Cartesius dimidius ...

Turing

'I don't want to give a definition of thinking, but if I had to I should probably be unable to say anything more about it than that it was a sort of buzzing that went on inside my head.'
—Alan Turing (BBC Third Programme, 14 January, 1952)

As a mathematician, Turing's achievements were of no small consequence. But he's also remembered for his hobbyist philosophising, for his speculative essays and public radio talks on the subject of thinking machines. Whence the more or less synonymous terms 'Turing test' and 'imitation game,' referring to the peculiar means by which he answered the question 'Can machines think?' As Turing rightly says, an answer 'should begin with definitions of the meanings of the terms "machine" and "think." ' ('Computing Machinery and Intelligence,' in Mind, 1950, p. 433). Well-defined terms (i.e. terms which are unequivocal, non-circular, extensionally-sufficient, etc.) are a necessary condition of sound arguments, alongside true premises and valid reasoning. But instead of defining his terms, Turing asks a new stand-in question:

'The new form of the problem can be described in terms of a game which we call the "imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart from the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A" ... We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?" (Ibid., pp. 433-434.)

Forget 'Can machines think?' It's 'too meaningless to deserve discussion' (ibid., p. 442). The new and 'more accurate version' (ibid.) of the question is: is it theoretically possible that machines play imitation games? An affirmative answer here is ipso facto an affirmative answer there (meaninglessness notwithstanding).

The logic wants an editor. But let's back up before moving ahead. Remember, Turing was a Cartesius dimidius, a Descartes halved. For Descartes, all matter is mechanical and all organisms are machines (as substantiae extensas), THE MACHINIST (God) super-adds minds (substantiae cogitantes) to some machines, and these divinely arranged marriages are called human beings. Turing accepted that all organisms are machines full-stop, rejecting mindish super-additions thereto. So why, then, ask the thinking-machine question at all? We're machines, and we think; the nervous system is a 'continuous machine' (ibid., p. 451); and so on. OK, then. We'll make the imitation game more exclusive. We'll 'exclude from the machines men born in the usual manner' (ibid., p. 435) and we'll 'only permit digital computers to take part' (ibid., p. 436). No, that's not the point. That thinking is mechanical is built into the bottommost premises. And thus the real work has already been done. Game-like tests à la Turing are unnecessary. If thinking is (and if believing and trusting and loving and grieving are) a micro-mechanical buzzing then it's only a matter of time—'at least 100 years' Turing surmised in 1952 (BBC)—before digital computers likewise buzz.

'If now some particular machine can be described as a brain we have only to programme our digital computer to imitate it and it will also be a brain. If it is accepted that real brains, as found in animals, and in particular in men, are a sort of machine, it will follow that our digital computer suitable programmed, will behave like a brain.' (BBC Third Programme, 15 May, 1951.)

In other words: if Cartesius-dimidius premises then Cartesius-dimidius conclusions. We have been here before, too, centuries ago. For is the seventeenth-century bête-machine not already an imitation gamer? Is it not 'what an engineer would call a "proof of concept," a proof designed to show that an automaton could be made to perform all the required actions in the appropriate circumstances'? (Dennis Des Chene, Spirits and Clocks: Machine and Organism in Descartes, p. 17; cf. p. 98 ff. and p. 107 ff. And note that forcing the issue to the advantage of mechanicism necessitates a Cartesius-totum position).

Suppose computers do well at imitation gaming. But further suppose that Cartesianism is not taken for granted. What follows logically? Not much. Concluding that, therefore, these computers are thinkers would be a non sequitur. For logical validation we'd have to conflate thinking and 'thinking' (i.e. a mechanical analogue thereof)—which would be a textbook example of petitio principii—and why would we do that? If we already believe (as Turing did) that thinking is a micro-mechanical process or state inside a machine then Turing tests are superfluous exhibitions. But if we don't believe that thinking is thus then Turing tests are impotent.

In his refutatio Turing presents several possible objections to his thesis. The first is what he calls the theological objection: 'Thinking is a function of man's immortal soul. God has given an immortal soul to every man and woman, but not to any other animal or to machines. Hence no animal or machine can think.' For some reason, Turing believes this to be the traditional religious position, though he includes a footnoted disclaimer ('Computing Machinery,' p, 443): 'Possibly this view is heretical. St. Thomas Aquinas (Summa Theologiae, quoted by Bertrand Russell, p. 480) states that God cannot make a man to have no soul. But this may not be a real restriction on His powers, but only, a result of the fact that men's souls are immortal, and therefore indestructible.' The last sentence bespeaks theological ignorance, but that's to be expected of readers who learn their Summa in Russellian summaria. (For a Thomist, God can't make a man to have no soul because a formless form-matter composite is contradictory nonsense. It would be like God making a sphere that had no sphericity.) Needless to say, what Turing puts forward as orthodox is heterodox. And a better name here would be the Cartesian-dualist objection—a most persuasive objection, if you're a Cartesian dualist, but neither you nor I are.

Turing's nemesis

The only objection that Turing thinks is strong is that of paranormal activity: precognition, cryptaesthesia, telepathy, etc. 'These disturbing phenomena seem to deny all our usual scientific ideas. How we should like to discredit them! Unfortunately the statistical evidence, at least for telepathy, is overwhelming' (ibid., p. 453). In this way Descartes' banished res cogitans makes an uncanny return. And all Turing can say is: 'If telepathy is admitted it will be necessary to tighten our test up' (ibid., p. 454). Such tightening! But what if we don't want to be Cartesians at all, neither fully nor by halves? Why would we? Turing himself says: 'I have no very convincing arguments of a positive nature to support my views' (ibid.). Thanks Alan.