Mr. Anderson on Subjunctive and Counterfactual Conditionals by A. C. LloydReview by: Charles A. BaylisThe Journal of Symbolic Logic, Vol. 18, No. 4 (Dec., 1953), pp. 338-339Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2266580 .

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338 REVIEWS

GIUSEPPE VACCARINO. Discussion. English translation. Ibid., pp. 117-120. B. V. JUHOS. Answer to Mr. Vaccarino. English translation. Ibid., pp. 120-122. The author discusses the relevance of quantification theory to certain traditional

metaphysical problems. He notes that the existence of a thing cannot be asserted by means of a quantified sentence unless the sentence attributes to the thing at least some relation or property. He then criticizes the concept of a thing-in-itself (which he identifies with that of a thing which has no properties and which is related to nothing) on the ground that the existence of such a thing cannot be asserted by means of a quantified sentence. He also discusses some of the philosophical problems associated with the concept of causality, but he does not touch upon the logical problems as- sociated with the contrary-to-fact conditional. RODERICK M. CHISHOLM

BELA VON JUHOS. Die Erkenntnisanalytische Methode. Zeitschrift fur philo- sophische Forschung, vol. 6 (1951-2), pp. 42-53.

A condensed version of the preceding paper. RODERICK M. CHISHOLM

A. C. LLOYD. On arguments for real universals. Analysis (Oxford), vol. 11 (1950 -1), pp. 102-107.

The author urges that although sound supporting arguments for realism may be derivable from mathematical logic, the traditional arguments based on ordinary discourse can be answered. His discussion focuses on two of these, the "in respect of" argument and the "resemblance" argument.

The former is to the effect that a nominalist who tries to define, say, 'red' by saying 'a is red =_ a resembles s," must add some such phrase as "in respect of color," where color is a universal. For any two individuals will be alike in an infinite number of respects and to indicate the resemblance intended without an infinite regress, some determinable must be referred to in the description. Lloyd urges that realists cannot prove that an infinite conjunction of resemblances is necessary, but agrees that nominalists cannot prove that a finite set is sufficient.

Lloyd states the "resemblance" argument this way: Nominalists define the "re- sembles" of "a resembles s" in some such way as this: (1) aRs = (aRs) R1 (sRt). But if R. be admitted to be the same as any other R, then they have admitted one universal, viz. resemblance. To avoid this they must define R, in some such way as this: (2) (aRs) R1 (sRt) - [(aRs) R1 (sRt)] R2 [(sRt) R1 (tRv)]; and so on, ad infinitum. Lloyd then tries to show that this infinite regress, if indeed there be one, is not a vicious one. But to state the argument in this way is, I think, to miss its point. The point is, rather, that even in step (1) a universal is admitted, for the R's of aRs and of sRt are two tokens of the same (universal) type. And the relations they symbolize are two instances of the same (universal) relation. CHARLES A. BAYLIS

ALAN Ross ANDERSON, A note on subjunctive and counterfactual conditionals. Ibid., vol. 12 (1951-2), pp. 35-38.

As evidence of his thesis that not even a true subjunctive conditional in the past tense implies the falsity of its antecedent, Anderson offers this example: Suppose a doctor investigating Jones's death states, "If Jones had taken arsenic, he would have shown just exactly those symptoms which he does in fact show." We should be in- clined to take such a statement as evidence that Jones had taken arsenic.

He proposes that we take subjunctive conditionals as not implying the falsity of their antecedents and define counterfactual conditionals as subjunctives in which the antecedent is false: (AcB) = df. AsB & -A. CHARLES A. BAYLIS

A. C. LLOYD. Mr. A nderson on subjunctive and counterfactual conditionals. Ibid., pp. 113-115.

The author rejects Anderson's account (above) on the ground that Anderson

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REVIEWS 339

neglected "the rhetorical situation (suppressed prefixes)" of the doctor, and thus that his example without such a prefix does not imply either the truth or the falsity of the antecedent. But Anderson does not urge that it has such an implication. He says merely that the doctor's (prefixless) statement does not imply the falsity of the antecedent.

Perhaps much of the disagreement between Lloyd and Anderson could be resolved by distinguishing between what a statement explicitly says and what is implicitly intended, as may be indicated, perhaps, by the circumstances rhetorical or otherwise.

CHARLES A. BAYLIS

JPRGEN V. KEMPSKI. Zur Logik der Ordnungsbegriffe, besonders in den Sozialwissen- schaften. Studium generate (Heidelberg and Berlin), vol. 5 (1952), pp. 205-218.

The article deals with the logical status of type concepts as used by some writers in the social sciences. The author rightly emphasizes that traditional logic with its restriction to class terms cannot provide an adequate formal analysis of typological procedures, and he indicates in outline how an explication and distinction of several kinds of typological concepts can be effected by means of the logic of relations and of functions; for this purpose, he draws on, and suggests certain extensions of, the analy- ses of type and gestalt concepts presented in II 61(2) and XV 61. CARL G. HEMPEL

TADEUSZ CZEZOWSKI. Uwagi o klasycznej definicii prawdy (Remarks on the classical definition of truth). Ksif ga pamiatkowa 75-lecia Towarzystwa Naukowego w Toruniu, Torufi 1952, pp. 35-41.

This is a historical review of various opinions concerning a "correct" definition of truth. Following a summary of the views of Aristotle, Aquinas, Mach, Poincar6, and others, the author informally sketches some of the ideas of Tarski. JAN KALICKI

BURTON DREBEN. On the completeness of quantification theory. Proceedings of the National Academy of Sciences of the United States of America, vol. 38 (1952), pp. 1047-1052.

The author combines arguments of Herbrand (3825) and Godel (4182) to obtain a proof of the following theorem. Every quantificationally valid schema q0 in prenex normal form is demonstrable. Every such demonstration, moreover, can be given a form, called a Herbrand Normal Form, which consists (a) of a first line which is a purely truth-functional tautology, and (b) of successive lines each of which is obtained from its immediate predecessor by applying one of the following three rules I, II, III. Given an alternation X as a line of a proof: (I) Replace any alternation clause 0 of X by r(3Lo) 1, where Q is any arbitrary variable such that if it appears in I - it is 6; (II) replace any alternation clause f - of X by r(e) -1, where 6 is not free in any other clause of X nor in f, LO 6 and e is any arbitrary variable such that if it appears in f - it is 6; (III) drop any re- petitions of an alternation clause of X.

The author also offers some comments as to what Herbrand considered to be a proper metamathematical question. He suggests that Herbrand omitted to infer from his theorems the result, that a formula which can not be established by a Herbrand Normal Form is not quantificationally valid, only because he did not consider such a theorem to have finitistic meaning. LEON HENKIN

H. RASIOWA and R. SIKORSKI. A proof of the Skolem-Ldwenheim theorem. Fun- damenta mathematicae, vol. 38 (for 1951, pub. 1952), pp. 230-232.

The theorem which is proved here may be expressed in the notation of the review of XVII 72 as follows: (*) Every consistent set A of formulas of the first order functional calculus So is simultaneously satisfiable in the domain I of positive integers.

The name which the authors attach to this theorem is historically inaccurate, as the following remarks are designed to show. In his papers of 1920 (2473) and 1929

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