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Footnote

Rez. in: JASIST 55(2004) no.1, S.89-90. (J. Warner): "This book is a review of the work of logicians, particularly mathematical logicians, who developed concepts crucial to modern computers. Leibniz, Boole, Frege, Cantor, Hilbert, Gödel, and Turing are covered, with some attention to their personal biographies. The prose style is lucid, with clear and potentially widely intelligible exposition of technical issues. The author, Martin Davis, has had a long and distinguished career, occupying a crucial locus between mathematical logic and engineering design and construction and accepting a responsibility to make the theory of computability accessible to non-technical readers. The clarity of presentation and themes developed are continuous with his previous publications, without repetition. The broad relevante of the work to information science is through the gestalt of the computer. More specifically relevant issues lie in the connections between mathematical and ordinary discourse concerns and in the intersection between logic and engineering. The idea of the computer as a universal machine, developed in mathematical logic in the 1930s and obscured in ordinary discourse by an emphasis an the stored-program concept as the revolutionary element, is discussed (pp. xi and 186). From the perspective of economics, the context of conceptualization (mathematical logic) is different from that of invention (wartime cryptography). Innovation and diffusion have brought the computer into further arenas: as Time (1999) noted: "every one who taps at a keyboard, opening a spreadsheet or a word-processing program, is working an an incarnation of a Turing machine" (p.192). The formal logic of the context of conceptualization may not be applicable to human and ordinary language concerns of the context of diffusion and more could have been made of this contrast. The received position, noted by Davis, has been that conceptualization and invention of the computer occurred largely separately, in mathematical logic and engineering. The position was questioned by Minsky, as long ago as 1967: "While it is often said that the 1936 paper [by Turingl did not really muck affect the practical development of the computer, 1 could not agree to this in advance of a careful study of the intellectual history of the matter." (Minsky, 1967, p. 104). Davis refers to the emerging evidente, whose release had been complicated and delayed by security considerations, indicating greater personal continuity and interaction, specifically between Turing and von Neumann, than had previously been allowed for (p. 192). A deeper cultural conflict between engineering and logic could also be detected, between a concern with robustness and developing and preserving robustness by incremental innovation and an interest in radical reconceptualization (curiously, Wittgenstein, who produced a robust account of formal logic, had trained as an engineer and designed a house). The image of the machine and its relation to mathematical reasoning is also considered and Poincare quoted: We might imagine a machine where we should put in axioms at one end and take out theorems at the other, like that legendary machine in Chicago where pigs go in alive and come out transformed into hams and sausages. It is no more necessary for the mathematician than it is for these machines to know what he is doing. (p.93) A stronger distinction between the process and product of mathematical reasoning, analogous to the distinction between the context of discovery and of justification in the philosophy of science and consistent with the Marxist view of the congealing of human labor in the product, might have reduced the need to identify the human process of mathematical reasoning with its mechanical analogue. A more radical move would to acknowledge both mathematics and technology as human constructions.