David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Philosophy and Phenomenological Research 69 (3):501–540 (2004)
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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References found in this work BETA
John Locke (2008/1995). An Essay Concerning Human Understanding. Oxford University Press.
Robert B. Brandom (1994). Making It Explicit: Reasoning, Representing, and Discursive Commitment. Harvard University Press.
Henry E. Allison (2004). Kant's Transcendental Idealism. Yale University Press.
Immanuel Kant (1998). Critique of Pure Reason (Translated and Edited by Paul Guyer & Allen W. Wood). Cambridge.
W. V. Quine (1953/1980). From a Logical Point of View. Harvard University Press.
Citations of this work BETA
Colin McLear (2014). The Kantian (Non)‐Conceptualism Debate. Philosophy Compass 9 (11):769-790.
Ian Proops (2005). Kant's Conception of Analytic Judgment. Philosophy and Phenomenological Research 70 (3):588–612.
R. Lanier Anderson (2005). Neo-Kantianism and the Roots of Anti-Psychologism. British Journal for the History of Philosophy 13 (2):287-323.
R. Lanier Anderson (2005). Neo-Kantianism and the Roots of Anti-Psychologism. British Journal for the History of Philosophy 13 (2):287 – 323.
William Mark Goodwin (2010). Coffa's Kant and the Evolution of Accounts of Mathematical Necessity. Synthese 172 (3):361 - 379.
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