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- Title
VERSIONI ALTERNATIVE DELLA LOGICA DEL SECONDO ORDINE: UN'INTRODUZIONE.
- Authors
Pedeferri, Andrea
- Abstract
Second order logic has been always considered by modern logicians quite problematic: so problematic that some of them don't even want to call it logic at all. The main features of second order logic is its high expressive power but, on the other hand, second order logic lacks of completeness, and this seems to be a 'shame' for a formal language who wants to be labelled as logic. Therefore the mainstream, following the idea of Quine, in the logical community has been that when we do second order logic we actually cross the border between logic and mathematics. However, is this line so sharp?, and are we sure that second order logic doesn't deserve a better place in logic? After all, although it is not complete, it can provide cathegorical characterizations for infinite structures, and this is not a bad point. In this paper I show some of the main attempts to "rescue" second order logic: the main points I deal with are both technical and more philosophical. On the one hand a big question is about the semantics: what is the right semantic for second order logic? On the other hand it arises the problem of the ontology: is it possible to accept at least a bit of the ontological entailments coming from second order logic, implications that look so similar to that ones coming from mathematics itself?
- Subjects
MODERN logic; LOGIC; FORMAL languages; MATHEMATICS; SEMANTICS; ONTOLOGY
- Publication
Epistemologia, 2007, Vol 30, Issue 1, p145
- ISSN
0392-9760
- Publication type
Article