La logique et les logiques : la question du pluralisme
Starting from the seminal work of Boole, Frege and Russell, the dissertation seeks to clarify the issue of logical pluralism in the era of the proliferation of non-classical logics and the developments in theoretical computer science and proof theory. Two “historical” chapters are scheduled: the first chapter articulate the absolutism of Frege and Russell, taking care to show how it condemns the possibility to consider alternative structures and logics; the fourth chapter describes the path that led Carnap from the adoption of the syntactic method to the formulation of the principle of tolerance, then goes on to display Carnap‟s instrumentalism in philosophy of Logic and mathematics. Opening with the analysis of an intuitive interpretation of linear logic, the second chapter then turns to the establishment of a form of logico-mathematical pluralism with the help of order theory and category theory. The third chapter delineates the playground of revisionism (philosophical positions surrounding the debate between monism and pluralism) and then provides an argument against the thesis that denies the reality of the conflict between rival logics, all this being done by adopting the substructural logic point of view. The fifth chapter shows that each of the three main approaches to the concept of logical consequence (model-theoretic, proof-theoretic and dialogical) supplies a framework sufficiently general to establish pluralism. In short, the dissertation is a defence of logical pluralism.
Philosophy of Logic Logical consequence Revisionism Monism Logical pluralism Principle of tolerance Proof theory Substructural logic