TURING, ALAN MATHISON. 1912-1954. Systems of Logic Based on Ordinals. London: C.F. Hodgson & Son, 1939.
Lot 95
TURING, ALAN MATHISON. 1912-1954.
Systems of Logic Based on Ordinals. London: C.F. Hodgson & Son, 1939.
US$ 20,000 - 30,000
£15,000 - 22,000

Lot Details
TURING, ALAN MATHISON. 1912-1954. Systems of Logic Based on Ordinals. London: C.F. Hodgson & Son, 1939.
TURING, ALAN MATHISON. 1912-1954.
Systems of Logic Based on Ordinals. London: C.F. Hodgson & Son, 1939. Offprint from: Proceedings of the London Mathematical Society, Second Series, Vol 45.
8vo (258 x 178 mm). Pp 161-228. Original printed wrappers. Pencil inscription "With corrections by ROG" on upper wrapper and some corrections and annotations in pencil by Robin Gandy in text. Lacking rear wrapper, spine worn with loss at head and foot, light soiling.
Provenance: From the library of Robin Oliver Gandy.

FIRST EDITION OF THE RARE OFFPRINT of Turing's doctoral dissertation, "one of the key documents in the history of mathematics and computer science" (Appel), the personal copy of Turing's close friend and fellow mathematician, Robin Gandy. One of his most formidable papers, Turing, working with Church as his advisor, represents the first systematic attempt to overcome Gödel's theory of incompleteness. In it, Turing proposes that, given an effective description of a sequence systems of logic, all of which share the same language and rules of inference, one can form a new system by taking the effective union of their axiom sets. The idea was significant enough that Church was able to expand upon it, even though Turing himself moved on to other ideas.
"Systems of logic based on ordinals is a profound work of first rank importance. Among its achievements are the exploration of a means of circumventing Gödel's incompleteness theorems; the introduction of the concept of an 'oracle machine,' thereby opening the field of relative computability; and, in the wake of the demolition of the Hilbert programme (by Gödel, Turing and Church), an analysis of the place of intuition in mathematics and logic" Copeland, The Essential Turing p 126. Appel, Alan Turing's Systems of Logic (Princeton, 2012).
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