Sunday, November 7, 2010

The Logic of Catastrophe: A Study in Arachnology, Part I

          Kant… This catastrophic spider…
        - Friedrich Nietzsche, The Antichrist (hat-tip Edward Feser)
In a discussion spawned by the last post's attempt to defend Heidegger against a common historicistic misreading, I was given occasion to sketch a rough, formal definition of that logical specimen which may serve, within certain limits, as a criterion according to which the difference between historicism and Heidegger's seynsgeschichte may be judged irreducible. The Liar's Paradox, as the specimen is sometimes called, was there specified as follows: 
The "Liar's Paradox" names any proposition the form of which contradicts that same proposition's content due to the manner in which the latter referentially contains the former." The Liar's Paradox as I have just formulated it can assume either a universal or a particular form, in keeping with the twofold possibility of the form of all predication (or if you prefer, propositional formation).
An example of its universal form would be: "All propositions are false". An example of its particular form would be "This proposition is false."".
The Liar's Paradox has a history whose origins may be traced at least as far back as the ancient Greek Cretan Epimenides, whose famous warning that "All Cretan's are liars" raised suspicion in regard not only to its credibility but, remarkably, also to its incredibility. But for the purposes of the present post, it is not its alleged ancient Greek origin but its alleged exemplification in modern transcendental idealism that is in need of some consideration: the author of Just Thomism has recently drawn attention to the way in which the "basic thesis" of Kant's first Kritik offers us a shining example of just such a logical fallacy:
The basic thesis of the Critique is that the mind cannot move beyond the bounds of possible experience. But the more often he argues and repeats the point, the more ironic it becomes, for sooner or later it becomes clear that Kant is giving page after page of non-empirical arguments to show that only empirical arguments are possible. To use Kant’s own language in his preface, when does he ever put the nature of the mind on the witness stand and force it to only answer the questions that he is putting to it? 
Is Kant, logically speaking, a bold-faced Liar? The question, however seemingly simplistic, is obviously an important one: perjury is perhaps least acceptable before the tribunal of Rational criticism. And while the objection is not an uncommon  one among intelligent readers of Kant, it is all the more pressing since Kant himself does not leave the peculiar character of his "thesis" unaddressed: 
That the understanding, therefore, cannot make of its a priori principles, or even of its conceptions, other than an empirical use, is a proposition which leads to the most important results. A transcendental use is made of a conception in a fundamental proposition or principle, when it is applied to things in general and in themselves, an empirical use, when it is applied merely to appearances , that is, to objects of a possible experience. (KrV A 239, B 298
If we are to examine Kant's words in the light of the aforementioned objection, then the first order of business is to ensure that no equivocation is afoot --or, in other words, that the terms to which the objection has been raised can be translated without significant remainder into those of the Kritik's actual proposition. Thinking along these lines we may be inclined to take observation of a state of affairs at once superficial and significant: the word Kant employs above which has been rendered as "understanding" is verstand. An immediate difference in terminology becomes apparent with the force of something obvious: Kant's work is not entitled "Kritik der Reinen Verstand", but "Kritik der Reinen Vernunft". It would be hard to overstate the importance of differentiating between the two faculties and of never losing sight of their difference, not only in the first Kritik, nor only in the entire critical project of Kant, but in German Idealism as a whole --even when, as in Hegel, the goal is to arrive at the Identity within this difference.

But for our present purposes, such a superficial  observation, while necessary, is insufficient. For what is at stake in the task at hand is not only that the powers of the mind cannot be reduced to verstand, but that the nature of verstand, when positively expounded and clearly specified, be unconfused with the source of Kant's proposition regarding the limitations of the employment of that same verstand. What does Kant mean by speaking of the "use of the understanding", in either its transcendental or its empirical variety? What is the nature of such "use" or "application"?  In his most general accounts, Kant speaks of verstand as "a spontaneity of knowledge" in distinction from the receptivity of sensibility (KrV A 126). At such a level of description we might very well be inclined to think of the understanding as identifiable with "mind" or with "the mental faculty" broadly conceived. But Kant also supplies his reader with far more specific accounts of the understanding: Kant's revolutionary claim is that it is possible "to reduce all acts of the understanding to judgements" and thus to regard the understanding specifically as "faculty of judgments" (KrV A 68, B 93). The precise sense then, of "the use of the understanding" here in question regards those functions whose combinatory power enables the setzen, the positing, that occurs in and is proper to all scientific, that is, synthetic judgment. Analytic judgments such as those that are to be found in logic, may well constitute a propaedeutic to science, but they can never constitute a body of scientific knowledge proper; they are not to be regarded as a use or application of the understanding, either in its transcendental or empirical variety. The use of the understanding, then, precisely in so far as it is so regarded, results in the acquisition of objective knowledge, i.e. not simply tautologous, but ampliative knowledge, which extends the wealth of what is already known,  and whose systematic possession constitutes, for Kant, the aims of all science. The use of the understanding is most properly referred to the acquisition of scientific knowledge, and that scientific knowledge, because it  must be ampliative (and therefore objective), must depend upon the possibility of categorial judgement, i.e. the capacity to say something about something

But it is here that the question is only begged all the more: when we revisit Kant's quotation above, isn’t Kant therein saying something ("cannot make any use other than empirical"about something ("the understanding" as it relates to its "a priori principles" and "conceptions")? But if we bear firmly in mind the specific meaning of the understanding that Kant has clarified, then an answer becomes detectable.  For what is meant by "saying something about something", i.e. by categorial judgment, is that act by which one can establish relations with an object --and not just any manner of relations, but precisely those in terms of which the object itself can be known and knowledge can thereby be amplified.  In other words the combination achieved in such judgment must be achieved in just such a way that that combination be justified and necessitated by nothing but the object itself; the grounds of our judgment must be looked for nowhere else than in the object itself. Only thus is knowledge truly objective. I can, on the other hand, say something about an object without my statement being objective knowledge (but only an opining about perception), as in Kant's famous example: "the rock in the sun over there is warm". This judgment does indeed refer to an object as to its matter. But --and this is the crucial point --it does not find the ground of its combination therein. Rather we should say in such a case that this combination is only to be found in the representing subject, in which the representations of  "rock" and "warmth" have happened to coincide. Such a judgement is a judgement of perception.  But if a judgment is to produce objective knowledge, if it is to truly say something about something, if it is to be a categorial judgment, then it must be a judgement of experience, the sole possibility of which depends upon the application of the categories and not upon subjective coincidence. Thus, when I say: "the sun causes the rock over there to increase in temperature", I am now relying on much more than a coincidence of representations to intend the object of my judgement; I am relying not on the mere subjective simultaneity revealed within time as inner intuition but upon the objective succession of time as universal intuition, i.e. as the element in which alone the matter of my representations (and not my representations qua form) can be given. Such a distinction is the fundamental basis of the second of Kant's Analogies of Experience, and, more generally of all dynamical determinations, and it must therefore be regarded as elementary to the entire argument, the "basic thesis", of the Kritik itself. 

To recapitulate: the use of the understanding, when specified as judgment, can be roughly spoken of as the act whereby one predicates or "says something about something", but such saying is itself a πολλαχῶς λεγόμενον. When we sort out the equivocation at play here, we discover that the primary sense of such "saying something about something" is the judgement qua judgment of experience, whose combination is objective, and not the judgment of perception whose combination is subjective. The case of Kant's proposition regarding the use of the understanding that we are discussing above can be classified in neither of the two ways just mentioned; the necessity of its connexion depends neither upon the use of the a priori principles of the understanding, nor upon the coincidence of representation, which is why the statement is properly logical in the transcendental sense; its matter, while belonging to a determinate domain (unlike General Logic, which bears no reference to material content whatsoever), is itself yet formal and only that. It is for this reason that Kant begins his second book of the Transcendental Analytic, namely, The Analytic of Principles, by noting the following regarding the material content of all knowledge proper to Transcendental Logic
As Transcendental Logic is limited to a certain determinate content, namely to the content of those modes of knowledge which are pure and a priori, it cannot follow general logic in its division...Understanding and judgment find, therefore, in transcendental logic their canon of objectively valid and correct employment.  (KrV A 131, B 170)  
Kant's point here bears repeating: a canon of the objective and correct employment of the understanding, and not that objective knowledge gained by such employment, is to provide the proper subject matter of the transcendental logic. For the Liar's Paradox to be operative in Kant's transcendento-logical statement that "the understanding, therefore, cannot make of its a priori principles, or even of its conceptions other than an empirical use", that statement must be a product of the use of the a priori principles or conceptions of the understanding, i.e. it must be establishing a categorial saying something about something. But this is not what it is doing, since categorial application, because it by definition is grounded in the object itself, always depends on the givenness of time in terms of which the appearance of that object is informed. If all objects of knowledge are in the first place given in and under the conditions of intuition as Kant has transcendentally exposited them, and if one accepts that the very application of the categories depends on those conditions and owes all of its (formal) meaning to them,  then his thesis regarding the empirical limits of the use of the understanding is logically unassailable. But however his exposition and analysis of the conditions of knowing be understood, it cannot be understood as vulnerable to the Liar's Paradox.