Logical inferentialists contend that the meanings of the logical constants are given by their inference rules. Not just any rules are acceptable, however: inferentialists should demand that inference rules must reflect reasoning in natural language. By this standard, I argue, the inferentialist treatment of quantification fails. In particular, the inference rules for the universal quantifier contain free variables, which find no answer in natural language. I consider the most plausible natural language correlate to free variables—the use of variables in the language of informal mathematics—and argue that it lends inferentialism no support.
References
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[4] Negri, S., and J. von Plato, Structural Proof Theory, with Appendix C by A. Ranta, Cambridge University Press, Cambridge, 2001. MR1841217 1113.03051[4] Negri, S., and J. von Plato, Structural Proof Theory, with Appendix C by A. Ranta, Cambridge University Press, Cambridge, 2001. MR1841217 1113.03051
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