The system R of relevant implication, a philosophical and logical presentation

Details

Supervisors

Verdée, Peter

Faculty

Faculté de philosophie, arts et lettres

Degree label

Master [120] en philosophie, à finalité approfondie

Abstract

Our goal is to present the logical system R of relevant implication. We start by highlighting the problems of classical logic that have motivated the construction of this recent system. The core idea is that in the way it characterizes validity (that is, in the way it provides a theory of what a « good argument » is), classical logic (CL) does not require the premises to be relevant to their conclusion. Alternatively, it does not require the antecedent of an implication to be relevant to its consequent. For example, the famous ex falso quodlibet, « from a contradiction, anything follows », can be represented in CL as : ⊢ (A & ~ A) -> B. This is true, according to CL, for any propositions A and B. So we present different aspects of R, and show how its construction has been motivated in order to stay as close to CL as possible while avoiding ‘fallacies of relevance’. The Hilbert-style, natural deduction and structural systems of R are presented, as well as its relational semantics (inspired by possible worlds semantics). In the course of the work, several problems appear to be faced by R, and we follow how the logicians and philosophers have tried to answer those problems. For instance, how are we to interpret the fact that our new system does not make valid the apparently innocuous and widely accepted disjunctive syllogism : from ~A and (A v B), infer B ? Which can be given the intuitive reading : « from the fact that it is not the case that A and from the fact that we know that one of A or B is the case, we can infer that it is the case that B ». In particular, two interpretations of R are presented throughout the book. Our work also presents and justifies a certain pragmatic approach to logic, approach which ultimately leads us to suggest a certain form of pluralism : why, after all, should we hypothesize that a single logical system can capture the whole of human reasoning ?