David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Grazer Philosophische Studien 66 (1):199-249 (2003)
The view that logic is true independently of a subject matter is criticized—enlarging on Quine's criticisms and adding further ones. It is then argued apriori that full reflective understanding of logic and deductive reasoning requires substantial commitment to mathematical entities. It is emphasized that the objectively apriori connections between deductive reasoning and commitment to mathematics need not be accepted by or even comprehensible to a given deductive reasoner. The relevant connections emerged only slowly in the history of logic. But they can be recognized retrospectively as implicit in logic and deductive reasoning. The paper concludes with discussion of the relevance of its main argument to Kant's question—how is apriori knowledge of a subject matter possible?
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Felix Mühlhölzer (2010). Mathematical Intuition and Natural Numbers: A Critical Discussion. [REVIEW] Erkenntnis 73 (2):265–292.
Tyler Burge (2013). Some Remarks on Putnam's Contributions to Semantics. Theoria 79 (3):229-241.
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