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Wittgenstein on Mathematics

2020-12-30 Philosophy
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Release : 2020-12-30
Genre : Philosophy
Kind : eBook
Book Rating : 29X/5 ( reviews)

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Book Synopsis Wittgenstein on Mathematics by : Severin Schroeder

Download or read book Wittgenstein on Mathematics written by Severin Schroeder. This book was released on 2020-12-30. Available in PDF, EPUB and Kindle. Book excerpt: 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 Gödel’s incompleteness theorems.

Wittgenstein's Philosophy of Mathematics

2006-12-05 Philosophy
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Release : 2006-12-05
Genre : Philosophy
Kind : eBook
Book Rating : 361/5 ( reviews)

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Book Synopsis Wittgenstein's Philosophy of Mathematics by : Pasquale Frascolla

Download or read book Wittgenstein's Philosophy of Mathematics written by Pasquale Frascolla. This book was released on 2006-12-05. Available in PDF, EPUB and Kindle. Book excerpt: Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, the three phases of Wittgenstein's reflections on mathematics are viewed as a progressive whole, rather than as separate entities. Frascolla builds up a systematic construction of Wittgenstein's representation of the role of arithmetic in the theory of logical operations. He also presents a new interpretation of Wittgenstein's rule-following considerations - the `community view of internal relations'.

Wittgenstein, Finitism, and the Foundations of Mathematics

1998-12-17 Philosophy
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Release : 1998-12-17
Genre : Philosophy
Kind : eBook
Book Rating : 325/5 ( reviews)

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Book Synopsis Wittgenstein, Finitism, and the Foundations of Mathematics by : Mathieu Marion

Download or read book Wittgenstein, Finitism, and the Foundations of Mathematics written by Mathieu Marion. This book was released on 1998-12-17. Available in PDF, EPUB and Kindle. Book excerpt: Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and by philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than on any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations. Marion shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy; and he also demonstrates that it has much to contribute to current debates about the foundations of mathematics.

Wittgenstein's Philosophy of Mathematics

2021-08-12 Science
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Release : 2021-08-12
Genre : Science
Kind : eBook
Book Rating : 534/5 ( reviews)

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Book Synopsis Wittgenstein's Philosophy of Mathematics by : Juliet Floyd

Download or read book Wittgenstein's Philosophy of Mathematics written by Juliet Floyd. This book was released on 2021-08-12. Available in PDF, EPUB and Kindle. Book excerpt: For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics (1934–1951) grew from his Early (1912–1921) and Middle (1929–33) philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.

Wittgenstein on the Foundations of Mathematics

1980 Mathematics
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Release : 1980
Genre : Mathematics
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Book Synopsis Wittgenstein on the Foundations of Mathematics by : Crispin Wright

Download or read book Wittgenstein on the Foundations of Mathematics written by Crispin Wright. This book was released on 1980. Available in PDF, EPUB and Kindle. Book excerpt:

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