A Note on an Article by R. K. P. Singh and R. Shukla by Erik GötlindReview by: Alonzo ChurchThe Journal of Symbolic Logic, Vol. 17, No. 4 (Dec., 1952), p. 277Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2266629 .

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REVIEWS 277

"true" and "false"; namely that some statements about future events, upon a plausible and at least not refutable assumption, are to be regarded as neither true nor false. The author objects to this that truth and falsehood do not depend on time: if (for instance) a prognosis is afterwards found to be false, it has been false from the beginning.

In the discussion of this point, Linke refers to the observation of Bolzano that the tense in a proposition only apparently belongs to the copula, but in fact belongs to the subject. (We might say that it belongs to what the assertion of the proposition is about.)

According to Linke truth is something purely ontological, it has to be conceived as relating originally, not to judgments (Urteile) but to states of affairs (Sachverhalte). He defines a state of affairs as the belonging of a quality to a thing or entity of any kind ("Zu- gehorigkeit einer Beschaffenheit zu einem Sachgebilde"), where "quality" is understood in a wider sense, so as to include relations. However, the artificiality of ascribing truth and falsehood to states of affairs appears in the introduction of an improper Zugehorigkeit, which is "an den die Zugehorigkeit herstellenden Akt geknupft," besides the proper Zuge- horigkeit, which is founded in the things themselves. The distinction between true and false states of affairs is made in accordance with the proper or improper Zugehorigkeit. The author has to admit that false states of affairs by his definition are states of affairs only in an extended sense.

In spite of his conviction that the disjunction of true and false must be maintained, the author realizes that propositional calculi of three or more truth-values can be important in treating some domains of facts. They then have the r6le of "logoide Formalismen," i.e., of calculi to be interpreted by means of concepts (such as the modalities) which ordinarily are dealt with under the head of logic though having only indirectly to do with truth and falsehood. But the difference between logic in such an enlarged sense and logic proper is emphasized by Linke. Thus he argues that, in quantum mechanics, the appearance that the two-valuedness fails is caused only by falsely identifying truth with certainty of truth, and falsehood with certainty of falsehood, or else by taking "meaningless"-a predicate that applies to sentences rather than judgments-as a truth-value.

Logic proper, on Linke's view, is mainly the science of negation and conjunction in their various combinations. He opposes the doctrine that the laws of logic concern directly not the world of things but only our language. Agreeing in this respect with Felix Kaufmann (see 4151, pp. 32-33) he maintains that negation and conjunction have their place in the real world. In particular as to negation he argues: negation is identical with diversity, but diversity doubtless exists in the world of things. And coming back to the opposition of true and false he declares that we call false "denjenigen Sachverhalt im weiteren Sinne, dessen Sachverhaltscharakter von dem des eigentlichen (wahren) Sachverhalts verschieden ist" (here of course the Sachverhalt must be meant in a definite respect).

The author has arrived at his theory of truth and falsehood by a modification of Bol- zano's doctrine of Sdtze an sich. His fundamental argument is that there are unknown truths.

However, it would seem that truth in this sense is the state of affairs (Sachverhalt) it- self, so that "wahrer Sachverhalt" is a pleonastic expression. In the purely ontological domain the distinction of true and false has no application-or else we must assume an ontology of intensions, as Mr. Linke surely is not willing to do, since he expressly denies that there are such things as ideal objects, or a category of ideal existence. This argument, of course, is not at all directed against an ontological conception of logic; only it seems that in a purely ontological logic one should abstain from speaking of true and false.

PAUL BERNAYS

ERIK GOTLIND. A note on an article by R. K. P. Singh and R. Shukla. The mathematics student, vol. 19 no. 3-4 (for 1951, pub. 1952), pp. 120-121.

In effect, the same criticism as in Rescher's review XVII 66(2). ALONZO CHURCH

EUGEN GH. MIHAILESCU. Cercetdri asupra subsistemelor calculului propozi~tilor (Re- searches on sub-systems of the propositional calculus). Roumanian, with abstracts in Russian and French. Studii si cercetari matematice, Academia Republicii Populare Ro- mane, Institutul de Matematica, vol. 2 (1951), pp. 1-44.

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