Knowledge Problems

The Fundamental Operation: Projection

2007-08-13T12:40:00.000-04:00

To illustrate a further important point, below is an actual object-property table. It shows 10 objects and 5 attributes. You can think of it as representing 10 objects that just came off an assembly line. Each of those objects has 5 properties, for example `\{P_1,P_2,P_3,P_4,P_5\}=\{text{color},text{shape},text{texture},text{size},text{orientation}\}`. Thus, for example, these objects can have three possible colors, `P_1 in \{0,1,2\}`, which might be `\{text{blue},text{red},text{green}\}`. It can be noted that not all of the objects need be distinct, and in fact there are several identical objects in this set. (Can you find them? Just kidding.)

Object	Property
	`P_1`	`P_2	`P_3`	`P_4`	`P_5`
`O_1`	1	2	0	1	1
`O_2`	1	2	0	1	1
`O_3`	2	0	0	1	0
`O_4`	0	0	1	2	1
`O_5`	2	1	0	2	1
`O_6`	0	0	1	2	2
`O_7`	2	0	0	1	0
`O_8`	0	1	2	2	1
`O_9`	2	1	0	2	2
`O_{10}`	2	0	0	1	0

The crucial fact that must be observed is that the distinguishability of objects depends on which attributes are considered. For example, in the table above, we can already note that objects `\{O_1,O_2\}` are indistinguishable, as are `\{O_3,O_7,O_{10}\}`. The objects in these sets correspond to the same point in feature space, even if they are physically distinct objects (which we assume they are). However, if we were to further assume that attributes `\{P_1,P_2,P_3\}` are inaccessible, and were therefore able to consider only attributes `P_4` and `P_5`, we would observe (table below) that several other objects now also become indistinguishable, collapsing to the same point in feature space.

Object	Property
	`P_4`	`P_5`
`O_1`	1	1
`O_2`	1	1
`O_3`	1	0
`O_4`	2	1
`O_5`	2	1
`O_6`	2	2
`O_7`	1	0
`O_8`	2	1
`O_9`	2	2
`O_{10}`	1	0

In particular, we now find that we have the following sets of indistinguishable objects:

`{(\{O_1,O_2\}),(\{O_3,O_7,O_{10}\}),(\{O_4,O_5,O_8\}),(\{O_6,O_9\}):}`

So there are only four discriminable kinds of objects represented in this knowledge system after attributes `\{P_1,P_2,P_3\}` have been dropped and consideration has been restricted to attributes `\{P_4,P_5\}`. These four kinds are called "equivalence classes" because the entities contained in each class are indistinguishable (equivalent) based on the attributes under consideration. The process of "dropping attributes" is called projection and corresponds to an orthogonal (parallel to axes) geometric projection in feature space. In the previous case, we would say that the data is projected onto dimensions `\{P_4,P_5\}`. In general, the projection onto a given set of attributes will produce a collection of equivalence classes containing objects which cannot be disambiguated based on those attributes. This will be extremely important in what follows.

A Basic Knowledge Representation Framework

2007-08-01T12:44:00.000-04:00

Reminder: There is some mathematical notation in this post. If you use Internet Explorer, you may need to download the free MathPlayer plug-in from Design Science. If you can see the equation below (rather than a bunch of ASCII text), you should already be good to go:

`sum_(k=1)^n k = 1+2+ cdots +n=(n(n+1))/2`

OK. On with the show...

Perhaps the most basic knowledge representation framework is the rectangular object-property table or array, in which rows represent individual objects or entities, and columns represent properties or variables. An example is shown below:

Object	Property
	`P_1`	`P_2	`P_3`	`\ldots`	`P_n`
`O_1`	2	1	100	`\ldots`	-0.01
`O_2`	3	0	430	`\ldots`	0.23
`O_3`	2	1	—	`\ldots`	0.30
`\vdots`	`\vdots`	`\vdots`	`\vdots`	`\vdots`	`\vdots`
`O_m`	3	0	430	`\ldots`	-0.43

Sometimes this format is simply called "raw data" or "flat data," because this is the basic representation for data acquired from multiple sensors, channels, etc., and the format used in familiar spreadsheet applications. In the Rough Set literature (pawlak_91), this framework is called an "information system" (pawlak_81), "knowledge representation system" (wong_ziarko_86), "attribute-value system" (ziarko_shan_96) or "information table" (yao_yao_02). In the case where the property values are binary (i.e., present or absent), the format is what Watanabe (1985) calls an "object-predicate table," or "Aristotelian table". It can be given a rigorous mathematical definition, but we'll skip that here, since it's pretty clear what's going on. A great many knowledge discovery problems can be represented in this model (ziarko_shan_96).

The `m \times n` attribute-value table above represents a set of `m` objects (also called entities or situations), wherein each object or situation (i.e., each row in the table) is described by a set of `n` properties (also called variables, attributes, features, or dimensions). We use these terms interchangeably as do others (goldstone_98,bruner_goodnow_86), although many authors also find it convenient to draw distinctions. In the example above, all properties have been coded numerically, although it makes no difference for our discussion. For example, the `P_1` property might represent "day of week," and the actual names of the days could be substituted for the numerical indices shown. The example also illustrates that different properties may have values drawn from different domains. For example, whereas property `P_1` appears to adopt single-digit integer values, property `P_2` appears to be a (binary) attribute adopting values in the domain `[0,1]`, property `P_3` appears to adopt larger integer values, and property `P_{n}` apparently adopts real (floating point) values, perhaps in the domain `(-1,1)`. The issue of missing values, such as that for property `P_3` on object `O_3`, will not be relevant to this discussion.

Observations

We will move to a more concrete example a bit later, but let us first pause to note a number of points about this kind of representation.

An object or entity in this representation is just a list of property values, called a "tuple" in database jargon. Thus, object `O_1` can be described as the property vector or ordered list `[2,1,100,\ldots,-.01]`, which is just convenient shorthand for `[P_1=2,P_2=1,P_3=100,\ldots,P_{n}=-.01]`. Geometrically, then, each object represents a point in an `n`-dimensional "feature space."
An object in this framework is just a list of property values. Two objects having the same set of property values are entirely indistinguishable. Depending on the application, it may still be the case that these objects are physically distinct from one another, but they are nevertheless indiscriminable based on their properties, and therefore completely interchangeable. Identical objects occupy the same point in feature space. There is in some respect a commitment here to something like Russell's "bundle theory" in which an object is nothing more or less than its descriptions (in all possible worlds), there being no "substrata" or essence to it; that is, there is no substrate in which the properties inhere. However, since all we can ever deal with rationally are descriptions of one sort or another, this doesn't seem like a shortcoming unique to this particular representational system. More on this later.
This kind of system can represent many kinds of knowledge. The objects in question may be individual entities, such as donuts on a shelf, where the properties may indicate donut attributes such as flavor, topping, calories, etc. Alternatively, the objects may represent the state of some system at discrete times. For example, an "object" or "situation" might be the weather in Central Park at a given moment, so that `O_1` is the weather at 9am, `O_2` is the weather at 10am, `O_3` is the weather at 11am, and so on. The attributes in this case could be descriptors of weather such as temperature, pressure, precipitation, cloud cover, etc. Thus, the knowledge base in this instance represents a multidimensional time-series or multidimensional signal. This idea is incredibly powerful, because each object/row then represents "the state of the universe" at a given moment in time. By "universe," I mean "universe of discourse," that is, the set of all properties that we are concerned about in a given application, which in the limit we can imagine to include all the properties in the actual universe. (We can imagine!)
A real-valued (i.e., "continuous") or high-cardinality variable such as `P_{n}` in the example above would typically need to be discretized (quantized) for purposes of analysis. Patterns in data often only become (statistically) visible when we step back and view the data at a distance, i.e., at a coarser level of resolution (ziarko_89). To do this, we represent an entire range of variable values with a single symbol, no different than when we round-off decimal numbers to the nearest integer. This process of quantization is actually a matter of categorization, which we will discuss in much greater detail later. In the examples that follow, we will play only with integer values.
In almost all cases of any interest, a given object-property table will be considerably smaller than the maximum size that such a data table might have if all combinations of attribute values were to occur. That is to say, in practice, not every object that can logically occur does actually occur (Mervis_Rosch81). For example, although one might logically conceive of a flying animal that weighs more than 300 pounds, in fact there are no such animals. This means that not every value of the attribute "able to fly" defined on domain `{yes,no}` co-occurs with every value of attribute "weight" defined on the real numbers. The observation that not all objects that can occur do occur, or — more generally — that their probabilities of co-occurrence are not uniform — this is an observation about the very essence of structure (pomerantz_lockhead_91). Structure in data manifests through the unequal co-occurrence of certain sets of attribute values, i.e., the tendency of certain attribute combinations to occur with greater or lesser frequency than other attribute combinations. The "empty locations" in feature space — the events that could logically have happened but did not — are the hallmark of structure. We will return to this important idea a little later.
There is an object-property duality that becomes apparent by rotating the object-property table 90° counterclockwise. Just as it is possible to describe an object as a vector or tuple of property values, it is possible to describe a property as a vector of "object values." A given property then corresponds to a particular point in "object space." This duality is very interesting and, as I understand it, forms the basis for the field of Formal Concept Analysis (FCA), but we will not be concerned with it here.

Finally, before we get to the major limitation of this framework, let us point out a minor limitation: The information system representation described above has been accused of failing to adequately represent relational information, (e.g., arnone_71). As Hahn & Chater (1997) point out, a "bird" is not just a collection of features {wings, beak, feathers, ...}, but is rather a collection of these features having a particular relationship to one another: "A creature with all the right features in the wrong arrangement would not be a bird!" However, while the information system may not be the optimal representation for relational information, it is still possible to represent such information within the system. If, for example, the distance from wing tip to wing tip is an important relational aspect of birds, we can introduce a property that represents this distance, and we can do the same for any other relational qualities. If there it is a relation among many features that is of importance, then we can introduce a new variable to code that as well. This is not to say that the information system gives us the reasoning apparatus by which to deduce new relational information, such as would automatically allow us to know, for example, that "A larger than B and B larger than C entails A larger than C." No, we are simply stipulating that it is possible to represent relational information within the object-property table, and this should be enough.

The Major Limitation

Now, having gotten the more neutral observations out of the way, it is crucial to point out a number of limitations on the sort of knowledge representation system we have been describing above. Principally, the very idea of there being "objects" and "attributes" is a philosophically troublesome one. Firstly, it is just not obvious that we can represent the totality of the external world in terms of objects (Watanabe_85). Who instructs us on what are the "correct" properties by which to distinguish legitimate objects? In the opinion of Bruner, Goodnow, & Austin (1986), all that is required of an attribute is that it be a distinguishable element: "An attribute, in brief, is any discriminable feature of an event that is susceptible of some discriminable variation from event to event. Indeed, if it did not vary it would very likely not be discriminable in any case — the fish will be the last to discover water." So essentially anything discriminable constitutes an attribute, which therefore places almost no constraint on the set of possible attributes for a given system. It goes without saying (maybe) that if we have a discriminable property `P_1` and a discriminable property `P_2`, we can always imagine an additional discriminable property `Q` that is equal to `P_1^2`, or `P_1 \times P_2`, or `\pi P_1 sqrt(P_2) + 42`. So what makes one feature set more legitimate than another? And if what distinguishes two objects is just their features, as our object-property representation scheme assumes, then this ambiguity on what constitutes legitimate features propagates to an ambiguity on what constitutes legitimate objects (watanabe_85).

More provocatively, are there indeed really such things as features or objects at all? This question did not appear to bother the medieval or ancient thinkers, who believed that objects and features were indeed objective aspects of the external world. "Tails" and "hooves" are indeed genuine features of horses, and "horses" are in turn genuine objects. The ancients could debate how significant the possession of tails or hooves is to a horse's horseness, but they could not debate the fact that these objects and attributes genuinely exist. However, in the wake of Berkeley and Kant, the confidence about what constitutes objects and features has evaporated, and it is now clear that the things we subjectively regard as objects and features are themselves the product of a complex interaction between what exists in the external world (distal stimulus) and a sequence of processing performed by our perceptual and cognitive apparatus. Thus, the features to which we have access are symbols employed by a knowledge representation system (our mind) that correspond in some consistent way to aspects of the external world (markman_99), but these features are still notably the product of a classification already imposed by the mind on the world. We cannot of course assume that features are strictly internal symbols, since then we would face a much larger problem of explaining in what way (if any) these features are grounded in reality (harnad_90).

This bifurcation between external and internal features has been given the catchy name of Occam's Cleaver (panaccio_05), which, stated poetically, instructs us that "we should be cautious not take as features of the things signified the features of the signs that signify them. In other words, we should not conflate representational features with ontological ones." This cautionary attitude toward features and objects certainly also characterizes the position of modern cognitive science, where the topic of how objects and features are "made" by minds remains a vigorous area of empirical study, often yielding surprising results. In machine learning and statistics, the question of "What are the features?" plays out practically in the areas of "feature selection" and "feature creation," which include such techniques as Independent Components Analysis and Projection Pursuit. Although there is no final answer to this question, it always being a matter of needs and expectations for a particular application, in some sense a learning theorist might say that the "right" set of features are those which capture the majority of intrinsic structure in a given system. Any set of features having this property is then the "right" set of features, and there may obviously be many such sets.

This last observation gives us a way to recover somewhat from criticisms regarding a severe over-commitment to objects and features. Let it be the case that an actual system (in the distal world) can indeed be described in a myriad of ways; that is, using a large or infinite variety of different feature sets. We can still assume that there is at least one such description that will adequately capture all the interesting structure in that system. In other words, there is some property-based description — not necessarily available to a given observer — but there is some description, in some property language, that adequately represents the phenomenon in question. This assumption can be rephrased to state that there is no system in the distal world that is completely impervious to description in some property language — i.e., by some set of attributes or variables. This is not an assumption that every distal system is describable by us — just that it is, in principle, susceptible to description.

The Major Objection

It will probably immediately be objected that in fact there is a perfect and devastating counterexample to the assumption that "there is no system in the distal world that is completely impervious to description in some property language," and that this counterexample is the Deity himself. After all, have not Rambam and a thousand lesser souls admonished us that God is beyond and above all description? Wasn't this their whole point: That there is at least one distal system, God, that is not amenable to any description whatsoever?

My answer is that, yes, in some instances this may have been exactly their point. But, I believe that many thinkers (e.g., Philo, Aquinas, see earlier) probably intended something much less sweeping, and meant by their remarks merely that God is not describable by or to human minds. Not that he is resistant to description altogether. (Can even God not describe God?) This more moderate unknowability proposal poses no problem for us, since all we are assuming of distal systems is susceptibility to some description, not necessarily description by the human mind. The more extreme claim, however — that God is resistant to property-based description of any kind whatsoever, whether the description be accessible by human minds or not — this would in fact pose a problem for us, if it were a coherent claim. But it is not.

It is certainly possible to say that "God is resistant to any description whatsoever," but this is writing a check that cannot be cashed. I do not believe we can claim to offer a coherent concept of "that which cannot be described in any possible description language." That is, we can neither offer an example of such an indescribable entity, nor can we provide an explanation of how or why it is that an entity would be resistant to description in every possible language. In light of this, we have to consider the idea of the absolutely indescribable entity to be incoherent. Now, I do realize that there are arguments made by Rambam and many others as to why it is that God cannot have qualities of any kind, which as I understand the arguments (see earlier posts) all come down to the issue of the unity or non-compositionality of God. And, as I said earlier as part of my "unavoidable heresy", the idea of non-compositionality is also incoherent, and so proofs from that direction cannot ameliorate the incoherence in the notion of a system that has absolute resistance to description.

And so my position here is as follows: The notion of an entity that is completely impervious to description under any possible description language is a notion that is incoherent, and a concept which can neither be explained nor exemplified. Hamilton (1864) writes that "What in reality has no qualities, has no existence in thought, — it is a logical nonentity," and by this I understand him to mean that it is incoherent to talk about a system or phenomenon which has no attributes whatsoever. Such a notion represents not profundity, but stupidity.

That being said, the idea that a system or phenomenon might be indescribable to some observer or by some property language is not stupidity. It may not be especially profound either, as it turns out, since we are well familiar with many observers having limited descriptive abilities; infants, mosquitoes, chess programs, etc. It is entirely coherent to state that a given phenomenon in the distal world is describable by certain observers and not by others. This is the approach we will take in what follows.

How Is God Unknowable?

2007-07-22T19:14:00.000-04:00

As I suggested earlier, in order for us to consider "unknowability of God" to be a coherent notion and to subject it to further examination, we need to be able to offer at least a tentative formal characterization both of the concept "knowable" and the concept "God". The failure or unwillingness to do this is, in my opinion, a tacit admission that such claims really have no meaning at all. As a first step in this direction, we have to be clear that when we use the term "unknowable" we are actually talking about a state of knowledge — a relationship that obtains between two entities, a knower and that which is to be known. This would appear so obvious as to not even need saying; after all, to what could a term such as "unknowable" refer if not to a state of knowledge? However, it seems to me that religious thinkers often feel at liberty to use terms without specifying the context within which those terms have meaning, and in particular I have often seen the term "unknowable" used independently of any knowledge representation framework that would grant it a concrete and fixed meaning. And so I stress that "unknowability" is a state of knowledge, and that therefore the term has a meaning only within the context of a knowledge representation system. This all seems straightforward to me.

Thus, as I say, we need a formal characterization of (1) knowledge, (2) knower, and (3) that which is to be known, before we can claim to understand what it means for "that which is to be known" to be "unknowable." Now, jumping ahead, since this essay is about the "unknowability of God," in the final analysis "that which is to be known" will be not just any phenomenon, but the phenomenon we call "God." However, the issue of unknowability extends far beyond the particular issue of knowing God, and by approaching the matter of knowledge representation formally, we can examine in detail issues concerning the general notion of "unknowability" without specifically making claims about God. In a sense, therefore, the question of whether and how we can know God is ancillary to the larger issue of whether and how we can know anything. So essentially we will be examining the consequences of allowing God to be a member of the class "unknowable," once this class is suitably and formally defined.

Not to belabor the point, but again, the approach here is not to declare God knowable or unknowable, but rather to examine what it would mean for God to be knowable or unknowable in a certain capacity, and what consequences would follow from such a status. Indeed, if we were to foolishly declare God to be unknowable, we would be invoking the very knowledge that we claim it is impossible for us to possess! Heschel (heschel_51) in fact has it right that "... he who insists that God is in every way unknowable claims to know that what he says cannot be known." This alone would seem to make many of the classical statements on God's unknowability and incomprehensibility highly suspect. Our goal in science and philosophy, as Nagel writes, is "... to reach a position as independent as possible of who we are and where we started, but a position that can also explain how we got there." And, as Heschel suggests, the matter of "how we got there" is the very first challenge that must be raised against the position that "God is unknowable". Simply, how do Rambam and Ramchal and Steinsaltz and Kaplan come to a position where they know that God is unknowable? In adopting this position, they are in fact professing a knowledge of God that is far more sweeping than what any of their opponents had ever claimed. To be able to assert that "it is inconceivable that man's understanding should be able to penetrate to the essence of the Infinite" (berkovits_04) would seem to itself demand a transcendent theory of both "man's understanding" and the "essence of the Infinite" that is far beyond anything that any thinker has ever offered. Likewise, to argue that "we have neither the words nor the mental processes that would enable us to actually describe God or understand Him" (Kaplan) would seem to require one to posses God-like insight into the structure of the Mind of Man and Mind of God.

Our purpose in this essay, therefore, is not to make such allegations, and our little project will hopefully not fall victim to such presumptions. (It will fall victim to other presumptions, however.) The current project is not to declare a particular entity (i.e., God) to be knowable or unknowable to human beings, but rather to provide a mathematical framework for discussing such questions intelligently, and one that might provide some general insights into the issue of knowability that will allow us to use the concept in a meaningful manner.

Still, one matter that must trouble the reader as we proceed is how we can possibly propose to obtain a formal characterization of the concept of God, or rather, how we can allow God to be subsumed in a class (i.e., the class "unknowable") that admits a formal characterization. Doesn't the very possession of any such formal characterization immediately make God knowable, so that whatever we might then prove about God's knowability would have been trivially assumed from the start? In other words, by the very act of formally specifying those three elements, (1) knowledge, (2) knower, and (3) that which is to be known, and then assuming that a process called "God" can be represented within the specified system, haven't we already committed ourselves to the idea that God is knowable?

Yes and no. And maybe. It is difficult to answer this question in the abstract, so as we go along I will try to be very clear on exactly what assumptions I am making about the entity or phenomenon known as God. And while almost all of the assumptions will be heretical according to someone, they are also so weak that it would be difficult to claim that these assumptions alone constitute knowledge of God.

So then, what does it mean, formally, to say that something can be know or cannot be known? There are a thousand legitimate answers to this question, for a thousand conceivable knowledge representation systems. In the next section I will review a very elementary knowledge representation scheme, and review a straightforward definition of unknowability that can be used within that system to express the issues we are talking about.

Kabbalism and Rationalism: A Point of Agreement

2007-05-17T23:05:00.000-04:00

So, in the end, what have the Jewish theologians told us about the knowability of God? On the kabbalistic account, God is represented by an unknowable component (En Sof) and a knowable component (Sefirot). On the rationalistic account, God is represented by an unknowable component (Essence and Attributes) and a knowable component (Actions). We therefore seem to have a point of agreement between the kabbalistic and rationalistic theological systems; in particular, both concede that God must be partially knowable and partially unknowable.

This agreement is, in itself, not very surprising. In the first place, both the kabbalistic and rationalistic systems are ultimately outgrowths of the Jewish religion, and therefore both require in the end that God remain somehow knowable to human beings. Were God to be completely and utterly cut off from human experience, nothing in the Jewish religion would make any sense, and, for the most part, Jewish thinkers are not willing or able to go this far. "Far from being able to serve as the basis for religion, the Absolute One renders religion meaningless" (berkovits_04).

This point of agreement between kabbalistic theology and rational theology is also unsurprising for the following simple reason: Rambam casts a large shadow. While the concept of En Sof may predate Rambam (although Kaufmann Kohler and Isaac Broydé, writing in the Jewish Encyclopedia, attribute the term to Azriel of Girona, who was Rambam's junior by a generation) and in any case owe more to Neoplatonic than Aristotelian ideologies, it seems unlikely that kabbalists thinking and writing about En Sof in any succeeding generation could have overlooked the 800-pound gorilla in the room, which is Rambam's denuded conception of God-as-He-is-in-Himself. What was left for the kabbalists after Rambam had completed his work was merely to pile poetical grandiosities upon the concept. From the kabbalistic standpoint, En Sof could certainly not be permitted to be less unknowable than Rambam's God, and since it is logically impossible for anything to be more unknowable than Rambam's God, the kabbalistic conception of the Unknowable was essentially forced into rough equality with that of Rambam. At least it seems so to me.

Still, it is beyond certain that both schools would reject a conclusion such as that "God is composed of two parts, one knowable and one unknowable." It is almost as certain that both schools would reject a more cleverly-worded conclusion such as that "God is composed of two aspects, one knowable and one unknowable." Cordovero writes, for example,

In the beginning Ein Sof emanated ten sefirot, which are of its essence, united with it. It and they are entirely one. There is no change or division in the emanator that would justify saying it is divided into parts in these various sefirot. Division and change do not apply to it, only to the external sefirot (matt_90).

There are hundreds of other testimonials to the absolute unity of God and to His imperviousness to division into "aspects," much less "parts". That being said, if it is to be admitted that God is somehow knowable and somehow unknowable (which is the only reasonable conclusion that can be drawn from both the rational and kabbalistic treatises), and if we are not to play games of equivocation with our own mundane terminology, such as by permitting "knowable" and "unknowable" both to inhere in the same subject without contradiction, then we are forced to accept one of the previous statements or a close cognate, however distasteful. Thus, kabbalists and rationalists alike must accept something like the following: "God is composed of two aspects or parts, one knowable and one unknowable."

One can choose to reject such a statement outright, but only at the risk of completely collapsing the distinction between "knowable" and "unknowable". If one rejects the above statement and all its cognates, it is no longer meaningful to talk about "En Sof vs. Sefirot" or about "Essence vs. Actions". There can be no meaningful distinctions to be had, and it is all holy nonsense. Certainly, one can debate what precise meaning we should attach to the notion of "part" or "aspect" in this context, and we will try to be more formal about this below, but if we desire that there be a distinction between knowable and unknowable, and we still wish to respect the law of contradiction, then it must be the case that there are in some sense multiple parts or aspects of God. So it is.

In any case, despite their point of agreement, neither the kabbalistic nor rationalistic system provides us with an explicit formal definition of "knowability," nor does either provide an explicit "knowledge-theoretic" explanation of the relation between the knowable and unknowable components/aspects of God. It is these two omissions that I will make a primitive attempt to address in the following section.

Unknowability of God In Jewish Rationalism V: So What's Left?

2007-05-13T00:12:00.000-04:00

Having concluded our little survey of Jewish rationalism, let us summarize. The position on God's unknowability found among many in the Jewish rationalist school (including, as I see it, Bachya, Rambam, and Albo) is that God's attributes are completely unknowable in the strongest possible sense. That is, there is no known predicate (i.e., one for which we can specify the classes induced by the predicate) which can be applied to God. Not even the predicate "one" or the predicate "exists" (if the latter even qualifies as a predicate) can be applied to God. The reason that we cannot know any of God's attributes is simply that God does not possess attributes, period. Naturally, objections both ancient and modern have been raised against this strong position on unknowability. I earlier mentioned the objections of Gersonides, Aquinas, and Berkovits, and I will return to consider their positions at the end of this essay (should I actually make it that far). Here, I just want to consider where the "strong unknowability" position leaves us in our relationship to God.

It could not have escaped a thinker of Rambam's caliber that by making God utterly unknowable and outside of any relation or likeness to mundane entities he was flirting with the possibility of God's complete irrelevance to the world of men, and thus of opening the door to the utter vanquishment of religion. He knew that while there might be some intellectuals who could achieve satisfaction and meaning through sublime meditations on the transcendental nothingness of the Unknowable Absolute, this task could hardly satisfy the majority of religious people, for whom "ponderation on ultimate unknowing" would scarcely constitute a religion of any sort at all, let alone the religion of the Bible that they had been taught from childhood. For the Jewish religion to make any kind of sense, God must have some tangible influence in the world of men — despite His unknowability. The solution that the Rambam proposes (and in which he is followed by many others) is that God is indeed yet knowable — not in His attributes, but through his actions:

Every attribute that is found in the books of the deity, may He be exalted, is therefore an attribute of His action and not an attribute of His essence, or it is indicative of absolute perfection (GP I:53)... Thus, God's emanation or connection with the world is his actions, and this is the intent of God's message to Moses in Exodus 33 (GP I:54)...

To recollect, Exodus 33 is perhaps the Bible's theological manifesto sui generis, if one reads it that way, of course: Moses had asked God, "Now, if I have truly gained Your favor, pray let me know Your ways, that I may know You and continue in Your favor," and "Oh, let me behold Your Presence." God had responded:

I will make all My goodness pass before you, and I will proclaim before you the name Lord, and I will grant the grace that I will grant and show the compassion that I will show. But," He said, "you cannot see My face, for man cannot see Me and live." And the Lord said, "See, there is a place near Me. Station yourself on the rock and, as My Presence passes by, I will put you in a cleft of the rock and shield you with My hand until I have passed by. Then I will take My hand away and you will see My back; but My face must not be seen.

Rambam sees in this passage evidence that God is providing an affirmative answer to Moses' first question concerning God's ways (actions). God shows "goodness" and "compassion" in the world of men, and it is through these actions that He can be known. The second entreaty of Moses, to behold God's Presence (God's attributes), is however denied. "Man cannot see Me and live." And the final statement that "you will see My back" can again be taken, as by Philo, as a reinforcement of the idea that it is solely by the effects of God's actions in the world that He can be known.

Albo makes a similar reading of Psalm 104, which begins "Bless the Lord, O my soul; O Lord, my God, you are very great; You are clothed in glory and majesty."

Alluding to the first aspect [God's essense], he says, "O Lord my God, Thou art very great," i.e. from the side of Thy quiddity Thou art very great, so that man can not speak about Thee, and with all this, "Thou art clothed with glory and majesty," i.e. from the side concerning which it is possible to speak about Thee, namely from the visible activities which come from Thee. They show Thy glory and Thy majesty. Therefore he describes in the sequel the creations which come from God, and which point to God's excellence and perfection by the perfection which is visible in them. (husik_29, p.6)

But what does it mean to say that God is knowable in His actions? I have not seen a coherent account of how one could know something about the actions of an agent, and simultaneously not know anything about the attributes of that agent. Is not to say that "agent X does action Y" just to say that "agent X has the attribute of doing action Y"? Is not an animal which digs holes in the earth just an animal that has the attribute of "burrowing"? How does one ascribe an action to an agent without simultaneously ascribing attributes? If God's attributes are utterly unknowable (or even nonexistent), then surely his actions are unknowable (or nonexistent) as well. I am hoping that I might find somewhere in Rambam a more coherent explanation of how this can work, but until then I cannot say much more.

A different problem related to God's actions which weighed on the minds of many medieval thinkers (and which indeed seemed considerably more pressing than the one I just mentioned), is the question of what the notion of "action" entails for alteration in the state of the Deity. From our own mundane experience, we recognize that (intelligent) action is generally precipitated by some sequence of changes in the cognitive state of the acting agent. We (as agents) speculate, we discover, we hypothesize, we deliberate and revise, we decide, we will, and then we finally act. However, the medieval thinkers absolutely rejected the idea that any such sequence of cognitive state-changes could obtain in the case of actions by the Deity. God's state cannot change, both because this would imply plurality in the Deity (multiple states), and because it would imply that the Deity's present state is not one of ultimate Perfection. If God is Perfect, why would he ever need to undergo change? The typical medieval opinion is that change is a defect, and so cannot be predicated of God (cf. Albo, husik_29, p.129).

The problem is even more keen on the view (cf. Aquinas, kreeft_90, p.136) that God's intellect, knowledge, and essence are all one and the same. If such is the case, a change in God's intellect would imply a change in God's essence, and, as Maharal suggests, "it is better to remain silent than say such things" (mallin_carmell_75).

The solutions to this problem are as a whole quite unsatisfying. Albo, for example, cannot deny of God a notion such as "will," because if God could be said to lack will, this would make him by any account an inferior kind of agent (if an agent at all). And yet to allow the notion of divine "will" leads to a lengthy sequence of logical dilemmas. Here is Albo capturing the conundrum:

...the term voluntary applies where the agent desires and does a given thing at a given time, which he did not desire before. The term voluntary does not apply to a thing which is always in the same condition. It follows therefore that the one who has will changes from a condition of not willing to a condition of willing. If so he is affected by, and receives change from another, for a thing can not be active and passive at the same time in the same relation. But God can not change, nor be affected by another. Nor can He be affected by Himself, for He would then be composed of two elements, an element by virtue of which He acts, and an element by virtue of which He is acted upon. But there can not be any composition in God at all, as we shall see. Nor can God be active and passive at the same time. It follows therefore that God's activity can not be voluntary, since He can not change. Moreover, an agent possessed of will lacks the thing which he desires. But God does not lack anything which He desires at any time and did not have before. Similarly one who exercises a choice chooses one of two things because that thing is more suitable to him than the other. He therefore lacks the thing which he chooses before he has chosen it. It follows, therefore, that God's activity can not be due to choice or will. But if He does not act with choice and will, nor like a natural agent, as light comes from the sun, as we explained, how can God be called an agent? (husik_29, p.13)... If God does not act with will, He can not act at one time rather than another, a supposition which leads to the doctrine of eternity in the absolute sense, and to the rejection of all the miracles in the Torah. Prayer ceases to be of any avail in time of distress, and right conduct and repentance are useless, and so on..." (husik_29, p.16).

The possible solution that God's actions in history (for example, the miracles retold the Bible) were somehow "planned out" from eternity (or from Creation), and therefore did require any proximal change in God's will, is dismissed by Albo as positively absurd:

Thus they say, God stipulated with the works of creation that the Red Sea should divide, that the fire should not burn Hananiah, Mishael and Azariah. From this it seems that their purpose was not to attribute to God a newly originated will at the time of the occurrence of the miracle. Therefore they say that the miracle occurred when it did through an eternal will, which determined that the miracle should take place when it did. But this opinion is far from intelligible. For if we examine the expression eternal will, we find that it is a spurious conception, and points to necessity rather than will. For the question remains as it was originally. When the world was created or when the miracle occurred through His eternal will, was it possible for God to postpone it to another time, or not? If He could postpone it, then the eternal will was nullified. For the reason He did not postpone it was not because of the eternal will, but because He did not desire at that moment to postpone it. If He had desired to do so, He would have postponed it. And if it was not possible for Him to postpone it because so the eternal will had decreed, then there is no such thing as will any more, and He becomes an agent acting by necessity and not with will, since He could not postpone the act if He would. We should have to say the same thing about all miracles and all acts proceeding from Him at any time, that they happen by necessity, and that the thing could not help being when it is, for so it has been determined by God's eternal will, which can not be changed... (husik_29, p.15)

And so what Albo, following Rambam, is forced to fall back on is simply the notion that we cannot understand what kind of an agent God actually is. That is, we do not know what it means for God to have "will" or "desire", or to make a "decision". These concepts simply cannot mean the same thing for Him as they do for us, and we thus have absolute equivocation in terminology. Albo again:

Because at first sight it might seem that there is a change in God's will, he says, "For My thoughts are not your thoughts, neither are your ways My ways...," i.e. as there is a difference between His knowledge and our knowledge, the two not belonging to the same class at all, so there is a difference between His will and our will, and between His ways and our ways, there being no similarity between them at all (husik_29, p.23)... It is clear therefore that since we see acts emanating from God which are similar to those acts which emanate from a voluntary agent, we speak of God as desiring and willing; though we can not understand how will and desire reside in God without causing change and affection. This is unknown to us, as the nature of His knowledge is unknown to us (husik_29, p.145).

Indeed, on Albo's opinion, the only alternative to absolute equivocation is to attribute ignorance to God (as does Ralbag, to whose views Albo is evidently contrasting his own below):

There is no way out of this difficulty except by saying either that His knowledge is not of the same kind as our knowledge, and that it does not cause change in Him as our knowledge causes change in us, or to commit the grievous heresy of attributing ignorance to God and saying that He does not know any particular thing that originates in the world, but the universal only, that He did not know Moses while he was in existence any more than He knew him before he existed and after he ceased to exist and that God does not know opposites, else He would have different kinds of knowledge. The best solution is to say that His knowledge follows His wisdom, and as His wisdom is of His very essence and not something added to His essence, and is absolutely unknown, so His knowledge and His will and His power, which follow His wisdom, are absolutely unknown (husik_29, p.21).

So if God's will is not like our will, and God's knowledge is not like our knowledge, and therefore God's actions are not like our actions, then how is it meaningful to talk about knowing God through his actions? I hope someone can explain this to me. In any event, on the rational view it seems that this is the very limit of what we can know about God.

Next section: Wrap-up of the Introduction! Hallelujah! (Yes, sadly, everything till now was part of the Introduction. Hopefully things will move more quickly now!)

Unknowability of God In Jewish Rationalism IV: Why Unknowable?

2007-04-29T23:11:00.000-04:00

In this section I will try to review some of the rational arguments for the unknowability of God that arise in particular from subscription in whole or in part to the Aristotelian system of the predicables described previously. Granted, the system that was inherited by Jewish thinkers had already been pawed over for hundreds of years by Neoplatonists and Islamic thinkers, but a certain degree of core commonality with Aristotle's original system remained. I will certainly not attempt to revisit every medieval rational theological argument, but only those that relate to God's unknowability.

So, now, what are the arguments the medieval Jewish rationalists give as to why it is necessary that God be unknowable? I will sketch out a few that I have seen, but it will imminently become clear that these are not independent arguments, rather variations on a single argument. I somehow feel, though, that the core epistemological issue here is eluding me. I want to find the cornerstone of these arguments — the singular fact from Aristotelean epistemology that positively requires God's unknowability — and I can't quite get it. I had thought that writing the previous post on the predicables would make it immediately obvious to me what the key issue is, but I was mistaken; it is still not clear to me. Perhaps a reader more familiar with Aristotelian thought will be able to provide the missing link for me. If so, I will hope to revise this section at some later time.

At least one common theme that I was able to see is that in the eyes of the medievals, having "knowledge of God" means knowing God's attributes. Thus, for God to be unknowable is for God's attributes to be unknowable, and most of the medieval arguments therefore focus on demonstrating the unknowability of God's attributes. As it turns out, this usually becomes a problem of demonstrating the nonexistence of God's attributes.

In a sense, though, I'm presenting the problem backwards: Unknowability is generally a consequence which falls out from more primary theological concerns, or at least that is how matters are presented. However, I am interested here in Unknowability in a primary sense, and I suspect that this may have been the interest of several medieval authors as well, although they do not say as much. (A completely cynical view would suggest that there is a very keen social imperative to establishing God's unknowability, since people who think they have intimate knowledge of God are often found to act in the most offensive ways toward their fellow humans. This sociological factor was I'm sure not lost on the Jewish thinkers of the middle ages, and thus even if we dismiss the cynical view as too cynical, I doubt that Unknowability can be regarded entirely as a by-product of other theological considerations. There must have been some desire on the part of theologians to establish God's unknowability as a bulwark against the nation of prophets actually behaving like a nation of prophets.)

On the assumption (i.e., my tentative assumption) that it is Unknowability which is a primary fact the medievals sought to demonstrate, it might be noted that there is a certain excessiveness in stripping God of all attributes. Isn't it enough to claim for the purpose of Unknowability just that we humans don't or can't know God's attributes, while yet allowing God to keep His (unknowable) attributes? Is it really necessary that God have no attributes? This seems to have been the position of Philo and his school, and it seems to have been the position of Aquinas as well. He writes in Summa (kreeft_90, p.115):

It is impossible for any created intellect to see the essence of God by its own natural power. For knowledge is regulated according as the thing known is in the knower. But the thing known is in the knower according to the mode of the knower. Hence the knowledge of every knower is ruled according to its own nature. If therefore the mode of anything's being exceeds the mode of the knower, it must result that the knowledge of that object is above the nature of the knower....

The implication here is that "unknowability" is a status that applies only to a set of two entities: (1) a knower and (2) a thing to be known. For a given knower and a given thing to be known, if the capacities of the knower are inadequate to know that particular thing, then we have a state of "unknowability". On this view, it would seem possible to allow unknowability of God without making Him completely naked of all attributes. We could say that God possesses attributes, but that our intellectual capacities fall short of being able to know these attributes. This, however, was not the tact of the Jewish medieval rationalists (with perhaps a couple exceptions). Rather, their approach was to equate unknowability with the complete absence of divine attributes, denying God even the attribute of "intellect" (cf. Maharal, mallin_carmell_75). As Rambam writes (GP I:50), "you must know that He, may He be exalted, has in no way and in no mode any essential attribute, and that just as it is impossible that He should be a body, it is also impossible that He should possess an essential attribute." The reasons behind this extreme position on unknowability seem to have been laid out already by Bachya ibn Pakuda, who gives us our first argument.

The problem of attribute priority

Bachya ibn Pakuda's argument for our essential inability to attribute properties to God is that, being the creator of all attributes, God cannot possess any of these same attributes Himself: "...whatever we could say about Him would refer either to His Essence or His properties, and the Creator of essences and properties cannot be described the way they are described" (pakuda_96, ch.9). It seems to me that what Bachya is saying is that if we were to suppose that God did possess an attribute of some kind, then we would be forced to conclude that God could not have created that attribute. To say otherwise, on Bachya's view, would be absurd. Thus, God cannot have any attributes.

While simple, Bachya's presentation of the problem seems to me to anticipate many of the later discussions. Maharal (mallin_carmell_75) seems to echo this idea when he writes that "Once we realize that all entity originates from His being, we understand that it has nothing in common with Him." We cannot attribute properties to God because doing so gives those properties an existence which is outside the creative control of — and in some sense prior to — God Himself.

On the other hand, Bachya's position is not completely convincing. If we were to say, for example, that God has "hands," does that logically imply that "hands" are somehow prior to God? It seems to me it does not. It is just a description of the way God is. To say that a bird possesses feathers is not to say that feathers exist independently and prior to the bird in question. The property "having feathers" is just a description of the way the bird is. In the case of God, it does not seem logically necessary that a property's existence requires the property to have existed prior to or outside of God (in some Platonic realm, for example), and if that's correct, then Bachya's argument loses some force on this account.

However, while the existence of the property in question (e.g., "hands") independent of God may not be logically implied, by naming a property (or by merely stipulating the existence of such a property in God) we do immediately raise the question of why God has this property instead of some other property, i.e., the question of why God is the way He is. This is a broader understanding of Bachya's question, I think. If God indeed has hands, then why does God have hands, instead of wheels or flippers? The same question would apply to psychological attributes as well. If God is indeed angry, then why is God angry, rather than silly or dopey? Since the medieval inclination was to see agency behind everything, in order to answer such question it would evidently be necessary to stipulate the presence of an agent, independent of God, who is responsible for God's having the attributes He has. Even without appeals to agency, unless one were to resort to brute facts (God is the way He is just because), the existence of particular attributes in God would still require some process to explain their presence there.

And if the attributes we attribute to God are shared by other entities as well, matters are actually even worse. Aristotle (Posterior Analytics, mure_01, p.120) informs us that "to know a thing's nature is to know the reason why it is," and that "we possess scientific knowledge of a thing only when we know its cause" (mure_01, p.112). In general, the knowledge that we seek about entities (why they have certain properties) is provided by identifying the superordinate category that endows those entities with the properties in question: "The proper function of science is to provide explanations, the canonical form of which is something like 'Xs are F because they are G.'" (hankinson_95). If an attribute which we apply to God is also applied to other entities as well, and we have scientific knowledge of those other entities in Aristotle's sense, then we will have genuinely identified a superordinate entity (i.e., class description) which is the "generator" of the attribute in question. In this case, since we do indeed "explain" the attribute in question by invoking an ancestral generator to which God as well as the other entities sharing that attribute would owe their properties, we would most likely be realizing Bachya's worst fears.

In summary, as I read it, attributes require explanation, and any explanation of God's attributes will have unacceptable theological consequences. Hence God cannot have attributes. We cannot escape by claiming that God possess attributes that are unknown to us, because whether they are known to us or not, their very existence implies an entity or entities which exist in some sense prior to God. This seems to me to be the liberal reading of Bachya's position.

The problem of compositionality

A second problem with the existence of attributes (and hence with knowing them) is that they introduce a kind of multiplicity into God. Many writers go on at great length about this issue. Rambam, for example, writes (GP I:50) that "no composition whatever is to be found in Him and no possibility of division in any way whatsoever." About God-as-He-is-in-Himself, Ramchal in Derech Hashem similarly tells us that "It is likewise necessary to know that God's essence is absolutely simple, without any structure or additional qualities whatsoever. Every possible perfection exists in Him, but in an absolutely simple manner." Albo (husik_29, p.128) also writes that God's attributes are unified in Him, while in us they are distinct (although his meaning is not clear to me).

It is likewise not entirely clear to me whether the insistence on divine unity is a philosophical imperative or a theological imperative. Aquinas (kreeft_90, p.83) writes that God cannot be composite because composite things must have a cause which causes them to unite, thus again setting up a problem of priority. If there are multiple attributes, we would be forced to seek both the reasons for the particular attributes instantiated in God, as well as the cause of their present combination in that subject. Aryeh Kaplan puts it this way:

The logic behind this is that any additional quality that we would ascribe to God would add an element of plurality to His being. Thus, for example, let us assume that we wish to speak of God's intellect as an entity in itself. We would then have to speak of two concepts, namely God's essence and His intellect. Since this would imply an element of plurality within God, it must be rejected. This is true of any other attribute which we may wish to ascribe to God, and therefore we must say that no such independent attributes exist. But if we cannot ascribe any attribute at all to God, then we must conceive Him as being absolutely simple. This indeed is the consensus of opinion among our great thinkers. Nevertheless, His very simple essence implies every attribute with which God rules the universe (kaplan_90).

It cannot even be said that God is therefore "one" in the numerical sense, because "quantity" too cannot be meaningfully predicated of God (cf. Cordovero, Rambam, etc.). As ibn Gabirol phrases it in Keter Malchut, "Thou art One, and at the mystery of thy Oneness the wise of heart are struck dumb, For they know not what it is... Thou art One, but not like a unit to be grasped or counted, For number and change cannot reach Thee" (zangwill_23, p.83, Ch.2).

Again, note that both here and with respect to Bachya's argument, the conclusion is not just that we cannot know God's attributes. The conclusion is that God cannot have attributes at all. Independent of what humans can or cannot know, if God were objectively to possess attributes, this would set up the objective theological dilemmas of attribute priority or multiplicity described above. On this account, the impossibility of knowing God is entirely self-evident: There is simply nothing to know. Since our knowledge of things is exclusively by way of predication — by attributing qualities to entities, if an entity is assumed objectively to have no qualities, then there is genuinely no possibility of acquiring knowledge about it.

And here I will pause to issue my first heresy alert: This notion of divine unity or structurelessness is one which I will most likely be forced to reject in another few posts. It is simply not possible to speak meaningfully of a dynamic entity which has no structure or no qualities. Ramchal already warns us that "admittedly, this is something far beyond the grasp of our understanding and imagination, and there hardly exists a way to express it and put it into words," but the fact remains that if we wish to explore the nature of God and his involvement in the universe, we simply cannot accept the notion of His structurelessness. The idea of objective structurelessness makes God into a nothing. Not a nothing in the sense that He has no describable attributes, but a nothing in the absolute sense that there is no possibility of His interaction or relationship with the universe, physical or otherwise. On Ramchal's account, God would be far less that a piece of chalk or lump of clay. Indeed, a wisp of tissue paper would be infinitely more powerful than God were we to insist upon his complete structurelessness.

The much-overtaxed excuse that God's structurelessness is "far beyond the grasp of our understanding and imagination" provides no remedy whatsoever. If we are willing to here admit into our theology an idea that is positively absurd on its face, then we might just as well do so whenever we please, and there is no longer any sense in which the process can be considered a rational theology. We could just say that it is "far beyond the grasp of our understanding and imagination" that a universe can create itself, and be done with it right there. If we are to pursue any kind of rational theology, then God must have structure, which means that God must have composition and/or attributes in some sense. This is simply an unavoidable heresy. As to whether such a view makes God contingent on his components or attributes, and thus gives those components or attributes priority in some sense, it may do. On the other hand, it may also be the case that the components could not exist in isolation, and that (like our own bodies) the constituent parts are in most respects inferior rather than superior to the whole. We will have more to say about this when the time comes.

The problem of subsumption of God within a class

Another problem with attributes as applied to God is the resulting subsumption of God within a class. I have not seen this problem directly expressed in this form by a medieval writer, but it has certainly been attributed to them often (and I assume correctly) by modern writers. Here is Aryeh Kaplan's version which I quoted in an earlier post:

Since everything conceivable — including any category of thought that the mind can imagine — was created by God, there is nothing conceivable that can be associated with Him. Let us say that I want to think about God. There is, however, no category in my mind in which I can place Him. Therefore, trying to depict God is like trying to see without eyes. When I try to see where there are no eyes, all I see is nothing. Similarly, when I try to think about God, all that my mind can depict is nothing (kaplan_85, p.89,90).

Kaplan's first statement simply echoes Bachya's position. The second line seems at first to suggest something different, though — that we cannot understand God because we have no category for God. However, as we mentioned earlier, classification is predication and predication is classification. Therefore, all that Kaplan is saying here is again that God cannot have attributes, the reason being that which Bachya has already laid out.

A closely related assertion that is often made is that God cannot be known because God cannot be defined. This would appear to be a weaker assertion than the previous, because definitions are a subset of the predicables. If we have already ruled out the applicability of any attributes to God, then we have certainly also precluded definitions. However, a weaker position might leave open the possibility that some attributes of God could be known, provided they are not essential (i.e., definitional) attributes. In any case, Louis Jacobs (jacobs_57) explains the problem this way:

God cannot be defined for definition is genus plus differentia. If, for example, man is defined as a rational creature, there is first the statement of the genus — the group to which he belongs — and then the statement of how he differs from other members of that group. We say that man is a member of the group 'creatures' and that by possessing reasoning faculties he differs from all other members of that group. But on any advanced view of Theism, God cannot belong to a group, for this would imply that the group to which He belongs is greater, i.e. more embracing than He.

Because in Aristotelian philosophy a definition requires specification of a genus, and genera are (as Porphyry points out) in some sense "generative" of their constituent species and therefor prior to those species, it is not possible that God has a genus. It may be noted that in Aristotle's system not everything actually needs a definition, since obviously such a demand would invoke an infinite regress. But nevertheless, for something to possess a definition requires that particular something to possess a genus, and therefore God cannot be said to possess a definition. Moreover, on the view of many, it cannot even be said that God belongs to the genus of "existing," since long-standing tradition dating to Aristotle asserts that "existence" is not a legitimate genus. As Albo writes (in typically muddled fashion),

In reality, however, it [existence] is neither a definition nor a description, God having no definition. For a definition is composed of genus and difference, but the word existent is not a genus which is predicated of all its subjects synonymously, as a genus is... For there is no genus in the world which includes God and another. The word existent is not applied synonymously to God and to other things. God's existence is real (absolute), whereas the existence of other existing things is acquired from His existence. But if existent is not a genus which includes God and other things, He has no difference (husik_29, p.36).

If the above explanation of God's resistance to definition is not adequate, Aquinas provides another. Aquinas (kreeft_90, p.81) points out that every member of a genus must have a difference, but yet possess the same quiddity (which is contributed by the genus). Hence, existence and quiddity must differ. But this is not so in God, and therefore he cannot have a genus. Whether this reasoning is entirely circular, which I believe it is, we will leave for another blog. The main point is that God cannot be known because God cannot be classified. The reason why God cannot be classified is again, at root, because any attribute when predicated of God (which immediately establishes a class in which God is a member) would in some Aristotelean sense assume precedence over God, which is theologically unacceptable.

The idea that God has no genus also has significant fallout for the notion of similarity between God and other entities. Aquinas (kreeft_90, p.89) puts it very simply by stating that entities in different genera cannot be compared, and since God has no genus, and hence no entity is in the same genus as God, there is not any possibility of comparison between God and other entities. Simultaneously, the lack of genus has consequences for relation between God and other entities, as Rambam points out (GP I:56):

Know that likeness is a certain relation between two things and that in cases where no relation can be supposed to exist between two things, no likeness between them can be represented to oneself. Similarly in all cases in which there is no likeness between two things, there is no relation between them. An example of this is that one does not say this heat is like this color, or that this voice is like this sweetness. This is a matter that is clear in itself. Accordingly, in view of the fact that the relation between us and Him, may He be exalted, is considered as nonexistent — I mean the relation between Him and that which is other than He — it follows necessarily that likeness between Him and us should also be considered nonexistent....

We may pause here to ask how convincing such arguments should be to a contemporary theologian. We no longer give metaphysical significance to predicates or categories, and thus for God to be subsumed in some arbitrary category would seem to hold little theological danger. If God were to be a member of the class of "things that have hands," would we consider this category to be somehow greater than God? Many categories may be constructed based on arbitrary feature conjunctions (Barsalou_83), but which have little or no ontological significance. The mere fact that "sitting on a yellow swivel chair in New Jersey within reach of a black coffee mug, purple pen, and unpaid credit card bill" defines a definite category which includes myself, some other people, and perhaps some animals, there is no deep ontological significance to this category. It is just an arbitrary grouping of entities that does not correspond in any way to the deep structure of the world. Most such categorizations have no deeper meaning, so merely belonging to a category does not by itself carry much epistemological weight.

Even so, it may not be possible to completely rid ourselves of the problem of class subsumption. While we can think of many categories with no ontological significance, many of the attributes on the basis of which such categories are formed would have been considered "accidents" — attributes which might have been and might yet be otherwise. The medievals were forced to reject such attributes of God for another reason (next post). Because of this, the kind of ad-hoc category contrived above is not the kind of category God could ever belong to. Therefore we are left asking whether we should still be troubled by the predication of essential attributes to God and what this entails for class subsumption. As it turns out, though, we can't really answer this question. In modern thought, there is not really any notion of "essential attributes," and so we are just returned to the question of whether God can have attributes at all.

So how persuasive is this argument of "unknowability due to unclassifiability"? It doesn't seem to me that this argument can any longer carry the weight it once did. By placing God in a category (or, more likely, a set of categories), we do not automatically promote those categories to an ontological status superior to God. The very notion of placing God in a category cannot therefore be offered by itself as providing a definitive demonstration of God's unknowability. However, if we do allow God to be classified in some fashion, we can still not escape Bachya's dilemma regarding the sources of God's attributes. There is no solution to that problem, but there may not need to be.

Unknowability of God In Jewish Rationalism III: The problem with predicates

2007-04-07T23:19:00.000-04:00

What follows is a modest digression into the topic of why the medieval thinkers were so insistent that God cannot be defined or categorized. It is their philosophical intuition on this point which, independent of any Scriptural attestations, leads thinkers such as Rambam into denying the application of any predicates to God. I will freely admit that I have not seen all the sources on the issue (which probably number in the thousands, across a half dozen languages), or even the best of the sources, so I will make do with what I have. Hopefully someone out there will be kind enough to illuminate matters further for me.

Let us begin by rehearsing the meaning of predication. A predicate is something that is affirmed or denied of a subject, yes, but we should strive to gain some more clarity on the matter than this. (It is precisely such clarity which has been the Holy Grail of every logician since Aristotle.) We could do worse than beginning with William Hamilton's concise summary of the nature of thought, which includes a few words on the nature of predication; if nothing else, it may help to clarify a few terminological issues. (W. Hamilton was a Scottish philosopher whose chief notoriety comes from his frequent impeachment in the writings of J.S. Mill. However, I think we can assume that there are good reasons Mill chose Hamilton as his prey, not simply the prospect of an easy kill.)

When we think a thing, this is done by conceiving it as possessed of certain modes of being, or qualities, and the sum of these qualities constitutes its concept or notion... As these qualities or modes are only identified with the thing by a mental attribution, they are called attributes... as it is only in or through them that we say or announce aught of a thing, they are called predicates, predicables, and predicaments, or categories, these words being here used in their more extensive signification... as it is only in and through them that we recognize a thing for what it is, they are called notes, signs, marks, characters... finally as it is only in and through them that we become aware that a thing is possessed of a peculiar and determinate existence, they are called properties, differences, determinations... (hamilton_64 p.55)

On Hamilton's view, as I read it, a predicate is a verbalizable quality of an object; however, the very same quality may also be called a "note", "sign", "determination", etc., when it is considered in certain contexts appropriate to those designations. Thus, really, a predicate is just some distinguishable quality of a perceived entity. What cannot be distinguished cannot be predicated of an entity, whereas conversely, anything than can be distinguished can be predicated. Thus, the necessary and sufficient condition for predication to take place is the existence of at least one distinguishable property or quality.

This is not altogether disjoint from the modern notion of predication, in which a predicate is defined simply as a relation, a function that maps its arguments to TRUE or FALSE (sowa_00; see also Sowa's mathematical review). That is, a predicate accepts a tuple of attributes or variables, and returns for each tuple a value of TRUE or FALSE. In some cases, a predicate can be expressed by a simple rule (i.e., intentionally), as for the unary predicate "is_positive_number(x)." Such an intentional description of a predicate is generally only viable when there is some simple algorithmic representation for the predicate in question (in the previous case, a division-by-2 remainder test), but more generally a predicate is just described by the set of entities for which it evaluates to TRUE, or, alternatively, by the set of entities for which it evaluates to FALSE. In these cases, the predicate is said to be described extensionally.

As an aside, classically, a predicate differs from a proposition in that a proposition is a sentence that has truth or falsity (Aristotle, On Interpretation, edghill_01b p.42). Thus, "a proposition is a portion of discourse in which something is affirmed or denied of something" (mill_36 p.51). In other words, a proposition is usually formed by explicitly evaluating a predicate or combination of predicates on a subject. Thus, "went to the store on Tuesday" is a predicate designating the class of people who went to the store on Tuesday. It is a relation which maps individual people (or their names) to TRUE or FALSE. A proposition which uses this predicate might then be "John went to the store on Tuesday," which evaluates to TRUE or FALSE depending on whether "John" is a member of the class represented by the predicate in question. Propositional logic deals with how truth is preserved when truth-bearing entities such as propositions are combined in various ways.

In the case of binary attributes (e.g., attributes which are either present or absent), the intentional description for a predicate would simply be the set of attributes shared by all the objects in the predicate-defined class, whereas the extensional description would be the set of objects themselves. As Hamilton puts it (hamilton_64 p.105), "The comprehension [intension] of a concept is nothing more than the sum or complement of the distinguishing characters, attributes, of which the concept is made up; and the extension of a concept is nothing more than the sum or complement of the objects themselves, whose resembling characters were abstracted to constitute the concept."

Note: See the note preceding the previous post about viewing mathematics. (You should see some red-colored mathematics below, if things are working on your end.)

To be a little more formal, a predicate (like a relation) is just some subset of the Cartesian product of the set of attributes or features by which the entities are described (i.e., some region of the "feature space"). For example, if we have a set `cc{X}` of three binary variables/attributes `cc{X}={x_1,x_2,x_3}`, each variable adopting value 0 or 1, then the full Cartesian product `ox cc{X}` is the set

`ox cc{X}={[000],[001],[010],[011],[100],[101],[110],[111]}`,

which is the set of every ordered combination of the attributes, i.e., the complete set of possible entities in the universe of discourse. (The notation `{010}` is shorthand for `{x_1=0,x_2=1,x_3=0}`, etc.) Any subset of `ox cc{X}` then defines a predicate. Thus, the subset `{000,010,101,110}` defines a ternary predicate, a relation which returns TRUE for just the previously specified objects (3-tuples), and returns FALSE for all other objects. This predicate defined by the set `{000,010,101,110}` has no compact intentional expression (i.e., rule), whereas, for example, the predicate defined extensionally by the set `{100,110,101,111}` admits the simple intentional description of `x_1=1` which we might capture verbally with a simple predicate label such as has_feature_x1(x1,x2,x3). (Note, however, that invoking an intentional description like this necessarily introduces inductive bias, which rears its head when new objects outside this set are observed, i.e., when the feature space is expanded.) The issue of simplicity and complexity (i.e., compressibility) of relations is a very deep one, and not directly relevant to this discussion. Also deep but not immediately relevant is the nature of the distinction between intentional and extensional description, and whether the two forms are not just points on a continuous spectrum of compressibility that includes many levels of "intentionality" or "extensionality" between the absolute poles of "intentional" and "extensional".

On the other hand, what is deep and immediately relevant is that the establishment of a predicate (intentionally or extensionally) immediately induces a categorization scheme on the universe; in particular, with the introduction of a predicate, two classes of entities are immediately distinguished — those for which the predicate evaluates true, and those for which the predicate evaluates false. Here then we begin to see the connection between predication and categorization: Indeed, "as soon as we employ a name to connote attributes, the things, be they more or fewer, which happen to possess those attributes, are constituted ipso facto a class... It is a fundamental principle in logic, that the power of framing classes is unlimited, as long as there is any (even the smallest) difference to found a distinction upon. Take any attribute whatever, and if some things have it, and others have not, we may ground on the attribute a division of all things into two classes; and we actually do so the moment we create a name which connotes the attribute" (mill_36 p.76,79). Thus, predication is categorization.

Mill makes a point that we do not predicate a class of an individual — we predicate membership in a class of the individual, or a name representing an attribute (mill_36 p.78). It is further notable (and Hamilton, for one, does not miss the opportunity to note it at great length) that there exists an inverse relationship between the sizes of the intention and extension of a concept or predicate. As the size of the intension increases through expansion of the set of attributes shared by the objects in the class, the extension is simultaneously decreased by the elimination of objects not sharing the specified features. Intuitively, the more rigorous the intentional description, the fewer objects can satisfy it. Conversely, as the extension of a concept or predicate increases through addition of non-redundant objects to the class, the intention is decreased by elimination of attributes which those objects fail to share. We will say more about this later.

It seems to me that the classical authors were generally concerned with unary predicates — those which accept only a single argument. Often these are "is-a" predicates, such as is_a_dog(x) or is_a_human(x), which return TRUE when x is a dog or human, respectively, although binary predicates such as has_a(x,y) or is_made_from(x,y) are also entertained. Such binary predicates would return TRUE when it is true (for instance) that object x possess a property y or that object x is made from y, respectively. (Lest anyone think that such primitive predicates as "is-a" are hopelessly antiquated, these sorts of relations are still very much current in modern ontologies, description logics, semantic networks, etc. The reason for their continued utilization is the same reason that found Aristotle pondering them 2000 years ago: There is a small set of common predicates which we humans use to describe our world, and any mechanical system that ultimately hopes to interact intelligently with humans must therefore cope with common predicates designating possession, composition, subsumption, etc.)

Aristotle, later amplified by Porphyry, distinguishes several different semantic classes of predication later to become known as "the predicables" (mill_36 p.77). It can probably go without saying that Aristotle himself is less than entirely clear on this issue (smith_95) — else he would not have so easily entertained great minds for two millennia — but in his Topics (pickard-cambridge_01 p.191) he at least lays out the following four types of predication: definition, property, genus, accident. In later treatments, definition seems to be replaced by the predicables species and differentia thus yielding the most common version of the hierarchy of predicables: genus, species, differentia, proprium, accidens, as is given in Porphyry's Introduction. Below, I review the two schemes as one, even though there may in fact be "radical differences" between the two, as suggested by the Wikipedia article (actually a 1911 Britannica article). In particular, the Britannica author suggests that Aristotle's system is the more secure because all of the predicates deal with universals (i.e., abstractions), whereas Porphyry's scheme by involving "species" intermixes predication of universals and individuals. I don't know whether I agree with that assessment or not, so I will just leave it alone.

Let us very speedily review these types of predicates, while simultaneously trying not to be sucked into Aristotle's interlocking theories of causation and "the categories". First, to paint the larger picture, it is best to think of the universe (of discourse) in terms of an inclusion hierarchy. The figure below shows a set of 10 individuals (bottom row). These individuals may be objects or events or any other entities which are susceptible to predication (i.e., which have distinguishable qualities), but it is only these individuals, i.e., the nodes in the bottom row, that are actually observable. The distinguishable qualities (i.e., feature set) in this universe are represented by capital English letters. (The letters themselves are, of course, just meaningless symbols; i.e., the label "ACH", for example, simply means "object having property A, and property C, and property H, and no other properties".) I think it is correct to say that this is the model of the structure of the world that most of the ancients were working with. They observed (as do we) that entities tend to have many common properties, and they took these common property clusters to be a guide to the deep structure of the universe; a structure in which entities share common features not by accident, but because in some sense these entities share a common genesis, a common connection to a particular generative node in an underlying (unobservable) reality.

The inclusion hierarchy model which results from this line of thinking is not wrong, per se. In fact, it can be an appropriate model both for understanding certain kinds of accretion-based artifacts (e.g., multiple-author documents) and certain natural systems (e.g., genetic inheritance, as per cladistics). Many other systems can be reasonably and profitably simplified into inclusion hierarchies (e.g., medical knowledge). The strict inclusion hierarchy is, however, certainly an incomplete model for any system of more than rudimentary complexity.

In any event, the method by which the inclusion hierarchy is inferred from observations is by recursive abstraction of common elements. For example, we note that in the figure three of the observed entities {ACH, ACI, ACJ} all share the feature complex AC. We therefore abstract the AC complex away from the entities, thus signaling our belief that there is an underlying entity (hidden node) which contributes this AC complex to all the entities which posses it. The same process allows us to abstract the feature complex AF from entities {AFK,AFL}. Recursively, we then note that hidden nodes AC and AF share the feature A in common, which can then be abstracted in the same way. After we construct the inclusion hierarchy in this manner, we may choose to apply special titles such as "genus" and "species" to some of the hidden nodes thus inferred. In the figure, AC and AF could be considered species of A, if certain conditions hold (discussed below). With this image in mind, we can now return to the definitions of "the predicables".

Genus and Species: Porphyry (barnes_03) explains that genus relates to "genesis" in the sense that genus is the "origin" for the things collected under it: Moreover, "genus is what is predicated, in answer to 'What is it?', of several items which differ in species; for example, animal." Species are then the subclasses within a genus, which are in turn comprised of individuals.

We can see already that there are going to be major problems. How does one know whether a given abstracted class should be given the special label of "genus" or "species"? Porphyry (barnes_03 p.6) already notes that "between the most general and the most special are other items which are at the same time both genera and species (but taken in relation now to one thing and now to another)." In other words, genus and species appear to be relative designations. Mill points out, for example, that "animal" is evidently a genus with respect to "man", but is a species with respect to "substance". One notion can always be regarded as subordinate or superordinate to another (hamilton_64 p.136).

It is possible to simply embrace the relativity of such terms, which amounts to an admission that the "generality" or "specificity" of classes are in the eye of the beholder, contingent on context, etc., etc. However, while this may work for the pure logician, it is not acceptable to Aristotelians who view the inferred inclusion hierarchy as descriptive of the order in the natural world. In their view, the classes abstracted at some level must have attributed to them Genus status with absoluteness. The Genus "animal" is not like the genus "shoe lace", although both are inferred by the selfsame process of abstraction; rather, the class "animal" corresponds to the structure of the world in a profound way that the class "shoe lace" does not. However, what exactly it is that makes something genuinely a capital-G Genus or capital-S Species (rather than no-capital genus or species) is rarely clear. Mill (mill_36 p.78) indicates that for Aristotelians, Genus and Species must reflect the essence of the subject, where the difference between essential attributes and non-essential attributes is just that the former are involved in the class name. (On Mill's interpretation, the essence of a subject is the essence (i.e. intension) of the class in which it is a member, this being the only notion of "essence" which he allows. This is clearly not how the ancients understood essence, however.) In any case, the appeal to essence just makes the entire endeavor completely circular, and provides no justification why one class is a Genus, a second is a Species, and a third is neither at all.

Mill provides a plausible, though weaker, approach to the designations of Genus and Species (mill_36 p.80). He writes that genera and species are those classes which are set apart from other classes by "vast numbers of features". Thus, plant is set off from animal by thousands of features, for example. This is a reasonable view, both because of naturalistic considerations relating to common descent in biology, and because it provides the rudiments of a procedure for assessing genericity and specificity. (Unfortunately, without constraints on features, the procedure cannot be implemented, but this is a common problem in all inference schemes.) Thus, the genera are classes that are separated from each other by vast numbers of features (classically, by all features, except perhaps "Being"), while species are the subclasses of a genus that are separated by vast numbers of features. Having now suitably confused matters, let us continue with our definitions.

Differentia: Differentia or differences are the distinctions between species within a genus. For example, the genus "animal" contains the species "human", "horse", "crab", etc. Whatever makes these subclasses distinct from one another — i.e., whatever features one of these subclasses possesses over and beyond what is contributed by its genus, that is its difference: As Porphyry writes, "a difference is that by which a species exceeds its genus" (barnes_03 p.10). "This surplus of connotation — this which the species connotes over and above the connotation of the genus — is the Differentia, or specific difference; or, to state the same proposition in other words, the Differentia is that which must be added to the connotation of the genus, to complete the connotation of the species" (mill_36 p.82). On Porphyry's view, "a difference is what is predicated, in answer to 'What sort of so-and-so is it?'" (barnes_03 p.10).

In the illustration, species AC differs from its genus (A) by the property C. Thus, C is its difference. Likewise, species BDC differs from its genus (B) by properties DC, which therefore constitute its difference. Again, this explanation raises many questions; for example, what kind of difference constitutes a capital-D Difference? Porphyry (barnes_03 p.9) indicates that "it is in virtue of those differences which make a thing other [not just otherlike] that divisions of genera into species are made... not just anything that happens to separate under the same genus is a difference but rather something which contributes to their being and which is a part of what it is to be the object" (barnes_03 p.11). Thus, true Differences must in some sense be categorical differences.

Property: The least-often discussed of the predicables, property, is a quality in members of the species which is non-essential, but which is characteristically present in members of that species (and in no others). For example (for argument's sake), possession of opposable thumbs or ability to laugh are special characteristics of human beings. However, opposable thumbs and laughter are not essential qualities of a human such that an individual's humanity would be called into question by their absence (as it would, for example, by the absence of rationality). Thus, properties are characteristic, but non-essential, qualities.

Accident: One can say that accident is any predication that does not fall into the other predicable categories. Loosely, accident is a quality of an individual that may have been other than what it is. The blue color of a house is an accident. The house could have been red, or yellow, or pale green, and at some other time it might indeed be one of those other colors. Accidents, in general, are any predications that are not universal and (like properties) do not go to the essence of the subject. Aristotle in Interpretation (edghill_01b p.53) points out that accidents do not combine in the subject to form a unity. (It is not clear to me what he means by this.) Accidents can also be described as those predicates which fail to counter-predicate with the objects they modify (see below).

Definition: Perhaps the most contentious of all the predicables, definition can be considered a derived predicable, given by the formula "genus + differentia" (Topics, pickard-cambridge_01 p.195; smith_95 p.52). That is, the definition of an entity is given by stating its genus followed by its differentia. The classical example is the definition of "human" as rational animal, or "animal + rational", where "animal" designates the genus to which humans belong, and "rational" designates the Difference which humans possess over and above the genus. Aristotle also describes definition as "an account which signifies what it is to be something" (smith_95 p.51).

Aristotle offers some additional hints to what definition means in his view: Along with genus, definition is one of the "essential predicates" which say of an entity "what it is" (smith_95 p.53-54), and which involve "essential attributes" — those which are essential to the nature of the object (Posterior Analytics, mure_01 p.116). In his Topics (pickard-cambridge_01 p.190) he indicates that "the peculiar" can be divided into definition (indicating essence) on the one hand, and property on the other. Indeed, the criterion of essentiality is really the ultimate test for definitionality: A weaker test, that of counter-predication (see below), does not in fact distinguish definition from property. Therefore, a definition must counter-predicate with the entity it describes as well as explain the essential nature of that entity (smith_95 p.53-54). Predicates which fail to do the latter, but which still counter-predicate, are simply properties. Predicates which fail to do both are accidents.

The notion of counter-predication is (in true Aristotelian fashion) simple but slippery. The idea is that a definition specifies both the necessary and sufficient conditions for the entity to be what it is (swoyer_06 p.141). Thus, if the definition of human is "rational animal," this means that human implies rational animal and rational animal implies human. Thus, the definition expresses the bilateral implication `mbox{human} \leftrightarrow mbox{rational animal}`. In other words, the class of `cc{X}` and the class of `cc{Y}` are exactly and necessarily the same classes when `cc{Y}` is the definition of `cc{X}`. (This notion of definition is what is known as a "concept" in formal concept analysis.) One can see that this counter-predication property holds for both property predicates as well as definition predicates, since a property is a peculiar quality shared by all instances (e.g., opposable thumbs). All humans and only humans have opposable thumbs (for argument's sake). Thus, an animal is a human if and only if it has opposable thumbs. Likewise for definition: an animal is a human if and only if it possess rationality. As indicated above, for a predicate to be a definition, beyond counter-predication it must also be descriptive of essential qualities, rather than nonessential qualities.

Aristotle provides no formal procedure for determining the definition of entities, although he disparages Plato's method of division (smith_95 p.52). However, he does indicate in Posterior Analytics (mure_01 p.179) that if we look for commonalities among entities, we can "persevere until we reach a single formula, since this will be the definition of the thing." This certainly suggests the kind of factoring procedure mentioned above for inferring inclusion hierarchies (figure above), but it is unclear what is meant here by "a single formula". For example, if the inclusion hierarchy is 37 levels deep, how do we know at which level are constituted the "definitions"? Perhaps connected to his reluctance to provide a procedure is Aristotle's insistence that definitions are not susceptible to proof or demonstration (Posterior Analytics, mure_01 p.162): "...there is no identical object of which it is possible to possess both a definition and a demonstration... all demonstrations evidently assume and posit the essential nature..." In other words, our knowledge of a thing's definition, since it is related to its essential nature, cannot come from any deductive argument; it must be assumed. This seems to make sense on a syllogistic view of proof; definition is Genus plus Differentia, but the Differentia cannot be implied by the Genus, since it is the nature of Difference not to be implied by Genus. In other words, if a Difference were implied by a Genus, then the Difference would simply be part of the description of the Genus, and be no difference at all.

It need not be mentioned that the entire system of "the predicables" is horribly question-begging, and leaves unanswered the question of which abstractions have a genuine existence as universals and which do not, as well as the essential nature (I know, I know) of universals such as "genus" or "definition". However, to one extent or another, this is the system that most religious thinkers of the middle ages had to wrestle with, and by acknowledging it we may better understand the particular positions they were forced to stake out. We will try to understand some of these theological positions vis à vis definition, predication, and categorization in the next section, but for the time being we will just conclude by pointing out that the Aristotelian system itself cannot be considered entirely wrong. In the wake of Occam and Mill and Wittgenstein and others, we can no longer seek "definitions" or "genera" in the absolute sense that the Aristotelians sought them; nevertheless, there is structure in the world, and this structure in many instances has a certain hierarchical character. Properties and features, whether they inhere in objects themselves or are merely mental constructions, do tend to cluster into groupings or modes. As Mill puts it, it seems undeniable that there are vast numbers of qualities by which plants differ from animals — far more than the number on which one plant differs from another, or one animal from another. Until this structure is acknowledged and modeled in some manner, science is impossible. Moreover, in some sense, the "universals" underlying this structure turn out to be even more real than the Aristotelians imagined them to be. Barring exercises in antirealism, there really are underlying genetic structures which explain the commonalities observed among organisms, and the manner in which these commonalities accrete and emerge is genuinely something that can be reasonably approximated by an inclusion hierarchy. As in many other areas of science (e.g., psychology), the instincts and ideas were right, but applied to the wrong constituents and at the wrong level of abstraction. Enough for now. חג שמח!

Unknowability of God In Jewish Rationalism II: Not Negative Theology

2007-02-05T13:28:00.000-05:00

Note: I am trying to work some mathematical notation into these posts, gratuitously at first, but later with the purpose of formalizing ideas. If you use the Firefox browser, you should be able to see the math no problem, I hope. If you use Internet Explorer, you may need to download the free MathPlayer plug-in from Design Science. (Because Microsoft makes things easy.) If you can see the red equation below (rather than a bunch of text), you should be OK:

`sum_(k=1)^n k = 1+2+ cdots +n=(n(n+1))/2`

OK. On with the show...

The greatest Jewish medieval rationalist proponent of the unknowable God is without any doubt Maimonides. His approach is frequently known as the "negative theology" or the doctrine of "negative attributes." The basic notion of negative theology probably dates back to Aristotle or Plotinus, but our interest here is not in tracing the intellectual history of the idea, and so we simply begin with Rambam. On a superficial level, the idea behind negative attribution is that instead of affirming attributes of God (by saying, for example, that God possesses "will" or "power"), it is appropriate that one should deny their opposites or privations (by saying, for example, that God is not lacking "will" or "power"). A typical selection from Rambam is as follows (GP I:58):

... we say of Him [God], because of these notions, that He is powerful and knowing and willing. The intention in ascribing these attributes to Him is to signify that He is neither powerless nor ignorant nor inattentive nor negligent... every attribute that we predicate of Him is an attribute of action or, if the attribute is intended for the apprehension of His essence and not of His action, it signifies the negation of the privation of the attribute in question... you come nearer to the apprehension of Him, may He be exalted, with every increase in the negations regarding Him...

The question that immediately leaps to mind is whether and how any advantage can possibly be gained by merely replacing affirmations with negations. Basic acquaintance with logic suggests that this approach will not achieve anything at all, and this was appreciated by all the significant medieval thinkers. Duns Scotus, for example, writes

For every denial is intelligible only in terms of some affirmation. It is also clear that we can know negations of God only by means of affirmations; for if we deny anything of God, it is because we wish to do away with something inconsistent with what we have already affirmed.

Crescas, I believe, makes the same point, as does Albo (husik_29):

For although it is true that all negations are predicable of God, still no wise man can negate any attribute unless he knows how the positive attribute applies to the thing characterized by it, and understands the aspect of perfection as well as of defect which the attribute contains.

It is clear that the negation of an attribute cannot be meaningful without the possibility of its affirmation, and that for classical logic the double-negation must equal the affirmation, `¬(¬x)=x`. In short, the problem is that without positive attributes there cannot be negative attributes (berkovits_04). Rambam himself was equally aware of the obvious difficulty in this interpretation of the negative attributes, and although he does give what appears to be a defense of this very position in GP I:60, he takes greater pains to explain that this superficial negation is not the sort of negation he is advocating. Rather, the negation that Rambam ultimately advocates is the negation of the very applicability of any attribute to God. Thus (GP I:58),

... those negations are not used with reference to or applied to Him, may He be exalted, except from the following point of view, which you know: one sometimes denies with reference to a thing something that cannot fittingly exist in it. Thus we say of a wall that it is not endowed with sight.

Thus, the application of any attribute to God constitutes what we today sometimes call a "category error." Just as there is some set of attributes which do not apply to walls (e.g., sight, wisdom, gender, etc.) and which can therefore not meaningfully be affirmed or denied of walls, there is a set of attributes which do not apply to God and which can therefore not meaningfully be affirmed or denied of God. Thus, Rambam's negation means that there are no attributes whatsoever that may be predicated in the same sense (i.e., univocally) of both humans and of God, a position which may be referred to as the doctrine of "absolute equivocation." More simply, as Steinsaltz puts it, we have no terminology to describe God. Thus, the predication of any attribute in regard to God is a predication which can neither be affirmed nor denied, but is one which falls into a critical third logical class of which the classical logicians often failed to take note:

A proposition must be either true or false, provided that the predicate be one which can in any intelligible sense be attributed to the subject (and as this is always assumed to be the case in treatises on logic, the axiom is always laid down there as of absolute truth). "Abracadabra is a second intention" is neither true nor false. Between the true and the false there is a third possibility, the Unmeaning ..." (mill_36)

Since Mill's time there has been some work on devising logics which incorporate the "unmeaning" valuation of predicates (see Haack, 1974), but that would be getting far afield for us, as it is hardly what Rambam could have had in mind. On Rambam's view, in the case of God as the "subject," the set of "Unmeaning" propositions is just the set containing every proposition. Let us then look at Rambam's position in his own words:

Now everything that can be ascribed to God, may He be exalted, differs in every respect from our attributes, so that no definition can comprehend the one thing and the other. (I:35)

... it behooves those who believe that there are essential attributes that may be predicated of the Creator—namely that He is existent, living, possessing power, knowing, and willing—to understand that these notions are not ascribed to Him and to us in the same sense... clear it is to all those who understand the meaning of being alike that the term "existent" is predicated of Him, may He be exalted, and of everything that is other than He, in a purely equivocal sense. Similarly, the terms "knowledge," "power," "will," and "life," as applied to Him, may He be exalted, and to all those possessing knowledge, power, will, and life, are purely equivocal, so that their meaning when they are predicated of Him is in no way like their meaning in other applications. (I:56)

Seeskin explains Maimonidean absolute equivocation in this way:

In God's case, the denial not only rejects the predicate in question but puts God outside the scope of the predicate or anything like it. To the question "How do we know which negations to make?" Maimonides' answer is that at one level we negate predicates that suggest imperfection to the average worshiper, but at another level we negate all predicates. In either case, there is no common core of meaning once we take into account the full extent of the negation (seeskin_00).

The only thing we can say about the nature of God is that whichever way we view it, or in whatever way we describe it, it is off the scale of intelligibility. In one way, this admission says more about us than it does about God. It says that when we try to understand God, we come face to face with our own limitations... (seeskin_91)

The negative theology is also strongly advocated by Albo, whose method he sees foretold in the "still small voice" of I Kings 19:12 (husik_29, 217). Concerning, in particular, the understanding of God's volition, he writes:

For God's will follows His wisdom and His power, and as His wisdom and His power are infinite and not of the same kind as our wisdom and power, so His will is not of the same kind as our will. And as the wisdom and knowledge of God are not something added to His essence, as we shall see later, but are of His very essence, and His essence is absolutely unknown, His wisdom is also absolutely unknown. And when we attribute wisdom to God, all that we understand is that we deny the attribute of ignorance, which is the opposite. In the same way we attribute will to God in the sense that we deny that He acts by necessity like the defective agents of finite power, God's activity being with infinite power. (husik_29, 20)

The reason why, on Albo's view, we even bother making attributions at all, is simply for the sake of appearances: God cannot be considered inferior to any merely physical contingent being, and since, for example, "volition" is a perfection among physical beings, we simply cannot deny that God has volition. Similarly, "We ascribe knowledge to Him because it is a perfection which it is inconceivable that God should be without." Fundamentally, it would be unseemly to deny to God attributes that are considered perfections among his creations. Still, Albo does not uniformly deny the applicability of all attributes, but distinguishes between desirable attributes (perfections) and undesirable attributes (imperfections). Only the former need be denied by way of absolute equivocation, while the latter can be denied in their mundane sense:

...not all attributes are negated in the same manner... If the attribute denotes a defect, it is negated in another way, namely in respect to its defective element. To deny everything of God without reason or understanding would not indicate God's perfection. All those attributes which we regard as defects, like dead, weak, ignorant, poor, bad, and so on, we negate absolutely, meaning that such attributes, which are defects, are not found in God, but that the opposite, which is a perfection, is found in Him. But when we negate the other opposite, which denotes a perfection in our estimation, like living, powerful, wise, rich, good, the meaning is not that this attribute does not exist in Him but the opposite, which is a defect, does. Such negation, far from ascribing perfection to God, is insult and blasphemy. What we do mean in the latter case is that the perfections which we understand by the terms living, powerful, wise, and so on, are not found in God as they are found in us but in a manner more honorable and more excellent, so much so that there is no relation between the perfection in us or as we understand it and the perfection when ascribed to God. The perfection or perfections in question are applied to man and to God as homonyms, considering the enormous difference that there is between them. (husik_29, 200)

I don't find Albo's remarks here to be particularly coherent, and perhaps his conclusion that "the most that we can understand about God is that we can not understand Him" (husik_29, 206) is an indication that Albo is not entirely pleased with his own analysis either. Returning to Rambam's "way of negation," or the doctrine of absolute equivocation, while one can justifiably admire Maimonides for this bold stroke of genius, it quickly becomes apparent that nothing was solved.

It is clear what price Maimonides pays for rejecting the doctrine of analogy. If there is no analogy between God's intelligence, power, and goodness and ours, we have no hope of understanding what these attributes are in God. We can say that they all must be identical or else God's unity would be compromised. But when it comes to how God thinks, how He generates power as a result of thinking, and why His power is necessarily benevolent, the only thing we know is that we cannot know. All we can do is confess ignorance. This is another way of saying that the internal nature of God is and will always remain a mystery... (seeskin_91)

The problem here is that while it is fine on the one hand to declare that predicates applied to God do not have the same meaning as predicates of the same name applied to man (i.e., that all such predicates are applied absolutely equivocally), the fact remains that all of the crucial arguments that the medieval rationalists offer in favor of God's existence, knowledge, power, incorporeality, etc., rely on the very fact that these two sets of predicates do mean the same things in both cases! This critique is clearly formulated by Gersonides in Wars of the Lord:

...since it is clear when we deny attributes of God that are found in us that such attributes are not completely equivocal with respect to God (may he be blessed) and us, the same is true when we affirm of God predicates that are true of us. For example, we say that God is immovable, since if He were movable He would be a body, for all moveable objects [are bodies]. Now it is evident that in this proposition the term "moveable" is not completely equivocal with respect to the term "moveable" when it is applied to nondivine things. For if it were, there would be no proof that God is not moveable, since the moveable object that must be a body is that which is moveable in the domain of human phenomena, whereas the term "moveable" (in the completely equivocal sense) would not imply that it is a body. Hence, since it is evident that the predicates we deny of God are not absolutely equivocal, neither are the terms that we affirm of Him. In general, if the terms used in affirming predicates of Him were absolutely equivocal, there would be no term applicable to things in our world that would be more appropriate to deny than to affirm of God or [more appropriate] to affirm that to deny of Him. For example, someone could say "God is a body" but not mean by the term "body," "a magnitude"; rather he would mean something that is completely equivocal with the term "body" as we usually use it. Similarly, someone could say "God does not have knowledge," since the term knowledge would not [on this view] have the same meaning for him in this statement as it does for us. (v.2 p.110, Feldman)

Ralbag's argument basically says that if an attribute is predicated of God in a completely different (and unknown) sense than that in which it is predicated of man, then when such a predicate is applied to God, it is no longer possible to use that term in any aspect of theological reasoning. Samuelson (1969) puts it succinctly:

Thus, in the case of a system of God-talk based on Maimonides' account, it makes no more sense to say, for example, "God is good" than to say that "xtqpr is qpryiz," since in both cases there are no rules governing the use of the constituent terms of the proposition. Actually, it is not even correct to call either letter sequence a proposition, since neither sequence constitutes anything that is in any way intelligible. Both are plain and simple gibberish.

The argument of Gersonides seems to me to be entirely cogent and final, although I might not go so far as Samuelson to say that "this argument is devastating against any form of the position that God is beyond human comprehension." It is only fatal against the use of inferential procedures involving the attributes of God, not against His essential unknowability. In any case, it is at least in part because of this thorny issue that Maimonides' position was rejected by most subsequent philosophers (wolfson_53). As to why his views were rejected among the masses, the greater problem may have been due to the inadequacy for religion of a propertyless, attributeless, featureless God, even if it could be shown conclusively that this is the only logically coherent understanding of God available within a radical monotheistic framework. As Berkovits puts it, "The negative attributes will never do. Religion cannot forgo the love and the mercy of God, or even his justice and anger. Such attributes have to be related to him in a positive sense, or else there is no basis for a living God or religious observance."

However, despite the dramatic distance that Rambam puts between man and God, he still strives to limit this barrier only to matters pertaining to God's essence or quiddity (God's "what-ness"). He seems to reserve room for knowledge of God in areas that do not impact the question of His quiddity, such as those areas that relate only to God's actions. We will try to assess this distinction below, but first we will make a short detour into the "problem of predicates," in which we try to gain some insight into why Rambam and other medieval thinkers were so adamant about the "indefinability" of God. Why can we not have a definition? Why can attributes only be applied to God equivocally? What would be so loathsome in attributing to God "knowledge" or "will" or "agency" in the same sense that we ourselves possess these attributes? Clearly, the medieval thinkers saw grave dangers in pursuing such a course. What was it they saw?

Unknowability of God In Jewish Rationalism I

2006-12-30T23:35:00.000-05:00

The rationalist approach to interpretation of the Bible and religious tradition is based on the fundamental doctrine that Torah and reason cannot be in conflict, and that an individual therefore need not adopt any position on matters religious which transgresses against reason. The basic spirit of Jewish rationalism — its motivation and method — is well captured, I think, by these two statements from Bachya and Ralbag:

And if he does not delve into the truth and certainty of the matter, he is disgraceful and is considered to be intellectually and functionally lax. He would be like the patient who knew all about his disease and its cure, but who depended entirely on his doctor to heal him, and was reluctant to use his own knowledge and judgment to determine if the doctor was doing the right thing or not... — Bachya ibn Pakuda (pakuda_96)

... when the Torah, interpreted literally, seems to conflict with doctrines that have been proved by reason, it is proper to interpret these passages according to philosophical understanding, so long as none of the fundamental principles of the Torah are destroyed... It is even more proper that we not disagree with philosophy when the Torah itself does not disagree with it. — Ralbag (feldman_84)

Thus, there is shame and disgrace attached to the failure to investigate matters of religious principle using the fullest powers of human reason. One cannot be considered wise or perceptive if one does not attempt to understand the origins, and establish the correctness, of one's beliefs. Moreover, at least on Ralbag's view, the "claim of reason" occupies a higher place than the "claim of tradition," and traditional understandings must be brought into conformity with the demonstrations of philosophy, rather than vice versa, to whatever extent this is possible.

Of course, one challenge of the "religion of reason" is that the dictates of reason change over time, and this approach — if it is to be pursued over the long term — demands a never-ending reinterpretation of tradition. This is because, as new principles are discovered and new facts uncovered, what earlier seemed a "reasonable" position slowly becomes an unconvincing, and, finally, untenable position. It is then replaced by a position that is more "reasonable" in light of current knowledge (and biases). This being the case, if Torah and reason are to remain free from contradiction, then the interpretation of Torah may need to change as often as do the artifacts of reason.

This observation has no doubt caused many to dismiss as foolhardy any effort to reconcile religion and reason. Those of a scholarly mindset will argue that the inevitable "tortured reconciliations" forfeit the original meaning and message of the text (e.g., Spinoza, sarna_66), while those more inclined to skepticism will wonder at the usefulness of a document whose only apparent remaining purpose is to be periodically "reconciled" with external evidence. They will see this as a symptom of pathology, as analogous to one who lugs around an old phone book from 1985, periodically updating the numbers in it with new information from www.yellowpages.com.

On the other hand, those of a traditional inclination will cite the short shelf-life of philosophical wisdom as evidence of its fallibility. If the claims of reason change every few years, then reason cannot be a genuine pathway to truth. Maharal (mallin_carmell_75) expresses this as follows:

Philosophers are interested in comprehending and revealing hidden matters, although they fail to understand the obvious, even the things that are before their very eyes. One school expounds one opinion about the essence of mind and soul, and another school expounds a different theory. And indeed none of the opinions are of any value, for what can material man understand? Granted, God has given man understanding and wisdom, but it is all relative to and connected with the material; all his rationality is subjective and related to matter. How can he grasp that which is abstract? A person would know nothing about the ways and actions of that which is far removed from his world had not Hashem revealed this to Moshe and the other prophets, who in turn passed this knowledge on to the Sages, who revealed these hidden things to us in the Midrashim and other teachings.

The implications of Maharal's statement are very much along the lines of the injunction of Ben Sira, later quoted by Bachya: "Do not inquire into what overwhelms you, and do not delve into what is hidden from you. Reflect upon what you have inherited instead; for you have no business occupying yourself with mysteries" (3:21). And one can certainly see Maharal's point regarding the questionable value of ancient philosophies (if not regarding the scientific merits of Midrashim). The "philosophies" with which the medieval rabbis were concerned to make the teachings of the Torah correspond are indeed among those untenable notions that have long since passing into the history of human ideas (though not without first fertilizing the ground for their successors), a situation which would seem retroactively to vindicate the opponents of medieval rationalism. In any case, Maharal has made his position clear, and it is readily adopted by the multitudes who are pleased to "remain silent" and to eschew any philosophical investigation of metaphysical matters. However, it is still worth considering the following words of Rambam (GP I:50):

If you belong to those who are satisfied with expressing in speech the opinions that are correct or that you deem to be correct, without representing them to yourself and believing them, and still less without seeking certain knowledge regarding them, you take a very easy road...

Regardless of how favorably one views the agenda of the rationalists, their efforts at reconciling Torah with what is (for us) an antiquated philosophical framework has from a practical standpoint diminished their appeal to modern readers. There is only so much one can read about the "Agent Intellect." If their commitment was indeed to Aristotelian theories of physics and cognition that vanished from sight 400 years ago, then we can wonder what relevance their work has for today's student. However, if their commitment was to the pursuit of reason, whatever its form, then at least their passion in pursuit of this commitment is still highly inspiring. Scholars like Rambam recognized, I think, that it is disingenuous to preferentially insulate religious beliefs from the critical evaluation that one brings to other beliefs about the world. In the words of a contemporary author, "Jewish apologetics... must not encourage that division of the mind in which incompatible ideas are allowed to exist side by side in water-tight compartments" (jacobs_57). It is therefore the rationalist attitude toward the study of religion, rather than the particular proofs or arguments yielded by this study in the medieval era, that is the most important contribution of the medieval rationalists. However, as our purpose here is not to assess the merits of the rationalist agenda, we will not dwell on this, and instead move on to presenting some of their actual opinions.

The greatest medieval proponent of the "unknowable God" is without any doubt Maimonides. But before approaching Rambam, we first briefly mention the treatment of the unknowability of God by two earlier scholars, Saadia and Bachya. Saadia in Beliefs and Opinions (Emunot V'dayot) informs us the following:

But we have arrived at the result that the world was created from nothing, and this being the character of the object investigated at that stage, it is necessary that the character of the object investigated at the next stage, namely, the Creator (be He exalted and glorified) should be more abstract than anything abstract, more profound than anything profound, more subtle than anything subtle, deeper than anything deep, more powerful than anything powerful, and higher than anything high, so that it becomes impossible to probe His quality.

This passage regrettably does not provide much insight into the nature of God's unknowability, and is perhaps even a regression from Philo's analysis, which at least offered a somewhat concrete Platonic notion of transcendence. Saadia's argument seems to be that each successive stage of investigation requires as its subject something more abstract than the previous stage (perhaps he intends here a reference to the relation between species and genus), and as the world came from nothing (a propertyless void), its Creator must be even more abstract — more propertyless — and thus presumably "beyond" nothing. However, without any further elaboration on this point from Saadia, it is difficult to say more about the particulars of his view.

Bachya ibn Pakuda in Duties of the Heart (Chovot Halevavot) is somewhat more explicit in his analysis, recalling in his remarks elements of Philo and ibn Gabirol — the latter of whom lived at around the same time — but adding (perhaps for the first time in Jewish thought?) the rudiments of the "negative theology":

There are three of them [expressions of God's Essence], and they are: that He exists, that He is One, and that He is Eternal and without beginning... But what you must understand about these terms is that they do not imply any sort of change or variation in God's Essence. They are there to deny their opposite in the Creator, and to have us understand that the Creator is not plural, He is not nonexistent, and He was not created... They do not mean to indicate change in God's Essence, nor do they imply the existence of properties or plurality in Him... (pakuda_96, p.45-47)

What you must also understand about God is that there is nothing like Him, and that when He is described one way or another, you are meant to take that description as a denial of its opposite. As Aristotle said, "It is better to describe what God is not than to describe what He is," because whatever we could say about Him would refer either to His Essence or His properties, and the Creator of essences and properties cannot be described the way they are described. Whatever, in fact, draws us away from such descriptions is undoubtedly true and suitable to Him, because He is beyond all description and attribution, and superior to all likeness and comparison... we cannot imagine or fathom His Essence... the only things we understand about Him are His name and the fact of His existence... (pakuda_96, p.47-51)

You only exhibit profound knowledge when you acknowledge and truly believe that you are utterly ignorant of God's Essence. (pakuda_96, p.54)

In the last passage we see resurfacing again the idea expressed by Philo (and many mystics) that the ultimate knowledge of God is only present in the stark realization of our absolute lack of knowledge concerning God. The more deeply this realization grabs an individual, the greater is the knowledge of God that individual can be said to hold. We also see again the idea of the absolute "beyondness" of God that is typical of the mystical writings, and is present as well in Saadia's position above.

What is new in Bachya is this notion that there is a difference between the positive description of God and the negative description of God. The reason, on Bachya's account, that we cannot affirmatively describe God in any way is that such descriptions would either be descriptions of his essence or properties, and that as the creator of essences and properties, God cannot be described in these same terms. However, the logic here seems to be somewhat muddled. Besides the problem of whether anything is gained by the use of negative attributions over positive attributions (a problem recognized by Rambam, Ralbag, and Albo, but perhaps not by Bachya), if God is the maker of essences and properties, and therefore cannot be said to have essences and properties, then what do we mean when we say there is such a thing as God? If He has no essence and has no properties, then aren't we deceiving ourselves in believing that the term God has any referent at all? It becomes just a nonsense word, designating nothing. If, on the other hand, God does have an essence or properties of some kind, but just not the kind that can be described by way of any predicates that we possess, then we return again to the question of why this should be the case. In what manner do our predicates fail to represent God's essence or properties?

What is also notable about Bachya, besides the nascent negative theology, is the distinction made between God's essence, God's properties, and God's actions. In Bachya's philosophy, our only exposure to God comes by way of God's actions or deeds. By contrast, His essence and attributes remain — as mentioned above — utterly unknowable:

Since the Creator is completely hidden and utterly at a distance from us in His Essence, we can only comprehend the fact of His existence. For we would lose whatever understanding of His existence we had trying to imagine Him, because we would have exceeded our reach (and it would be like trying to experience something physical with the inappropriate sense). So, we should pursue God's existence through the signs of His deeds in creation, and they will prove Him to us. (pakuda_96, p.55)

But "expressions of God's deeds" speak of God in terms of His deeds, and we are allowed to compare them to those of His creations. Yet, we are only permitted to use them in reference to Him because of our pressing need to know about Him and grasp His existence in order to take service to Him upon ourselves.(pakuda_96, p.47)

Here we see the idea, taken up later by Rambam, that God is partly unknowable (in His essence and His attributes) and partly knowable (in His actions). We will have an opportunity to discuss this dichotomy at greater length later, but here we just point out that there is an ambiguity in this stance, since a priori we don't know which particular events in the world reflect the actions of God and which do not. The only reason we would attribute certain actions to God in the first place is because we have prior reason to believe that certain events are representative of the kind of things that the Deity might do, and yet the kind of things that the Deity might do depends on the particular traits that the Deity possesses (i.e., his psychological profile, as it were). Thus, any analysis of God's "actions" is inextricably bound up with analysis of God's attributes and essence (spero_73), and yet on Bachya's account this is precisely the information to which we do not have access. How then do we learn about God from God's deeds?

What is also interesting here is Bachya's analogy of this problem to that of using an "inappropriate sense." He expands on this idea as follows:

Each sense is limited in what it can do, and none can extend beyond its limit. So while you can easily see things close up, they are harder to see further away, until you cannot see them at all (which goes for hearing, and the other senses). It is also impossible to perceive with anything but the appropriate sense and if you try to, you will fail. So, for example, you could not listen to a song by "seeing" it; you could not see things by "listening" to them; and you could not taste things by "touching" them — even when the objects of your efforts are right in front of you. Because you cannot experience things with the inappropriate sense organ.

Bachya extends this idea from modalities of sensation also to modalities of cognition — i.e., memory, thought, imagination etc. — indicating that each of these has a particular domain of activity beyond which it fails to operate. What Bachya gives us here (even only by analogy) is something seemingly richer than the idea of Platonic transcendence presented by Philo and ibn Gabirol. It is not just that each creature perceives (or receives) God according to his mental "grasp" or intellectual level, where this capacity is viewed as a single parameter. Rather, Bachya's analogy rests on a kind of faculty psychology (cf. Fodor_83), positing that within a given individual there are multiple information channels that are dedicated to particular modes of information processing. A particular event in the environment may simultaneously be represented within the sensory apparatus dedicated to vision, olfaction, or audition, etc., or it may only be represented in a subset of these modalities, or in none of them. Thus, it might not be reading too much into Bachya to think of the cognitive system as effecting a representation of variation (i.e., of variables) in the environment. Different environmental variables are made available to the intellect in different perceptual modalities. It is possible that a variable exists in the environment that is represented in one sensory or cognitive mode and not in another, or in no mode at all.

Now, Bachya intends this as a metaphor for the problem of knowing God's essence, not as an explanation of the problem. He says "it would be like trying to experience something physical with the inappropriate sense," not that this is what it would be in actuality. But what his analogy may be getting at is that even though God is very near — to the point even that information concerning Him is in fact present in our cognitions (i.e., "even when the objects of your efforts are right in front of you") — there is nevertheless some intrinsic mental limitation that prevents us from encoding this information in the manner necessary to facilitate understanding. Perhaps there is more to this metaphor than meets the eye.

Unknowability of God In Jewish Mysticism, Part III (Existentialism)

2006-12-05T01:49:00.000-05:00

We may mention alongside the mystical view also the existential or experiential attitude, wherein it is denied that our approach to God has anything whatsoever to do with knowledge; that is, God is not something that is known, but something that is experienced. In this sense, the kabbalistic (and rational) view that God is utterly Beyond — in the teasing words of Heschel (1951), that "the difference between Him and man is far greater than the difference between unconscious matter and conscious man; that man, consequently, may know as much about Him as a bubble knows about the theory of relativity; that God has nothing to do with this wretched globe; that he is aloft and so far above the forms of existence known to us that nothingness alone is where he dwells" — this view is not even wrong. There can be no sense at all in which God is Beyond or Unknowable, because the relationship between man and God is not characterized by "knowledge" at all. One cannot say that God is far beyond man's conception, because "conception" has nothing whatsoever to do with this relationship. The approach to God in this view is thus non-noetic, i.e., not by way of the intellect or by way of reason.

Since I can't claim to understand this approach well at all, I will let Heschel speak for himself:

The encounter with reality does not take place on the level of concepts through the channels of logical categories; concepts are second thoughts. All conceptualization is symbolization, and act of accommodation of reality to the human mind. The living encounter with reality takes place on a level that precedes conceptualization, on a level that is responsive, immediate, preconceptual, and presymbolic...

Particularly in religious and artistic thinking, the disparity between that which we encounter and that which is expressed in words and symbols, no words and symbols can adequately convey. In our religious situation we do not comprehend the transcendent; we are present at it, we witness it. Whatever we know is inadequate; whatever we say is an understatement. We have an awareness that is deeper than our concepts; we possess insights that are not accessible to the power of expression...

Man's walled mind has no access to a ladder upon which he can, on his own strength, rise to knowledge of God. Yet his soul is endowed with translucent windows that open to the beyond. And if he rises to reach out to Him, it is a reflection of the divine light in him that gives him the power for such yearning. We are at times ablaze against and beyond our own power, and unless man's soul is dismissed as an insane asylum, the spectrum analysis of that ray is evidence for the truth of his insight. (heschel_56)

To think of God is not to find Him as an object in our minds, but to find ourselves in Him... God is neither a thing nor an idea; He is within and beyond all things and all ideas. Thinking of God is not beyond but within Him... He remains beyond our reach as long as we do not know that our reach is within Him; that he is the Knower and we are the known; that to be means to be thought of by Him... We often know Him unknowingly and fail to know Him when insisting upon knowing. (heschel_51)

While Heschel is always very eloquent in presenting his viewpoint (and probably the best poet-theologian we've had — or will have — for a long time), one has to wonder whether the view of God as "presymbolic experience" really captures the Jewish notion of the Deity. From my perspective, it does not. But regardless, it remains unclear to me in exactly what way Heschel believes man's mind to be "walled," and in what way this particular "wall" prevents knowledge of God. What is it about God that prohibits expression in words or symbols? Why is it that some things can be conceptualized, and some cannot? For Heschel to say that "no words and symbols can adequately convey" what this distinction might be is, in my opinion, to openly admit that he doesn't know what the distinction is, or, indeed, whether there really is one.

There is at least a superficial similarity between the existential approach and the Kabbalistic approach, not only in that both approaches for the most part elude my understanding, but also insofar as such Kabbalistic references to En Sof as "that which is not conceivable by thinking" (Isaac the Blind, in Scholem 1954) and "Who can in no way be comprehended by any thought" (Schneur Zalman, in Mindel 1969) also suggest a non-noetic relationship between man and God. However, it seems to me that many kabbalists do not truly reject the noetic approach in the way the existentialists do. They reserve a place for reason and intellect in the approach to God, and therefore the concept of "unknowability" retains its relevance for them.

Consider the following statement of Buber:

God is an unknown Being beyond this world only for the indolent, the decisionless, the lethargic, the man enmeshed in his own designs; for the one who chooses, who decides, who is aflame with his goal, who is unconditioned, God is the closest, the most familiar Being that man, through his own action, realizes ever anew, experiencing thereby the mystery of mysteries. Whether God is "transcendent" or "imminent" does not depend on Him; it depends on man... (glatzer_66)

This does not seem to be the same idea that the Kabbalistic writers were working from. For them, the concept of "unknown Being" is a coherent one, and is indeed ultimately the final and most satisfactory way that we can describe God-in-Himself. But beyond this, it seems that in both Kabbalah and rationalism the approach to God is precisely not by way of being "aflame" with some unidentified passion! The "ecstatic" approach to God, if that is what we should call it, would not require anything like the vast literature that the Kabbalistic or philosophical writers produced. Rather, both these approaches to God call for the meticulous and arduous study of a certain body of knowledge, which then enables one to begin to understand the Deity. In the case of Kabbalah, it is the esoteric knowledge of the Sefirot which requires meticulous study and contemplation:

Thus Scripture states, Know the God of your father and serve Him (I Chron. 28:9). [This verse] teaches that in order to serve [God] properly one needs [to acquire] knowledge concerning Him — that is, knowledge of his sefirot, His conduct with them, and His unification with them. (Cordovero, in robinson_94)

In the case of philosophy, it is obviously the proofs of physics, metaphysics, and logic that require mastery in order to begin the approach to God. Neither the Kabbalistic nor rationalistic approach disregards reason and intellect in the way that Heschel or Buber appear to. Moreover, while I will grant that expressions such as "God is neither a thing nor an idea; He is within and beyond all things and all ideas" are poetically masterful, I don't know what they mean. To me, such an expression evokes a feeling of mystery and awe, but does absolutely nothing to in any way clarify the situation in which we find ourselves vis-à-vis God. It is a Jabberwocky-esque collection of words that stimulates feelings but conveys no insight, knowledge, or information. I hate to say it, but this is what we in less delicate moments refer to as "nonsense," and in more delicate moments as "holy nonsense."

Frankly, I don't think anyone in the modern age (i.e., anyone, for example, who accepts the "neuron doctrine") will be able to formulate the approach to God other than in terms of knowledge or information. One can speak of "experience" and "encounter," but unless a radically dualistic theory of mind is entertained, all these phenomena must in some way be grounded in the nervous system, and there is every good reason to believe that the nervous system does represent concepts and knowledge. While only a small fraction of those representations may be consciously accessible, they are nevertheless legitimate knowledge representations. It is true that there are levels of the nervous system that one might regard as subsymbolic (spinal cord reflex, retinal processing, etc.) but it strikes me as very backward to situate our relationship with God in those surroundings. In any event, even these systems are representational and hence conceptual in the sense that they track features external to the nervous system, something we will discuss later.

On top of this, it seems to me that Heschel's approach transgresses against Berkovitz's claim that Judaism is essentially non-mystical. According to Berkovitz, if there is to be religion at all, there must be a relationship between distinct entities, one of them being man, and the other being the Deity. Man and God must necessarily be distinct, and the entirety of the Torah speaks to such a distinction:

God addresses himself to man, and he awaits man's response to the address. God speaks and man listens; God commands, and man obeys. Man searches, and God allows himself to be found; man entreats and God answers. In the mystical union, however, there are no words and no law, no search and no recognition, because there is no separateness (berkovits_04).

If there is to be a relationship between distinct entities, as it seems there must be on Berkovitz's analysis, this must then be a relationship based on knowledge of some kind. Hermann Cohen, for example, writes

Moreover only through reason, through the ability of knowledge does that man arise who can come into correlation with God... Reciprocity enters man's knowledge of God in accordance with correlation. It is as if God's being were actual in man's knowledge only, so tremendous is the effect of the correlation. Man is no longer merely God's creature, but his reason, by virtue of his knowledge and also for the sake of it, makes him at least subjectively, as it were, the discoverer of God...

Prayer also recognizes this relation to knowledge. In the main daily prayer, the "Eighteen Benedictions," the first of the supplications reads: "Thou favorest man with knowledge." It is as if it were to say: the first of God's favors is the endowment of knowledge, and there can be no other kind of favor but that which is dependent on knowledge. Thus knowledge plainly becomes the fundamental condition of religion, of reverence for God...

While I don't pretend to completely understand Cohen's view of the man-God relationship, it seems clear enough that its basis is in knowledge and reason, those unique capacities of man which differentiate man from other animals in the classical view.

Finally, to the extent that the man-God relationship is not one based on knowledge or information, then it is not the topic of this paper. Here we deal with issues related to knowledge-based or information-based relationships between man and God, which are the kind of relationships that I believe are indicated when people speak of God being unknowable. If one insists that the relationship between man and God is not through knowledge in the first place, then there is no meaningful sense in which to say that God is "unknowable," and we have no need to complete this paper. However, my opinion is that — while knowledge- or information-oriented approaches to the relationship between man and God may ultimately fail to lead to religion (cf. Sherwin_06, p.57) — approaches to the relationship between man and God that are not based on knowledge or information will ultimately fail to lead to coherence and comprehensibility. From the perspective of one who seeks understanding, the latter is far worse. I will take my chances with the former.

Next time, the Philosophers...

Unknowability of God In Jewish Mysticism, Part II

2006-11-27T12:03:00.001-05:00

In this section we will examine a bit further what the classic sources have to say about the unknowable component of God, the En Sof, and then discuss what two recent kabbalistically-influenced scholars have written on the subject. Let us first just give the following quotes about En Sof, and see if we can gather from them anything substantial. Again from the Zohar, we have the following:

It is taught in the Book of Concealment: The Most Ancient One, the Most Secret, the Most Concealed, is formed [128b] and prepared so that, in his formations, he is like an eldest Elder — more ancient than the ancient ones, more concealed than the concealed ones. In his formations he is both known and unknown... In the hollow of the skull is the membrane of the air, the cover of the secret supernal Wisdom that cannot be discovered or expounded or revealed. The membrane envelopes the brain, which is the secret Wisdom. That is, the Wisdom is covered by the membrane that cannot be opened, the brain itself being the secret Wisdom. It is at rest and tranquil in its place, like good wine upon the lees, and thus it is said of the Elder, that his mind is concealed, and his brain is concealed and tranquil... It is written (Dan 7:9) "The Ancient of Days did sit." He sits in his place, but no man can know where it is. He sits but is not found... (rosenberg_73)

The following additional statements are quoted in Matt (1990):

Ein Sof cannot be conceived, certainly not expressed, though it is intimated in every thing, for there is nothing outside of it. No letter, no name, no writing, no thing can confine it. The witness testifying in writing that there is nothing outside of it is: "I am that I am." Ein Sof has no will, no intention, no desire, no thought, no speech, no action — yet there is nothing outside of it (Azriel of Gerona).

No letter, vowel, or image can be applied to it, for even Keter, the beginning of emanation, is devoid of name and image in letter or vowel. How much more so with Ein Sof, whom we cannot depict, of whom we cannot speak, of whom we cannot posit either judgment or compassion, excitement or anger, change or limit, sleep or motion, or any quality whatsoever, either prior to the emanation or now (Moses Cordovero).

Elijah opened and said, "Master of the worlds! You are one — but not in counting. You are higher than the high, concealed from the concealed. No thought grasps you at all... About you, no one knows anything..." (Tiqqunei Hazohar).

Ein Sof is a place to which forgetting and oblivion pertain. Why? Because concerning all the sefirot, one can search out their reality from the depth of supernal wisdom. From there it is possible to understand one thing from another. However, concerning Ein Sof, there is no aspect anywhere to search or probe; nothing can be known of it, for it is hidden and concealed in the mystery of absolute nothingness (David ben Judah Hehasid).

The depth of primordial being is called Boundless. Because of its concealment from all creatures above and below, it is also called Nothingness. If one asks, "What is it?" the answer is, "Nothing," meaning: No one can understand anything about it. It is negated of every conception. No one can know anything about it — except the belief that it exists. Its existence cannot be grasped by anyone other than it. Therefore its name is "I am becoming" (Joseph Gikatilla).

While one can probably find a thousand additional poetic expressions in the kabbalistic literature of the unknowability of En Sof, my suspicion is that there is little to be learned over what might already be gleaned from just the above statements. It is possible, of course, that the statements given above are intended to stoke a certain feeling of mystery and awe in the reader — as well as a recognition of the individual's insignificance besides God — rather than to actually convey any insight about the nature and scope of God's unknowability. Nevertheless, let us try to gather what we can.

It seems to me that the recurring idea here is that the human mind is incapable of representing to itself knowledge concerning either God's wisdom and/or God's nature. In the quotation from the Zohar, it seems that it is the Divine wisdom which remains beyond reach, sealed away and forever inaccessible. In the other citations, it seems rather that it is the Essence of the Divine, the phenomenon of En Sof itself, that is not approachable. But I think we can do a bit better: Azriel and Cordovero both intimate that the problem of God's unknowability is, to a certain extent, a problem of description; that is, we are somehow lacking the tools that we need in order to describe the Divine. Attributes such as intention, desire, compassion, excitement, etc., that we are tempted to apply to God, these attributes — for unspecified reasons — fail utterly to describe the Divine essence. We thus have the sense that the "un-graspability" or "incomprehensibility" of En Sof is due to its essential indescribability by whatever mental or spoken languages we have available to us. Rav Kook provides an analysis of God's unknowability along similar lines (Pangs of Cleansing):

The foundation of religious faith is rooted in the recognition of the greatness and perfection of the Infinite. Whatever we conceive of it is insignificant in comparison with what by right we should conceive of it, and what we should conceive of it is not much more significant in comparison to what it really is. ... All the divine names, whether in Hebrew or in any other language, give us only a tiny and dull spark of the hidden light to which the soul aspires when it utters the word "God." Every definition of God brings about heresy, every definition is spiritual idolatry; even attributing to Him intellect and will, even the term divine, the term God, suffers from the limitations of definition. Except for the keen awareness that all these are but sparkling flashes of what cannot be defined these, too, would engender heresy.

We see here again a conceptualization of the unknowability of God as the indescribability of God, and, in particular, the indefinability of God. I assume here that "definability" is a refinement (i.e., restriction) on "describability," but without further specification it is difficult to know exactly in what ways these notions differ. Nevertheless, I think it is appropriate to interpret Rav Kook as saying — along with earlier kabbalistic thinkers mentioned above — that there is a key failure of description in the case of En Sof, and it is this failure of description that is the cause of our inability to know the Divine. However, the actual mode of failure remains unspecified.

Among the contemporary thinkers who have written on this topic, two individuals of unique stature are Aryeh Kaplan and Adin Steinsaltz. Aryeh Kaplan was a prolific author and outstanding scholar who wrote and translated many books on spiritual topics related to kabbalah and meditation (in addition to his classic Living Torah). I'm not certain, however, that among his many achievements can be counted any elucidation of the nature of God's unknowability, at least not beyond what was achieved by earlier scholars. In any case, Kaplan writes as follows:

God Himself, of course, is absolutely and ultimately unknowable. There is absolutely nothing in our experience that can be used as a means of comparison. There is nothing in human or any other language that can be used when speaking of God Himself (kaplan_90).

Our minds can only think in material terms, and therefore, it is almost impossible for us to picture any existence outside of space and time. This is but another reason why God's essence is absolutely unknowable (kaplan_90).

Ultimately, God is so high above us that we cannot comprehend Him at all... We have neither the words nor the mental processes that would enable us to actually describe God or understand Him. This is not only true of mortal man, but even of the highest celestial beings (kaplan_90).

Since everything conceivable — including any category of thought that the mind can imagine — was created by God, there is nothing conceivable that can be associated with Him. Let us say that I want to think about God. There is, however, no category in my mind in which I can place Him. Therefore, trying to depict God is like trying to see without eyes. When I try to see where there are no eyes, all I see is nothing. Similarly, when I try to think about God, all that my mind can depict is nothing (kaplan_85).

When a person imagines nothingness, he should realize that this is the closest that it is possible to come to imagining God. Most certainly. this does not mean that God is nothingness. In every possible way, God is more real than anything else that exists. However, it means that since there is nothing in the human mind that can relate to God as He actually is, nothingness is the closest thing to a perception of God that we can obtain. When a person depicts nothingness, he must realize that behind the nothingness is God (kaplan_85).

Of course, even to use the word "being" with relation to God is a misnomer and anthropomorphism. The only reason that we think of God as a "being" is so that we can speak to Him, and "being" is the only category into which we can fit that to which we can speak. Of course, the fact that "being" is the closest category into which we can place God does not mean that he is a being. As we have discussed earlier, there is no category into which can place God (kaplan_85.)

One may be tempted to say, "God is a principle." However, as I discussed earlier, the sentence "God is..." is a statement that cannot be completed. God is the creator of all categories and therefore cannot fit into any of them. Both "principle" and "being" are approximations that we use because the mind has no category into which it can place God. It may be that a third, intermediate category might be a better explanation, but the mind has no example of it, and therefore, such a category cannot be imagined. Nevertheless, through meditation, one can gain a glimmer of the nature of this third category (kaplan_85).

We will leave alone that last remark about meditation, except to make the following point (not for the last time): It seems to me that once we begin to discard reason we can no longer consider ourselves to be doing theology. Although Bayle claims that "you are accustomed by your theological mind to abandon reason as soon as you believe yourself to be in the presence of a mystery," this is a bad habit that we really cannot tolerate. Theology is the study of God and religion, and as far as I am aware, study of anything requires reasoning. When we give this up, we give up the only tool by which we can assess the relative merits of competing claims, and thus we again descend from constructive argument into "rhetoric and vituperation" (in Fackenheim's words). "Faith is different from reason and transcends reason but reason is the only tool we have by which to distinguish faith from credulity, truth from superstition" (jacobs_57).

In this connection, it might occur to one to suggest that perhaps the very notion of an "unknowable God" is intrinsically irrational or mystical, but that is very far from the truth, in my opinion. While the proposition that God is unknowable may have undesirable consequences for the grounding of religion in "metaphysical truth," the idea itself is rational and coherent since "unknowability" can be formalized mathematically for knowledge representation systems. To the extent that the human mind is a knowledge representation system of one sort or another, there is therefore nothing essentially irrational in positing the existence of "unknowable entities." However, this does not mean that every particular claim about unknowability is a coherent one, and so every such claim needs to be thoroughly vetted.

Now, to return to Rabbi Kaplan, he gives us a lot to digest, although — as we'll see — most of the claims he makes about God's unknowability were already made by the medieval rationalists. The most important of these claims are, as I see them, the following:

There is nothing to which we can compare God.

There is nothing in the world that can be associated with God.

There is nothing in our verbal language that is useful in describing God.

There is nothing in our mental language that is useful in describing God.

There is nothing in the mind that is related to God.

There is no category in which we can place God in order to depict Him.

There is no predicate capable of completing the sentence "God is..." (although, judging from the above quotes, this does not prevent Kaplan from using such sentences frequently).

The mind has no example of the category into which God might be placed.

It seems to me that some of these points have substance, and indeed constitute an essentially rational understanding of the problem in the classical mode, which we will take up in greater detail later. By "rational," I particularly mean that these types of assertions are formalizable, and thus open to some sort of debate or discussion. For example, in Claim 1, if by "compare" we mean something like feature-matching, then the statement that we have nothing to which we could compare God is (in its extreme interpretation) a claim that our mental representation of God does not share representational features with any other cognitive representation. This is an idea that we can at least attempt to formalize, and whose coherence and consequences we can therefore study. Similarly for the other claims.

However, as I see it, the above claims can all be formalized simultaneously within a single framework, because — to quote Joseph — it is the same dream. That is, from different angles, Kaplan is describing a single problem of unknowability, and it is the same problem of description which emerged from the sources cited earlier. The entire idea is essentially captured in Claims 4 and 5 (which I take to be synonymous), that there is nothing in our mental language that is useful in describing God. To the extent that mental description is achieved through a listing of features or relationships among features (something we will certainly pick up again below), what this claim means is that there are no features in our internal representational language that are applicable to describing God. From there it follows all the following claims.

Claim 3 follows, since we do not expect that our verbal language could compose descriptions that our mental language cannot compose.

Claim 2 follows — if by "association" we mean the sharing of features, since if anything in the perceived world shared features with God, this would imply that such features can be represented (in contradiction with Claim 4).

Claim 1 follows, since if there are no representational features that apply to God, then there are no representational features by means of which any feature-based comparison could be made.

Claims 6 and 8 (which I take to be synonymous) follow, since (classically speaking) the subsumption of an entity in a category or class is occasioned by abstracting from that entity those features which are shared between it an the other members of the class. As Rambam writes (GP I:58), "an attribute does not particularize any object of which it is predicated in such a way that it is not associated by virtue of that particular attribute with other things." (E.g., the things I am eating right now are in the category of "legume" because they have certain properties or features in common with other entities in this category.) If no features or properties of an entity can be represented in the first place, then it is impossible for the entity to be classified in this traditional sense. The distinction between Claim 4 and Claim 6, if there is one, is probably between categories considered in their extensional sense (as being characterized by their members) and categories considered in their intensional sense (as being characterized by the attributes shared by their members). We will say much more about this later.

Claim 7 follows since "is a" relationships are category (inclusion) relationships, and are therefore not possible for the reason just mentioned.

We will not delve too much into these claims right now, except to mention that Kaplan's presentation leaves open many issues (beyond the naked question of why Kaplan's personal knowledge of God seems to exceed so dramatically what his own philosophy permits: "Yet, he who insists that God is in every way unknowable claims to know that what he says cannot be known" (heschel_51).) In particular, how should we frame the problem of describability to which Kaplan alludes? Why is it so impossible for us to acquire a category for God? It cannot, after all, simply be that we do not innately have such a category; there are many mundane categories which we do not possess innately, but that we develop over the course of our lives. As infants we did not have categories for "automobile" or "Jewish philosopher" or "information theory," and yet at some point we did nevertheless acquire these categories. (What is perceived as a "feature" also changes during development (smith_linda_89,younger_03), which may also point to the evolution of perceptual categories: "Shape" becomes a useful feature only when category for "shape" exists.) Indeed, one can reasonably say (and later we probably will say) that the essence of learning is the acquisition of categories — the abstraction of information, and if that is the case, then the process of category formation is clearly a process that humans and animals execute with proficiency and intelligence.

What Kaplan must therefore mean when he says that we do not "have the category" is both that we do not have the category a priori (i.e., innately), and also that it is impossible in principle that we should ever obtain the category. But why is it so? What is it about the structure of God and the structure of our cognitive system that prevents us from knowing about Him? What kind of category would be suitable, and how can we know that we don't have it? Does "entities that create everything conceivable" not constitute a valid category? If it does, then haven't we indeed categorized God? If it does not, then what does it mean to say that God is "the thing that creates everything conceivable," as Kaplan does above? So, while providing some very tantalizing ideas, Kaplan definitely leaves us with a lot of work to do in order to understand anything concrete about the kind of unknowability that confronts us in approaching God.

An approach very similar to Kaplan's seems to be adopted by Rabbi Adin Steinsaltz, who is considered to be one of Orthodoxy's preeminent contemporary thinkers. He provides a brief treatment of the nature of God which fuses kabbalistic mysticism with Maimonidean equivocation (which we will cover later). The reader can judge for themselves whether, besides the updated language, this version adds anything new to the account of Ramchal, Philo, or Rambam.

No created intellect, whether of man or angel, can possibly bridge the gap between the works of Creation and the Creator. Just as the creature is unable to grasp the Infinite Divine, so is it unable to grasp his attributes. Indeed, when speaking of any of the Divine attributes or Sefirot, we are only bringing the incomprehensible down to our human level because we are confronted with an insoluble dilemma. We can either use terms that are obviously imprecise and incorrect, but have some meaning for us as humans, or we can try to use precise terms that only make us totally inarticulate, unable even to begin to express ourselves. In a sense, as soon as one wishes to be absolutely correct in speech, there are no words any longer, none that satisfy the requirements....

Compare the above statement to Rambam's observation (regarding, there, in particular, the notion of that "God is one not through oneness") that "These subtle notions that very clearly elude the minds cannot be considered through the instrumentality of the customary words, which are the greatest among the causes leading unto error. For the bounds of expression in all languages are very narrow indeed, so that we cannot represent this notion to ourselves except through a certain looseness of expression" (GP I:57). However, I am not sure what Steinsaltz has in mind when he claims that "we can try to use precise terms that only make us totally inarticulate," since precision in language is generally found to improve comprehension, and it is the lack of precision that ordinarily leads to misunderstanding.

In any event, the general thrust of his remarks are that we do not have the right terms (descriptors, predicates, etc.) by which to describe God, and therefore we cannot understand God. As I mentioned above, I believe that the proposal that "we do not have the right terms" (really Rambam's proposal) is the same as Kaplan's proposal that we do not have the right "category" for God (also Rambam's proposal). It is the same dream. Steinsaltz continues:

To be sure, it may be claimed that I am a product of Divine grace. If so, how is it that I do not have any way of knowing Him? It is as though a creature of three dimensions were to draw a picture of two dimensions. This two-dimensional picture could never grasp the concept of three dimensions or comprehend that which brought it into existence. We, too, are thus a sort of transfer or a projection from some higher plane of being, constantly receiving from it and even endeavoring to grow into it, but altogether unable ever to grasp it or understand it.

There can be no direction to God's being — above or below in any meaningful way as far as geography is concerned; it can only be in terms of levels, in the sense of different planes of existence. Only thus can it be said that the dimension of Ein Sof is above and beyond the world. To be sure, this other-worldly dimension has become, in a manner of speaking, the point of departure for those philosophies that maintain that, since Ein Sof or God is beyond the world, then there is no connection between them, and there is an essential, unbridgeable gap between Divinity and reality as we know it...

Steinsaltz invokes the ever-beguiling Flatland metaphor as a way in which to understand the unknowability of En Sof, and it is not a bad start (although it would be a far better start if he would cite Plato or Abbott for the idea). I have previously written about the limitations of this sort of metaphor, but it is not the general use of the metaphor with which I find fault here. What is troublesome is the unwillingness of Steinsaltz to pursue the idea with greater rigor and detail. Geometry is certainly a formal discipline. If Flatland is the appropriate metaphor, then isn't it imperative to investigate it from every angle and aspect? If geometry or vector space is a sound metaphor, then each part of his statement that "We, too, are thus a sort of transfer or a projection from some higher plane of being, constantly receiving from it and even endeavoring to grow into it, but altogether unable ever to grasp it or understand it" would seem to cry out for some formalization within the framework of geometry or linear algebra. If he was not planning on using the tools of geometry or linear algebra to investigate this idea, then why introduce the geometric metaphor in the first place?

My conclusion is that while the Flatland metaphor is very important, it is used by many religious writers — and by Steinsaltz here — as a primitive "intuition pump." It all sounds very plausible at first — sure enough, everyone agrees that the two dimensional picture could never grasp the concept of three dimensions. But, when we consider it further, we must begin to wonder in what sense "a picture of two dimensions" is like "human cognition" and in what sense "a creature of three dimensions" is like the En Sof. What is the likeness between a picture and the human mind? What is the likeness between a "third dimension" and En Sof? Moreover, is it even coherent to say that "a two-dimensional picture could never grasp the concept of three dimensions"? Is "grasping" an activity that we can predicate of pictures? I personally have never observed a picture to "grasp" anything. As far as I am aware, "grasping," in the sense of "conceiving," is something which is only done by minds (or, if you like, information processing systems), so it is incoherent to talk about anything other than a mind or information processing system grasping something in this sense. However, as I said, there is something profound about the Flatland metaphor, and we will hopefully later see what it is.

Since we've already strayed quite a ways from Kabbalah, we can wrap things up here. The "unbridgeable gap between Divinity and reality as we know it" mentioned above by Steinsaltz — the tension between the imminent (Sefirot) and transcendent (En Sof) aspects of God — would seem to be the principle dilemma in kabbalistic thought. Indeed, "a great part of the history of religions, including the religion of Israel, consists of the quest for the solution of the problem of bridging the abyss that cannot be closed" (urbach_75), and so Kabbalah is unique not for its identification of the central problem, but in its approach to reaching a resolution. Although some of the kabbalistic literature evidences an attempt at systematicity — for example, in the attention given to the particular relational structure of the Sefirot, I am not aware of any true formalization of this system which uses any of the tools of knowledge representation. In particular, while "the sefirot reveal what can be conveyed of the divine nature" (matt_90) it is not clear what the relationship between the Sefirot and the En Sof might actually be, if any, and it is therefore not clear in exactly what sense the En Sof remains unknowable.

Finally, to end this little discussion of the God's unknowability in Kabbalah, there is the following consideration: "The language of truth is unadorned and always simple." It seems to me that for the most part the kabbalistic literature exhibits the very opposite of unadornment and simplicity, which makes me wonder whether there is really to found within it (i.e., in the classic sources) a genuinely coherent statement of the essential problem of God's unknowability. While I'm not nearly familiar enough with the sources to draw a definite conclusion, my feeling is that the clearer exposition of the problem is likely to be found within the writings of the rationalist philosophers.

Unknowability of God In Jewish Mysticism, Part I

2006-11-19T04:12:00.000-05:00

It is impossible to say exactly when the mystical approach within Judaism was inaugurated. There are mystical works dating from the Talmudic period (i.e., Sefer Yetzirah), and, as we saw above, Philo's own writings weave together Greek mysticism with Scriptural exegesis to create something which can only rightly be described as Jewish mysticism. In this connection, another unique figure who was heavily influenced by Greek mystical thought is the early medieval poet-philosopher Solomon ibn Gabirol. In his long poem Keter Malchut, he expresses thoughts about God's remoteness and unknowability which would be by no means foreign to Philo:

(I) Thine is the might in whose mystery our thoughts can find no stay, so far art Thou beyond us.... Thine are the mysteries that transcend understanding and thought... (XXVI) Who can approach Thy seat? For beyond the sphere of Intelligence hast Thou established the thrown of Thy glory... Thus far reacheth Intelligence, but cometh here to a standstill, For higher still hast Thou mounted, and ascended Thy mighty thrown, "And no man may go up with Thee." (zangwill_23)

Again, we find the idea that God-in-Himself somehow exceeds the reach of man's intelligence, that although thought can embrace and measure many things, it cannot embrace and measure God. In another respect like Philo, ibn Gabirol remains an ambiguous figure in Jewish philosophy, not only because of his Scholastic alter-ego "Avicebron", but because he doesn't fit comfortably into a particular Jewish intellectual tradition. If nowadays he is perhaps seen as less of a mystic and more of a poet, this is probably due to the manner in which Jewish mysticism came to be exclusively identified with the system of thought known as the Kabbalah, thus leaving other Jewish mystics out in the cold.

At least since the Middle Ages, "Jewish mysticism" has indeed meant "Kabbalah." But the Kabbalah as we know it popularly today (much like rational theology as we know it popularly today) might be said to bear the marks of having been abandoned by serious scholars. Esoteric terms are thrown around with a wink and a nod and a hope that someone, somewhere, actually understands how it all works. While the abandonment of rational theology by scholars may be blamed on the advent of modernity — the sweeping vistas of natural philosophy and science luring contemplative thinkers away from the stodgy confines of Scholastically-shackled theological ponderations, in the case of the Kabbalah, Scholem sees the opposition of Jewish scholars to the Hasidic movement as a principle reason for the abandonment of the Kabbalah by serious scholarship. Guilt by association, as it were. And inevitably, says Scholem (1954,p.2), in place of scholarship came instead credulity and silliness: "The natural and obvious result of the antagonism of the great Jewish scholars was that, since the authorized guardians neglected this field, all manner of charlatans and dreamers came and treated it as their own property." One may be tempted to say that such a statement was probably never truer than it is today, when Kabbalah is associated in many people's imaginations with "myth and magic" of various varieties; however, a quick survey of the history of Jewish mysticism shows that Kabbalah always presented an irresistible attraction to individuals of questionable motivations and sanity (e.g., Nehemiah Hayyun, Judah Leib Prossnitz, Nathan of Gaza, etc.). In any event, here we will limit ourselves to what some of the classic kabbalistic sources say about the unknowability of God, and try as best we can to understand them.

While the evolution of the Kabbalah was probably fairly organic, the classic work that nevertheless stands at the center of this world is the Zohar, which was circulated and — in all likelihood — partially written by Moses de Leon in the 13th century. We will therefore begin our review of the mystical approach to God's unknowability with this key work. The Zohar on Exodus (scholem_49) says the following:

If one should ask: Is it not written, "For ye saw no manner of similitude" (Deuteronomy 4:15), the answer would be: Truly, it was granted us to behold him in a given similitude, for concerning Moses it is written, "and the similitude of the Lord doth he behold" (Numbers 12:8). Yet the Lord was revealed only in that similitude that Moses saw, and in none other, of any creation formed by his signs. Therefore it stands written: "To whom then will ye liken God? Or what likeness will ye compare unto Him?" (Isaiah 40:18). Also, even that similitude was a semblance of the Holy One, be blessed, not as he is in his very place which we know to be impenetrable, but as the King manifesting his might of dominion over his entire creation, and thus appearing to each one of his creatures as each can grasp him, as it is written: "And by the ministry of prophets have I used similitudes" (Hosea 12:11). Hence says He: Albeit in your own likeness do I represent myself, to whom will you compare me and make me comparable?

Because in the beginning, shape and form having not yet been created, He had neither form nor similitude. Hence is it forbidden to one apprehending him as he is before Creation to imagine him under any kind of form or shape, not even by his letters "hay" and "vav," not either by his complete holy Name, nor by letter or sign of any kind. Thus, "For ye saw no manner of similitude " means, You beheld nothing which could be imagined in form or shape, nothing which you could embody into a finite conception.

But when He had created the shape of supernal man, it was to him for a chariot, and on it he descended, to be known by the appellation YHVH, so as to be apprehended by his attributes and in each particular one, to be perceived. Hence it was he caused himself to be named El, Elohim, Shaddai, Zevaot and YHVH, of which each was a symbol among men of his several divine attributes, making manifest that the world is upheld by mercy and justice, in accordance with man's deeds. If the radiance of the glory of the Holy One, be blessed, had not been shed over his entire creation, how could even the wise have apprehended him? He would have continued to be unknowable, and the words could not be verily said, "The whole earth is full of His glory." (Isaiah 6:3)

We can certainly see here echoes of Philo in the statement that God appears "to each one of his creatures as each can grasp him," but it remains entirely unclear what is meant by the notion of "grasping" in this context. It seems that we are referring here to some powers of the mind and some capacities of "conception" (or lack thereof), as indicated by the expression "nothing which you could embody into a finite conception." The passage goes on to suggest that God makes himself known to man through his "attributes," which provide an avenue of access without which God would have been utterly unknowable.

What begins to take shape here is the idea that God-as-He-is-in-Himself is utterly beyond mental conception, but that nevertheless there are some aspects of God which do fall within the realm of man's knowledge. In the kabbalistic system, the Divine comes to be regarded in terms of a remote unknowable component or essence referred to as En Sof or Ayin (Ayin may alternatively refer to the first Sefirah, if that is considered to be other than an aspect [scholem_74] or identity of En Sof [robinson_94,sherwin_06]. cf. Deus absconditus), along with a collection of Sefirot which represent aspects of God which are capable in some way of interacting with created world.

"Of God as He is in Himself — En Sof — nothing can be said at all, and no thought can reach there" (jacobs_73). En Sof itself is sometimes referred to as a realm of "pure Thought" (scholem_74), so as to detach it completely from any merely mortal variety of thought. The names En Sof and Ayin themselves (respectively, "Without End" and "Nothing"), and their other synonyms in the kabbalistic literature all are suggestive of the fact that nothing can be known about this entity — that it is beyond thought and exceeds human conceptual capacities (scholem_74).

In many ways, the kabbalistic stance of "mystical agnosticism" (scholem_74) regarding En Sof, inasmuch as En Sof is represented as transcending the "limits of human apprehension," is really no different than the stance taken by the Maimonides and the rationalists regarding the "infinite supreme eternal entity" (sherwin_06,dan_06), and is also very close to the Neoplatonic ideas of Philo and ibn Gabirol. Indeed, "the concept of an infinite, perfect supreme being that cannot change, a concept absent from Jewish thought in antiquity, is dominant in both philosophy and kabbalah" (dan_06). Certainly, to the extent that God-in-Himself is claimed by both rationalists and kabbalists to be utterly impervious to description, it is probably permissible to regard the En Sof of the kabbalists and the Divine Essence of the philosophers as the self-same (and empty) concept.

The unique idea of Kabbalah concerns the manner in which God interacts with the world and with humanity in particular, and this is by way of the Sefirot. Indeed, if there is one feature that most distinctly characterizes kabbalistic mysticism, it is the notion of Sefirot. However, what exactly the Sefirot are is difficult to say — not because there is a dearth of sources describing the Sefirot, but because there is an excess of sources describing them, and describing them in an excess of different ways (dan_06). In Cordovero's introduction to Kabbalah, the Sefirot appear to play the same role as God's "actions" does for Maimonides:

[The beginner] needs to know that Eyn Sof caused and emanated His sefirot, and His actions are [performed] through them. They constitute the ten "sayings" through which he acts. They serve him as vessels for the [34a] actions which derive from Him in the World of Separation and below. Truly His being and essence extend themselves in them... the [divine] names [themselves] are the sefirot, and the names are appellations of Eyn Sof according to His actions. (robinson_94)

However, there are disagreements as to whether the Sefirot actually represent actions or instruments of God, as above, or whether they are manifestations of divine attributes, aspects of the Divine essence, or something else (robinson_94, sherwin_06, scholem_74). In the later Kabbalah, the Sefirot are generally regarded as being both of the essence of God, and yet separate from Him (scholem_74). In this paper, we will not go into any details about how the Sefirot are hypothesized by various authors to function. Rather, when we later present a formal knowledge representation framework, we will try to show how it might map onto the kabbalistic ontology of En Sof and Sefirot, at least when these are conceived of in something like Cordovero's model. For the present, let us try to understand a little bit better — by considering some more sources — what is the nature of the peculiar limitation that places En Sof forever beyond the reach of human conception.

Jerusalem and Athens

2006-10-30T11:00:00.000-05:00

It remains far beyond me to detail the avenues by which Platonic and Aristotelian ideas came to influence Judaism. However, it seems that the Greek conception of transcendence (e.g., the Absolute) along with the general rigor of Greek reasoning drove Jewish thinkers to envision a God that was ever more static and remote. The great medieval thinkers who wrote on this topic are well known, especially Rambam, Ralbag, and Crescas. But a millennium before Moreh Nevuchim was written, one of Judaism's most neglected philosophers and mystics gave us a surprisingly modern exposition of God's transcendence. Philo, "the first theologian," introduces the Jewish conception of unknowability (matt_90) with a Platonic expansion on the famous Exodus 33 conversation between God and Moses:

[Moses says] "But what Thou art in Thy essence I desire to understand, yet find in no part of the All any to guide me to this knowledge." [...] [God] replies, "Thy zeal I approve as praiseworthy, but the request cannot fitly be granted to any that are brought into being by creation. I freely bestow what is in accordance with the recipient; for not all that I can give with ease is within man's power to take, and therefore to him that is worthy of My grace I extend all the boons which he is capable of receiving. But the apprehension of Me is something more than human nature, yea even the whole heaven and universe will be able to contain. [...] But while in their essence they [God's powers] are beyond your apprehension, they nevertheless present to your sight a sort of impress and copy of their active working. You men have for your use seals which when brought into contact with wax or similar material stamp on them any number of impressions while they themselves are not docked in any part thereby but remain as they were. Such you must conceive My powers to be, supplying quality and shape to things which lack either and yet changing or lessening nothing of their eternal nature. Some of you call them not inaptly 'forms' or 'ideas,' since they bring form into everything that is, giving order to the disordered, limit to the unlimited, bounds to the unbounded, shape to the shapeless, and in general changing the worse to something better. Do not, then, hope to be ever able to apprehend Me or any of My powers in Our essence."

Further, Philo warns us that

To be anxious to continue his course yet further, and inquire about essence or quality in God, is a folly fit for the world's childhood. Not even to Moses, the all-wise, did God accord this, albeit he had made countless requests, but a divine communication was issued to him, "Thou shalt behold that which is behind Me, but My face thou shalt not see." This meant, that all that follows in the wake of God is within the good man's apprehension, while He Himself alone is beyond it, beyond, that is, in the line of straight and direct approach, a mode of approach by which (had it been possible) His quality would have been made known; but brought within ken by the powers that follow and attend Him; for those make evident not His essence but His subsistence from the things which he accomplishes.

While in Philo's view it certainly seems that aspects of God are unknowable by the human mind, he, like Maimonides later, does not take this as a cause for despair and disenchantment. Rather, Philo regards the recognition of God's unknowability as the highest goal of human inquiry:

When therefore the God-loving soul probes the question of the essence of the Existent Being, he enters on a quest of that which is beyond matter and beyond sight. And out of this quest there accrues to him a vast boon, namely to apprehend that the God or real Being is apprehensible by no one, and to see precisely this, that He is incapable of being seen.

Thus, in some sense, it is the recognition of the limits of human knowledge that itself represents the highest form of human knowledge, a sentiment echoed 1800 years later in R'Nachman's dictum that "The end of knowledge is [the realization] that we do not know" (green_92). Perhaps all mystics think alike, after all.

Next, the mystical approach...

Talmudical Unknowability

2006-10-19T11:27:00.000-04:00

It would be a major oversight not to include the opinions of Chazal on the unknowability of God, but it appears to me that the Talmud contains very little of any substance on this topic, perhaps because of the "theological functionalism" to which Chazal largely adhered (lachs_93). I will cite two passages which I found mentioned in (montefiore_loewe_74): In the Midrash on Psalms (braude_59), we have

...when Moses said to the Holy One, blessed be He, Show me now Thy ways (Ex. 33:13), He showed them to Moses, as is said He made known His ways unto Moses (Ps. 103:7). But when Moses said: Show me, I pray Thee, Thy Glory (Ex. 33:18), that is to say, "Show me the rule whereby Thou guidest the world," God replied: "My rules thou canst not fathom!"

A perhaps even less informative passage is found in the Sifre on Deuteronomy (hammer_86):

Who rideth upon the heavens as thy help — when Israel is upright and performs the will of God, He rideth upon the heavens as thy help, but when they do not perform His will — and in His excellency on the skies (33:26) — if one dare say such a thing. And in His excellency on the skies: All of the people of Israel gathered around Moses and said to him, "Our master Moses, tell us, what is the glory (of God) really like on high?" He replied, "You can surmise what the glory (of God) is like on high from the appearance of the lower heavens." A parable: To what may this be likened? To a man who said, "I wish to behold the glory of the king." He was told, "Go to the capital city and you will see him." He went there and saw a curtain set with precious stones and pearls and spread out at the entrance of the city. He could not take his eyes off of it, until he collapsed in a swoon. They then said to him, "If you could not take your eyes off of a curtain set with precious stones and pearls and spread out at the entrance of the city, until you collapsed in a swoon, how much more so had you entered the city (and beheld the glory of the king)." Hence it is said, And in His excellency on the skies.

In both passages, the assertion is that God is somehow unapproachable. The distinction, I think, is that previously mentioned (last post) regarding the interpretation Exodus 33. In the Sifre above, the remoteness of God is characterized in terms of his radiance overloading the senses — the notion that God is somehow too intense for human perception, whereas in the Midrash on Psalms the unapproachability of God appears to be due to a genuine failure of comprehension. It is not that the attempt to understand God would cause us to be struck blind or "collapse in a swoon," but rather that the human mind cannot fathom the kind of Entity that is God — that the human mind is in some way incompatible with the kind of knowledge that characterizes this particular Entity. However, the exact nature of this incompatibility is not further discussed, as far as I can tell, and is probably not of any great interest to the author of the Midrash.

While there well may be other Talmudical passages which remark on God's remoteness and inaccessibility (and which I hope someone will bring to my attention!), it seems fair to say that the real history of the unknowable God begins when Judaism encounters Greek philosophy. This will be our next topic.

Biblical Unknowability

2006-10-16T18:54:00.000-04:00

One finds early hints to the idea of the unknowable God in the Pentateuch. The classic passage is found in Exodus 33, where Moses makes various entreaties of God which might be interpreted as part of a quest to understand the Divine nature. Moses asks, "Now, if I have truly gained Your favor, pray let me know Your ways, that I may know You and continue in Your favor," and a few verses later, "Oh, let me behold Your Presence."

To this, God famously responds as follows:

I will make all My goodness pass before you, and I will proclaim before you the name Lord, and I will grant the grace that I will grant and show the compassion that I will show. But, "He said, "you cannot see My face, for man cannot see Me and live." And the Lord said, "See, there is a place near Me. Station yourself on the rock and, as My Presence passes by, I will put you in a cleft of the rock and shield you with My hand until I have passed by. Then I will take My hand away and you will see My back; but My face must not be seen.

The metaphysical reading of this passage is either that God is in His essence somehow too "intense" to be directly perceived by human senses without damage to the perceptual apparatus, or, more abstractly, that God in His essence cannot be comprehended by mortal (i.e., living) creatures because His essence in some way transcends their representational or computational capacities. Both interpretations have been offered by various commentators, and sometimes (it would appear) even by the same commentator.

In Neviim and Ketuvim we find many additional passages that accommodate themselves to interpretations involving the unknowability of God. Kohelet claims in 3:11 that "He also puts eternity in their mind, but without man ever guessing, from first to last, all the things that God brings to pass," and later in 11:5, that "Just as you do not know how the life-breath passes into the limbs within the womb of the pregnant woman, so you cannot foresee the actions of God, who causes all things to happen." Likewise, The Psalmist proclaims (Ps.145) "Great is the Lord and much acclaimed; His greatness cannot be fathomed," and (Ps.147) "Great is our Lord and full of power; His wisdom is beyond reckoning." The Jewish Apocrypha also contains similar references to God's unknowability. From Ben Sirah 43:27 (skehan_dilella_87), we have

More than this we will not add;
let the last word be "He is the all."
Let us praise Him the more, since we cannot fathom Him,
[...]
Extol Him with renewed strength,
and weary not, though you cannot fathom Him.
For who has seen Him and can describe Him?
or who can praise Him as He is?
Beyond these, many things lie hid;
only a few of His works have I seen.

However, the passages most frequently cited in support of God's ultimate unknowability are those from Isaiah and Job:

Who measured the waters with the hollow of His hand,
And gauged the skies with a span,
And meted earth's dust with a measure,
And weighed the mountains with a scale
And the hills with a balance?
Who has plumbed the mind of the Lord,
What man could tell Him His plan?
Whom did He consult, and who taught Him,
Guided Him in the way of right?
Who guided Him in knowledge
And showed Him the path of wisdom?
[...]
To whom, then, can you liken God,
What form compare to Him?
[...]
Do you not know?
Have you not heard?
The LORD is God from of old,
Creator of the earth from end to end,
He never grows faint or weary,
His wisdom cannot be fathomed.
(Isaiah 40:12-28)

For My thoughts are not your thoughts, neither are your ways My ways, says the Lord. For as the heavens are higher than the earth, so are My ways higher than your ways, and My thoughts than your thoughts. (Isaiah 55:8-9)

Behold, God is great, and we know it not, nor can the number of his years be searched out. (Job 36:26)

Would you discover the mystery of God?
Would you discover the limit of the Almighty?
Higher than heaven — what can you do?
Deeper than Sheol — what can you know?
(Job 11:7-8)

Although all these Biblical passages are wonderfully pregnant with metaphysical possibilities, and have of course been the subject of uncountable interpretations of metaphysical character, it is not completely clear whether the biblical authors generally intended their words to be understood as claims about the unknowability of God. The context of some of these passages often makes it seem more plausible that they are intended to highlight the great power of God or his great fidelity and consistency, rather than speaking to metaphysical issues. (For example, "My ways are not your ways" because "the word that issues from My mouth...does not come back to Me unfulfilled, But... achieves what I sent it to do.")

There are certainly also many passages that seem to convey the contrary idea, that God can be known. For example, in Proverbs (2:1-5) we have,

My son, if you accept my words
And treasure up my commandments;
If you make your ear attentive to wisdom
And your mind open to discernment;
It you call to understanding
And cry aloud to discernment,
If you seek it as you do silver
And search for it as for treasures,
Then you will understand the fear of the LORD
And attain knowledge of God.

More significantly, it seems to me that the entire message of Tanach is the knowability of God, and that most Biblical authors therefore do not have a conception of God as being unknowable. Rather, in most cases, God communicates his desires and attitudes plainly enough, and without any great sense of mystery. Nevertheless, the extent to which the Biblical authors where actually interested in metaphysics is something that can be endlessly debated, and which probably will.

A Brief History of God's Unknowability

2006-10-16T12:46:00.000-04:00

Since this is not a scholarly review, I will not give an exhaustive history of the idea of the unknowable God. (Nor could I, since I am just learning most of this material for the first time myself.) The following brief sketch will therefore have to suffice. Also, I am not a student of medieval rationalism or kabbalism, so I hope that where I have gone astray in describing these movements, someone with greater knowledge and insight will be willing to correct me. (You know who you are.) Certainly, there are many other sources which may be consulted by the reader interested in a more thorough review of these issues altmann_73, seeskin_00. Also, it will be apparent that I am covering only the classical Jewish approaches to the issue, and neglecting even the most significant non-Jewish Western thinkers such as Aquinas, Scotus, or Avicenna. To attempt to survey both Jewish and non-Jewish philosophers in this short paper would be (for me) beyond futile. As it turns out, though, this is not the major deficiency that one might think, since the important Jewish philosophers were all heavily influenced by non-Jewish sources (and, in some cases, vice-versa), so most of the major extant ideas are expressed in one way or another by the various Jewish thinkers.

Unknowability of God, In Parts

2006-10-10T13:38:00.000-04:00

My epochal post on the "Unknowability of God" is taking an epoch to write, so I will start posting the introductory material in parts. This was B. Spinoza's suggestion, and I think it is a good one, although I am sure he (and everyone) will be disappointed at the quality of what they see. Nevertheless, I don't envision the introductory parts getting any better, so I will post them now in the hope that people who read them can offer me some help in improving this material. I hope at least that B. Spinoza, Chardal, and David Guttman, and BenAvuyah will give me some feedback. I will really appreciate it! Thanks a lot. Stand by for imminent posting.

Complexity, Simplicity, Dimensionality

2006-09-06T11:42:00.000-04:00

I want you to go on to picture the enlightenment or ignorance of our human condition somewhat as follows. Imagine an underground chamber like a cave, with a long entrance open to the daylight and as wide as the cave. In this chamber are men who have been prisoners there since they were children, their legs and necks being so fastened that they can only look straight ahead of them and cannot turn their heads. Some way off, behind and higher up, a fire is burning, and between the fire and the prisoners and above them runs a road, in front of which a curtain-wall has been built, like the screen at puppet shows between the operators and their audience, above which they show their puppets. (Plato, The Republic)

And even as we, who are now in Space, look down on Flatland and see the insides of all things, so of a certainty there is yet above us some higher, purer region, whither thou dost surely purpose to lead me — O Thou Whom I shall always call, everywhere and in all Dimensions, my Priest, Philosopher, and Friend — some yet more spacious Space, some more dimensionable Dimensionality, from the vantage-ground of which we shall look down together upon the revealed insides of Solid things, and where thine own intestines, and those of thy kindred Spheres, will lie exposed to the view of the poor wandering exile from Flatland, to whom so much has already been vouchsafed. (Abbott, Flatland)

Don't run the movie yet! Just look at the first frame when it loads. What do you see? Eight dots inside a box? I hope so. Is there anything unusual about the arrangement of the dots? Some pattern, perhaps? Maybe yes, maybe no.

OK, then, run the movie. Do you detect any kind of order or coherence that you did not see before? Would it help if I told you that the dots mark the eight vertices of a rotating cube? (The cube is rotating at a different rate about each of its three axes.) There are a few observations that I think are interesting:

What might have initially looked like a random collection of dots in 3-space was in fact far from random, being a projection of a very simple and coherent structure, the cube.

Even before you recognized the rotating cube for what it was, you probably became sensitive to the fact that there was some structure or organization to the motion.

The rotating cube is not always easily recognizable as a cube. As is the case in the opening frame, there are many static views of the cube's vertices from which it is very difficult to infer the underlying structure (most of these views look like semi-random dot patterns in 2D). But I think you will agree that there are also sequences of the movie during which the cube seems to disintegrate into just a collection of moving dots. This also seems to happen if you close your eyes for about 5 seconds during the movie, and then reopen them. For the first second or so you may not see the cube, but only the dots.

Go through the same exercise with the second and third movies. First assess whether you detect any structure or coherence in the pattern of dots on the initial frame. Then run the movie and reassess the situation. It's unlikely you will deduce the actual structure underlying the motion of the dots (as you may have been able to do for the first movie), although you may still observe the motion to be highly organized, perhaps more so at some points than at others. In fact, the actual structures determining the motion of the dots in second and third movies are very similar to that in the first movie. In the second movie, a 6-D hypercube spins at a different rate along each of its axes. The dots again represent the vertices of the hypercube, of which there are 64, projected into 3-space. In the third movie, it is a 9D hypercube that rotates, the dots marking the 512 vertices.

What is the point, you ask?

Well, besides the point of "keeping the blog alive" while I work on preparing my epochal post on the Unknowability of God (coming soon to an epoch near you!), there is also the following point:

What people usually intend when they invoke Plato's Allegory of the Cave (or Abbot's Flatland) is that information is lost when a high-dimensional structure is projected into a lower-dimensional space. (Obviously, the "spaces" in question need not be physical spaces. The argument goes through for vector spaces in general). Thus an entity or system which exists in 10 dimensions — and whose dynamics are described by relationships among 10 variables — will probably not be completely observable when viewed through a reduced subset of those dimensions. ("Probably" is the correct term to use there.)

The intuition is that what you will get when you observe, say, only three of the phenomenon's 10 dimensions is some diminished and highly oversimplified view of that phenomenon — in a sense only seeing 30% of the actual phenomenon, and thus utterly missing the other 70%.

But that is not typically the case, as the movies show. What you get on projecting a N-dimensional structure into lower set of M dimensions is a compression of the N dimensions into M dimensions, and while there is certainly a loss of information, there may also be a dramatic increase in apparent complexity. Thus, a phenomenon that is simple and compact to describe in 10 dimensions, may prove difficult and verbose to describe in three dimensions. In the extreme, a high-dimensional structure may appear essentially random when projected into lower dimension.

The Cave Allegory is a favorite of theological dabblers. Most people, when they first hear of it, feel that they have been hit by a bolt of pure wisdom from God. And maybe they have, although most probably do not realize that dimensional compression is the bread-and-butter of many specialties in science and engineering — e.g., pattern recognition, optimum signal processing, relational databases, etc. — and that there is an entire area of statistics called "projection pursuit." In any case, people immediately latch onto the idea (like Plato, perhaps) that this physical world is just a simplified projection of some transcendent realm — a pale shadow of some grander and more real reality that actually exists in much higher dimensions.

The prospect that things might appear simpler in some other dimensions is very attractive, and it provides the motivation for the development of most scientific models (although the preference is usually to find lower-dimensional representations rather than higher-dimensional representations). However, the appeal of this idea should be tempered by the fact that structures projected from higher dimensions may appear considerably more complex or even random in lower dimensions.

As a result of projection, diverse and unrelated dimensions in the higher dimensional space might be collapsed together or "confounded." From studying the resulting projection in lower dimensions, how then do you determine what the actual dimensions of the original space are? Perhaps, as a result of projection, what we observe in our reduced-dimension space as a seemingly unitary variable "X" is actually the combined effect of variables A,B,C,D,E,F,G,H,I,J which exist in 10-dimensional space. It is therefore not the case that the "real" 10 dimensional reality simply adds nine more variables to the observed variable "X"; It is rather that there is no variable "X" in the real reality — there is no spoon!

So when the amateur theologians ask us to "imagine that our world is a projection from a higher-dimensional space," what exactly is it that we are supposed to imagine? It is not fair to simply imagine a reality like this one, but with a lot more properties. Even if we knew the exact nature of the projection in question, we would still be left with inductive ambiguity due to the resulting compression, but the fact of the matter is that no theologian has offered us even the slightest idea about the nature of the proposed projection. In the absence of this, it is possible to imagine almost any situation obtaining in the higher-dimensional world while yet being compatible with (and in some sense identical with) the observed events of our own shadowy world.

In summary, the Allegory of the Cave may provide the welcome insight that there is something beyond the world of our experience, but it cannot provide any genuine theological comfort, because in the absence of constraints we have no idea how the world of our experience corresponds to that "greater world," the real reality, the more spacious Space, the more dimensionable Dimensionality. We are still lost.

Yeridat Hadorot: Beleiving DOES Make It So.

2006-06-19T23:08:00.000-04:00

All the precious things she had
In the days of old
Jerusalem recalled
In her days of woe and sorrow,
When her people fell by enemy hands
With none to help her;
When enemies looked on and gloated
Over her downfall. (Eichah)

Tho we are not now that strength which in old days
Moved earth and heaven, that which we are, we are... (Tennyson)

We are a failing people, a springless autumn... We are become Middle Men, of the Twilight, but with memory of other things. (Faramir, Lord of the Rings)

The notion of yeridat hadorot (the decline of the generations) is one that permeates Orthodox though and attitudes. The idea that earlier rabbinical figures were inestimably greater than later rabbinical figures is a cornerstone of Orthodox Jewish life. Every Baal Habos and 4th grade-student can tell you that this is true without any reservations or conditions. Contemporary rabbinical figures, be they neighborhood rabbeim or the present gedolai hador, are in no way comparable to figures of generations past; the Chafetz Chaim, the Netziv, the Vilna Gaon. And yet those figures are likewise in no way comparable to earlier figures such as Rambam, Rashi, or R'Saadya, whose greatness is scarcely conceivable to us. And those figures are likewise incommensurable with earlier authorities, R'Akiva, R'Yehuda HaNasi, Hillel. And those individuals are finally in no way comparable to the prophets, Eliyahu, Shmuel, and ultimately Moses, Aaron, and the Patriarchs.

The idea that present generations are in some way but a pale shadow of former generations can be found broadly in both Jewish and non-Jewish culture. One might say that a first hint of this attitude in Judaism is already present in the exaggerated life spans reported in Genesis chapter 5, and then again in Genesis 6:4, where the Nephilim are referred to as "the heroes of old, the men of renown." Genesis chapter 11 suggests that the early civilization of Babylon was so advanced that "nothing that they propose to do will be out of their reach." Later, we have the Talmudic expressions of this idea, such as that from Shabbos 112b (Soncino): "R. Zera said in Raba b. Zimuna's name: If the earlier [scholars] were sons of angels, we are sons of men; and if the earlier [scholars] were sons of men, we are like asses..."

One can see in the mythology of many other culture (Greek, for example) also the idea that the men of former times had capacities far beyond those of contemporary men, and were capable of deeds which contemporary men can scarcely comprehend. Indeed, the accomplishments of those early men where of such a magnitude that even the gods were forced to take note. In modern storytelling, this idea has perhaps its most potent presentation in the fiction of Tolkien, where the Men of earlier ages had near-supernatural powers, exaggerated life spans, and were closely affiliated with the gods and other transnatural agents (e.g., Elves). In Tolkien's mythology, those early Men left behind majestic stone cities and monuments, silent testimony to a level of achievement and power at which the diminished men of the present age can only gape and marvel, and then weep at how far they have fallen.

But in the wearing of the swift years of Middle-earth the line of Meneldil son of Anárion failed, and the Tree withered, and the blood of the Númenoreans became mingled with that of lesser men. Then the watch upon the walls of Mordor slept, and dark things crept back to Gorgoroth. (Elrond, Lord of the Rings)

This belief in declining aptitudes and capacities can be found also in the regard of the medievals for the works of Greek philosophy and medicine. In encountering the works of Aristotle and other Greek thinkers, the intellectuals of the Middle Ages were awed by the products of an intellectual culture which seemingly surpassed their own in every conceivable way. Indeed, the profundity and scope of Greek thought made it seem almost a sacrilege for one to raise critical questions about received Greek wisdom. And therein lay the problem, of course. As it has been pointed out, the worship of Greek thought may well have delayed the dawn of the empirical method and with it modern science.

With regard to the current Jewish perspective on this idea, it is difficult to say in exactly what way later generations are supposed to be inferior to previous generations. Is it in brute intelligence? Is it in creativity? Is it in spirituality? Is it in access to some mystical divine knowledge — ruach hakodesh? There is a recent book by Menachem Kellner which explores how Rambam understood this idea, but it's a pretty safe bet that Rambam's interpretation is not the popular understanding. I would suggest that the popular understanding is rather a loose fusion of all of the above. Thus, earlier generations were incomparably greater in intelligence, knowledge, wisdom, spirituality, creativity, and any other desirable attribute we can think of. I suspect that a poll of Orthodox people would probably reveal such an understanding to be the dominant one.

As usual, it is not my intention (nor within my capacity) to do a scholarly exercise in the concept of yeridat hadorot. I suppose you should read Kellner's book if you want that. Rather, here I just want to make the following simple suggestion:

"Yeridat Hadorot" is a self-fulfilling prophecy.

It's very simple: If the contemporary intellectual community collectively believes that its faculties and capabilities are far inferior to those of previous generations, then it will be loathe to amend, revise, or replace any of the ideas and rulings of earlier generations. One can see this effect in the reluctance of the medievals to revise Aristotelian accounts of the cosmos, and one can see it in the resistance of Orthodox Jews to modify halachic practices or to permit hashkafic innovation. Under an attitude of yeridat hadorot, one cannot propose any idea that might run contrary to the position of an earlier luminary, because — in virtue of yeridat hadorot — the earlier luminary must be correct, and thus the later innovation must be inferior, if not heretical.

Thus every potential expression of a halachic and hashkafic idea must be carefully censored by its author to make sure that it does not run contrary to the sanctified expression of a previous generation. If a new idea in fact does present the appearance of conflict with earlier ideas, then it is necessarily wrong and must never see the light of day. One can observe this self-censorship even within Orthodox music, which is so fearful of saying something hashkafically incorrect that it resorts to endlessly repeating passages from Tehillim, which are very old and therefore very safe.

The contemporary intellectual community is therefore constrained by their idolization of earlier generations to work "between the cracks," filling the small gaps in earlier ideas or tentatively extending them to modern situations, but never truly challenging, defending, constructing, deconstructing, revising, or replacing.

By embracing the attitude of yeridat hadorot, the present generation thus guarantees that it IS in fact far diminished in all senses from previous generations.

By fearfully restricting themselves to a much narrower set of allowable halachic and hashkafic positions than was allowed to their predecessors, our present-day Jewish intellectuals ensure that their creative output, their intellectual productivity, and their spiritual expression, cannot be anything but a pale and unflattering imitation of what previous generations had been able to achieve. There is thus no doubt that future generations will lament the depravity of our own generation in comparison to former ones, because by embracing the yeridat hadorot attitude we have already ensured that it is so.

I don't mean to suggest that our esteemed predecessors weren't indeed exceptional people. There was only one Vilna Gaon. Only one Newton. Only one Maimonides. But their greatness was a product of both their intrinsic intellectual/motivational capacities and the times and circumstances in which they lived. There are certainly people alive today who have intrinsic intellectual/motivational capacities comparable to these larger-than-life figures. There are Newtons and Rambams growing up among us. However, if these individuals are taught from the start that they need to censor all their ideas and insights to conform with sacred prior doctrine (and so as not to disturb anyone's fragile religiosity), then they will certainly never develop their full potential for intellectual achievement. They won't become the next Rambam or the next Newton because they have been taught that this path is not permitted to them.

Yeridat Hadorot, true or false? True, but only when we make it so.

You are not required to complete the task, yet you are not free to withdraw from it. (Avos)

Don't say, "How has it happened that former times were better than these?" For it is not wise of you to ask that question. (Kohelet)

Other evils there are that may come; for Sauron is himself but a servant or emissary. Yet it is not our part to master all the tides of the world, but to do what is in us for the succor of those years wherein we are set, uprooting the evil in the fields that we know, so that those who live after may have clean earth to till. What weather they shall have is not ours to rule. (Gandalf, Lord of the Rings)

Fin

Moral Lessons from Haibane Renmei and the Book of Ruth

2006-06-04T10:17:00.000-04:00

Oy. This blog is getting really off-topic (it was intended to be about epistemology), but now I decided I want to write a post about Megillat Ruth in the light of the anime Haibane Renmei that I watched recently. I previously wrote about the existential aspects of Haibane Renmei which got my brain going, but I was equally moved by the emotional and humanistic aspect of this series. (The characters in Haibane Renmei are not technically human but it is still a tale of humanism.) And because I saw this anime just shortly before Shavuoth, certain similarities between the humanistic aspects of Haibane Renmei and the Book of Ruth became very apparent. Both feature an interaction between two female characters, where the older character has lovingly nurtured the younger character, and the younger character is then forced to decide what sacrifice they must make in order to repay this kindness when the older character falls into distress. On reflection, while Haibane Renmei is in no sense a "modernization" of the Book of Ruth, I would not be surprised if the Japanese director had been exposed to Ruth, and had seen a glimmer of something in that story which he indirectly re-expressed in Haibane Renmei.

One caveat on what follows: I use the term "salvation" a lot below. I do not mean big-S "Salvation" in the Christian sense that a person is (or needs to be) saved from the damnation they incur simply in virtue of being flesh-and-blood. Rather I mean small-s "salvation" in the psychological sense that many people experience an inner turmoil and strife — often resulting in a pattern of self-destructive behavior — from which they find themselves unable to escape, and from which they therefore require salvation. Like struggling swimmers being swept out to sea on a powerful current, there are many people in this world (and in our communities) who for whatever reason are in a psychological state that interferes with their ability to direct their lives, to effect positive changes, and ultimately to grow. The kind of salvation that I refer to below is the small-s salvation which is needed by such individuals, and which is provided through the concerned intervention of their fellow human beings. Likewise, if I mention something about "sin" here and there, it should be obvious that I am not referring to the commission of crimes nor the transgression of religious observances. Rather, what I am referring to are the sins that one commits against themselves by embracing despair, conceding defeat, and ultimately forfeiting hope for themselves. Thus, the sin and salvation which I talk about below are psychological concepts.

Ah well, I'm afraid this post will end up sounding very Christian anyway, but read to the bottom, and you'll see that it's ultimately all about psychology! (I may be turning Japanese, but I'm not turning Christian. After this post, I will return you to your regularly-scheduled epistemology.)

For one mitzvah leads to another mitzvah, and one sin leads to another sin; for the consequence of a mitzvah is a mitzvah, and the consequence of a sin is a sin. (Avos)

Sometimes a sin is its own punishment. (Wise Rabbi)

"One who recognizes their own sin, has no sin." That is a riddle called the Circle of Sin... Perhaps that is what it means to be bound by sin: To keep going around in the same circle looking to find where the sin lies, and at some point losing sight of the way out. (Haibane Renmei)

You are not required to complete the task, yet you are not free to withdraw from it. (Avos)

When I read the Book of Ruth this year after having recently watched Haibane Renmei, Ruth really came across to me in a different light than it ever has previously. Certainly, there are many ways to read Ruth. One might read it as kind of a historical record, perhaps as a "back-story" for the epic of the Davidic dynasty. One might read it as an polemic in favor of sweeping acts of kindness, or as a lofty vision of how devotion and commitment may be manifested in their purest and most unselfish forms.

I had previously read Ruth in all these ways, and I can't say that any of them are right or wrong. But when I started reading it this year, it occurred to me that the Book of Ruth is perhaps most profoundly a tale of humanistic salvation. That is, Ruth is not just a story of people helping each other. Rather the Book of Ruth offers a vision of how one human being is delivered from utter annihilation — not by God — but by the selfless intervention of a fellow human being. This is humanistic salvation, and I believe that this is the theme of the Book of Ruth. The essential salvation story is densely compressed within the first chapter, while the rest of the book unfolds the consequences.

The Book of Ruth begins, of course, not with Ruth but with Naomi. And indeed, the story is as much about Naomi as it is about Ruth, perhaps even more so. Such a duality, such a collaboration, is required in any example of humanistic salvation. As in Haibane Renmei, salvation does not ultimately come from the "self-actualization" of a suffering individual, nor does it come from their heartfelt pleadings to an unknowable God. Instead, salvation ultimately comes from the willingness of a suffering human being to accept the helping hand that is offered to them, and the willingness of another human being to offer it. This is the necessary human partnership that is so eloquently captured in Ruth.

In a story of humanistic salvation, it is not necessarily the case that God is absent, callous, or indifferent. There is certainly a Providential component in both the Book of Ruth and in Haibane Renmei. However, in these stories God appears to only bestow his blessing for salvation on parties who have demonstrated their readiness to receive it. Crucially, this readiness cannot be demonstrated by anything that the suffering individual can do in isolation, whether by prayer or by deed. Likewise, this readiness cannot be demonstrated by anything the benevolent individual can do in isolation, whether by prayer or by deed. The requisite demonstration occurs only when the two human beings connect with each other, the one to offer assistance and the other to accept it. It is as though God stands back and says, "I want to see what you are willing to do for yourselves and for each other."

Within the first few verses of Ruth, we learn of a woman named Naomi who loses her husband and two sons in rapid succession. The text, while a model of brevity, here does us a disservice by introducing this tragedy so early and so quickly. We don't know who Naomi is, and we don't know anything about her husband or sons, so it's difficult to identify with any of these characters. In a sense, it feels like we're missing the first half of the book, which would have provided the essential character development. Because of this odd structure, I think it's easy for the modern reader to overlook what is the essential fact presented in the beginning of this first chapter.

The essential fact is that Naomi regards herself as having been annihilated. Within a short period of time, the entire meaning of her existence has been utterly erased. She says to her daughters-in-law, "My lot is far more bitter than yours, for the hand of the Lord has struck out against me," and when arriving in Bethlehem, she tells the townsfolk, "Do not call me Naomi. Call me Mara, for Shaddai has made my lot very bitter. I went away full, and the lord has brought me back empty." It's not just that Naomi is a sad individual, but that Naomi has utterly given up hope for herself.

As in Haibane Renmei, in the Book of Ruth a person's name symbolizes the meaning of their existence, their true identity, their unique narrative, the essential characteristics that makes them an irreplaceable individual. By changing her name from "Pleasantness" to "Bitterness," Naomi indicates that she has fundamentally altered her personal narrative, her essential meaning. She has changed her personal epic from the "story of Naomi, the woman who showed pleasantness to everyone" to the "story of Naomi, an unfortunate woman who was consumed by bitterness."

Naomi believes that her life is now irredeemable, that her doom has been assured. She will go on living, but without direction, purpose, or meaning. She has come to deeply believe that the "Story of Naomi" has reached its bitter conclusion, and she has already composed in her mind the final chapter: Naomi died and was forgotten, and it was as though she had never lived. Naomi prepares to utterly abandon herself.

But something happens on the way to oblivion. As Naomi falls ever further away from life, another human being unexpectedly reaches out to grab her. Wait, says Ruth, I will not let you go.

Naomi is surprised by Ruth's attitude: What could Ruth possibly see worth saving in an old, empty, defeated woman? Naomi's story is finished, and so she pushes Ruth away. She urges Ruth to leave her, to pursue a marriage amongst her own people, to secure her own future, to start rebuilding the Story of Ruth. In all her words to Ruth, Naomi is in essence saying, Build your own life, for my life is ended. Craft your own story, for my story has concluded. Forget about me, as I have forgotten about myself. I am not deserving of any kindness. I will quietly disappear. Moreover, by saying "the Lord has struck out against me," Naomi is arguing, as many despairing individuals do, that external events — indeed, God himself — have certified her worthlessness. She sees the tragedies that have befallen her as proof that she is indeed an intrinsically tragic figure, the kind of person who is — and always was — simply destined for tragedy. She is telling Ruth, "Can't you see that I am a doomed figure? Can't you see that there is no possible hope for me?"

It is easy to recognize — as everyone does — that what follows in verses 16-17 is a key moment in the story. Ruth determinedly deflects Naomi's attempts to distance herself, resists Naomi's efforts to convince Ruth that the failure of the woman Naomi is absolute and irreversible. Ruth refuses to participate in Naomi's exercise of self-condemnation, and will not be persuaded either that Naomi's cause is lost, or that Naomi is an intrinsically doomed person. Ruth dedicates herself to saving Naomi:

Do not urge me to leave you, to turn back and not follow you. For wherever you go, I will go; wherever you lodge, I will lodge; your people shall be my people, and your God my God. Where you die, I will die and there I will be buried..."

Thus Ruth extends her hand for Naomi to grab. But, as eloquent as it is, Ruth's decision to offer her support regardless of external circumstances and Naomi's protestations is not the pivotal moment of the story, because Naomi's salvation is not something over which Ruth has control. Rather, at this point Naomi's salvation hangs on Naomi's own response to Ruth's intervention. Naomi faces a decision, a decision which is as crucial as Ruth's own decision to persist in attempting to aid Naomi. Naomi must decide whether she will amplify her efforts to resist Ruth's aid and thus persist in attempting to sabotage Ruth's devotion, or whether she will acquiesce to accept the help that Ruth is offering.

While Naomi's choice may seem an obvious one to the reader, such matters are not necessarily clear to an individual in distress. Naomi has already rewritten her own narrative as the story of a failed human being, and by doing so has spared herself from any further pain or uncertainty. Future misfortunes may come to her, but since she has already conceded that she is the kind of person who deserves such misfortune, much of the sting will have been diminished. She has resigned herself to accept things as they come, greeting them with the attitude of "I am the kind of person who experiences misfortune." In accepting Ruth's offer, there is therefore the threat that Naomi may have to let go this new narrative, and once again face the possibility of pain and uncertainty.

Moreover, because Naomi considers herself worthless in the aftermath of her tragedies, she must overcome a tremendous guilt barrier in accepting Ruth's help. In effect, she sees Ruth throwing away Ruth's own prospects of future happiness out of a misguided dedication to a worthless, unsalvageable corpse. The fear that — in addition to everything else — she might now also become guilty of dragging Ruth down into her own miserable world must have weighed very heavily on Naomi's mind. How can she justify keeping Ruth with her, when she, Naomi, is a figure destined for tragedy? In addition to the arguments she makes in the text, it seems Naomi must have had a hundred other reasons with which to push Ruth away. It is easy to push people away.

Therefore, it is verse 18, in which Naomi finally accepts the support that Ruth is offering, which may be the pivotal moment in the Book of Ruth:

When Naomi saw how determined she was to go with her, she ceased to argue with her.

In accepting Ruth's aid and companionship, Naomi is forced — perhaps unknowingly — to once again revisit the "Story of Naomi," and to begin to reconsider that last chapter. However, unlike the instant salvation achieved in Haibane Renmei, the Book of Ruth conveys the impression that Naomi's rehabilitation is far from rapid. In real life, a person's narrative cannot be rewritten in just a moment. However, the story does suggest that the ultimate resurrection of Naomi is the inevitable consequence of that first connection between herself and Ruth, the moment where Ruth selflessly offered her devotion and assistance to Naomi, and the moment where Naomi overcame her barriers to accept it.

Therefore, let me summarize what I see as the moral lessons contained in the Book of Ruth and Haibane Renmei:

Question: When is it permissible to finally give up hope on a struggling individual?

Answer: It is NEVER permissible to give up hope on a struggling individual. One must continuously seek to provide aid to a struggling person, even when that person vigorously resists assistance. It is difficult for us to see what barriers that person may be facing. Thus, even when a person seems completely intent on abandoning themselves, it is required that we continue to attempt to intervene. Although it may very well be beyond our control to pull that person back through our own efforts, the concern that we show for them in the process might very well be the one thing that keeps them hanging on. Perhaps when they see that someone else believes in them, that someone else thinks their existence has value, they might begin to see something of that value in themselves. When at some point the suffering individual comes to a place where they can attempt to look for a helping hand and a way out, someone must always be there to offer it to them. Never give up hope.

Question: When is it permissible to finally give up hope on yourself?

Answer: It is NEVER permissible to give up hope on yourself. There are many reasons that we may come to a point of despair, but we must always keep looking for a way to improve our situation. This is our obligation. Past failures are massively incriminating and continuously play on our mind, but dwelling on the past feeds the "cycle of sin" mentioned in the quotes above. People in despair are drawn to asking impossible metaphysical questions that have no answers:

Where did I go wrong?
Why was I chosen to suffer?
Why is the universe set against me?
Why didn't I ever get a chance?
Why am I the broken one?

Don't ask these questions. They only lead in circles. Instead, just look for the way forward. Look for the helping hands that are extended to you. Try something you haven't tried before. Tell a friend about your trouble. Tell your doctor, rabbi, priest. Don't give up. It is not your fate to suffer forever. You've paid your dues, and now it's time to find your way out.

When we have been suffering for a long period of time, it is easy to begin thinking that "it's just too late to fix matters at this point." One feels the weight of lost time pressing down upon one's shoulders, time that we know can never be recovered. And there is the sense that, as in a video game or sporting event, if we didn't play our best game from the start, then it is impossible for us to catch-up and get a good score in the end. There's a tendency to want to quit the game and give up trying. But life is not a video game, and no one knows how it is ultimately scored. Moreover, we often tend to inflate our own failures, and from an objective standpoint our life is not nearly the disaster that we perceive it to be.

And finally, as Victor Frankl points out, there is meaning in suffering. The suffering that we experienced was not wasted or empty. It was not for nothing. It deepened and enriched us. But nevertheless, we should not seek to suffer further. We should accept those experiences as part of ourselves, and then move forward. Never give up hope.

Existential Anime

2006-05-28T20:29:00.000-04:00

Where were you when I laid the earth's foundations,
Speak if you have understanding.
Do you know who fixed its dimensions
Or who measured it with a line?
Onto what were its bases sunk?
(Job)

Ring the bells that still can ring
Forget your perfect offering
There is a crack in everything
That's how the light gets in.
(Leonard Cohen)

I just saw an amazingly sad and thought-provoking Anime yesterday called Haibane Renmei. It is 13 episodes and available on DVD from Amazon (i.e., legally) and on BitTorrent. Except for a couple of moments, it is free of those Anime elements that make some Americans uncomfortable (e.g., manifestations of the cavalier Japanese attitude toward nudity and sexuality), so I would recommend it without reservations. I suspect it's best viewed with subtitles.

The story is heavy with Christian themes of sin and salvation (which is very unusual for Japanese animation), although there is no reference to any particular Christian mythology. But these themes of sin and salvation are in some measure also Jewish, and indeed are now largely universal. We all wonder what will become of us ultimately, whether and how anything we do here and now can influence our final disposition, and we all hope that somehow even if we've gotten everything completely wrong, that there might be a compassionate Father-in-Heaven who knows how we struggled, and will accept us even if we have nothing to offer other than our failures. But our deepest wish of all is not to be left alone. If our loved ones do indeed go somewhere after this life, our dearest hope is that we will be able to rejoin them someday. (One can see this desire already in Genesis, where the patriarchs when they die are "gathered to their kin.") There is no concept more devastating or painful than the idea that at the end of our days, we might be somehow be left all alone, never again to be reunited with our loved ones. There could be no fate more cruel than that.

(Incidentally, the depth of this fear is why religion has gotten so much mileage out of bludgeoning people with visions of Hell and Purgatory. The fear of Hell is not ultimately the fear of fire and torture, but the fear of being forever separated from the people you love.)

The premise of Haibane Renmei itself is in some regards strangely similar to the The Prisoner, and yet it is utterly different. The outline of the story is that there are certain children who are periodically born into a small village which is sealed off from the outer world by impenetrable walls. These special children are not born as infants from human mothers, but emerge mysteriously from cocoons at the ages of between 5 and 12 years old. They are called "Haibane" because that is what they have always been called. (Haibane might mean "Charcoal Feather" in Japanese. Not sure.) There is no rhyme or reason to any of this: At random periods, a cocoon will spontaneously grow in some isolated location in the village, and eventually a Haibane child will emerge. The Haibane children are fully aware that they have had some prior existence before emerging from the cocoon — an existence that included a home somewhere and a family — but they cannot remember anything in particular about that prior existence, not even their own names. After emerging from the cocoon, each child is given a new name by the older Haibane children based on the dream that the child experienced while in the cocoon. Each child sprouts cute little wings and is given a halo, so they look like the classical figure of an angle. However, the wings are flightless, the halos functionless, and in every respect the Haibane children remain just ordinary children. There is no information available to the children about where they came from, why they appeared in this village at this time, or what purpose their existence might serve. The Haibane's existence is a complete and utter mystery to the Haibane themselves.

In addition to these Haibane children, the village also contains a majority of normal humans who reproduce in the classic fashion. However, neither the Haibane nor the humans are permitted to leave the village. The human villagers generously give the Haibane children jobs to do, and the two species coexist peacefully. However, while the human villagers go through the normal human life cycle of aging and death, it's a different story for the Haibane. At a certain time in the life of these children, they just disappear. That is, at some moment — usually a few years after their "birth" — they suddenly begin to feel that "their time has come," and they walk alone into the Western Forest where they are mysteriously "beamed-up" as a column of light. This is their "Day of Flight." And just as they have no knowledge of how or why they came to this village in the first place, there is no knowledge of how or why they leave it. It's just how it ever was, from time immemorial: A new Haibane is born into the village, lives, laughs, and loves for a short few years, and then mysteriously disappears. Some of the older Haibane children have watched many of their friends disappear in this fashion and have almost become accustomed to it, wondering only when their own turn will come. Others of the children find it very difficult to be suddenly abandoned by their close friends in such an abrupt manner. (Since they have no parents, their friends are their family.) But again, there is no rhyme or reason. It's just the way things are.

Naturally, the fondest wish of every Haibane child is that when their Day of Flight comes, they will be reunited with their dear friends who have previously left them. And their greatest fear is that they might for some reason be left behind (as some indeed are), to live alone and die alone.

This is all food for thought, but besides the great sadness of the story itself, what is even sadder in some ways is the "knowledge deficit" of these children. What do they know about anything? At any given time, the oldest of the Haibane children are perhaps 16 years old. (Only a few children reach this advanced age without yet having had their Day of Flight.) And the knowledge that any of these "seniors" possess is just the scattered bits of lore that the previous generations told them over the years. The older Haibane have certainly witnessed many new Haibane being born, and they have witnessed many of their friends depart. They therefore know something of how to care for and acculturate the "newborn" Haibane, and they know something of how to grieve for their departed companions.

But they have no insight. They have no answer to the question of "Why?" Indeed, the most painful fact is that there is no one to whom they can even ask their questions: "Who am I? Why am I here? What is my purpose? What should I do? Where will I go on the Day of Flight?" There is no one who has the answers. There are only the children themselves.

All they can do is live day to day, enjoy the time they have together without knowing how long it will last, and ultimately just accept the essential mystery of their existence. Perhaps on their Day of Flight they will finally learn the answers to their questions, but perhaps not. Perhaps the Day of Flight is simply The End, after which they will have no existence at all. Or perhaps the Day of Flight is the entrance to a new level of existence, a new cocoon, a new village. Or perhaps it is a passage back to the forgotten place they originally came from. All they really know is that it is a journey they cannot refuse. And so they all hope for and believe in the best-case scenario... that wherever they do end up going on the Day of Flight, it will be somewhere that they will be reunited with all of their friends that they had lost.

And so my first reaction after watching this series was "Those poor children." They have to live this existence of uncertainty, not knowing who they are, where they came from, where they are going, or what the meaning of their very existence is. They have no answers. They have no teachers. They have no oracle or prophet. No one has been beyond the village walls. The Haibane children have nothing but a few scraps of mythology passed down by prior generations of Haibane children who were as much in the dark as they are. "Those poor children," I think.

But then I think, isn't this exactly our own situation? We are those poor children. We have no oracle to whom we can ask questions such as "Why am I here? Where did I come from? What is my purpose?" Indeed, "Who can possibly know what is best for a man to do in life — the few days of his fleeting life? (Kohelet)" There are none of us who stand at some Archimedean vantage point, and to whom we might entreat, "What is the view from there?" Likewise, we know not what will become of us when our time is finished. "For who can enable him to see what will happen afterward? (Kohelet)"

Like those poor Haibane children, we too have no one who has been beyond the walls. All we have are the snippets of mythology which were given to us by former generations who were even more in the dark than we are. Indeed, we are all abandoned children, with no adults to guide us, to teach us. When our newborns ask us "Why?" we tell them the same story that was told to us. Whether we tell them a scientific story or a religious story, all we can ultimately say to them is "Here is what I was told. I don't know if it's right or wrong. Perhaps some day you will know more."

I hear babies cryin', I watch them grow,
They'll learn much more than I'll ever know.
And I think to myself, what a wonderful world,
Yes, I think to myself, what a wonderful world.

Plato Lets Us Off Too Easily

2006-05-03T18:23:00.000-04:00

What do you see when you play this movie? If your vision is at all intact, you perceive motion, and you almost certainly also recognize that there is structure and coherence to the motion. In other words, you probably feel fairly confident that the motion you observe is not random, but reflects some underlying process — that there is an explanation of some sort that accounts for what you are seeing. And you would be right. Congratulations — that's no small achievement.

But how much more can you say about what the process actually is? It could be a lot of things, right? You don't really know, other than that it's structured motion, as already stipulated. But you might take the evident periodicity of the motion to be suggestive of rigid body rotation, and you'd be right about that. This inference might be reinforced if you recognize the shiny blue thing to be some kind of semitransparent glass or crystal, in which case you might conclude that it either contains or stands in front of the rotating rigid body. And knowing this would allow you to further deduce that some of the evident curvature of the rotating object might be a mere "trick of the light" as light is refracted and reflected within the glass. And if you can get as far as dismissing the curvature as artifactual, then you may find that some of the angles suggest something vaguely cube-like in nature. And you'd be right there too.

As shown in the second movie, the source of motion is in fact a rotating wire-frame cube, which happens to be located a considerable distance behind the spherical glass, and illuminated from behind.

What I am trying to get at here is how difficult it can be to get to the "truth" of the matter — to describe the way things really are. You might protest that "actually, it wasn't that difficult at all." Maybe you instantly detected a rotating cube behind or within a glassy substance. Well, OK. But remember that besides the unusual wire-frame cube (whose actual structure I assume you did not guess from the first movie) there was nothing spectacularly alien about the scene. Identifying an object lit from behind and viewed through heavy glass is not categorically different than identifying an object lying under a few feet of moving water in a river or creek, something we are fairly good at most of the time. (To make the example stronger, try to imagine the appearance of the cube after being refracted or reflected through a series of heterogeneous materials, rather than just one piece of glass.)

My point is this: Plato's Allegory of the Cave paints our epistemological challenge as one of inferring the true structure of reality from a linear projection of that reality into a lower-dimension subspace. Information is lost in this projection, since features which exist independently in the real world are collapsed together in our perception, just as in the allegory three dimensions are collapsed into two dimensions (shadows on the wall). However, by invoking an analogy involving mere linear projection, Plato lets us off the hook too easily. Indeed, one might protest that Plato's shadows actually yield a good deal of information about the structure of the real world. Provided we know the manner in which the shadows are produced and that we have the capacity (!!) to conceive and reason about a third dimension, we denizens of the cave could probably make some fairly good inferences about what goes on in the three dimensional world beyond our experience.

For example, imagine the simple 2-dimensional projection (shadow) of the rotating wire-frame cube. Seeing this shadow on a wall, you would very quickly deduce the structure of the actual 3-dimensional object, because this projective mapping is very simple. [We of course have to note the inevitable presence of inductive ambiguity that arises when dimensional information is lost. In the case of the wire-frame shadow, the direction of rotation will be underdetermined because the "front" and "back" of the cube cannot be distinguished in the shadow.]

A naive extrapolation of Plato's analogy might therefore lead one to believe that the problem of ontology is just figuring out how many actual physical dimensions are linearly projecting into the three dimensions of our experience, and then making inferences about what actual n-dimensional entities correspond to the 3-dimensional entities we observe in our perceptual subspace. We then end up with a naive "Flatworld" ontological attitude, which holds that what actually exist in the world are n-dimensional entities which project linearly (or worse, orthogonally) into our own three dimensions. So, in this view, while we do not perceive the real world, we perceive a subspace of the real world in which objects have a fairly simple relationship to their actual n-dimensional counterparts.

The problem is that there is no reason a priori to think that the world of our experience is a simple linear projection of some higher-dimensional reality. This is what I am trying to illustrate with the movies. What if, like the image of the cube refracted through heavy glass, the entities in your observational subspace are related to actual entities in the world in some highly-complex manner, and that the actual nature of this relationship is utterly unknown to you? This is our actual epistemological situation. It is certainly reasonable to think, like Plato, that the objects of our experience are related to some broader reality beyond our perception. But it is wrong to think that we know anything about the structure of that relationship. Indeed, how can we ever characterize the properties of that relationship without first knowing something about the broader reality itself. One cannot characterize a relationship between two sets of entities when only the properties of one set are actually known. And yet...

Is There a Crisis?

2006-04-23T00:38:00.000-04:00

A self-transcendent conception should ideally explain the following four things: (1) what the world is like, (2) what we are like, (3) why the world appears to beings like us in certain respects as it is and in certain respects as it isn't, (4) how beings like us can arrive at such a conception.
(Nagel, "The View from Nowhere")

Tho' much is taken, much abides; and tho'
We are not now that strength which in old days
Moved earth and heaven, that which we are, we are, —
One equal temper of heroic hearts,
Made weak by time and fate, but strong in will
To strive, to seek, to find, and not to yield.
(Tennyson, "Ulysses")

He went like one that hath been stunned,
And is of sense forlorn:
A sadder and a wiser man,
He rose the morrow morn.
(Coleridge, "The Rime of the Ancient Mariner")

Despite all my rage I am still just a rat in a cage.
(Smashing Pumpkins)

It seems to me that there is an essential dilemma in the scientific endeavor, one that can best understood through the allegory of The Prisoner. Sometime while I was in high school, PBS ran an old British television series called "The Prisoner." I assume it was originally made some time in the 60's. Suffice it to say that it was extremely weird — definitely not what you would ever expect to find on American TV.

During the opening music and credits, we watch this James Bond-like hero character driving a small British sports car into an underground garage, and then moments later striding purposefully down a long tunnel into an obscure basement office (evidently the seat of some unsavory state security operation with which he is affiliated). He has a brief and agitated conversation with the mysterious figure behind the desk before bitterly thrusting down a letter of resignation and storming out. He races back to his apartment and anxiously throws a few belongings into a small suitcase, evidently preparing to make a hasty escape. But someone has other plans for him. A mysterious figure arrives at the apartment, and within a matter of seconds the hero is lying prone on the floor — unconscious from the poisonous gas injected through the door's keyhole.

He awakens some time later, alone in the living room of a strange post-modern apartment. Alarmed and afraid, he rushes to the window, preparing to confront his unknown assailants. But what he sees outside is not a military complex, nor are there any signs of guards, interrogation squads, or other trappings of captivity. Rather, what he sees from the window is a peaceful and almost surreal little village. He is stunned. What exactly had happened to him? Where is he? How did he get here? Confused and angry, he bolts out of the apartment looking for answers. He finds a shopkeeper just opening her store. "Where am I?! What is this place?!" he demands.

The shopkeeper's matter-of-fact reply: "Why, you're in the The Village, of course."

Frustrated, the hero questions several other people, but none of them is any more forthcoming. All they can tell him is that he is in The Village. No one can explain to him where or what The Village is, or how he or any of them came to be there. What is even more infuriating and alarming is that none of them seem to share his discomfort at not knowing anything about their present situation. They show no concern about where they are, how they got there, or why. For that matter, they show no interest in who they are, as they are all referred to by numbers instead of names. (Our hero is Number 6.) These people are simply not bothered by the absurdity of it all — they just go on about their mundane business. For them, "You're in the The Village, of course" is the beginning and end of all knowledge. There are no questions; Everything is perfectly as it should be, and was ever thus.

The story continues from there, and you can trust me when I tell you that it gets much weirder. (The final episodes are essentially incomprehensible.) But the allegory I have in mind relates to the opening sequence of Episode 1 that I just described. Let us consider the Prisoner awakening in his strange Village as an allegory for our own cognitive awakening. Put yourself now in the role of the Prisoner. Indeed, you are the Prisoner, and the Village in which you suddenly and inexplicably find yourself is the World that you see every morning when you wake up. Don't forget that.

Unlike the Prisoner, we do not have the benefit of a sharp moment of discontinuity demarcating the break between a normal "prior existence" and an abnormal "current existence". Rather, we are brought to our current existence by a subjectively smooth and seamless evolution in awareness and cognitive-perceptual capacities. We first enter this world as a primitive creature capable only of seeking food, warmth, and affection. Over a long period of pre-reflective development, we successively add perceptual and cognitive capacities as dictated by a genetic program which has been tailored to provide maximally synchronous meshing of organism to environment. Capacities and parameters that are not evolutionarily hard-coded into alignment with the environment are nevertheless tuned over the course of development by various learning mechanisms to respond in optimal fashion to the statistics of the particular environment on which they are trained. Thus, long before we ever achieve verbal competence or the capacity for abstract thought and advanced symbolic operations, our minds have already been thoroughly adapted, acclimated, tuned, and conditioned to this particular world that we refer to as reality.

It is because of the fact that by the time we achieve our adult mental competencies and the ability for reflection we have already become so well adapted to our environment that there scarcely seems anything worth reflecting about — it is because of this that most individuals are never troubled by what we call "philosophical problems." Certainly, if someone whacked them on the head and they woke up in a Mexican warehouse, they would run about in a panic yelling "Where the hell am I?" But this emotional alarm is only the result of the sharp discontinuity in state that occurs under those circumstances. Because the manner in which organisms are introduced into this world produces little or no subjective discontinuity, few people ever find the opportunity to recognize that there is anything noteworthy about the world and about their place in it. Rather, most humans are so acclimated to their world that they cannot conceive that anything about their existence might be otherwise. Certainly, they can conceive that they might have been born in Africa or China or perhaps on a Moon Base, circumstances permitting, but they will never be able to formulate the essential existential questions:

What the hell am I...
Where the hell am I...
What the hell am I doing here?"

The expletives above are important to indicate the emotional state that must accompany a true realization of the nature of the problem. Like the Prisoner, who reacts to his situation with confusion, anger, fear, perplexity, and ultimately purposeful action, the appropriate reaction to the coalescence of the essential existential questions must be confusion, anger, and fear, and then ultimately a burning desire to find the answers to these questions at any cost. To strive, to seek, to find, and not to yield. The Prisoner upon awakening in his strange Village does not say "Oh well, whatever... seems like a nice place to retire." No! The Prisoner needs to know what the hell is going on, and there is no way he can rest until he gets some answers.

In moments when I think of myself (like the Prisoner) as having unexplainably awoken in this strange world, I do indeed become agitated, anxious, frightened. I want to stop everything and demand an immediate explanation. I want to scream "What the hell is going on here!" or "What am I?" I want to wave my hands madly through the air, pointing to everything and nothing and cry out "What is all THIS!?" and "Why is all this the way this is!?"

And I need to have answers now, today — not tomorrow, not next week. How can the Prisoner even think of eating or sleeping when he doesn't know the first thing about his circumstances? And what about you and me? Should we not all run through the streets yelling, "What happened?! Where am I?! What am I?! What the hell is going on?!" Like the victims of an sudden earthquake awakening amidst the rubble, should we not be gripped by the most severe terror, anger, and confusion? Like the Prisoner awakening in his strange Village, should we not furiously demand immediate answers? The Prisoner does not first shave, shower, put on deodorant, prepare breakfast, and only THEN demand an answer. There is nothing of greater importance to the Prisoner than discovering the facts of his present circumstances.

Our first instinct should be to scream.

Strange as it sounds, I think it's fair to view the scientific endeavor as our most effective substitute to screaming. When we feel the existential mystery pressing in on us, there are moments when we indeed would wish to scream at the top of our lungs, "Give me answers! I want answers!" But like the Prisoner, we quickly discover that our impassioned demands, pleas, and threats are met by Nature with contemptuous silence. Whatever is "out there" is clearly not disposed to providing straight answers to straight questions. And when the Prisoner realizes that his captors are likewise unforthcoming, he does not give up. He does not resign himself to being manipulated by unknown forces, he is not happy with his lot. Rather, he takes the offensive. He improvises, manipulates, investigates, pursues every indirect avenue that might shed light on his situation. And so too, when our screams failed us, we found methods by which to improvise, manipulate, investigate — to scratch and claw our way toward some understanding of our own existence. This is science. It is thus far the only mechanism that appears to provide any genuine insight into our circumstances.

But we must remember that while science remains the effective substitute to screaming, it is hideously slow and often painfully indirect. And that is the danger. What we admire most about the Prisoner is that he never loses his passion, never becomes complacent or resigned, at least not for long. He does not becomes entranced and enchanted by the intricacies of his own manipulations and improvisations. While his manipulations may take him far afield and require him frequently to "play the game" as his captors intend, the Prisoner never forgets his own agenda, his own questions... Whenever given the chance he demands, "Who is Number 1?", meaning "Who is in charge? Who has the answers?"

While we scientists don't expect that there is some clandestine antagonist hiding the answers from us, shouldn't the scientific endeavor nevertheless be pursued with a similar atmosphere of panic and urgency? For God's sake, we have no idea who we are or what we are doing here! How do we have the time and patience to train rats, teach undergraduates, or run ANOVAs? Why aren't we confused, perplexed, and angry, demanding answers? Don't we realize the utter mystery of our existence?

I indeed suspect that most scientists have forgotten that they are supposed to be screaming. Perhaps they never knew this to begin with. They, too, like everyone else, have become comfortable with the world of their experience, and they find little or nothing amiss. Sure, they have questions about the function of a particular protein they study, or the conductivity characteristics of some new material they created. Questions, yes. But screaming? Why on Earth would they want to scream? Did something bad happen? Did someone get hurt?

Perhaps this is all for the best, in a way. Few good insights have ever come out of a truly agitated, unruly, or impatient mindset, as far as I am aware. Those who feel that they must have their answers right-now-today are often forced to settle for the very first piece of detritus that drifts by. Impatient people are left embracing Towers of Babel, Alien Invasions, and various other lightweight and ridiculous explanations of why things are the way they are. Clearly, more insightful accounts come out of greater deliberation and perseverance, but even they only provide a peek at how things might be. Whatever small insights eventually come to us usually are the result of the most deliberate and patient investigations. Scratching and clawing.

Still, there is an aspect in which this is deeply unfortunate, because it requires that human beings make careers of scientific investigation, with all the afflictions that this situation can be expected to bring. The cutting urgency to uncover the circumstances of our existence is lobotomized to the dull necessity of publishing five journal papers a year and teaching basic principles to 800 disinterested undergraduates. The impassioned crusade for Truth metamorphoses into the Post Office. The mentality becomes one of individual career advancement, of "getting by" in the institution from day to day and year to year. Perhaps somewhere in a dark recess of the researcher's mind remains a dim recollection that they thought they had something to do, but what was it?

It is possible that there is another reason for the apparent absence of panic and urgency one sees among scientists. It is possible that many scientists believe that the circumstances of our existence have been adequately explained and accounted for with the discovery of Evolution. Thus, I suppose they would say, with the Theory of Evolution in hand we need no longer feel the pressing panic and confusion of the Prisoner, because we pretty much know, at least in broad terms, how we came to be here, why the world appears the way it does, and whether there is some ultimate purpose to any of this. (Apparently not.)

But frankly, any sense of tranquility derived from the Theory of Evolution is truly undeserved. The Theory of Evolution is the very last place that we should look for comfort about our situation. The Theory tells us that the particulars of our existence and many particulars of the world around us all owe to a long-term process of environmental adaptation. But the Theory also tells us that our mind — the "citadel itself," our entire mechanism of apprehension and cognition, of knowing about the world — also owes to the very same process of environmental adaptation.

But then arises the doubt, can the mind of man, which has, as I fully believe, been developed from a mind as low as that possessed by the lowest animals, be trusted when it draws such grand conclusions? (Darwin)

In my opinion, the evolutionary origins of the human mind throws us into an even greater state of perplexity about the circumstances of our existence. What guarantee do we have that a brain which evolved millions of years ago for tasks of hunting and mating would ever be adequate to the task of comprehending the true nature of the cosmos and our place in it? Not only can I not imagine any such guarantee, but the very notion that such a brain might possess such capacities seems ludicrous. So while the Theory of Evolution is clearly a huge advance in every regard, it gives us yet another level of perplexity: What are the constraints and biases of minds such as ours, and how can we ever characterize these constraints and biases without knowing a great many things a priori about the nature of the world that we are attempting to discover through the use of these very capacities.

What we want is to reach a position as independent as possible of who we are and where we started, but a position that can also explain how we got there. (Nagel)

It's that last part that has to give us all headaches. Who are we that our minds can discover the Truth? This is the greatest source of perplexity in the modern age. Even with all the impressive fMRI and single-cell recording studies now being done, I don't think scientists have really yet gotten a grasp of the nature of this problem. Perhaps it's best just to scream, after all.

A noiseless patient spider,
I mark'd where on a little promontory it stood isolated,
Mark'd how to explore the vacant vast surrounding,
It launch'd forth filament, filament, filament, out of itself,
Ever unreeling them, ever tirelessly speeding them.

And you O my soul where you stand,
Surrounded, detached, in measureless oceans of space,
Ceaselessly musing, venturing, throwing, seeking the spheres to connect them,
Till the bridge you will need be form'd, till the ductile anchor hold,
Till the gossamer thread you fling catch somewhere, O my soul.
(Whitman, "A Noiseless Patient Spider")

The Lay of the Land

2006-04-11T15:29:00.000-04:00

How can we ever know which of the above landscapes describes the relation between the physical world and our capacity to know that world? Does this matter in any practical sense? I suspect it does, because just as the topology of an error surface affects the convergence properties of optimization algorithms, the topology of the "knowledge surface" should affect the convergence properties of knowledge acquisition algorithms, i.e., science. Thus, we must find out what the landscape really looks like, but how?

Parasitic Religion

2006-03-19T18:36:00.000-05:00

I see a good deal of truth in the argument (per Dawkins) that religion is a kind of parasite, a set of memes that replicate themselves from generation to generation by cleverly commandeering certain critical mental faculties to ensure their reproduction. (And even recognizing this, I find myself unable to take any kind of measured stand to prevent my own exploitation as a receptive host.) As hard as it is to internally revise or reject religious beliefs learned in childhood, it is much harder yet to resist conveying these beliefs to one's children. Religious beliefs do seem to force one inexorably to communicate them to the next generation. They hijack one's rationality by playing to emotions of guilt and fear. Religious people who don't really believe any of the religious fairytales will still transmit religion to their children, either directly or through the schools in which they enroll them. This process is rarely ever disrupted by a host declaring "I will not transmit!" Rather, disruption occurs when a host transmits ineffectively, for example, when a parent sends their child to an after-school religious program. While such a measure may satisfy the parent's compulsion to transmit religion, it is not adequate to implant the religious memes into the new host. Thus we find that completely secular people are generally not raised on secularism, but are more often raised on "religion-lite". For these individuals, someone indeed did attempt to infect them with the relevant memes, but the effort was not adequate for the memes to take root and the religious parasite was extinguished. Am I being too negative?

Learning Religion

2006-03-19T18:22:00.000-05:00

I am unimpressed with the manner in which religion and theology are taught, or rather to who they are taught. In particular, I am unimpressed with the traditional practice of teaching theology to children. Oughtn't educated people, religious and irreligious alike, find this practice to be very suspect?

Imagine that you are the parent of an 7-year old child. You are divorced, and share custody of the child with your former spouse. Unfortunately, your former spouse has become a member of an obscure cult that preaches a variety of apocalyptic beliefs, very different than your own mainstream religious beliefs. One day, a friend informs you that your child has been inducted into the cult and has begun attending daily classes with the cult leader, all with the enthusiastic encouragement of your former spouse. Does this bother you?

I think that you would be VERY bothered by this news. Why? Because such a young child can't possibly have the wherewithal to objectively assess the claims that they are likely to hear? Because such a young child can't possibly have the experience to know how such claims are regarded by others, or to have had exposure to competing claims? Because such a young child is predisposed to give maximal credence to the claims that are made by authority figures in their lives? Because such a young child is predisposed to give maximal credence to the claims made by a parent? Because such a young child is predisposed to think or do whatever will be rewarded by social acceptance among peers and the affection and respect of authority figures and parents? Because strong beliefs adopted during childhood may be difficult and painful to dispel or revise at a later time? Because indoctrinating such a young child is tantamount to coercion?

I think all of the above arguments have some degree of validity. Indoctrinating a young child is indeed a coercive process. A young child has no choice but to believe what they are told, especially when everything of importance to them is made to be contingent on this belief. But such utter contingency is always the case in a very religious environment. Should thinking people be upset with this state of affairs only when the indoctrination is carried out by an esoteric cult leader, but not when it is carried out within their own mainstream Jewish or Christian home? What is the essential difference? Let me offer a couple more quotes from the Joshi reader:

To my mind, the inculcation of religious belief into the young — a process that can scarcely be termed anything but brainwashing — is religion's great crime against humanity. Billions have been prejudiced in favor of one religion or another by this kind of indoctrination, and it requires a tremendous strength of mind and will to overcome it in later years. [...] One would suppose that religionists would wish their adherents to have come by their beliefs freely and of their own accord; so why do they insist that religious training begin at an age when the child is not able to think for itself and is incapable of questioning the authority of its parents or other adult figures (Joshi 2000).

If religion were true, its followers would not try to bludgeon their young into an artificial conformity; but would merely insist on their unbending quest for truth, irrespective of artificial backgrounds or practical consequences. With such an honest and inflexible openness to evidence, they could not fail to receive any real truth which might be manifesting itself around them. The fact that religionists do not follow this honorable course, but cheat at their game by invoking juvenile quasi-hypnosis, is enough to destroy their pretensions in my eyes even if their absurdity were not manifest in every other direction. (Lovecraft, in Joshi 2000).

Well, taking a few steps back, I'm not sure that outrage is necessarily in order. Parents have always indoctrinated their children with their own beliefs, and they will continue to do so regardless of Joshi's indictments or my own half-hearted objections. And such indoctrination will always play on a child's immature fears and desires, because that is all the child has at its disposal.

But I think there needs to be some acknowledgment of the following truth: There is a certain educational dynamic created when Professor Smith lectures to a class of 22-year-olds about the life of Jesus, and there is another, very different, educational dynamic created when Mommy cuddles her 8-year old child and lovingly reassures him that everything will be OK as long as he always loves Jesus. These are not equivalent forms of education, nor are they even in the same category.

Obvious? Perhaps. But I don't think that this gross inequivalence is registered by most religious people. One argument that I often hear in friendly discussions on religion is that if so many millions of people believe in God, then surely there must be a good deal of truth to the notion. Well, of course this is wrong in so many ways. But for just one, it implicitly compares belief in God with other beliefs that have never had the kind of reinforcement that has been lavished upon the former. Consider, for example, that there is probably a small group of people who believe that Immanuel Kant was the greatest Western philosopher of all time. And every year there are probably a few additional students who will make such an assessment after encountering Kant in a philosophy course. Should we conclude because of the huge disparity in the number of God-believers and Kant-believers that God's existence is therefore so much more self-evident than Kant's philosophical greatness?

I think before we can honestly do that, we ought to strive to level the playing field. One way to attempt this would be to instruct children about Kant at the earliest ages, telling fascinating stories about him that might excite the childish imagination, and stressing ad nauseam how he was the greatest philosopher of all time, how no one before or since could hold a candle to his wisdom, how he loved all people, how he freed our minds, etc. (And of course we should not neglect to seriously instruct the child about the unimaginably horrible fate that awaits them should they choose to believe otherwise.)

But this project is probably hopeless if we wish to retain any trace of truth in our tale. Rather, we should level the playing field by deferring any instruction about God until about the same time and place where we begin instruction about Kant. Let a 22-year old university student who has not been previously indoctrinated take one class on Western religion and another on Western philosophy, and let us then see which he or she finds more compelling, the self-evidence of God's existence or the self-evidence of Kant's greatness. If we repeated this experiment several times, I think we would see the great disparity evaporate. As Robertson writes in regard to Christianity (see Joshi 2000),

Clergy and flock alike act in the spirit of self-interested corporations. They feel that if children are not trained to accept Christian doctrines before they can reason for themselves, the chances are ten to one that they will not join any church in later life. [...] None of them dares to trust to the process of persuading grown men and women.

My point is not that Kant is greater than God. I couldn't even finish Kant's book. My point is that religious thinkers somehow always manage to overlook the many (unearned) competitive advantages that accrue to their beliefs sheerly in virtue of the way that those beliefs permeate every aspect of the child's developmental environment. Oddly, many religious thinkers seem to have convinced themselves that most people who hold religious beliefs have indeed arrived at them against all odds, through Herculean effort and heroic sacrifice. Please. In most cases, religious beliefs are first delivered with the mother's milk, and continue to be delivered without cessation throughout all of childhood and adolescence. Few other beliefs get such privileged treatment. What is finally required to produce a religious adult from a religious child is not Herculean effort, but common intellectual inertia.

In conclusion, I think that the theologians — the people who actually think about religion rather than just performing the motions — really have something to ask themselves. They tell us that one can arrive at religious truths through rational deduction, or through study of nature, or through study of self. All these endeavors require certain capacities that are characteristically present in adults and not in children. Why then not defer instruction on theological matters until adulthood, when the capabilities will be present for the successful completion of the task? Shouldn't religious thinkers indeed be embarrassed that rather than instructing and educating the most mature and most critical minds, they have chosen to coax and cajole the least competent and least critical minds?

Persuasion and Coercion

2006-03-19T14:00:00.000-05:00

I think one must be deeply skeptical about any set of beliefs that incorporates among it a meta-belief regarding the consequences of nonbelief in the set. Besides the obvious logical problems (i.e., the belief regarding the consequence of nonbelief will only be relevant to those who already accept the belief set), it seems to me that the threats of unpleasant consequences for the nonbeliever and of rapturous consequences for the true-believer just erodes the credibility of the belief set itself. It leads one to think that any argument in favor of the belief set is more one of "bullying" than "convincing". If people must be threatened with unimaginably horrible mental and physical afflictions for themselves and their loved ones in order to be persuaded to subscribe to a given belief set, it can only be concluded that the beliefs themselves must be extraordinarily unpersuasive. This is very much what we see in religion since the Biblical era. Time and time again the flock strays from the path of belief, and time and time again must be terrorized by the prophets with threats of awful punishments and calamities.

Welcome to the Dark Side

2006-03-19T13:39:00.000-05:00

Did you ever notice that while some people thrive in the religious social environment, others seem never to find a sense of comfort and belonging?

Here's a metaphor of my own: I think that religion can be likened to a river that runs through a rocky terrain. The water at some distance from the banks and the bottom runs smoothly and easily, making gentle curves, perhaps occasionally hitting a dip or making a rapid adjustment around an obstacle. Most of the water in the river has a genuinely serene property. Drop a leaf into this part of the river, and you would watch it move effortlessly downstream and be gone from sight.

On the other hand, the water that has the misfortune to run along the rocky bank has a turbulent and unpleasant existence, constantly colliding with massive, immovable objects, being turned back on itself, sprayed up into the air, sucked into vortices, churned in chaotic eddies. A leaf dropped into these waters has an uncertain future. Perhaps it will be sucked into a crevice, flattened against the side of a rock, or just ripped fiber from fiber under massive and uncomprehending forces.

I think that people raised within a strong religious tradition can be thought of as a million leaves scattered randomly on such a river. By good fortune, a majority will find themselves some distance from the banks, moving placidly downstream amongst the thousands of similarly situated leaves. Indeed, if any one such leaf could "see" only what lay in its immediate vicinity, it would scarcely recognize any motion at all — just the small dipping and bobbing of the other leaves relative to itself.

But there will be a small fraction of people that find themselves near the rocky banks of this river, or that through misfortune will drift closer and closer to those shores over time. And those leaves will inevitably be ripped and battered mercilessly until their very shape and structure is obliterated, their torn remnants eventually left to decay forgotten under a rock.

Picture the leaf that has come to be pinned against some undistinguished rotted tree stump. The other leaves amongst which it began its journey have long ago disappeared from sight, transported by the river's mighty flow to distant places. Yet if this trapped leaf could escape the confines of its watery prison for just a moment — to majestically leap from the water onto the dry river bank, to safety... but that moment can never come. Wet and soggy and decaying, the leaf's fate is sealed. "Stay with me!" the water cries irresistibly, as the leaf slides into the muck.

I think that this frightening boundary region, this rocky bank, is an intrinsic feature of every socio-religious system. The most obvious victims are those whose mental or sexual predispositions are certified by the pious masses to be "an affront to God". They will certainly be the first into the grinder. But they won't be the last, because their sacrifice cannot diffuse or erase the boundary region. The boundary is created along with the belief system; it is created by the belief system. In order for the water in the center of the river to flow smoothly, there must exist a region of water at the edges that is continuously punished, harassed, confounded, destroyed.

The grinder never stops grinding, and the grinder is never empty.

Review of "Off The Derech" by Faranak Margolese

2006-03-13T19:42:00.000-05:00

I just finished reading Off The Derech by Faranak Margolese, and I thought it was very interesting. She discusses a lot of the causes that drive people off the derech, and does so in a fairly perceptive and truthful manner. She herself appears to be quite religious, and therefore invokes God about as often and as naively as other religious authors do, frequently sounding as though she just recently chatted with Him about his views on chinuch and whatnot.

God created Adam and immediately gave him free choice, knowing full well that not one page later Adam would stumble and choose sin. But God determined that it was better to allow Adam to fall, better to have him betray His will with free choice, than not have that choice at all.

God wants us to walk in his ways, but he doesn't force us to. He leads but does not push. He gives us free will and then does what He can to preserve it by delaying punishment.

This sounds like the climax of a really bad d'var Torah, but if you can read past the midrashic drivel (which, ironically, is what probably drove me off the derech as much as anything else), you will find that most of Ms. Margolese's analyses are pretty sound. I will now discuss some of the issues she raises.

One of the author's recurring points is that Judaism must be able to compete in the free marketplace of ideas on its own merits. That is, it is no longer enough to "scare" people into remaining frum with visions of Gehinom or God's wrath, or to coerce observance through emotional manipulation (e.g., fear of losing the respect or love of one's parents). In the modern world, these classic techniques are ineffective or counterproductive, and often produce nominally Orthodox Jews whose Judaism is extremely shallow or cynical. Instead, Orthodox Judaism must prove itself to be more emotionally and intellectually rewarding than any other available option, or it will continue to lose adherents. This is especially true in the modern era, when one really doesn't have to believe anything. In earlier times, the alternatives to Judaism were largely limited to Christianity and Islam, and for a wide variety of reasons these options were never very appealing to Jews. Today, one can live a completely normal and fulfilled life without subscribing to any religious system at all. Orthodox Judaism must therefor prove that it can provide its members a better option than all the other options available:

The outside world is no longer painful or perceived as evil, but rather enjoyable, attractive and welcoming. So today, in order for observant Judaism to be chosen, it cannot merely be neutral. It must be better than the alternative.

Ms. Margolese focuses heavily in the beginning of the book on "rejection" as a cause of people leaving Yiddishkeit, and I think there's a lot of truth in that. She discusses a number of kinds of rejection, all valid, but I think she underplays the rejection felt by individuals who can't buy into the hashkafa of Orthodox Judaism. Certainly, there is more than a single legitimate Orthodox hashkafa, but it is nevertheless the case that most Orthodox Jews believe that God (literally) gave the Torah to Moses at Mount Sinai about 3300 years ago, and that this exact same Torah is the one we read today every Shabbos. Most Orthodox Jews believe that God created the universe less than 6000 years ago in pretty much the same state as we see it today, and many or most believe that this creation occurred over a literal 6-day period. These are basic aspects of Orthodox Judaism today.

Orthodox Jews (me included) who at some point discover they can no longer suspend their disbelief in such stories will undoubtedly feel rejected, regardless of whether or not they actually give voice to their discontentment. Moreover, for the most part, these discontented Jews will not give voice to their concerns, because they realize the incredible emotional and psychological pain that doing so would bring to their friends and family, and to any other true believers. (They realize this because they themselves almost certainly experienced this very same emotional anguish in the course of revising their own deepest-held beliefs about the world.)

So what recourse exists for Orthodox Jews in this situation? What they see all around them in the Orthodox world is rank intellectual dishonesty; that is, the coddling of religious beliefs, and the unwillingness to examine cherished ideas with the dispassionate scrutiny that is the hallmark of all critical reasoning and empirical investigation. How can Jewish people who also value rationality and empiricism find a place in such a culture? I don't know.

On a related note, Ms. Margolese has a chapter on Truth, and how issues related to the search for truth drive people away from Orthodoxy. Again, I agree with most of her points, but find that she underestimates the role of theology and hashkafa. For example, she writes,

So how can we strengthen belief in God? By discussing with students and children, on a level they can understand, the reasons for believing in God: why it makes sense, if it makes sense, what the alternatives are, what some of the arguments are for God's existence and against it.

This is not easy to do. In fact, it can be quite tricky for, while we can make good arguments for the rationality of God's existence, we cannot prove it.

Yes, it is tricky, isn't it? That's the problem that a lot of us have with Orthodox theology and hashkafa. We've been told from the earliest ages how obvious is the existence of God, and how foolish and ignorant are all those agnostics and atheists. (Indeed, they are considered far worse than Christians and even Reform Jews, probably because their arguments are so much harder to refute.) At some point, however, when we are able to think and read for ourselves, we come to realize that the very best arguments for the existence of God were already discredited by the 17th century. The author's position that "there are good arguments for the rationality of God's existence" is really quite weak, and it is the historical failure to honestly recognize this that bothers many of us so much. The "good arguments" that the author refers to are really just post-hoc justifications, and have only rarely convinced anyone who wasn't already a believer.

Moreover, the author's suggestion for discussing with students "what some of the arguments are for God's existence and against it" is disturbingly wishful thinking. Does she really think that a yeshiva rabbi discussing God's existence with his students would paint a fair picture of "the alternatives." Or will the yeshivas invite atheists and agnostics to present the evidence in favor of their positions? I think not. No, the "discussion" envisioned by Ms. Margolese will ultimately be nothing other than the same hashkafic brainwashing that has defined Jewish education ever since the Middle Ages. I think the following opinion from a contemporary book on off-the-derech Hasidim comes much closer to the truth of the matter:

Among people who believe that there is only one truth — and that they are in possession of it — tolerating other points of view is, by definition, impossible. (Winston, 2005)

Also, although I realize that Off The Derech is not a theological treatise, one too-often hears this "we can make good arguments" line without ever actually hearing one of these good arguments. So what's the good argument? The Argument to Design? The Ontological Argument? These arguments do not convince anyone except those who already believe. That is not what I consider a "good argument." I think it will be when Orthodoxy comes to grip with the tentativeness of the God-hypothesis — with the idea that God's existence and involvement is something we wish to be true rather than know to be true — that genuine religious inclusiveness will be possible. In the meantime, the zealous and absolute adherence to metaphysical beliefs which have zero empirical support will continue to make a mockery of the notion of religious rationality or rational religiosity.

Ms. Margolese goes on to propose that

If we succeed in intellectually establishing that there is a God, that He gave the Torah, and that rabbinic leaders have the authority to make halachah, we will have succeeded in establishing an important foundation for observance.

Well, yes, sure, but it's crucial to note that the Orthodox educational process does not actually work by establishing any of these things intellectually. If we wanted to establish these beliefs intellectually, we should wait until a person is 20 years old and has experience with the ways of world and some capacity to distinguish fact from fiction, and then we should make our best intellectual arguments about the existence of God, the authenticity of the Torah, and rabbinic authority. What we actually do is brainwash children with religious fairytales from the time they are 2 years old until the time they are 22 in the hope that it will become impossible or irrelevant for them to ever seriously entertain real hashkafic questions, either because we have made them completely ignorant of anything other than Talmud, or because we have constructed their belief systems in such a way that raising such issues would simply be too cognitively or emotionally painful. As Ms. Margolese writes,

Our parents believed, they told us we should believe, and therefore we do, without giving it the kind of thought and exploration that makes it our own. Thus belief in God begins in childhood and pervades the lives of observant people.

As an example of the Orthodox educational approach, consider this charming advice from Wagschal's Successful Chinuch:

[we] need to show children the beauty of Torah and emptiness of the secular way... [we] need to answer questions before children can ask them for themselves... [the] child must be warned not to be taken in by what he may see, read or hear and, above all, to avoid temptations.

This certainly does not sound like a recipe for an open and honest evaluation of "alternatives," and I think it unfortunately represents the typical approach to chinuch in the Orthodox community. All the talk about intellectual honesty and openness and alternative beliefs is really just hogwash, I'm sorry to say. Strictly religious parents and teachers want their children and students to believe the same things they themselves believe, and a long-term process of brainwashing is without any doubt the most reliable way to accomplish this. Individuals who ultimately reject this brainwashing may leave religion entirely, or remain within the religious world as cynics, hypocrites, and antonymous bloggers.

A couple more things I'd like to quote from the book:

Michael, who went off the derech as an adult, experienced intellectual dishonesty when observant people would engage in what he called "selective reporting" as they tried to prove that Judaism was true. He says they would "sometimes look for various scientific discoveries to prove certain age-old truisms in the Talmudic system and, at the same time, disregard scientific studies that disprove them... They don't even necessarily believe in the tools they are using to prove the Torah. They just figure, 'Hey. It's useful. Let's use it.' And when someone discovers that it's not useful, they dump it... It is not the evidence that drives the system; the system drives the evidence."

I could not have said it better myself, but there are still a couple of points to make. The first is that Ms. Margolese treats Michael's story as a "for instance," when actually the intellectual dishonesty Michael describes is completely rampant in the yeshiva world, and widely embraced by kiruv organizations. (Note the liberal use of "Torah Codes" nonsense in certain kiruv programs.) Michael's story is far from an isolated incident. But the essential problem is that it's almost inevitable. When people have a certain unassailable belief — a view of the world that cannot possibly be wrong, then all valid evidence must inevitably point to that particular conclusion, and all contrary evidence must be in error. What we therefore see in the yeshiva world is that when empirical evidence cannot be suitably twisted to fit the Jewish mythology, this evidence is then recast as the deceptive production of evil, amoral, atheistic scientists, who are worse than Nazis and would dissect their own mothers given half a chance. (If you think I am overstating things, please read Avigdor Miller.) Thus, any evidence scientists produce which does not happen to support prevailing Jewish fairytales is immediately attributed to Satan.

So the essential problem of Truth is that Judaism, like all other religions, is not about Truth at all. It's about a particular set of beliefs and traditions which come from an age of mystery and magic, long before the introduction of critical reasoning, empirical methods, and natural laws. Those who try to sell Judaism as a "quest for truth" are selling a bill of goods. The closest thing any of us have to a real "quest for truth" is the scientific method. Even with all its imperfections, the achievements of science in illuminating the workings of the natural world long ago surpassed the sum total of everything religion had ever accomplished in this capacity.

The author goes on:

So truth must be acquired truthfully. If we want to argue effectively for the truth of Torah, we must not only speak of truth, we must speak with it in the classroom, in our actions, and all our pursuits. We must be honest about ourselves and honest about Judaism. Hiding the truth undermines truth, which is one of the strongest arguments for Torah observance...

The basic problem is that true intellectual honesty would require that we modulate our belief in God and Torah in correspondence with the evidence presented in the favor of these propositions. In science and critical reasoning, hypotheses are "believed" with a strength that is largely proportional to their evidential support. For example, the causal role of smoking in cancer is strongly believed because of vast empirical findings that support this hypothesis. On the other hand, the existence of life beyond our solar system engenders more tenuous belief, because although we suspect that other habitable planets may exist and may produce life by the same mechanisms that produced life here, we thus far have no actual evidence of life outside of Earth. We also have available rational and quantitative methods for belief evaluation (Bayesian probability, for example) that are frequently used in artificial intelligence. In any case, the main point is that intellectual honesty (i.e., rational cognition) requires that the strength of beliefs be contingent on the strength of evidence. Unfortunately, the fact is that Orthodox Jews are not prepared to appropriately modulate their beliefs in God or Torah. Instead, they put God and Torah beyond the reach of evidence or argument, thereby ensuring that Orthodox Judaism cannot achieve true intellectual honesty. I think it's really that simple.

The author claims that "After all is said and done, we must take a leap if we are to believe in God." I simply ask "Why must we?" The intellectually honest approach is to attach a degree of belief to the God-hypothesis and Torah-hypothesis that reflect their evidential support. Why can't we just do the honest thing?

Omissions and Commissions

Let me now mention something that "Off The Derech" leaves out entirely, as does almost every other "frum" book on child-rearing, such as Successful Chinuch, Love is Not Enough, Timeless Parenting, Being and Becoming, More Effective Jewish Parenting, Chinuch in Turbulent Times, and so on, and so on.

That is sexuality.

From reading almost any "frum" book on child and adolescent development, you would think that nothing of any significance happens to boys and girls between the ages of 12 and 15. They just get bigger and possibly become "moody." The wholesale omission of any discussion of the sexual aspects of puberty reflects the monstrous fear of sexuality in the Orthodox world. The approach to sexuality adopted by frum authors, educators, and parents alike has been to ignore as thoroughly as possible any discussion of sexual development, and to rely on the hope that God will make it all just go away.

We can conclude, therefore, that as long as a child is sheltered, his heart will remain pure and he will be protected from sin. (Wagschal 1999)

In other words, sexuality is a kind of alien virus that is beamed in from the "outside world," a contagion that can be prevented by carefully surrounding a child with fedoras, shaitles, and rabbinical fairytales. This hear-no-evil, see-no-evil attitude toward sexuality (along with the inevitable cover-up of sexual abuse and sexual maladjustment) is one more factor that gives the lie to the notion of intellectual honesty in Orthodox Judaism. The Orthodox approach to sexuality is not honest; it is cowardly.

What To Do About Religion?

2006-02-24T15:50:00.000-05:00

The next few posts just contain some random and non-denominational ruminations on religion. Personally, I can't embrace the faith as I did in my youth, but neither have I been willing or able to walk away from it. The resulting divergence between my belief and behavior has been a source of considerable distress to me in recent years. But as I don't foresee myself either renewing a faded romance with religion or marshalling the masochistic fervor to perform a radical amputation, I guess I'll just have to try to make myself comfortable where I am... straddling the fence. Ouch.

As fair warning, the tenor of these posts is currently fairly negative toward religion, although I don't intend it to remain that way indefinitely. (I see positive aspects to religion as well as negative.) On the one hand, I'm sure that organized religion doesn't need any more critics, especially not from the likes of myself. Over the past centuries, secularists like Hume, Russell, Sagan, and those French guys have been largely effective in exposing the problems of religious belief, at least for an intellectual audience. Many religious people who posses some level of intellectual curiosity will eventually come into contact with those challenging and abrasive points of view (as did I). Whether or not they can succeed in insulating their beliefs during this encounter, they will probably come away from it with a good deal less certainty about the rationality of those beliefs. And uncertainty is what this all comes down to...

On the other hand, none of what anyone says seems to make the slightest difference. People seem to need religion, and what people need they will have.

My biggest problem with religion is the unusual degree of certainty that becomes attached to its constituent beliefs, such as those regarding the nature of God or the occurrence of certain distant historical events (e.g., the Resurrection, the Exodus, etc.). In my opinion, this degree of certainty is, on average, so radically undersupported by the quality and quantity of evidence that it just cries of pathology. Key religious beliefs are largely excused from the critical scrutiny and evaluation given to other issues. The problem is not just that "extraordinary claims require extraordinary evidence," which is true, but also that any claim should only accrue a degree of belief that reflects the weight of evidence in its favor. So even if certain propositions about God or distant historical events have some evidence in their favor, these propositions could only accrue a degree of belief proportional to the strength of that evidence. And while one can argue over the actual quality and quantity of this evidence, it seems plain to me that the known facts are never remotely adequate to justify the metaphysical levels of belief that key religious propositions seem to engender. Thus, the belief attached to these propositions is essentially irrational. Some would say that this irrationality is the essence of faith, which would probably get a nod of agreement from the "schoolboy who said Faith is believing what you know ain't so" (Mark Twain), but as something of a rationalist I can't generally see much intellectual merit in "leaps of faith."

And so, to begin...

Perhaps the day will come when the most solemn concepts which have caused the most fights and suffering, the concepts "God" and "sin," will seem no more important to us than a child's toy and a child's pain seem to an old man — and perhaps "the old man" will then be in need of another toy and another pain — still child enough, an eternal child!

— Nietzsche, W. Kaufmann translation

Man is not far above beast, for all is vanity.

— Kohelet

Religion is a big problem for me. I was raised in a religious environment (Jewish), and have a lot of affection for the religious traditions that I grew up with. But the theology... aye, there's the rub.

Although I'm generally sympathetic to theological arguments that seek to cast doubt on the scope of human cognition (e.g., What gall to imagine that our puny human minds can comprehend the universe!), I don't see how these arguments lead anywhere other than profound skepticism and metaphysical doubt, which are certainly not the desired ends of most theological projects.

Sooner or later we are told that when such attributes as omnipotence, mercy, justice, and love are ascribed to God they do not mean what they mean applied to men. [...] One might as well claim that God is purple with yellow dots, or circular, or every inch a woman — provided only that these terms are not used in their customary senses. (Kaufmann, in Joshi 2000)

Skeptical possibilities are those according to which the world is completely different from how it appears to us, and there is no way to detect this. (Nagle 1986)

But if theologians fail to see where this road leads, that's their problem. For myself, I'm certainly prepared to believe that there's something big going on "out there" all around us, a something to which we are not privy. And I won't argue with those cosmic universalists who choose to call that unknown something "God," but I don't see how simply branding the unknown with those three magic letters really adds anything to our understanding of the universe. Just call the unknown "the unknown" if that's what you mean. Now, I realize that some folks who like to identify "the unknown" with God may do so just to make a cold an indifferent universe seem a bit more friendly, but I think others have probably missed the point entirely.

Why, when no honest man will deny in private that every ultimate problem is wrapped in the profoundest mystery, do honest men proclaim in pulpits that unhesitating certainty is the duty of the most foolish and ignorant? Is it not a spectacle to make the angles laugh? [...] [W]hen one of us ventures to declare that we don't know the map of the universe as well as the map of our infinitesimal parish, he is hooted, reviled, and perhaps told that he will be damned to all eternity for his faithlessness... [He is told] Stick to the words which profess to explain everything; call your doubts mysteries, and they won't disturb you any longer; and believe in those necessary truths of which no two philosophers have ever succeeded in giving the same version. (Stephen, in Joshi 2000)

As to inquiries into the particulars of what or who God is and what he likes to do on weekends, I think this is probably a waste of time and energy but not an essentially dishonest pursuit. It seems that every system of thought has its axioms, and if one chooses to make God's existence Axiom #1 and God's inclination to do good stuff Axiom #2, then it would be desirable to explore the consequences of those choices. The common problem is that these axioms (and others underlying theological exploration) are almost certainly not selected in virtue of their overwhelming "productivity" — their ability to generate new theorems or hypotheses. Nor are they generally selected for their "self-evidence," although perhaps they might have been at a time when commerce in metaphysical ideas was much more limited than it is now.

Rather, it is my informal observation that when a theologian sets out to construct a religious system from axioms such as these, that person is really trying to retrofit an established set of religious doctrines to which he or she is already committed. And while there is no essential shame in this endeavor, from a practical standpoint this is a different process than constructing a theory from the ground up, and should not be advertised as such. The true constructive process places primary importance on the method by which new insights are produced. It specifies this method in detail, and insists on rigor and formality in the application of the method at each step. By contrast, the process of religious justification (apologetics) implicitly places primary importance on the generation of particular conclusions, such as that "Man should worship God" or that "The Bible is true." When metaphysical importance is attached to a particular conclusion, in effect requiring the inevitability of that conclusion, then the method by which the result is produced becomes a mere annoyance to be dispensed with at the earliest opportunity. And experience shows that when the critical eye is removed from the application of method, what soon remains is no method at all. I have found this absence of method to be palpable in the few works of religious apologetics that I have encountered. As Eliot writes (see Joshi 2000),

So long as a belief in propositions is regarded as indispensable to salvation, the pursuit of truth as such is not possible, any more than it is possible for a man who is swimming for his life to make meteorological observations on the storm which threatens to overwhelm him.

This is not to say that I can produce an example of the perfect constructive process. Geometry and other axiomatized systems may provide a model, although even in processes which exhibit immaculate attention to method, the desire to produce particular conclusions can bias the selection of axioms in ways which are not ultimately justified or fruitful. Rather, attention to method exists along a continuous spectrum. However, in mathematics and in most branches of science, it seems that every possible step is taken to reduce ambiguity in method, whereas in many areas of theology, every step is taken to preserve ambiguity in method. One might consider the overuse in theological presentations of metaphor, analogy, and their accompanying obfuscatory idioms (e.g., "as it were", "in a manner of speaking", "in a certain sense", etc.) as the symptoms of this desire to preserve ambiguity in method.

In any case, I think that the speculation induced by theological inquiry can be extremely engaging and rewarding in its own right, and indeed often provides the motivation (that few other things do) for people to think about themselves, their individual fate, and their place in the universe. But I feel very differently about pronouncements on matters related to God's psychological state — who or what he likes and dislikes, what his hopes and dreams are, etc. Such pronouncements cannot come from any honest investigation of the subject, because such an investigation could only produce the most tentative strings of hypotheticals: "If there is a God, and if he has a personality, and if that personality includes hopes and dreams in the same sense that human beings have hopes and dreams, and if those hopes and dreams include among them the desire that everyone will worship him in the same sense that a human being might experience the desire to be worshiped, then...". What degree of certainty could ever attach to the conclusions of such reasoning?

In matters of the intellect do not pretend that conclusions are certain which are not demonstrated or demonstrable. (Huxley, in Joshi 2000)

No, theological pronouncements on the nature of God have a different source than the intellectual curiosity that drives theological inquiry, and I don't like what I think it is. [Hint: I think it is social control.]