On Formally Undecidable Propositions of Principia Mathematica and Related Systems.

GODEL, Kurt.

$1,200.00

Item Number: 144686

Edinburgh and London: Olivier & Boyd, 1962.

First edition of this classic work. Octavo, original cloth. Translated by B. Meltzer. Near fine in a near fine dust jacket. With an introduction by R.B. Braithwaite. Rare in the original dust jacket.

In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics. The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.