The Peripatetic Program in Categorical Logic: Leibniz on Propositional Terms – Marko Malink, Anubav Vasudevan

Greek antiquity saw the development of two competing systems of logic: Aristotle’s categorical syllogistic and Stoic propositional logic. Some Ancient logicians took propositional logic to be prior to categorical logic on the grounds that Aristotle’s syllogistic presupposes modes of propositional reasoning such as reductio ad absurdum. By contrast, Peripatetic logicians sought to establish the priority of categorical over propositional logic by reducing various modes of propositional reasoning to categorical syllogisms. In the 17th century, this Peripatetic program was championed by Gottfried Wilhelm Leibniz. In the Specimina calculi rationalis, Leibniz develops a theory of propositional terms which allows him to derive the rule of reductio ad absurdum in a purely categorical calculus in which every proposition is of the form A is B. We reconstruct Leibniz’s categorical calculus and show that it suffices to establish not only reductio but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the non-monotonic variant of this categorical calculus is a natural system of relevance logic known as RMI.

Marko Malink (New York University) & Anubav Vasudevan (University of Chicago)

Logic and Metaphysics Workshop Fall 2017:

September 11 Lovett, NYU

September 18 Skiles, NYU

September 25 Jago, Nottingham

October 2 Greenstein, Private Scholar

October 9 GC Closed. No meeting

October 16 Ripley UConn

October 23 Mares, Wellington

October 30 Woods, Bristol

November 6 Hamkins, GC

November 13 Silva, Alagoas

November 20 Yi, Toronto

November 27 Malink, NYU

December 4 Kivatinos, GC