[MaFLa] invitation to a philosophy talk on`Kant's Case for the Syntheticity of Mathematical Judgments in the First Critique and Afterwards`

Krisztina Biber Biberk at ceu.hu
Tue May 17 14:44:16 CEST 2011

The CEU Department of Philosophy cordially invites you to a talk 
Katherine Dunlop (Brown University)
`Kant's Case for the Syntheticity of Mathematical Judgments in the First
 Critique and Afterwards`
Friday, 3 June, 2011, 4.00 PM, Zrinyi 14, Room 411
In the _Critique of Pure Reason_, especially the "Doctrine of Method" portion, Kant seems to argue that mathematical judgments are synthetic  because they are justified by "pure intuition", where intuition represents  particulars (and pure intuition is a priori). 
But it is not easy to understand how representation of a particular can justify a priori  conclusions. In this paper, I develop a further reason to seek an another way to understand Kant's argument that mathematical judgments are synthetic. I show that the position Kant takes in the first Critique is vulnerable to objections made by followers of Christian Wolff in the 1790s. These opponents argued that the predicate of any mathematical judgment could be incorporated into an appropriate definition of its subject. The judgment would then be justified by conceptual analysis--without any contribution from intuition--and so would be analytic. Kant is vulnerable to the objection because he maintains that mathematical definitions are "arbitrary". I argue, however, that Kant has the resources to withstand the objection. Kant can argue that the definitions introduced by the Wolffians presuppose the same cognitive capacities used to prove the result in question, in particular, the capacity to construct figures in space. However, this cognitive power is not easily understood as representation of a particular, i.e., intuition as Kant defines it in the first Critique. Kant should instead maintain that definitions of concepts presuppose, on the part of the sensible faculty, general constructive abilities. I show that Kant indeed formulates his view this way in response to the Wolffians.
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