Remarks on the Foundations of Mathematics
Oxford: Basil Blackwell, 1956. Presumed First Edition, First printing Thus. Hardcover. Text is in German and English. xix/xixe, 196/196e, 197-204 (index) pages. "e" indicates the text on that page is in English. Includes Editors' Preface; Table of Contents; and Foundations of Mathematics. Illustrations (some with color). Cover shows wear and soiling. Some underlining to the text. Ink notation inside front cover. Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. From 1929 to 1947, Wittgenstein taught at the University of Cambridge. In spite of his position, during his entire life only one book of his philosophy was published, the relatively slim 75-page Logisch-Philosophische Abhandlung (Logical-Philosophical Treatise) (1921) which appeared, together with an English translation, in 1922 under the Latin title Tractatus Logico-Philosophicus. His only other published works were an article, "Some Remarks on Logical Form" (1929), a book review, and a children's dictionary. His voluminous manuscripts were edited and published posthumously. The remarks on the philosophy of mathematics and logic, which are published in this book, were written in the years 1937-1944. After that time, Wittgenstein did not again return to this topic. He had written a great deal on the subject in the period 1929 to roughly 1932. The tables of contents and the index are intended to help the reader to survey the whole, and also to make it easier to look up passages. The editors had the sole responsibility for the division of the material. Remarks on the Foundations of Mathematics (German: Bemerkungen über die Grundlagen der Mathematik) is a book of Ludwig Wittgenstein's notes on the philosophy of mathematics. The text has been produced from passages in various sources by selection and editing. The notes have been written during the years 1937–1944 and a few passages are incorporated in the Philosophical Investigations which were composed later. The text offers an extended analysis of the concept of mathematical proof and an exploration of Wittgenstein's contention that philosophical considerations introduce false problems in mathematics. Wittgenstein in the Remarks adopts an attitude of doubt in opposition to much orthodoxy in the philosophy of mathematics. Particularly controversial in the Remarks was Wittgenstein's "notorious paragraph", which contained an unusual commentary on Gödel's incompleteness theorems. Multiple commentators read Wittgenstein as misunderstanding Gödel. In 2000 Juliet Floyd and Hilary Putnam suggested that the majority of commentary misunderstands Wittgenstein but their interpretation has not been met with approval. The debate has been running around the so-called Key Claim: If one assumes that P is provable in PM, then one should give up the “translation” of P by the English sentence “P is not provable”. Wittgenstein does not mention the name of Kurt Gödel who was a member of the Vienna Circle during the period in which Wittgenstein's early ideal language philosophy and Tractatus Logico-Philosophicus dominated the circle's thinking; multiple writings of Gödel in his Nachlass contain his own antipathy for Wittgenstein, and belief that Wittgenstein willfully misread the theorems. Some commentators, such as Rebecca Goldstein, have hypothesized that Gödel developed his logical theorems in opposition to Wittgenstein. Condition: Fair.
Keywords: Mathematics, Logical Inference, Calculation, Provability, Irrational Numbers, Betrand Russell, Reproducibility, Self-evidence, Axioms, Empirical Proposition, Intuition, Calculating Machine, Existence Proofs, Games
[Book #81839]
Price: $135.00