Remarks on the Foundation of Mathematics - Softcover

Wittgenstein, Ludwig

Softcover

ISBN 10: 0631125051 ISBN 13: 9780631125051

Verlag: Wiley-Blackwell, 1981

Über diesen Titel

Reseña del editor:

This substantially revised edition of Wittgenstein's Remarks on the Foundations of Mathematics contains one section, an essay of fifty pages, not previously published, as well as considerable additions to others sections. In Parts I, II and III, Wittgenstein discusses amongst other things the idea that all strict reasoning, and so all mathematics, are built on the 'fundamental calculus' which is logic. These parts give the most thorough discussion of Russell's logic. He writes on mathematical proof and the question of where the proofs of mathematics get their force and cogency, if they are not reducible to proofs in logic. Thsi leads him to discuss'contradiction in mathematics' and 'consistency proofs'. He works against the view that there is a sharp division between 'grammatical propositions' and 'empirical prepositions'. He asks us at one point to imagine a people who made no distinction between the applied mathematics and pure mathematics, although they counted and calculated. Could we say they had proofs? Here is a feature of his method which becomes more imporatnt; what Wittgenstein calls, at least half seriously, 'the anthropological method in philosophy'. This emerges in Parts V, VI and VIII. In Part VI, published here for the first time, Wittgenstein brings togeher the view that in mathematics proofs ae 'concept forming' and the view that language and logic and mathematics 'presuppose' common ways of acting and of living among the people who give tham and are convinced by them. Part VIII now has a fuller discussion of difficulties in the notion of 'following a rule' in calculation and the notion of logical necessity.

Contraportada:

This analyzes in depth such topics logical compulsion and mathematical conviction; calculation as experiment; mathematical surprise, discovery, and invention; Russell's logic, Godel'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.

Über diese Auflage

• Verlag: Wiley-Blackwell
• Erscheinungsdatum: 1981
• ISBN 10: 0631125051
• ISBN 13: 9780631125051
• Einband: Tapa blanda
• Anzahl der Seiten: 448
• Herausgeber: Anscombe G. E. M., Rhees Rush, Von Wright G. H.