Stable Philosophical Systems and Radical Anti-realism

The target of this paper is twofold. The first part develops firstly a very general and abstract topic, by describing what philosophy of logic is, when it is embedded in a genuine philosophical system, and it secondly provides an explanation of the reason why intuitionism, assumed as genuine philosophical system, is in total harmony with the contemporary intuitionistic formal logic. This part ends on the definition of what is a stable philosophical system, and explains why Platonism and Intuitionism are stable. The second part deals with the contemporary critics against Intuitionism made by a logico-philosophical tentative to give a new rise of Stric Finitism in philosophy of logic. I give arguments to show that, at the moment, the Radical Semantic Anti-Realism does not provide a philosophical system as stable as Intuitionism. 1 Philosophical systems and philosophy of logic 1.1 Vuillemin’s classification Roughly, there are two main ways of developing what one calls ‘a philosophy of logic’. The first way consists in starting from the actual scientific knowledge of logic, with the goal of exposing, and if possible of solving, some problems linked with language and knowledge in general. Such questions could be for example, “how defining the logical consequence?”, “how defining negation?”, “how can we make use of deduction of an absurdity?”, “how can we compare a logical system to another one?”, and so on. It is obvious that this way has the Joseph Vidal-Rosset Archives Poincaré UMR 7117 Nancy. e-mail: [email protected]