¹ In Der logische Aufbau der Welt, p. 41.

² Not in the book mentioned in the previous note—there this possibility was explained away—but only in The logical syntax of language, p. 169.

³ These parenthesized es will be omitted hereafter.

⁴ The restrictive phrase in this theorem ‘which do not form partial es of other sts’ may look strange at first sight. The need for it will be soon exemplified. Cf. note 6.

⁵ For the sake of economy, quotes will be printed only around the first member of a list of es, wherever misunderstandings will not be likely to arise.

⁶ This exemplifies T3.13. The oddity involved could, of course, have been avoided by the use of auxiliary ss such as parentheses, or by making use of additional rules of scope.

⁷ I am not sure whether the geometrical C dealt with by Hilbert-Ackermann, , Grundzüge der theoretischen Logik, 2nd ed., p. 82Google Scholar, is an exception. This model-C contains two prs: ‘Λ(x, y)’ (‘x lies on y’), where ‘x’ belongs to the mgn of point-names and ‘y’ belongs to the mgn of straight-line-names, and ‘≡(x, y)’, the pr of identity, where ‘x’ and ‘y’ may belong to both mgna. “Of course, the assertion of the identity of a point with a straight line is always to be regarded as false.” But there are no hints as to whether we are to look on the s-sq ‘Λ(x, y)’, where, say, both variables belong to the mgn of point-names, as an always false st or as a non-st. In the first case, all ind-es would be not only ist but also isg; in the second case, the two mgna forming the type of ind-es would be c-rel.

Later on, pp. 83ff., Hilbert and Ackermann show how to construct for every C which contains more than one domain of ind-es an equivalent C with one domain of ind-es only.

Cf. also Schmidt, A., Ueber deduktive Theorien mit mehreren Sorten von Grunddingen, Mathematische Annalen, vol. 115 (1938), pp. 485–506CrossRefGoogle Scholar.

⁸ Cf. Carnap, C., Testability and meaning, Philosophy of science, vol. 3 (1936), pp. 442–443CrossRefGoogle Scholar.

⁹ Cf. Kaplan, A., Definition and specification of meaning, The journal of philosophy, vol.43 (1946), pp. 281–288CrossRefGoogle Scholar.

¹⁰ Cf. R. Carnap, Introduction to semantics, section 12, with further references there.

¹¹ Cf. Testability and meaning, Philosophy of science, vol. 4 (1937), p. 5Google Scholar.

¹² Urban, W. M., Language and reality, p. 198Google Scholar.

¹³ Cf. op. cit. in previous note, pp. 647–648, 651. It is very hard to reconcile the various apparently contradictory evaluations which Urban gives of this st. The confusion seems to me symptomatic for the still prevalent neglect of the all-important distinction between pragmatical description of certain linguistic usages and the syntactical (or semantical) proposals to reform or unify these usages by construction of artificial language-systems.

Here are two more examples of confusions arising out of this neglect which have immediate relevance to our subject.

In his article Meaningfulness, Mind, vol. 46 (1937), pp. 347–364Google Scholar, A. C. Ewing opposes the generally held view that statements such as ‘Quadratic equations go to race-meetings’ or ‘Virtue is a fire-shovel’ are meaningless. He is right in so far as Ci may be constructed in which the corresponding s-sqs will be sta. But when he continues to assert dogmatically that these statements are self-contradictory, he is wrong, when his assertion is interpreted pragmatically as a description of common usage, since this usage is far from being univocal in this respect—no statistical investigations have been made, as far as I know, but I am sure that each of the mutually exclusive predicates ‘meaningless,’ ‘self-contradictory,’ and ‘factually false’ will find its followers among common people and philosophers alike—, and this interpretation is the only possible one in our case.

In conformance with the three mentioned possible evaluations, various language-systems may be constructed in which the corresponding s-sqs will have one of these properties. A discussion of the advantages and disadvantages of these language-systems will be important and fruitful, but only when held without any dogmatic prejudices.

Belief in the uniqueness of a “logical grammar” corresponding to a given language leads Josef Schaechter to make several mistakes in his otherwise interesting and stimulating book Prolegomena zu einer kritischen Grammatik, Vienna, 1935Google Scholar. On this assumption is based his distinction between “essential” and “inessential” grammatical rules, between the “grammar of significance” and the “grammar of material.” Starting from these distinctions, he concludes that there are not only linguistic usages which are impeccable according to usual grammar but which are meaningless word-sqs according to his logical grammar (p. 26)— his examples ‘I am travelling into the past,’ ‘Virtue is triangular,’ ‘The leaf wishes,’ show, incidentally, that Schaechter fails to make the important distinction between s-sqs which are not in conformance with the rules of formation of the language dealt with and s-sqs which are sts whose falseness follows from the semantical rules alone, a distinction which corresponds roughly to that stressed already by Husserl under the names ‘nonsense’ (‘Unsinn’) and ‘countersense’ (‘Widersinn’)—, but that there are also logically impeccable usages which are nevertheless incorrect according to usual grammatical standards, since they sin against “inessential” rules. This remark is valuable so long as we bear in mind its relativity to the language-systems chosen for this comparison, but Schaechter's insistence on the absoluteness of his “logical grammar” leads him astray.

His example for a logically correct but grammatically incorrect st is: “Die Mädchen gehte auf dem Strasse.” He points out that this word-sq, in spite of its three grammatical mistakes, i.e., ‘die’ instead of ‘das,’ ‘gehte’ instead of ‘ging,’ ‘dem’ instead of ‘der,’ is a logically impeccable st, since all these mistakes are “inessential.”

But how does Schaechter know that the utterer of the original word-sq intended to say (or write) “Das Mädchen ging auf der Strasse” rather than “Die Mädchen gingen auf der Strasse,” or “Das Mädchen geht auf der Strasse,” or “Das Mädchen ging auf dem Strand,” or just anything else you like, meaningful or meaningless? The original word-sq is neither grammatically nor logically meaningful, and there is nothing in it which points to its meaningful substitute. But as soon as certain pragmatical considerations induce me to replace it by some logically meaningful st, this st will be meaningful also grammatically.

¹⁴ Or, for a non-empiricist, can possibly be of some importance (in a certain sense to be specified).

¹⁵ This happy term is Reichenbach's.

¹⁶ A history of Western philosophy, pp. 157, 831.

¹⁷ An article dealing with the interesting history of the syntactical categories and their importance for an effective criticism of certain recent logico-philosophical discussions is in preparation.