It Adds Up After All: Kant's Philosophy of Arithmetic in Light of the Traditional Logic
Author: Anderson, R. Lanier
Source: Philosophy and Phenomenological Research, Volume 69, Number 3, November 2004 , pp. 501-540(40)
Publisher: International Phenomenological Society
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 (<7+5>) bear two relations to number concepts: <7> and <5> are inputs, <12> is output. To capture both relations, hierarchies must posit overlaps between concepts that violate the exclusion rule. Thus, such truths are synthetic.
Document Type: Research article
Publication date: 2004-11-01
- This journal is now published by Blackwell Publishing. Current issues of this journal are available from here . Backfile content is in the process of being reloaded by Blackwell, and will shortly be removed from this page and available only from the Blackwell link above. If you have any queries about continued access to this journal please contact mailto:email@example.com.
- Information for Authors
- Subscribe to this Title
- ingentaconnect is not responsible for the content or availability of external websites