A Theory of Subjunctive Conditionals by Robert L. StanleyReview by: Alan Ross AndersonThe Journal of Symbolic Logic, Vol. 22, No. 3 (Sep., 1957), pp. 324-325Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2963647 .

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324 REVIEWS

description. If the falsity of the antecedent were entailed by a counterfactual about the past, then neither of the statements 'If Seneca had written the tragedies, then he would have written in metrical verse' and 'If Seneca had written the tragedies, then he would not have written in metrical verse' would be true: but surely one of these is true.

He discusses the part that counterfactual conditionals play in ordinary language by pointing out that they are central for the distinction between general statements of law and general statements of fact; and that they play an important part in the meaning of singular causal statements. If someone argues that one historical event took place because of another, then one might refute him by arguing that, on the other hand, if the first had not taken place, still the second would have. This does not refute him, since it might be that if the first had not occurred, its place would have been taken by another cause of the second. JOHN WATLING

ROBERT L. STANLEY. A theory of subjunctive conditionals. Philosophy and phenomenological research, vol. 17 (1956), pp. 22-35.

Previous writers on subjunctive conditionals have frequently had as their goal the discovery of a uniform translation of subjunctive conditionals (subjunctive in virtue of natural language verb-forms) into an extensional formalism, involving only truth-functions and quantification. This attack is bedevilled by a number of well-known difficulties, especially (a) the trivial truth of certain truth-functional and universally quantified conditionals, e g., of p D q when -p and of (x) (Px D Qx) when (x)-Px; and (b) the difficulty of distinguishing "accidental" from "non-acci- dental" universal conditionals. (See Schneider XIX 68 for a summary of recent discussion.)

Stanley's novel approach presents a method for deciding (independently of natural language verb-forms) whether a given conditional has subjunctive sense. His quasi- formal method is not effective, but it is constructive: a proof that a candidate has subjunctive sense can be effectively recognized as such (given agreement that certain expressions are atomic "declarative clauses" in the "everyday grammatical sense"). When the premises of the proof (construction of which is motivated by, loosely speaking, search for appropriate initial conditions and general laws) are true and non-trivial, the conditional is subjunctively true.

Formally, the idea is roughly as follows (terminology adapted from Stanley's): a particular or universal conditional is subjunctively true if it is deducible from true atomic declarative clauses and true non-trivial generalizations with the help of universal instantiation and a rule of "truth-subtraction," which comes in the applications discussed to inferring ip D q from p and (p.tp) D q, where p and q are declarative clauses and ip is a non-void conjunction of declarative clauses. Generali- zations of the form (xl) . . . (xn) (po'.V' :) q') (where p', V', and q' are like p, t, and q, except that certain naming terms are replaced by variables) are trivial if (i) the ante- cedent is "wholly counterfactual": all substitutions of terms for variables make p'. V' false; (ii) the consequent is "wholly profactual": all substitutions of terms for variables make q' true; or (iii) the antecedent is not "completely relevant": one of the conjuncts in p'.yp' may be deleted, yielding a .; such that (xl)... (xn)(O D q') is true. Otherwise they are non-trivial.

The author discusses applications of his method to a number of familiar problematic examples, of which the following (showing that 'If I had been Bach, I would have written the Coffee Cantata,' as accented, is subjunctively true) is typical. (1) is a non- trivial generalization, (3) is a declarative clause, and (2) and (4) follow by rules mentioned above.

(1) (x)(y)(I am x . x wrote y I wrote y).

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REVIEWS 325

(2) I am Bach. Bach wrote CC: D: I wrote CC. (3) Bach wrote CC. (4) I am Bach: D: I wrote CC. Discussion of this and other examples is designed to show that this method gives

a reasonably accurate criterion for distinguishing trivial from non-trivial conditionals. The reviewer finds the arguments convincing.

Remark. Stanley's suggestions are original and ingenious, but though they help clarify the intuitively felt distinction (a), above, we are still at a loss regarding (b). True, as Stanley points out, his theory is no worse off than other extensional theories in this respect, but to the reviewer this situation seems again to point up difficulties in the attempt to analyze all informative discourse extensionally. Logicians who are not intimidated by Quine's eloquent condemnation of modal logic might well feel that a modal reconstruction of subjunctive conditionals (in elaboration of Burks XVI 277, say) would be more to the point. In any event, if a modal analysis can be reduced to an extensional one, then extensionalists should have no quarrel with a modal analysis; if not, then the extensionalists seem committed to eternal perplexity re- garding the distinction (b), in spite of the fact that we can all handle it reasonably well in practice. ALAN Ross ANDERSON

ARNOLD REYMOND. Quelques considerations sur la nature de la logique et de son objet. Bulletin de la Soci&45 Fran!aise de Philosophie, vol. 45 (1951), pp. 33-57.

G. BtNPZ1:, JEAN-LouIs DESTOUCHES, PAULETTE DESTOUCHES-FtVRIER, R. LE SENNE, R. POIRIER, ARNOLD REYMOND. Discussion. Ibid., pp. 57-70.

R. BLANCHt. Lettre de M. R. Blanche. Ibid., pp. 71-74. See Erratum, ibid., p. 131. ARNOLD REYMOND. Rdponse d'Arnold Reymond a la lettre de M. Blanche'. Ibid.,

pp. 74-82. R. BLANCHI. Passages d'une lettre. Ibid., p. 82. ARNOLD REYMOND. Rdponse. Ibid., pp. 82-83. G. B1:NtZt. Lettre de M. G. Bdndzd: Note sur la logique en general. Ibid., pp.

83-84. ARNOLD REYMOND. Rdponse de M. Arnold Reymond a la lettre et a intervention

de M. Bendze. Ibid., pp. 84-90. Reymond's paper deals with a variety of questions bearing on the biological and

psychological aspects, the ontological import, and the formal apparatus of logic. Beginning with some observations on judgment in organisms ranging from inverte- brates to man, the paper turns to rational judgment, the nature of truth and of the logical modalities, logistic systems and intuitionism, and finally the logic of the possible and the probable, with special reference to many-valued systems. The dis- cussion of these topics is so sketchy, however, and couched in so vague and often metaphorical language that an attempt to give a fuller account and a critical appraisal seems unprofitable, and indeed unwarranted in view of the scope of this JOURNAL.

What seems to the reviewer the most lucid and pertinent contribution to the dis- cussion is made in two letters by Blanch6 criticizing Reymond's characterization of the four modalities of the necessary, the impossible, the possible, and the contingent. Blanche shows that Reymond's definitions lead to consequences that run counter to standard principles of modal logic; for example, Reymond construes possibility in the narrow sense in which nothing that is possible is necessary; but as he also character- izes impossibility as the complement of possibility, it follows that what is necessary is impossible. - Destouches, in his contribution to the discussion, adds some remarks on negationless systems of logic. CARL G. HEMPEL

ROBERT BLANCHt. Quantity, modality, and other kindred systems of categories. Mind, n.s. vol. 61 (1952), pp. 369-375.

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