Por Joan San-Millán (Centro de Filosofia das Ciências da Universidade de Lisboa).
In Begriffsschrift, Frege presented a logical system and used it to formulate logical definitions of arithmetical notions and to deduce some noteworthy theorems by means of logical axioms and inference rules. It is often assumed that all derivations in this work - despite some oddities that should be corrected - can be reproduced in a second-order formal system.
In this talk, I argue that the deductive system of Begriffsschrift must not be reconstructed as a second-order calculus. An analysis of the nature of its language, logical axioms and inference rules leads me to argue that Begriffsschrift’s deductions do not need any correction but, on the contrary, can be explained in coherence with a global reading of this work.
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