I argue that a compulsive seeking for just one sense of consistency is hazardous to rationality, and that observing the subtle distinctions of reasonableness between individual and groups may suggest wider, structuralistic notions of consistency, even relevant to re-assessing Gödei's Second Incompleteness Theorem and to science as a whole.

The following paper deals with the notion of existence, especially as concerns natural languages. In Section 1, starting from some quite obvious examples drawn from logic, I sketch the problem of the existential presupposition usually ascribed to noun phrases. My opinion is that the point of view frequently adopted in this case is unduly restrictive, for the existence which is believed to be presupposed here is actual existence. Accordingly, I emphasize the need for having a weaker notion of existential presupposition, (...) such that the existence (if this word can still be used) here referred to is relevant only to linguistic goals. Section 2 sketches this notion, by assimilating existence (in the weak sense) to identification in a linguistic space. (I deal here only with intuitive considerations: a more formal account will be given, I hope, in another paper.) Finally, in Section 3, the notion of actual existence is examined by contrast with the linguistic (or weak) notion of existence: and this is a question which of course can't be tackled in terms of a purely linguistic analysis, for it needs a general, epistemo-logical approach. (shrink)

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...) We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis. (shrink)