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

Philosophy and Phenomenological Research 69 (3):501–540 (2004)
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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

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Ryan Anderson
University of St. Thomas, Minnesota

Citations of this work

World and Logic.Jens Lemanski - 2021 - London, Vereinigtes Königreich: College Publications.
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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References found in this work

From a Logical Point of View.Willard Van Orman Quine - 1953 - Cambridge: Harvard University Press.
An essay concerning human understanding.John Locke - 1689 - New York: Oxford University Press. Edited by Pauline Phemister.
The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Critique of Pure Reason.Immanuel Kant - 1998 - Cambridge: Cambridge University Press. Edited by J. M. D. Meiklejohn. Translated by Paul Guyer & Allen W. Wood.

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