Remarks on the Foundation of Mathematics [Paperback]

Ludwig Wittgenstein (Author), Rush Rhees (Editor), G. H. von Wright (Editor), G. E. M. Anscombe (Editor)

Book Description

ISBN-10: 0631125051 | ISBN-13: 978-0631125051 | Publication Date: January 15, 1991 | Edition: 3

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.

Editorial Reviews

Review

Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

--This text refers to an out of print or unavailable edition of this title.

Language Notes

Text: English, German (translation) --This text refers to an out of print or unavailable edition of this title.

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Product Details

• Paperback: 448 pages
• Publisher: Wiley-Blackwell; 3 edition (January 15, 1991)
• Language: English
• ISBN-10: 0631125051
• ISBN-13: 978-0631125051
• Product Dimensions: 8.3 x 5.5 x 1.3 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #535,148 in Books (See Top 100 in Books)

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27 of 27 people found the following review helpful:

5.0 out of 5 stars Some remarks on Remarks..., April 30, 2000

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Gayle (USA) - See all my reviews

This review is from: Remarks on the Foundations of Mathematics, Revised Edition (Paperback)

If you are interested in the philosophy of mathematics, this is the book for you! No special knowledge of mathematics or philosophy is needed to read and understand this book. Some prior experience with philosophy would be helpful, though,just to get you used to discussing philosophy. Some reading of other philosophy books by Wittgenstein, especially Philosophical Investigations or On Certainty would be helpful, to get you used to Wittgenstein's unusual style of writing. But if you haven't read any philosophy before reading Remarks on the Foundations of Mathematics, don't worry, it isn't necessary.

Wittgenstein seems to think that mathematics is a language as German, or French, or English are languages. Mathematics is a human language, he says.He discusses the way we learn mathematics and also what constitutes proofs of mathematical theorems.

This is an extremely interesting book to read, but it is not something you can sit down and read in one sitting. It will take a few sittings to get through it all. For myself, this was because I had to stop frequently and think of the implications of what Wittgenstein was saying. For example, he says that the mathematiciam creates essences. I had to re-evaluate my conception of mathematics after reading this statement.

Overall, this was a very enjoyable book to read and it changed the way I view the world of mathematics.