REMARKS ON THE FOUNDATIONS OF MATHEMATICS BY LUDWIG WITTGENSTEIN, BEMERKUNGEN ÜBER DIE GRUNDLAGEN DER MATHEMATIK von LUDWIG WITTGENSTEIN. (BILINGUAL VERSION ENGLISH-GERMAN, VERSIONE BILINGUE INGLESE-TEDESCO)

EDITORS' PREFACE. The remarks on the philosophy of mathematics and logic 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, part of which we hope to publish later, together with other material. This earlier work belongs to a stage of Wittgenstein's development which is still fairly close to the thought of his Tractatus Logico-Philosophicus. The remarks presented in this volume are of a piece with the thought of Philosophical Investigations. It appears to have been Wittgenstein's original intention to incorporate his ideas on mathematics and logic in Philosophical Investigations. In fact the first of the fragments here published (Part I) was part of an earlier version of the MS. of the Investigations. It begins with two entries which are in all essentials identical with 189 and 190 of the Investigations. This Part I is obviously the earliest of the fragments presented here. It must have been written in 1937. It is the only part of this collection which existed in typescript, and is certainly the most worked over of them all. The last portion of the MS. has been left out; its contents occur in an improved version in the Investigations, 547-568. The entries 122-130 are in great part the same as 193-197 of the Investigations, but have been retained on account of their context. Two appendices were attached to Part I. One dealt with surprise in mathematics. It has not been included in this volume. The other discusses Gödel's theorem about the existence of unprovable but true propositions in the system of Principia Mathematica. (Appendix I.) It must have been Wittgenstein's intention to attach appendices on Cantor's theory of infinity and on Russell's logic, as well as the appendix on Gödel's theorem, to the contributions to the problem of the foundations of mathematics which he planned for Philosophical Investigations. Under the heading Addenda (probably at the beginning of 1938) he wrote a certain amount on problems of set theory: namely on the diagonal procedure and the different kinds of number-concepts.

Bibliographic description
Title: Remarks on the Foundation of Mathematics
Original title: Bemerkungen über die Grundlagen der Mathematik
Author: Ludwig Wittgenstein
Editors: Rush Rhees, G. H. von Wright, G.E.M. Anscombe
Translated by: Gertrude Elizabeth Margaret Anscombe
Publisher: THE M.I.T. PRESS, June 1967
Length: 204 pages; 23 cm
Language: German, English
Series: Paperback
ISBN: 0262730170, 9780262730174
Subjects: Osservazioni sopra i fondamenti della matematica Scienza Filosofia Manuali Trattati Calcolo Logica Bertrand Russell Teorema Kurt Gödel Circolo di Vienna Tractatus Logico-Philosophicus Nachlass Teoremi Rebecca Goldstein Cantor Dedekind Dimostrazioni matematiche Contraddizione Proposizioni matematiche Concetti Linguaggio Saggi Libri Vintage rari fuori catalogo Collezionismo inglese Edizioni bilingue Tedesco Testo originale a fronte Letture Lezioni Corsi Gasking J.N. Findlay Stephen Toulmin Alan Turing Bernard Bosanquet Norman Malcolm Yorick Smythies Coerenza Sistemi formali Logicismo Frege Platonismo Negazione Verità Aritmetica Assiomi Numeri cardinali Scacchi Cerchio Poligoni costruibili Definizione Equazioni Geometria euclidea Esperimenti Espressioni Figura Formula Grundgesetze Eptacaidecagono Ettagono Idea Infinito Intuizione Leggi Pensiero Lewy Dimostrazione Media Metodo Misurazione Errore Moltiplicazione Correlazione Pentagono Pentagramma Predicato Principia Mathematica Hardy Equazione quadratica Domanda Quantica Realtà Risultato Radici Regole Quadrato Tecnica Parola Analitica Ricerche filosofiche Georg Kreisel Critica Interpretazione Finitismo Begriff Beweis Paradigma Regel Logik Zahlen Zwang Sprache Philosophie Sprachspiel Grammatica von Wright Falso Wrong Calculation Queer process Behaviorismo Relazioni Assurdo Comportamento Prova Intuizione David Pinsent Cambridge Ramsey Keynes Piero Sraffa Pascal Confessioni Sant'Agostino Lichtenberg Otto Weininger Friedrich Waismann Luitzen Brouwer Familienähnlichkeit Libro blu marrone Giochi linguistici Tatsache Paul Feyerabend Lewy Significato Tautologia Novecento Matematici Regola Costruzione Diagonale Text mirrored Science Philosophy Manuals Treatises Calculus Logic Theorem Circle Theorems Mathematical demonstrations Contradiction Propositions Concepts Language Essays Rare books out of print Collectibles Bilingual editions Original text facing Readings Lessons Courses Coherence Formal systems Logicism Platonism Negation Truth Arithmetic Axioms Cardinal numbers Chess Circle Constructible polygons Definition Equations Euclidean geometry Experiments Expressions Figure Heptacaidecagon Heptagon Infinity Intuition Laws Thought Demonstration Average Method Measurement Error Multiplication Correlation Pentagon Pentagram Predicate Quadratic equation Question Quantum Reality Result Roots Rules Square Technique Word Analytical Philosophical research Criticism Interpretation Finitism Grammar False Behaviorism Relations Absurd Behavior Arithmetic Proof Intuition Confessions Saint Augustine Book blue brown Language games Meaning Tautology Twentieth Century Mathematicians Rule Construction Diagonal