Published online by Cambridge University Press: 05 March 2012
It is my firm conviction that, if ever a history of the rational philosophy of the earlier half of this century should be written, this book [Carnap's The Logical Syntax of Language] ought to have a place in it second to none. … It was through this book that the philosophical world, to the west of Poland, was first introduced to the method of analysing languages in a “metalanguage,” and of constructing “object-languages” – a method whose significance for logic and the foundations of mathematics cannot be overrated; and it was in this book that the claim was first made, and, I believe, completely substantiated, that this method was of the greatest importance for the philosophy of science.
Popper, Conjectures and RefutationsWe now know what Carnap knew early in 1931 when his thoughts on Wittgensteinian grammar and metamathematics finally converged. The product of that fusion was The Logical Syntax of Language, a book that displayed a new theory of mathematical knowledge and offered it as a model for epistemology.
The single most decisive stimulus to the train of thought that culminated in that book was Gödel's 1931 paper on the incompleteness of formal theories of arithmetic, “Uber unentscheidbare Sätze,” which contains a discovery whose intellectual significance was comparable to Einstein's relativity theory.
The relevance of Gödel's conclusions to Hilbert's program are widely acknowledged. But its relevance to what one might call “Wittgenstein's program“ was no less decisive.
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