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TURING, Alan and Maxwell Herman Alexander NEWMAN. 'A formal theorem in Church's theory of types.' Offprint from: The Journal of Symbolic Logic, vol. 7, no. 1. Princeton, NJ: 1942. 8° (253 x 175mm). 8pp., 28-33. Original stapled wrappers. [With:] TURING, Alan. 'The use of dots as brackets in Church's system.' Offprint from: The Journal of Symbolic Logic, vol. 7, no. 4, Princeton, NJ: 1942. 8° (253 x 175mm). 12pp., 146-156. Original stapled wrappers (light staining and ring mark to upper cover, first leaf loose). Provenance: R.O. Gandy (pencil numbering in margins).
TURING, Alan and Maxwell Herman Alexander NEWMAN. 'A formal theorem in Church's theory of types.' Offprint from: The Journal of Symbolic Logic, vol. 7, no. 1. Princeton, NJ: 1942. 8° (253 x 175mm). 8pp., 28-33. Original stapled wrappers. [With:] TURING, Alan. 'The use of dots as brackets in Church's system.' Offprint from: The Journal of Symbolic Logic, vol. 7, no. 4, Princeton, NJ: 1942. 8° (253 x 175mm). 12pp., 146-156. Original stapled wrappers (light staining and ring mark to upper cover, first leaf loose). Provenance: R.O. Gandy (pencil numbering in margins).

Details
TURING, Alan and Maxwell Herman Alexander NEWMAN. 'A formal theorem in Church's theory of types.' Offprint from: The Journal of Symbolic Logic, vol. 7, no. 1. Princeton, NJ: 1942. 8° (253 x 175mm). 8pp., 28-33. Original stapled wrappers. [With:] TURING, Alan. 'The use of dots as brackets in Church's system.' Offprint from: The Journal of Symbolic Logic, vol. 7, no. 4, Princeton, NJ: 1942. 8° (253 x 175mm). 12pp., 146-156. Original stapled wrappers (light staining and ring mark to upper cover, first leaf loose). Provenance: R.O. Gandy (pencil numbering in margins).

Turing was by now working full-time at Bletchley Park, but he continued to correspond with Newman who was still teaching the Foundation of Mathematics at Cambridge. When not working on Enigma, Turing used his limited spare time to focus on the theory of types, elaborating on Alonzo Church's work of 1940. It was highly technical work, involving separation of mathematical 'nouns' and 'adjectives'. 'The use of dots as brackets in Church's system' promises two further papers from Turing which never appeared. (2)

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