As to the misconceptions: In the first place, the existence of "undecidable propositions" or "unsolvable problems" has only remote connections with the failure of excluded middle. More precisely, from the fact that a certain problem is unsolvable, one cannot infer that the affirmative and negative answers to that problem are both incorrect. Both Gödel's and Church's theorems were originally proved for systems with the excluded middle, i.e. for systems in which 'p or not p' is provable for every proposition 'p'; (...) though in the light of Gödel's theorem there are propositions 'p' such that neither 'p' nor 'not p' is provable in those systems. Careful distinction should be made between the following locutions. (shrink)
Our first aim is to make the study of informal notions of proof plausible. Put differently, since the raison d'étre of anything like existing proof theory seems to rest on such notions, the aim is nothing else but to make a case for proof theory; ...
A notation for the language of physics is given, and a system of axioms constructed. It is argued that from the standpoint of a 'realistic' ontology our method is preferable to Carnap's 'coordinate languages.' The primitive ideas are the part-whole relation μ and the set H of coordinate systems. Only such statements are intended in the axioms as are non-controversial; i.e. no open cosmological questions are prejudged.
Unlike all other present-day nationalities, Arab nationality is defined exclusively in terms of a single written language, which encompasses a huge range of mutually incomprehensible speech forms—the better to make the “Arab nationality” as large as possible, and to establish continuity between today's “Arabs” and the glorious past of the early Islamic conquerors. The secular version of Arabic nationalism lost its appeal when the Arab countries failed to unite politically and when they were defeated by Israel in 1967. The apparent (...) Islamization of Arabic society since 1967 is actually a response to these failures. When “Arabs” perceived that secular ideology had failed to achieve their national goals, they turned to Islamism as a different strategy for achieving the same objectives. (shrink)