On the Dummettian understanding, anti-realism regarding a particular discourse amounts to (or at the very least, involves) a refusal to accept the determinacy of the subject matter of that discourse and a corresponding refusal to assert at least some instances of excluded middle (which can be understood as expressing this determinacy of subject matter). In short: one is an anti-realist about a discourse if and only if one accepts intuitionistic logic as correct for that discourse. On careful examination, the strongest (...) Dummettian arguments for anti-realism of this sort fail to secure intuitionistic logic as the single, correct logic for anti-realist discourses. Instead, antirealists are placed in a situation where they fail to be justified in asserting monism (that intuitionistic logic is the unique correct logic). Thus, antirealists seem forced either to accept pluralism (i.e. one or more intermediate logic is at least as `correct’ as intuitionistic logic–an option I take to be unattractive from the anti-realist perspective), or they must be anti-realists about the realism/anti-realism debate (and, in particular, must refuse to assert the instance of excluded middle equivalent to logical monism or logical pluralism). (shrink)

This is the first part of a paper concerning intermediate propositional logics with the disjunction property which cannot be properly extended into logics of the same kind, and are therefore called maximal. To deal with these logics, we use a method based on the search of suitable nonstandard logics, which has an heuristic content and has allowed us to discover a wide family of logics, as well as to get their maximality proofs in a uniform way. The present part illustrates (...) infinitely many maximal logics with the disjunction property extending the well-known logic of Scott, and aims to provide a first picture of the method, sufficient for the reader who wish to achieve an overall understanding of it without entering into the further aspects developed in the second part. From this point of view, the latter will not be self-standing, but will be seen as a prosecution and a complement of the former, with the aim that the material presented in the whole paper can be used as a starting point for a classification of the subject. (shrink)

In the paper the views and tendencies in the philosophical reflection on mathematics in Poland between the wars are analyzed. Views of most outstanding representatives of Lvov–Warsaw Philosophical School and of Polish Mathematical School are presented. Their influence on logical and mathematical researches is considered.