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Abstraction principles provide implicit definitions of mathematical objects. In this paper, an abstraction principle defining categories is proposed. It is unsatisfiable and inconsistent in the expected ways. Two restricted versions of the principle which are consistent are presented. |
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I argue that three main interpretations of the aim of Russell’s early logicism in The Principles of Mathematics (1903) are mistaken, and propose a new interpretation. According to this new interpretation, the aim of Russell’s logicism is to show, in opposition to Kant, that mathematical propositions have a certain sort of complete generality which entails that their truth is independent of space and time. I argue that on this interpretation two often-heard objections to Russell’s logicism, deriving from Gödel’s incompleteness theorem (...) |
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It is known that the Restricted Predicate Calculus can be embedded in an elementary theory, the signature of which consists of exactly two equivalences. Some special models for the mentioned theory were constructed to prove this fact. Besides formal adequacy of these models, a question may be posed concerning their conceptual simplicity, "transparency" of interpretations they assigned to the two stated equivalences. In works known to us these interpretations are rather complex, and can be called "technical", serving only the purpose (...) |
