Socratic Proofs and the Logic of Questions

What

Lecture

When

24/01/2003 - 00:00

Where

To be announced

Speaker(s)

Andrzej Winieuwski (Ugent)

Website

http://logica.ugent.be/centrum/events/abstracts/24_01_03.htm

Let us imagine that we are confronted with the following problem: (1) Is s Ú Øq derivable from: p, Ør, p Ù q ® r ? Is it possible to solve it by pure questioning? A logician would not be surprised if instead of solving problem (1) in a direct way one would move to the following auxiliary question: (2) Is Øq derivable from: p, Ør, p Ù q ® r, Øs ? Yet, no answer to (2) is evident at first sight. But we can transform (2) into: (3) Is it the case that: Øq is derivable from p, Ør, Ø(p Ù q), Øs, and Øq is derivable from p, Ør, r, Øs ? and (3) can be further transformed into: (4) Is it the case that: Øq is derivable from p, Ør, Øp, Øs, and Øq is derivable from p, Ør, Øq, Øs, and Øq is derivable from p, Ør, r, Øs ? At this point there is no need for further auxiliary questions: all the constituents of the affirmative answer to (4) are evident and so is the affirmative answer to it. Thus the answer to the initial question (1) is YES. But if at least one constituent had remained non-evident and no further transformations of it had been possible, the answer would have been NO. The aim of my talk is to show that the method sketched above can be described in exact terms and that it leads to reliable results. I will consider as proofs certain sequences of questions ended with a question whose affirmative answer is, in a sense, evident. These sequences are called Socratic proofs. For simplicity, I will concentrate upon Classical Propositional Calculus (CPC). I extend the language of CPC in a way that enables us to talk about CPC-derivability and ask questions about it

Centre for Logic and Philosophy of Science

Paginanavigatie

Socratic Proofs and the Logic of Questions