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Remarks on the Foundations of Mathematics (Paperback, revised edition)
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Remarks on the Foundations of Mathematics (Paperback, revised edition)
Series: The MIT Press
Expected to ship within 10 - 15 working days
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Wittgenstein's work remains, undeniably, now, that of one of those
few philosophers who will be read by all future generations. The
Remarks analyzes in depth such topics as logical compulsion (the
"must") and mathematical conviction; calculation as experiment;
mathematical surprise, discovery, and invention; Russell's logic,
Goedel's theorem, Cantor's diagonal procedure, Dedekind's cuts; the
nature of proof and contradiction; and the role of mathematical
propositions in the forming of concepts. Wittgenstein's later
philosophy was much involved with the concept of "language-games,"
of which mathematics was one. It was his feeling that a proper
analysis of the use of language would clarify concepts and lead to
the solution of (what seem to be) philosophical problems.
Sometimes, Wittgenstein's expository method is pre-Socratic: a flow
of disconnected statements, not unlike Heraclitean fragments, that
range from clear aphorisms to cryptic oracles. Elsewhere, there are
brief Socratic dialogues with imaginary persons, opponents of
equally severe seriousness, representatives of the other half of
Wittgenstein strove for total clarity of language as a means of
solving philosophical problems, but some of his most meaningful
statements here are expressed suggestively, subjectively,
poetically.
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