Minds and Machines by Hilary Putnam; Alan Ross Anderson; Sidney HookReview by: Joseph S. UllianThe Journal of Symbolic Logic, Vol. 36, No. 1 (Mar., 1971), p. 177Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2271581 .

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REVIEWS 177

tive sentences. The metaphysician can hold that his talk about real freedom is not intended to describe new empirical facts but rather to prescribe how we should look at facts already familiar " (p. 237). The reviewer concurs, and would like to see the program carried through.

RONALD J. BUTLER

HILARY PUTNAM. Minds and machines. Minds and machines, edited by Alan Ross Ander- son, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1964, pp. 72-97. (Reprinted from Dimensions of mind, A symposium, edited by Sidney Hook, New York University Press, New York 1960, pp. 148-179.)

Putnam argues for the thesis that the traditional mind-body problem is no genuine theoretical problem, but rather " wholly linguistic and logical in character." He likens the relation between a human being's mental and physical states to that between a Turing machine's "logical" and "structural" states, where the former are machine states in the usual sense and the latter are bound up with the machine's physical embodiment (vacuum tubes, electronic relays, etc.). He asserts that "every philosophic argument that has ever been employed in connection with the mind-body problem... has its exact counterpart in the case of the 'problem' of logical states and structural states in Turing machines." In particular, such counterparts are offered for various contentions about (i) "private knowledge" (as of pain) and (ii) the permissibility of identifying mental and physical events with each other. The parallels staked out are highly suggestive. JOSEPH S. ULLIAN

GUSTAV BERGMANN. Propositional functions. Analysis (Oxford), vol. 17 no. 2 (1956), pp. 43-48.

EDWIN B. ALLAIRE. Types and formation rkles: a note on Tractatus 3.334. Ibid., vol. 21 no. 1 (1960), Pp. 14-16.

Bergmann attempts to show that "the notion of a propositional function is both useless and harmful." It is useless because "anything that can be said or done by mentioning or using a propositional function (e.g. 'F(x)', where 'F' is a predicate constant and 'x' an individual variable] can also be said or done by mentioning or using the predicate which is its constituent." And the notion is harmful because it lends "specious plausibility" both to a bad argument for nominalism and to the doctrine that a sentence names something.

Throughout the paper Bergmann insists-quite correctly-that there is no significant syn- tactical difference between a predicate and an individual constant. In particular, neither is better suited than the other to serve on interpretation as a name. More specifically, syntactical con- siderations lend no support to the erroneous view, suggested by the notation of propositional functions, that an individual constant standing alone can make some sense (as a name of an individual) which a predicate cannot (as a name of a "character"). (Bergmann does not refer to, but it is instructive to compare, Frege's Function and concept (XVIII 92), especially pages 31-32.)

In developing his thesis, Bergmann writes as if there were no good reason to have ("no real use" for) the notion or notation of propositional functions. But surely there are the same reasons-some of them no doubt good- as there are for quantifying over individual and not predicate variables in elementary logic. (For example, there may be far more interesting sen- tences of the sorts 'Every thing has this particular property' and 'Every thing which has this particular property has that one as well' than of the sorts 'This particular thing has every property' and 'This particular thing has every property which that one has.') We cannot write, for instance, '(Vx)F(x)' without also writing both '(Vx)' and 'F(x)'. And just as we want a term for the first part, "the quantifier," we also want a term for the second part, "the propositional function." The risks which Bergmann points out will not induce us to get along without a term for this part. But his and other considerations certainly justify our using some less misleading term, like "propositional form," ".open sentence," "quasi-sentence, " or "matrix."

Allaire extends Bergmann's catalogue of the harmful effects of the notation of propositional functions, especially of a sort used by Frege and Wittgenstein. There is first the "erroneous belief" that the formation rules of a formal language may be implicit in, and thus follow from, the division of its signs into types by shape. (Wittgenstein is taken to express this belief in 3.334-" the rules of logical syntax must follow of themselves, if only we know how every single

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