Remarks on the foundations of mathematics

Author(s)

• Wittgenstein, Ludwig
• Rhees, Rush
• Wright, G. H. von (Georg Henrik)
• Anscombe, G. E. M. (Gertrude Elizabeth Margaret)

Bibliographic Information

Remarks on the foundations of mathematics

by Ludwig Wittgenstein ; edited by G.H. von Wright, R. Rhees, G.E.M. Anscombe ; translated by G.E.M. Anscombe

B. Blackwell, 1978

3rd ed., rev

• : pbk

Other Title

Bemerkungen über die Grundlagen der Mathematik

Note

Translation of Bemerkungen über die Grundlagen der Mathematik

Includes index

Description and Table of Contents

Description

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.

Table of Contents

Preface to The Revised Edition Part I Circa 1937-1938 Part II 1938 Part III 1939-40 Part IV 1942-1944 Part V 1942-1944 Part VI ca. 1943/1944 Part VII 1941 and 1944 Index

by "Nielsen BookData"

• NCID: BA01387726
• ISBN:
  • 0631164502
  • 0631125051
• LCCN: 78326059
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: ger
• Place of Publication: Oxford [Eng.]
• Pages/Volumes: 444 p.
• Size: 23 cm
• Classification:
  • LCC : QA8.4
  • DC : 510/.01
  • NDC8 : 410.1
• Subject Headings:
  • LCSH : Mathematics -- Philosophy