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Remarks on the Foundations of Mathematics

av Ludwig WITTGENSTEIN

Andra författare: G. E. M. Anscombe (Översättare), Rush Rhees (Redaktör), G. H. Von Wright (Redaktör)

Andra författare: Se under Andra författare.

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364271,649 (4.47)1
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.… (mer)
Senast inlagd avM.A.H., AMAbrams, KallipolisLibrary, Sbark, avoidbeing
Efterlämnade bibliotekEeva-Liisa Manner
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Mark Liberman linked to some pages in this on LLog, and it seemed approachable. I'm not getting a lot from it, though. It's a neat piece of history, seeing Wittgenstein in conversation with Turing, plus some interesting ideas and styles of argument, but transcribed lecture / dialogue format makes for poor pedagogy, I think. I actually wanted to learn a little something about the mathematics and contradiction, and there's really only a few sentences here dealing with that, not the full exposition I wanted.
  leeinaustin | Jul 15, 2009 |
Originally in German?
  richardhobbs | Nov 28, 2010 |
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inga recensioner | lägg till en recension

» Lägg till fler författare (3 möjliga)

Författarens namnRollTyp av författareVerk?Status
WITTGENSTEIN, Ludwigprimär författarealla utgåvorbekräftat
Anscombe, G. E. M.Översättaremedförfattarealla utgåvorbekräftat
Rhees, RushRedaktörmedförfattarealla utgåvorbekräftat
Von Wright, G. H.Redaktörmedförfattarealla utgåvorbekräftat
DIAMOND, CoraRedaktörmedförfattarevissa utgåvorbekräftat
NYMAN, Heikkimedförfattarevissa utgåvorbekräftat
TRINCHERO, MarioÖversättaremedförfattarevissa utgåvorbekräftat

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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.

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