Wittgenstein on the Foundations of Mathematics
Author: Crispin Wright
Publisher: Bloomsbury Academic
Published: 1980
Total Pages: 518
ISBN-13:
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Author: Crispin Wright
Publisher: Bloomsbury Academic
Published: 1980
Total Pages: 518
ISBN-13:
DOWNLOAD EBOOKAuthor: Ludwig Wittgenstein
Publisher:
Published: 1972
Total Pages: 204
ISBN-13: 9780262730174
DOWNLOAD EBOOKAuthor: Mathieu Marion
Publisher: OUP Oxford
Published: 1998-12-17
Total Pages: 272
ISBN-13: 0191568325
DOWNLOAD EBOOKMathieu 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.
Author: Severin Schroeder
Publisher: Routledge
Published: 2020-12-30
Total Pages: 200
ISBN-13: 100031829X
DOWNLOAD EBOOKThis 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.
Author: Pasquale Frascolla
Publisher: Routledge
Published: 2006-12-05
Total Pages: 318
ISBN-13: 1134974361
DOWNLOAD EBOOKWittgenstein'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'.
Author: Juliet Floyd
Publisher: Cambridge University Press
Published: 2021-08-12
Total Pages: 96
ISBN-13: 1108616534
DOWNLOAD EBOOKFor 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.
Author: Frank Plumpton Ramsey
Publisher: Psychology Press
Published: 2000
Total Pages: 312
ISBN-13: 9780415225465
DOWNLOAD EBOOKFirst Published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.
Author: Penelope Maddy
Publisher: Oxford University Press, USA
Published: 2014
Total Pages: 147
ISBN-13: 0199391750
DOWNLOAD EBOOK"Maddy's short monograph looks at Wittgenstein's philosophy of logic, from the perspective of the form of naturalism that she calls "second philosophy." That view takes an empirical approach to logical truth -- essentially arguing that if philosophers want to understand the world, they should start from a position informed by scientific understandings of the world, because science is often a reliable guide to how the world works. Similarly, just like science, logic is also grounded in the structure of our world, and our basic cognitive machinery is tuned by evolutionary pressures to detect that structure where it occurs. Ludwig Wittgenstein (particularly in the "Tractatus") also linked the logical structure of representation with the structure of the world, but still insisted that the sense of our representations must be given prior to -- independently of -- any facts about how the world happens to be. When that requirement is removed, Wittgenstein's position in the Tractatus approaches Maddy's Second Philosophy -- that logic is grounded in the structure of the world and our representational systems reflect that structuring. The later Wittgenstein also hews closely to Second Philosophy, holding that our logical practices are grounded in our interests and motivations, and our natural inclinations, and the features of the world. In this sense, logic is no different from other descriptions of the world -- just more general and responding to features so basic and ubiquitous that they tend to go unnoticed. Maddy's Second Philosophy finds Wittgenstein as an important precursor and kindred spirit, and promotes a new view of him as a naturalistic phliosopher"--
Author: Arthur Gibson
Publisher: Springer Nature
Published: 2020-12-13
Total Pages: 490
ISBN-13: 3030360873
DOWNLOAD EBOOKIn this volume we witness Wittgenstein in the act of composing and experimenting with his new visions in philosophy. The book includes key explanations of the origin and background of these previously unknown manuscripts. It investigates how Wittgenstein’s philosophical thought-processes are revealed in his dictation to, as well as his editing and revision with Francis Skinner, in the latter’s role of amanuensis. The book displays a considerable wealth and variety of Wittgenstein’s fundamental experiments in philosophy across a wide array of subjects that include the mind, pure and applied mathematics, metaphysics, the identities of ordinary and creative language, as well as intractable problems in logic and life. He also periodically engages with the work of Newton, Fermat, Russell and others. The book shows Wittgenstein strongly battling against the limits of understanding and the bewitchment of institutional and linguistic customs. The reader is drawn in by Wittgenstein as he urges us to join him in his struggles to equip us with skills, so that we can embark on devising new pathways beyond confusion. This collection of manuscripts was posted off by Wittgenstein to be considered for publication during World War 2, in October 1941. None of it was published and it remained hidden for over two generations. Upon its rediscovery, Professor Gibson was invited to research, prepare and edit the Archive to appear as this book, encouraged by Trinity College Cambridge and The Mathematical Association. Niamh O’Mahony joined him in co-editing and bringing this book to publication.
Author: Alfred North Whitehead
Publisher:
Published: 1910
Total Pages: 688
ISBN-13:
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