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Volume 25, 2008

Philosophy of Mathematics

Jody Azzouni
Pages 69-88

The Compulsion to Believe
Logical Inference and Normativity

The interaction between intuitions about inference, and the normative constraints that logical principles applied to mechanically-recognizable derivations impose on (informal) inference, is explored. These intuitions are evaluated in a clear testcase: informal mathe­matical proof. It is argued that formal derivations are not the source of our intuitions of validity, and indeed, neither is the semantic recognition of validity, either as construed model-theoretically, or as driven by the subject-matter such inferences are directed towards. Rather, psychologically-engrained inference-packages (often opportunistically used by mathematicians) are the source of our sense of validity. Formal derivations, or the semantic construal of such, are after-the-fact norms imposed on our inference practices.