The aim of this paper is twofold. First of all I want to present some old ideas revisited in the light of some of the many interesting new developments occurred in the course of these last ten years in the field of the foundations of fuzziness. Secondly I desire to present a tentative general framework in which it is possible to compare different attitudes and different approaches to the clarification of the conceptual problems arising from fuzziness and soft computing. In what follows, then, I shall use some names as banners to indicate a (crucial) problem (i.e., Carnap’s problem, von Neumann’s problem, Galileian science, Aristotelian science and so on). Although it will be clear by reading the following pages, the use of these reference names (the association of a name to a certain problem) should not be considered as the result of a historically based profound investigation but only as a sort of slogan for a specific position and point of view, an indication which, of course, I hope (and trust) does not, patently, contradict historical evidence regarding the scientific attitudes, approaches and preferences of the named persons. In some cases the problem associated to a certain scientist could be not so central in his scientific interests as it could appear from the connection proposed here and as my slogan could suggest.