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Wittgenstein on Mathematics (Hardcover)
Loot Price: R4,582
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Wittgenstein on Mathematics (Hardcover)
Series: Wittgenstein's Thought and Legacy
Expected to ship within 12 - 17 working days
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This book offers a detailed account and discussion of Ludwig
Wittgenstein's philosophy of mathematics. In Part I, the stage is
set with a brief presentation of Frege's logicist attempt to
provide arithmetic with a foundation and Wittgenstein's criticisms
of it, followed by sketches of Wittgenstein's early views of
mathematics, in the Tractatus and in the early 1930s. Then (in Part
II), Wittgenstein's mature philosophy of mathematics (1937-44) is
carefully presented and examined. Schroeder explains that it is
based on two key ideas: the calculus view and the grammar view. On
the one hand, mathematics is seen as a human activity - calculation
- rather than a theory. On the other hand, the results of
mathematical calculations serve as grammatical norms. The following
chapters (on mathematics as grammar; rule-following;
conventionalism; the empirical basis of mathematics; the role of
proof) explore the tension between those two key ideas and suggest
a way in which it can be resolved. Finally, there are chapters
analysing and defending Wittgenstein's provocative views on
Hilbert's Formalism and the quest for consistency proofs and on
Goedel's incompleteness theorems.
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