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- W2794967327 abstract "Solomon Feferman has expressed skepticism or reserve about set theorySet theory, especially higher set theory, in many writings, and in his mathematical work he has largely stayed away from set theory. The paper undertakes to describe and diagnose Feferman’s attitude toward set theory, especially higher set theory. Section 1 discusses his opposition to Platonism in relation to some understandings of what Platonism is. Section 2 discusses his interest in predicativity, his analysis of predicative provability, and his sympathy for “predicativism,” although he denies being an adherent and has used impredicative methods in his own metamathematical work. It also notes his reconstruction of Hermann Weyl’sWeyl, Hermann attempt to construct the elements of analysis on a predicative basis. Section 3 concerns his attitude toward proof theory. Section 4 turns more to philosophy. His anti-platonism is compared with the well known platonism of Gödel. Unlike GödelGödel, Kurt, Feferman views concepts as human creations. He notes that basic mathematical concepts can differ in clarity and argues that less clear concepts, in particular those of set theorySet theory, can give rise to questions that do not have definite answers. It is questioned whether Feferman’s conceptual structuralism gives mathematics the degree of objectivity that its application in science requires. In Sect. 5 remarks are made about Hilary Putnam’sPutnam, Hilary criticism of Feferman’s claim that a predicative system conservative over PA is adequate for the mathematics applied in science. The difference is seen to turn on Putnam’s scientific realism." @default.
- W2794967327 created "2018-04-06" @default.
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- W2794967327 date "2017-01-01" @default.
- W2794967327 modified "2023-09-23" @default.
- W2794967327 title "Feferman’s Skepticism About Set Theory" @default.
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- W2794967327 doi "https://doi.org/10.1007/978-3-319-63334-3_20" @default.
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