Remarks on the Foundation of Mathematics by Ludwig Wittgenstein

Remarks on the Foundation of Mathematics by Ludwig Wittgenstein

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.

Ludwig Wittgenstein (1889 - 1951) was an Austrian-British philosopher who taught at the University of Cambridge and is known as one of the most important philosophers of the 20th century. He worked in the areas of logic and the philosophy of mathematics, the mind and language.

SKU	Nicht verfügbar
ISBN 13	9780631125051
ISBN 10	0631125051
Titel	Remarks on the Foundation of Mathematics
Autor	Ludwig Wittgenstein
Buchzustand	Nicht verfügbar
Bindungsart	Paperback
Verlag	John Wiley and Sons Ltd
Erscheinungsjahr	1981-03-19
Seitenanzahl	448
Hinweis auf dem Einband	Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.
Hinweis	Nicht verfügbar