It Adds Up After All: Kant’s Philosophy of Arithmetic in Light of the Traditional Logic


Authors
Ryan Anderson
University of St. Thomas, Minnesota
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
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ISBN(s) 0031-8205
DOI 10.1111/j.1933-1592.2004.tb00517.x
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References found in this work BETA

From a Logical Point of View.W. V. Quine - 1953 - Harvard University Press.
Critique of Pure Reason.Immanuel Kant - 1998 - Cambridge: Cambridge University Press.
An Essay Concerning Human Understanding.John Locke - 1689 - Oxford University Press.
Kant's Transcendental Idealism.Henry E. Allison - 1988 - Yale University Press.

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Citations of this work BETA

Kant on Perceptual Content.Colin McLear - 2016 - Mind 125 (497):95-144.
Kant on Animal Consciousness.Colin McLear - 2011 - Philosophers' Imprint 11.
The Kantian (Non)‐Conceptualism Debate.Colin McLear - 2014 - Philosophy Compass 9 (11):769-790.

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