Du Jugement Hypothétique. by Roman IngardenReview by: Rose RandThe Journal of Symbolic Logic, Vol. 21, No. 4 (Dec., 1956), pp. 390-392Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2268393 .

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between the various classical theories of logic have their origin in the question of the existential import of these basic categorical forms. It is not the purpose of the present work to defend a particular school of logic which has evolved as a result of some selected interpretation. Rather, its main purpose is to clarify the alternative logical theories by making full use of the powerful instruments of translation which modern symbolic logic makes available. In particular, the author makes use of the predicate calculus and the calculus of classes.

A wide range of logical theories and problems is developed to satisfy the purpose of the book. Such early modern theories of classical logic are considered as those of Frege, Boole, Venn, Schrdder, De Morgan, Bentham, and William Hamilton. Among the more recent theories which are investigated are those of Lukasiewicz, Bochefiski, Wedberg, Ivo Thomas, and the author. Within this varied context, such problems are treated as the nature of logical existence, questions relating to the quantification of predicates, the status of the null class, and the exact relationship between traditional logical systems and the modern calculus of classes.

Of particular interest is the author's theory for reproducing in the first-order functional calculus both the principles of immediate inference and the categorical syllogism as developed in traditional logic. In constructing his theory, Menne extends the method used by J. N. Keynes in 631, and concludes that the results obtained in the present work are equivalent to those established by Jaskowski in XVII 268(2). However, Menne fails to mention the earlier work by H. B. Smith (for example in, 25913) which gives results that are equivalent to those of Jaskowski. Also, Menne's formulas (p. 115) which are said to be equivalent to Jaskowski's are incorrect, although his general theory is sound. As a guide to correcting these errors, let As, A,, and Am denote the translations of the traditional A form of a categorical proposition as given respectively by Smith, Jaskowski, and Menne (assuming that Menne's formula for the form A on page 115 has been corrected). A rather natural translation of As, A,, and Am into the first-order functional calculus would then be as follows:

As (x)(a(x) D b(x))(((x)(b(x) D a(x))) v ((Ex)(a(x)b(x)) (Ex)(-.a(x) _b(x)))).

A j (x) (a(x) Db(x))(((x) (b(x) Da(x))) v ((Ex)a(x) (Ex)-a(x) (Ex)b(x) (Ex)_b(X))).

Am (x)(a(x) D b(x))(((x)(b(x) Da(x))((Ex)(a(x)b(x))v(Ex)(.a(x)

_b(x))))v((Ex) (a(x)b(x)) (Ex) (-a(x) _b(x)))),

One may now show that A -A and As - Am are both provable in the functional calculus of first order. Hence, Smith's, Jaskowski's, and Menne's results are essentially the same. It is interesting to note that Smith's result was published in 1924 while Jaskowski's appeared in 1950.

In addition to the serious errors already mentioned in connection with Menne's formulas on page 115, the reader must guard against other errors in formulas which appear throughout the present work. For example, additional signs of negation are required in such formulas as 2.18, 4.22, 4.24, 5.12, and 5.14. A sign for conjunction is missing from formula 6.09, and P should be replaced by 0 with corresponding corrections made in formulas 26.22 through 26.25. A. R. TURQUETTE

ROMAN INGARDEN. 0 sadzic warunkowymn (Du jugement hypothitique). Kwartal- nik filozoficzny, vol. 18 (1949), pp. 263-308. French resume, ibid., pp. 324-325.

The problem of the nature of hypotheticals - i.e., of judgments of the form "If p, then q" or "If A is B, then C is D" - is approached by Ingarden from the phenomeno- logical point of view. The hypothetical has been regarded either as an assertion or as the expression of an argument or inference, either as a unity or as a combination

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of two sentences to which truth and falsehood can be ascribed. These were the views held by Kant, Sigwart, Meinong, and Kotarbifiski, among others.

Though the hypothetical can be used with the meaning of a categorical description of the facts ("If there is frost, an outside thermometer will fall below the freezing point") or with the meaning of an assertion made with a certain restriction ("You will be happy if you live hygienically"), Ingarden's interest centers upon a type of hypothetical in which the "if ... then" has a special meaning. The answer to the question What is a hypothetical? is not to be given by a definition but by a description and clarification of its use.

Ingarden takes as his point of departure the concept of material implication, ascribed by him simply to "the logicists," according to which the hypothetical is composed of a pair of sentences not necessarily having any connection in their content, and only the respective truth-values of the sentences are relevant for the logical sense. Against this he undertakes to show that the hypothetical is not an assertion about two facts, and that it cannot be true or false.

One might attempt to transform the hypothetical into a categorical by saying that there exists a necessary connection between such and such states of affairs, and to express it symbolically by "There exists R(P, Q)," where 'R' means 'necessary con- nection' and takes the place of a subject. But 'R' here occurs in a structure of higher order than the structure "If p, then q"; for while 'p' and 'q' describe facts, 'P' and 'Q' are only names for 'p' and 'q'. "If p, then q" has for its intention a certain connection of facts, but "R(P, Q)" refers intentionally only to the expression "If p, then q."

On analysis of the hypothetical, "If electric current flows through a copper wire, the wire becomes hot," it will be seen that the parts of the hypothetical, 'is,' 'p', 'q', have a different meaning in the context of the hypothetical than if they stood alone or in a simple sentence. Because of its dependence upon 'if' and 'then,' the 'is' loses its assertive or predicative function. Nevertheless the antecedent is not merely a supposition, as in Meinong's view, but expresses something which can exist. Goblot (TraitM de logique) is right in calling the parts of the hypothetical assertions possibles. The 'is' in the consequent marks the content of 'q' as a necessary complement of the content of 'p', the predicative function of 'is' being so modified that D is ascribed to C only in case A is B. Thus a hypothetical is an organic whole, and not merely a compound of two categorical sentences. In an inference in which "If p. then q" is used as a premiss, the conclusion, being an assertion, can be obtained only by taking an assertion as second premiss.

Although the parts of a hypothetical are not assertions, the hypothetical as a whole has an assertive function. The hypothetical asserts the existential interdependence of p and q so that with the occurrence of p, q must occur. Not being an assertion, a hypo- thetical cannot be true or false. But having stated its assertive function, one may ask whether truth and falsehood could in some sense be applied to it. A hypothetical is true, says Ingarden, if the fact described by the values of 'q'does not exist independently, apart from the occurrence described in the hypothetical, and if the fact described by the 'q' of the given hypothetical is existentially dependent upon that described by 'p'. And a hypothetical is false if these conditions are not fulfilled. This is in disagreement with the interpretation by material implication, according to which a hypothetical is false if and only if 'p' is true and 'q' is false, because it is held that a pair of categorical judgments that have no connection in content cannot stand in the relation of existential dependence, even if both true.

Also, if both parts of a hypothetical in the modus realis are false, the hypothetical is false. But the same hypothetical expressed in the modus potentialis may change into a true one. For instance it is not true that people have legs like apes nor that they climb trees rather than walk. But it is true that "If people had legs like apes, they

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would climb trees rather than walk." The hypothetical is true because there is an exis- tential dependence between these two possible facts. The truth of a hypothetical in the modus irrealis depends again on the existential dependence between the two facts, though these be self-contradictory. Such a hypothetical is true if q, as described in "If p then q," would be existentially dependent upon p if this p could exist at all.

Thus Ingarden holds that the analysis of the hypothetical leads to special criteria for its validity. Material implication would be proved to be a necessary tool for science only if no discovery were possible without it. On the other hand nothing can be said against its use, as long as the difference between the hypothetical as commonly used and material implication is kept in mind.

Comments of the reviewer. The concept of "existential dependence" is applied not only to real facts but also to possible and impossible facts. Therefore the concept of existence is used here in a different way than in everyday life. Perhaps Ingarden understands it as accidental dependence, or as causal or logical connection, and then of course it could be applied also to possible facts. Yet it is entirely incomprehensible what "dependence" between impossible (self-contradictory) facts could mean. More- over, the meaning of truth of a hypothetical in the modus realis is not the same as that of truth of a hypothetical in the modus potentialis. In the first case truth would mean that there is a real dependence between two real facts as described by 'p' and 'q' of the hypothetical. Such dependence, not indicated by a special expression but only given implicitly by the facts, cannot be called real unless the two facts are real. But dependence between two possible facts means a logical connection between the parts 'p' and 'q' of the hypothetical in the modus potentials, and truth refers here only to the statement about such structural relation.

Ingarden has the merit of stressing the importance of a connection between the two parts of a hypothetical, stating that an analysis which refers to the truth-values only is neither sufficient (in the modus realis) nor necessary (in the modus potentialis). But his view is obscure and difficult to understand, by the very form of its expression. Thus the vague concept of "existential dependence" does not explain the meaning of the hypothetical, and especially not of the conditional contrary to fact (modus potentialis and irrealis). The case of a complex hypothetical, in which the antecedent is again a hypothetical, is altogether ignored - although this is no modern innovation but was considered already by the Stoics. RosE RAND

G. P. HENDERSON. Causal implication. Mind, n.s. vol. 63 (1954) pp. 504-518. This deals with the system of causal implication invented by A. W. Burks (XVI

277(2)). The writer discusses the general questions raised when a new logic is put forward for acceptance, and the application of Burks's system to problems of universal, hypothetical, and counterfactual statements and to Lewis Carroll's barber shop puzzle. His first conclusion is that "causal" logic is not a technical answer to any metaphysical question about the concept of causal connexion. Secondly, if it is granted that the context of a natural argument may show a "rhetorical intention" to restrict the assignment of possible truth-values, then ' there is no specific work, which Burks has proposed, which [material implication] cannot do." T. J. SMILEY

A. J. BAKER. Incompatible hypotheticals and the barber shop paradox. Mind, n.s. vol. 64 (1955) Pp. 384-387.

Lewis Carroll's paradox (that from the rules 'A, B, and C must not all be out at once' and 'If A goes out B goes with him,' it seems to follow that C can never go out) depends in part on the incompatibility of the hypotheticals 'If A then B' and 'If A then not-B'. The present writer discusses this question with reference to the "causal" implication used in the solution of Burks and Copi (XV 222(3)), and goes on to say that even their solution may lead to paradox - 'If A ever goes out C never does' - unless a

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