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Turing’s Responses to Two Objections

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Abstract

In this paper I argue that Turing’s responses to the mathematical objection are straightforward, despite recent claims to the contrary. I then go on to show that by understanding the importance of learning machines for Turing as related not to the mathematical objection, but to Lady Lovelace’s objection, we can better understand Turing’s response to Lady Lovelace’s objection. Finally, I argue that by understanding Turing’s responses to these objections more clearly, we discover a hitherto unrecognized, substantive thesis in his philosophical thinking about the nature of mind.

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Notes

  1. For example, Jerry Fodor writes, “… the question arises, how a machine could be rational? …the great logician Alan Turing proposed an answer to this question. It is, I think, the most important idea about how the mind works that anybody has ever had. Sometimes I think that it is the only important idea about how the mind works that anybody has ever had” (Fodor 1992, p. 6).

  2. Some of the articles discussed here appeared in print first in Furukawa et al. (1999), with B. J. Copeland editing them, and then, collected with corrected versions of other materials in which Turing discusses machine intelligence, in Copeland (2004).

  3. Notice that the generation of m involves applying a similar method to one used in a proof of what is often called the recursion theorem for computability (see, for example, Rogers 1967, p. 180).

  4. Here, as in general (and as Turing did), by infallible, I mean infallible for questions that can be expressed as theorems of first order arithmetic, as can statements of the halting of a particular Turing machine on a particular input.

  5. Perhaps, then, it should be the ‘Turing–Gödel–Kreisel–Benacerraf maneuver/analysis/conclusion’.

  6. See, for example, ibid., p. 123.

  7. I have not presented all of the logicians and philosophers who have taken the response to the first mathematical objection that Turing does. A notable early example of such a response is made by Putnam in 1960: “Given an arbitrary machine T, all I can do is find a proposition U such that I can prove (3) If T is consistent, U is true, where U is undecidable by T if T is in fact consistent. However, T can perfectly well prove (3) too! And the statement U, which T cannot prove (assuming consistency), I cannot prove either (unless I can prove that T is consistent, which is unlikely if T is very complicated)!” (Putnam 1960, p. 77, emphasis in original). It is therefore preferable to have some name for this response other than hyphenating the names of luminaries who make this response to the first mathematical objection.

  8. Arguments that Turing intended his test to have related, but different empirical content can be found in Dennett’s 1985 postscript to his paper ‘Can Machines Think’ (Dennett 1985, p. 21).

  9. The transcripts of the competitors for the ‘Loebner Prize’ are striking instances of these; see links from http://www.loebner.net/Prizef/loebner-prize.html for examples.

  10. I use the word ‘created’ here instead of ‘designed’, as Bringsjord et al. do, since design seems to give away at least some of what is at stake. Things that are designed typically are intended to behave in some way conceived by the designer, whereas created objects may not—e.g. the described creation, by God, of free human beings in Genesis.

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  1. Department of Philosophy, Dalhousie University, Halifax, NS, Canada, B3H 4P9

    Darren Abramson

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Abramson, D. Turing’s Responses to Two Objections. Minds & Machines 18, 147–167 (2008). https://doi.org/10.1007/s11023-008-9094-6

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