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Remarks on the Foundation of Mathematics (Paperback, 3rd Edition)
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Remarks on the Foundation of Mathematics (Paperback, 3rd Edition)
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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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