Deductive Systems with Unified Multiple-Conclusion Rules. Alex Citkin

Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.

Logic and Metaphysics Workshop

Feb 3 Hartry Field, NYU

Feb 10 Melissa Fusco, Columbia

Feb 17 GC CLOSED NO MEETING

Feb 24 Dongwoo Kim, GC

Mar 2 Alex Citikin, Metropolitan Telecommunications

Mar 9 Antonella Mallozzi, Providence

Mar 16 Mircea Dimitru, Bucharest

Mar 23 Jenn McDonald, GC

Mar 30 David Papineau, GC

Apr 6 ? Eoin Moore, GC

Apr 13 SPRING RECESS NO MEETING

Apr 20  Michał Godziszewski, Munich

Apr 27 Michael Glanzberg, Rutgers

May 4 Matteo Zichetti, Bristol

May 11 Lisa Warenski,GC

May 18 PROBABLY NO MEETING