Abstract

As I am not at all a specialist on Gottlob Frege’s work, my comments intended initially to be focused on an aspect that emerges in the last part of Peter Clark’s paper “Frege, neo-logicism and applied mathematics” 1, where he treats the question of “applied mathematics” — an aspect that appealed to me and that was triggered by Frege’s relationship between numbers and concepts, and reasoning. Starting with this concern, I have been led by my subject to propose some considerations about foundations and rationality which will go — briefly — in two directions. The first direction is that of a distinction between logical and rational foundations, whilst the second direction is that of taking into account as a fact the historical development of mathematics among the sciences, which modifies the terms of any foundational program. In delineating these considerations, I found that what I had in mind could apply to mathematics itself as well as to “applied mathematics”, thus deviating somewhat from my first explicit intention. In conclusion I shall consider the possibility of a rational foundation programme for mathematical and physico-mathematical sciences which would take into account the changes in the scientific contents and the widenings of the forms of rationality that, in my view, make these changes possible. Such foundations for knowledge would not be any more static, but dynamical and would be possibly considered only retrospectively: they would be “forward foundations”, in a sense that will be discussed in detail elsewhere.