Abstract
THE starting-point of Prof. Carnap's work is the distinction between two aspects or tendencies in logic. On one hand, there is the tendency to emphasize form, the logical structure of sentences and deductions, relations between signs in abstraction from their meaning: this is Hilbert and Bernays' Beweistheorie, Carnap's syntax. In contradistinction to it is the emphasis on meaning, interpretation, relations of entailment and compatibility as based on meaning, the distinction between necessary and contingent truth, etc.: this is semantics, and corresponds generally to Hilbert and Bernays' mengentheoretische Logik. Prof. Carnap is planning a series of studies on semantics, of which the volume under review is the second (the first being an "Introduction to Semantics"); it deals with the application of his methods to a criticism of the formalization of logic, that is, its representation by a formal system or calculus. The problem is to determine to what extent the logical calculi that have been constructed hitherto have actually effected the task of formalizing logic in such a way that the principal logical signs can be interpreted only in terms of the accepted logic of meaning; a question which the author answers in the negative. He shows, however, that a full formalization of prepositional logic, and also of the logic of functions, can be effected by making use of new basic concepts, the most important step being the introduction of junctives, that is, of sentential classes in conjunctive and in disjunctive conception.
Formalization of Logic
By Prof. Rudolf Carnap. (Studies in Semantics, Vol. 2.) Pp. xviii + 159. (Cambridge, Mass.: Harvard University Press; London: Oxford University Press, 1943.) 16s. 6d. net.
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[Book Reviews]. Nature 153, 8 (1944). https://doi.org/10.1038/153008a0
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DOI: https://doi.org/10.1038/153008a0