Abstract
Since the publication of Alan Turing’s famous papers on “machine intelligence” over six decades ago, questions about whether complex mechanical systems can partake in intelligent cognitive processes have largely been answered under the analytical rubric of their capacity successfully to simulate symbol-mongering human behavior. While this focus on the mimetic potential of computers in response to the question “Can machines think?” has come to be accepted as one of the great bequests of Turing’s reflections on the nature of artificial intelligence, I argue in this paper that a closer look at Turing’s oeuvre reveals an especially informative tension between the pragmatic and normative insights, which enabled him in 1936 to formulate his pioneering version of the theory of mechanical computability, and his later attempt to argue for a simplistic notion of “machine intelligence” as an effectual imitation of the human mind. In fleshing out the source of this tension, I endeavor to show how the mimetic model of “thinking machines” that Turing eventually embraces is ultimately at cross-purposes with the normative-pragmatic insights by which he reached his original innovations in computability theory and combinatorial logic.
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Notes
- 1.
This is Gandy’s phrase and the theme around which he organizes “The Confluence of Ideas in 1936.”
- 2.
- 3.
Notably, a distinction of this sort arises much earlier in analyses of logic but then again even more forcefully in the process philosophy of Alfred North Whitehead. It takes on a more semantic complexion in the work of Black, Sellars, and Searle (1968, p. 422).
- 4.
This occurs in Nicomachean Ethics 1170a28–1171b35. See also (Agamben 2009, pp. 25–38).
- 5.
- 6.
The elemental role of these dimensions of authority and responsibility in the practice of giving and asking for reasons has been stressed most recently in the writings of Robert Brandom. On his view, the undertaking of inferentially articulated commitments in dialogical processes of meaning redemption constitutes the basis of the normative-pragmatics of rational communication. In the stress he places upon this normative character of the sociality of reason, Brandom writes in a broadly Kantian-Hegelian heritage and, in so doing, joins the ranks of Humboldt, Peirce, Sellars, Apel, and Habermas. See especially his (1994), (2000), (2009, pp. 52–77).
- 7.
There is, in fact, a third step we must take here to flesh out fully the ethical-pragmatic preconditions of the social practice of computing, but one to which, in keeping with the scope of this paper, I can only allude. I want to suggest that, by situating the central limitative claims set forth by Turing (1936/2004) within the context of the reconstruction of these preconditions I have been offering, we can begin to discern a largely unrecognized bridging concept that links the programmatic significance of the Church-Turing Thesis to that of the undecidability results Turing achieved in offering his negative answer to the Entscheidungsproblem. As is well-known, Turing accomplished the latter by, as he put it, correctly applying “the diagonal process” (Turing 1936/2004, p. 72) to what has since come to be known as the halting problem. Once Turing had established a perspicuous definition of an algorithm under the rubric of his machines, it then became possible for him, first, to Gödelize an enumerable set of the latter by arithmetizing them and, then, to apply the tool of diagonalization in order to exploit the operative limitations exposed by the fate of self-referential foundering thereby met in the process of computing. It is in this pragmaticizing “application of the diagonal process” that, I want to suggest, we can identify a third precondition of the social practice of computing. By resituating the predicament of unsolvability in the tangible milieu of the human process of calculating, Turing shows that the embodied computor is always subject to a certain irreducible factor of alterity (instantiated in the iterative constituents of the anti-diagonal sequence). The latter both determines the absolute limitation of the finite calculative practice and transgresses that very limitation in virtue of the unincorporability of the antidiagonal sequence into the diagonal process which delimits that calculative practice as such. The factically manifesting architectonic of undecidability, which Turing derives therefrom, can be seen as an enabling condition of the radical openness of mathematical experience, a condition of possibility of mathematical possibility, if you will. It animates the unbounded exigency to mathematical communication and operates, in turn, as a precondition of the social practice of calculating more primitive than intersubjective compositionality and agentially-situated generalizability inasmuch as these latter two are themselves spurred by the barb of living doubt emergent from such a predicament of unsolvability per se.
- 8.
Gödel appended this comment in 1963 to his 1931, “On Formally Undecidable Propositions of the Principia Mathematica and Related Systems” (Gödel 1986, p. 191).
- 9.
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Leslie, D. (2016). Machine Intelligence and the Ethical Grammar of Computability. In: Müller, V.C. (eds) Fundamental Issues of Artificial Intelligence. Synthese Library, vol 376. Springer, Cham. https://doi.org/10.1007/978-3-319-26485-1_5
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