Space, Geometry, and Kant's Transcendental Deduction of the Categories
Thomas C. Vinci
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Thomas C. Vinci aims to reveal and assess the structure of Kant's argument in the Critique of Pure Reason called the "Transcendental Deduction of the Categories." At the end of the first part of the Deduction in the B-edition Kant states that his purpose is achieved: to show that all intuitions in general are subject to the categories. On the standard reading, this means that all of our mental representations, including those originating in sense-experience, are structured by conceptualization.
But this reading encounters an exegetical problem: Kant states in the second part of the Deduction that a major part of what remains to be shown is that empirical intuitions are subject to the categories. How can this be if it has already been shown that intuitions in general are subject to the categories? Vinci calls this the Triviality Problem, and he argues that solving it requires denying the standard reading. In its place he proposes that intuitions in general and empirical intuitions constitute disjoint classes and that, while all intuitions for Kant are unified, there are two kinds of unification: logical unification vs. aesthetic unification. Only the former is due to the categories.
A second major theme of the book is that Kant's Idealism comes in two versions-for laws of nature and for objects of empirical intuition-and that demonstrating these versions is the ultimate goal of the Deduction of the Categories and the similarly structured Deduction of the Concepts of Space, respectively. Vinci shows that the Deductions have the argument structure of an inference to the best explanation for correlated domains of explananda, each arrived at by independent applications of Kantian epistemic and geometrical methods.
actually exists. This, I submit, is work already accomplished in the first part by means of the Analytic Bridging Principle. According to Keller, we make the transition from (primitive) “self-knowledge” to knowledge of the empirical self by introspection: ...I represent myself as the formal subject of thought. I can, however, enrich this formal notion of subject through introspection and more (p.231) indirect empirical evidence (included in the term “self-intuition”). This empirical
continues: Of course, even then it is incomprehensible how the intuition of a thing that is present should allow me to cognize it in the way it is in itself, since its properties cannot migrate over into my power of representation; but even granting such a possibility, the intuition still would not take place a priori, i.e., before the object were presented to me, for without that no basis for the relation of my representation to the object can be conceived...(Ak 4, 282; Hat., 34) What is
branches, and leaves themselves, and I abstract from the quantity, the figure, etc., of these; thus I acquire the concept of a tree. (¶6) My claim will be that what Kant calls “the general concept of spaces in general” cannot be derived from experience by abstraction because it cannot be derived by abstraction at all, and this because there is no thing(“nothing”) in common among spaces. The “thing” that there would have to be would be a universal of some kind but spaces are thoroughly
Prolegomena. This means that the prescriptivist explanation cannot be operating in part I. The only remaining option for Kant is that pure intuition is a form-space for both pure and empirical objects, as it is in the KV interpretation. But what then are we to make of the passages fromProlegomena, part II, 38, and the letter to Kästner which both appear so unequivocal in their denial of this? Surely Kant cannot have it both ways? I offer three resolutions of the conundrum, in decreasing order of
are any such conditions. We should be on the lookout for something more than is on offer in the Metaphysical Deduction to provide it. We have been speaking a good deal so far of two sides to the argument of the Deduction: one side subjective, the other objective. Kant himself speaks in the Preface to the A edition of a “subjective” and an “objective” side to the Deduction: One side refers to the objects of the pure understanding, and is supposed to demonstrate and make comprehensible the