Syntheticity, Intuition and Symbolic Construction in Kant's Philosophy of Arithmetic

Dissertation, Columbia University (1997)
Abstract
Kant notably holds that arithmetic is synthetic a priori and has to do with the pure intuition of time. This seems to run against our conception of arithmetic as universal and topic neutral. Moreover, trained in the tradition constituting the aftermath of W.V. Quine's attack on the the a priori and on the analytic/synthetic distinction, the modern philosopher of arithmetic is likely to consider Kant's position a nonstarter, and leave settling the question of what Kant's philosophy of arithmetic is exclusively to the Kant scholar and the historian of the philosophy of arithmetic. I argue that this conclusion is misguided because it rests on the unfounded supposition that the pure intuition of time is the basis for Kant's syntheticity and a priority theses. I recover Kant's grounds for holding those theses and their significance to contemporary philosophy of arithmetic. ;I consider and reject Friedman's eliminativist attempt at making Kant palatable to the contemporary philosopher. I argue that Kant's ideas about the mathematical method in 1763, before he explicitly draws the analytic/synthetic distinction, inform the appreciation of Kant's mature view. The idea of construction in intuition is a key to Kant's Critical position that explains the relation between the intellectual and the sensible aspects in Kant's thought. I show that Kant employs a distinct notion of pure formal intuition that is associated with arithmetical necessity construed as peculiarly mathematical; irreducible to logical or sensible modality. Kant's claim is not that the intuition of time serves to justify arithmetical judgments, I argue, but that we cannot represent time as we do unless we think of it arithmetically. According to Kant, arithmetic is not reducible to logic but it is nonetheless just as fundamental to thought in general. The singularity numerical judgments in relation to the category of quantity is shown to involve a notion of a form of an object that is primary with respect to the concept of an object in general. Finally, I reconstruct Kant's notion of symbolic construction and explicates Kant's conception of a constructive procedure. I argue that a Kantian view of the ontology of arithmetic takes the numbers to be nominalizations of construction procedures for intuitable symbolic types
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,655
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Monthly downloads

Sorry, there are not enough data points to plot this chart.

Added to index

2015-02-07

Total downloads

1 ( #872,133 of 2,158,232 )

Recent downloads (6 months)

1 ( #355,837 of 2,158,232 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums