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The Department of Philosophy Undergraduate Colloquium presents:
Paraconsistent Logics for Non-Classical Arithmetic
Speaker: Joseph MacDonald
Day/Date: Thursday, November 24, 2016
Time: 4:00 p.m.
Location: C-630
My research covers areas of metalogic, paraconsistent logic, and their applications in non-classical arithmetic (theory of number). For the purposes of this talk, I will place a strong emphasis on consistency by discussing various extensions and deviations of standard negation consistency. I will also give a very brief outline of how strong soundness and completeness results for the classic propositional calculus are obtained, since the solutions give a clear demonstration of the relation between proof-theoretic and semantically valid consequence relations. This will lead into a discussion of various paraconsistent logics that have been modelled for the purpose of offering more constructive approaches to dealing with inconsistencies, rather than allowing for the trivial extension of any inconsistent set, by the principle of explosion. Then, I will discuss the models of arithmetic that are obtainable from these paraconsistent logics and why they are significant. As we will see, these models offer an alternative meta-mathematical framework to Peano Arithmetic, and thus avoid the devastating results of Kurt Gödel’s undecidability proofs.
Everyone is welcome.
Contact:
Bev Garnett | bev.garnett@uleth.ca | (403) 380-1894
