Tuesday, March 08, 2016

there is no pure metalogic.

Let us say that an inquiry is purely metalogical just in case an inquirer makes no assumptions about the validity of any inference rule. Now suppose that a metalogical inquirer turns his gaze upon two logics which go by the names ‘classical’ and ‘intuitionist’. He observes that the former accepts the validity of double negation elimination and the latter does not. He then concludes that classical logic and intuitionist logic are not the same. Oh snap, our inquirer has left the realm of pure metalogic, for our inquirer just employed Leibniz’s Law and modus ponens. Ergo, there is no such thing as a purely metalogical inquiry. 


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