THE FOUNDATION FOR MODERN COMPUTER LOGIC

CHURCH, ALONZO (+) EMIL L. POST.

[Church:] A note on the Entscheidungsproblem (+) Correction to A note on the Entscheidungsproblem (+) [Post:] Finite combinatory processes-formulation I. [In "Journal of Symbolic Logic", Volume 1, number 1 + 3, 1936]

Wisconsin, The Association for Symbolic Logic, 1936.

Lev8vo. Entire volume one of "Journal of Symbolic Logic" (i.e. number 1-4), March, June, September, December 1936) BOUND WITH ALL THE ORIGINAL WRAPPERS in a blue half cloth with gilt lettering to spine. Crossed-out library paper-label to lower part of spine and top left corner of front board. Two library stamps (in Chinese) to back of front free end-paper. Chinese library-stamp (red) and stamped inventory-number lower part of all four front wrappers. Minor bumping to lower corner of nr. 4, otherwise internally a very fine and clean copy of the entire volume. [Church:] Pp. 40-1; 101-2. [Post:] Pp. 103-5. [Entire volume: 218 pp.].

First publication of Church's seminal paper in which he proved the solution to David Hilbert's "Entscheidungsproblem" from 1928, namely that it is impossible to decide algorithmically whether statements within arithmetic are true or false. In showing that there is no general algorithm for determining whether or not a given statement is true or false, he not only solved Hilbert's "Entscheidungsproblem" but also laid the foundation for modern computer logic. This conclusion is now known as Church's Theorem or the Church-Turing Theorem (not to be mistaken with the Church-Turing Thesis). The present paper anticipates Turing's famous "On Computable Numbers" by a few months.

"Church's paper, submitted on April 15, 1936, was the first to contain a demonstration that David Hilbert's 'Entscheidungsproblem' - i.e., the question as to whether there exists in mathematics a definite method of guaranteeing the truth or falsity of any mathematical statement - was unsolvable. Church did so by devising the 'lambda-calculus', [...] Church had earlier shown the existence of an unsolvable problem of elementary number theory, but his 1936 paper was the first to put his findings into the exact form of an answer to Hilbert's 'Entscheidungsproblem'. Church's paper bears on the question of what is computable, a problem addressed more directly by Alan Turing in his paper 'On computable numbers' published a few months later. The notion of an 'effective' or 'mechanical' computation in logic and mathematics became known as the Church-Turing thesis." (Hook & Norman: Origins of Cyberspace, 250)

The volume also contains first printing of Post's seminal paper, in which he, simultaneously with but independently of Turing, describes a logic automaton, which very much resembles the Turing machine. The Universal Turing Machine, which is presented for the first time in Turing's seminal paper in the Proceedings of the London Mathematical Society for 1936, is considered one of the most important innovations in the theory of computation and constitutes the most famous theoretical paper in the history of computing. "Post [in the present paper] suggests a computation scheme by which a "worker" can solve all problems in symbolic logic by performing only machinelike "primitive acts". Remarkably, the instructions given to the "worker" in Post's paper and to a Universal Turing Machine were identical." (A Computer Perspective, p. 125).

"The Polish-American mathematician Emil Post made notable contributions to the theory of recursive functions. In the 1930s, independently of Turing, Post came up with the concept of a logic automaton similar to a Turing machine, which he described in the present paper [the paper offered]. Post's paper was intended to fill a conceptual gap in Alonzo Churchs' paper on "An unsolvable problem of elementary number theory" (Americ. Journ. of Math. 58, 1936). Church's paper had answered in the negative Hilbert's question as to whether a definite method existed for proving the truth or falsity of any mathematical statement (the Entscheidungsproblem), but failed to provide the assertion that any such definite method could be expressed as a formula in Church's lambda-calculus. Post proposed that a definite method would be written in the form of instructions to a mindless worker operating on an infinite line of "boxes" (equivalent to Turing's machine's "tape"). The worker would be capable only of reading the instructions and performing the following tasks... This range of tasks corresponds exactly to those performed by a Turing machine, and Church, who edited the "Journal of Symbolic Logic", felt it necessary to insert an editorial note referring to Turing's "shortly forthcoming" paper on computable numbers, and ascertaining that "the present article... although bearing a later date, was written entirely independently of Turing's" (p. 103)." (Origins of Cyberspace, pp. 111-12).

Even though Post's work to some degree has been outshined by Turing's, the present paper is of seminal importance in the history of the foundation for modern computer logic and the ideological basis for the modern computer.

The volume also contains the following important papers by W. V. Quine:
1. Toward a Calculus of Concepts. Pp. 2-25.
2. Set-theoretic Foundations for Logic. Pp. 45-57.


Hook & Norman, Origins of Cyberspace, 2002: 250 + 356
Charles & Ray Eames, A Computer Perspective, 1973: 125.

Order-nr.: 43552