Remarks on the Foundations of Mathematics, Revised Edition
By Ludwig Wittgenstein
* Publisher: The MIT Press
* Number Of Pages: 448
* Publication Date: 1983-05-10
* ISBN-10 / ASIN: 0262730677
* ISBN-13 / EAN: 9780262730679
Product Description:
Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.
Summary: Remarks and Mathematical Philosophy
Rating: 5
From back cover:
"The 'Remarks' analyzes in depth such topics as logical compulsion (the 'must') and mathematical conviction; calculation as experiment; mathematical surprise, discovery, and invention; Russell's logic, Godel's theorem, Cantor's diagonal procedure, Dedekind's cuts; the nature of proof and contradiction; and the role of mathematical propositions in the forming of concepts.
Wittgenstein's later philosophy was much involved with the concept of 'language-games,' of which mathematics was one. It was his feeling that a proper analysis of the use of language would clarify concepts and lead to the solution of (what seems to be) philosophical problems.
Sometimes, Wittgenstein's expository method is pre-Socratic: a flow of disconnected statements, not unlike Heraclitean fragments, that range from clear aphorisms to cryptic oracles. Elsewhere, there are brief Socratic dialogues with imaginary persons, opponents of equally severe seriousness, representatives of the other half of Wittgenstein's mind. Paradoxically, Wittgenstein strove for total clarity of language as a means of solving philosophical problems, but some of his most meaningful statements here are expressed suggestively, subjectively, poetically."
Summary: The Differentiation of Reality through language
Rating: 5
This is the Calculus we all ought to be studying in school. Not since Whorff have we come this close to the heart of Languages.
Summary: Some remarks on Remarks...
Rating: 5
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.
http://ifile.it/93jn06s/Wittgenstein_06_Remarks_on_the_Foundation_of_Mathematics.rar
