Outline of a theory of appeal to intuition in formal reasoning

Salman Panahy (University of Melbourne), Salman Panahy

Salman Panahy (Melbourne) will give present "Outline of a theory of appeal to intuition in formal reasoning". The talk will start at 11 in G14 Old Quad.

Abstract: This paper is an attempt to reread some existing accounts of appeal to intuition in formal reasoning in fields such as arithmetic and logic and give a more formal sense to a less appreciated one of them. The ultimate goal is having a clear answer to the following question: whether appeal to intuition distinct arithmetical reasoning from logical reasoning or not. By logical reasoning I mean using logical words such as ‘and’, ‘or’, ‘if… then…’, ‘all’, ‘some’, and substitution in reasoning either as inference rules or axioms. And by arithmetical reasoning I mean expanding the logical vocabulary by adding notions such as number and order either as axioms or as inference rules.

It will be argued that if we take intuition as a source of justification to hold some propositions or axioms or to accept some inferential moves, then there are ways to show the difference between arithmetical reasoning and logical reasoning in terms of appeal to intuition. However, if we understand intuition as a sort of guiding power to build a proof in a formal apparatus, then there is no difference between arithmetical and logical reasoning.