We will be hearing from Eylem Özaltun on her paper entitled, 'Paralogisms revisited: transcendental object as arbitrary object'

Abstract:  

 I start by registering that Kant’s concern in the passages where he talks about I think is the possibility of objective thought and rational discourse. Hence any account of Kant’s I think must first and foremost make its role in establishing this possibility intelligible. The main claim of my paper is that any account of I think according to which “I” refers to an individual cannot meet this adequacy criterion. I show this by investigating a curios expression Kant uses, namely, “=X”. This expression appears in B404: “Through this I, or He, or It (the thing), which thinks, nothing further is represented than a transcendental subject of thoughts = X”. I argue that “=X” is Kant’s device for emphasizing the indeterminacy of a certain representation. It is a specific kind of indeterminacy which makes this indeterminate representation suitable for figuring in deductive inferences like universal instantiation and universal generalization. “=X” is a vehicle for generality for Kant. I further argue that Kant models the vehicles of generality he employs in his metaphysics on the use of such devices in ordinary mathematical discourse. Namely, he models his notion of the transcendental on the notion of the arbitrary in mathematics. I take it that when Kant uses “transcendental” to modify “object” or “subject” he uses it as synonymous with “arbitrary” as in “Let X be an arbitrary triangle”.

How do arbitrary objects work as a vehicle of generality in ordinary mathematical discourse? In order to answer this question in a way that will help us to interpret Kant, we need a study of the discourse as a study of natural language of mathematics. After all Kant did not look at mathematics via the post-Fregean logical reconstructions of its reasonings. Now if there are some significant mismatches between such reconstructions and the ordinary practice, we cannot use the former to see what Kant saw in mathematical reasoning. What we need is a study of how mathematicians use arbitrary objects as a vehicle of generality without explicit quantification. I find what we need in Kit Fine’s work: in his account of arbitrary objects as variable objects constructed by Locke-Cantor abstraction.  

I show that Locke-Cantor conception of abstraction is the best model for how Kant abstracts to get to the arbitrary objects of his metaphysics, namely, the transcendental object and transcendental subject. Being abstract objects, they are logically distinct type of objects than the individual objects that fall in their range. (For example, an arbitrary integer is not identical to any particular integer. Such an identity claim would not only be false but a category mistake). I argue that Kant appeals to their being of logically distinct type to expose the formal mistakes of rational psychologists in Paralogisms. I show that Kant’s criticism can be summarized with a slogan: do not confuse a reference to an arbitrary object with a reference to an individual object in its range! Then I argue that thinking that the “I” of I think refers to an individual is just this confusion. Finally, I show that the same confusion would result in reduction of Kant’s account of recognition of others as rational beings to an argument from analogy.