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| Author | : S.G. Shanker |
| Publisher | : Routledge |
| Total Pages | : 571 |
| Release | : 2013-12-19 |
| Genre | : Philosophy |
| ISBN | : 1317832035 |
First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.
| Author | : S.G. Shanker |
| Publisher | : Routledge |
| Total Pages | : 373 |
| Release | : 2013-12-19 |
| Genre | : Philosophy |
| ISBN | : 1317832043 |
First published in 2005. Routledge is an imprint of Taylor & Francis, an informa company.
| Author | : Stuart Shanker |
| Publisher | : |
| Total Pages | : 540 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Pasquale Frascolla |
| Publisher | : Routledge |
| Total Pages | : 318 |
| Release | : 2006-12-05 |
| Genre | : Philosophy |
| ISBN | : 1134974361 |
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'.
| Author | : Stuart Shanker |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : V.H. Klenk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 160 |
| Release | : 2012-12-06 |
| Genre | : Philosophy |
| ISBN | : 9401013918 |
Wittgenstein's remarks on mathematics have not received the recogni tion they deserve; they have for the most part been either ignored, or dismissed as unworthy of the author of the Tractatus and the I nvestiga tions. This is unfortunate, I believe, and not at all fair, for these remarks are not only enjoyable reading, as even the harshest critics have con ceded, but also a rich and genuine source of insight into the nature of mathematics. It is perhaps the fact that they are more suggestive than systematic which has put so many people off; there is nothing here of formal derivation and very little attempt even at sustained and organized argumentation. The remarks are fragmentary and often obscure, if one does not recognize the point at which they are directed. Nevertheless, there is much here that is good, and even a fairly system atic and coherent account of mathematics. What I have tried to do in the following pages is to reconstruct the system behind the often rather disconnected commentary, and to show that when the theory emerges, most of the harsh criticism which has been directed against these re marks is seen to be without foundation. This is meant to be a sym pathetic account of Wittgenstein's views on mathematics, and I hope that it will at least contribute to a further reading and reassessment of his contributions to the philosophy of mathematics.
| Author | : Juliet Floyd |
| Publisher | : Cambridge University Press |
| Total Pages | : 96 |
| Release | : 2021-08-12 |
| Genre | : Science |
| ISBN | : 1108616534 |
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.
| Author | : Cora Diamond |
| Publisher | : University of Chicago Press |
| Total Pages | : 301 |
| Release | : 2015-05-14 |
| Genre | : Philosophy |
| ISBN | : 022630860X |
For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured on the philosophical foundations of mathematics. A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.
| Author | : Severin Schroeder |
| Publisher | : Routledge |
| Total Pages | : 200 |
| Release | : 2020-12-30 |
| Genre | : Philosophy |
| ISBN | : 100031829X |
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.
| Author | : Bob Clark |
| Publisher | : Springer |
| Total Pages | : 225 |
| Release | : 2017-11-14 |
| Genre | : Mathematics |
| ISBN | : 3319639919 |
This book uses Ludwig Wittgenstein’s philosophical methodology to solve a problem that has perplexed thinkers for thousands of years: 'how come (abstract) mathematics applies so wonderfully well to the (concrete, physical) world?' The book is distinctive in several ways. First, it gives the reader a route into understanding important features of Wittgenstein’s writings and lectures by using his methodology to tackle this long-standing and seemingly intractable philosophical problem. More than this, though, it offers an outline of important (sometimes little-known) aspects of the development of mathematical thought through the ages, and an engagement of Wittgenstein’s philosophy with this and with contemporary philosophy of mathematics on its own terms. A clear overview of all this in the context of Wittgenstein’s philosophy of mathematics is interesting in its own right; it is also just what is needed to solve the problem of mathematics and world.
