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11Chapter Three. Modal LogicIn J. W. Davis (ed.), Philosophical logic, D. Reidel. pp. 40-70. 1969.
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39The completeness of intuitionistic propositional calculus for its intended interpretationNotre Dame Journal of Formal Logic 22 (1): 17-28. 1981.
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174Alan Weir. Truth through Proof: A Formalist Foundation for Mathematics. Oxford: Clarendon Press, 2010. ISBN 978-0-19-954149-2. Pp. xiv+281: Critical Studies/Book Reviews (review)Philosophia Mathematica 19 (2): 213-219. 2011.Alan Weir’s new book is, like Darwin’s Origin of Species, ‘one long argument’. The author has devised a new kind of have-it-both-ways philosophy of mathematics, supposed to allow him to say out of one side of his mouth that the integer 1,000,000 exists and even that the cardinal ℵω exists, while saying out of the other side of his mouth that no numbers exist at all, and the whole book is devoted to an exposition and defense of this new view. The view is presented in the book in a way that can ma…Read more
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69One textbook may introduce the real numbers in Cantor’s way, and another in Dedekind’s, and the mathematical community as a whole will be completely indifferent to the choice between the two. This sort of phenomenon was famously called to the attention of philosophers by Paul Benacerraf. It will be argued that structuralism in philosophy of mathematics is a mistake, a generalization of Benacerraf’s observation in the wrong direction, resulting from philosophers’ preoccupation with ontology.
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