Leibniz entre logicisme, formalisme et intuitionnisme ? - David Rabouin (Philosophia Scientiæ)
Leibniz has often been presented as one of the precursors of logicism or formalism but more rarely a precursor of intuitionism. He was a staunch defender of the Tertium non datur, reasoning in forma and blind thought, so at first glance he appears far removed from this school of thought. After demonstrating some weaknesses of logicist and formalistic interpretations, this article aims to highlight features that are close to intuitionism, particularly in Leibniz’s conception of the mathematical continuum. A first conclusion might be that in Leibniz’s case we gain nothing and actually lose by applying to his thought the categories of later mathematical philosophy. A more positive and certainly more fruitful conclusion is that if we accept that Leibniz’s thought can be related at one and the same time, and in different ways, to logicism, formalism and intuitionism, this is because traits that seem irreconcilable to us are not in terms of his mathematical practice. It can borrow from them without lapsing into inconsistency and, as I shall sketch out in conclusion, this provides some interesting avenues for the current philosophy of mathematical practice.