Remarks on Mathematics and Logic

The second of five planned volumes, this book collects Wittgenstein’s unabridged writings on mathematics and logic composed between 1939 and 1941.In 1956, a significant but abridged portion of Ludwig Wittgenstein’s 1937–1944 writings for a continuation of what became Philosophical Investigations was published as Remarks on the Foundations of Mathematics. Now, in these five German-English facing-page volumes, the writings of Remarks on Mathematics and Logic are presented in full as Wittgenstein wrote them: in chronological order, without editorial omissions, selections, or rearrangements.Volume III contains materials from 1939 to 1941, including previously unpublished—one manuscript and four manuscript parts—and one manuscript from which selections were made for previous abridgements. The topics covered in this volume include surveyability and perspicuity in mathematics; Cantor and Gödel; Russellian logicism; geometrical cogency of proofs; consensus as part of the phenomenon of our calculating; rule-following and unwinding; consistency proofs; calculation as invention rather than discovery; superstitious fear of contradictions; why mathematicians cannot philosophize about mathematics; mathematical propositions are overdetermined; the idea of a mathematical reality; the connection between the sense of a mathematical proposition and its use; positioning a proposition in a system; an unproved mathematical proposition as the expression of a problem; the role of mathematical propositions in descriptions (of reality).This edition will be the authoritative source for Wittgenstein’s writings in their original context.