It adds up after all: Kant's philosophy of arithmetic in light of the traditional logic

Abstract
Officially, for Kant, judgments are analytic iff the predicate is "contained in" the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia(e). Hierarchies afford a straightforward sense of containment: genera are contained in the species formed from them. Kant's thesis then amounts to the claim that no concept hierarchy conforming to division rules can express truths like '7+5=12.' Kant is correct. Operation concepts ( ) bear two relations to number concepts: and are inputs, is output. To capture both relations, hierarchies must posit overlaps between concepts that violate the exclusion rule. Thus, such truths are synthetic
Keywords Analytic Philosophy  Contemporary Philosophy  Philosophy of Mind
Categories (categorize this paper)
ISBN(s) 0031-8205
DOI 10.1111/j.1933-1592.2004.tb00517.x
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: 27,606
Through your library
References found in this work BETA
Kant's Transcendental Idealism.Henry E. Allison - 2004 - Yale University Press.
From a Logical Point of View.W. V. Quine - 1953 - Harvard University Press.
An Essay Concerning Human Understanding.John Locke - 1700 - Oxford University Press.

View all 45 references / Add more references

Citations of this work BETA
Kant on Perceptual Content.Colin McLear - 2016 - Mind 125 (497):95-144.
The Kantian (Non)‐Conceptualism Debate.Colin McLear - 2014 - Philosophy Compass 9 (11):769-790.
Neo-Kantianism and the Roots of Anti-Psychologism.R. Lanier Anderson - 2005 - British Journal for the History of Philosophy 13 (2):287-323.
Kant's Conception of Analytic Judgment.Ian Proops - 2005 - Philosophy and Phenomenological Research 70 (3):588–612.

View all 9 citations / Add more citations

Similar books and articles

Monthly downloads

Added to index

2009-01-28

Total downloads

114 ( #43,005 of 2,168,588 )

Recent downloads (6 months)

5 ( #61,319 of 2,168,588 )

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