How many syllogisms are there?

History and Philosophy of Logic 9 (1):77-85 (1988)
Abstract
The incompleteness and artificiality of the ?traditional logic? of the textbooks is reflected in the way that syllogisms are commonly enumerated. The number said to be valid varies, but all the numbers given are of a kind that logicians should find irritating. Even the apparent harmony of what is almost invariably said to be the total number of syllogisms, 256, turns out to be illusory. In the following, it is shown that the concept of a distribution-value, which is related to the traditional theory of distribution, and the familiar concept of quantity together suffice to produce a far better way of enumerating syllogisms and a more complete understanding of the systematic features of syllogistic logic
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References found in this work BETA
P. T. Geach (1960). Distribution: A Last Word. Philosophical Review 69 (3):396-398.
P. T. Geach (1962/1968). Reference and Generality. Ithaca, N.Y.,Cornell University Press.
W. V. Quine (1982). Methods of Logic. Harvard University Press.
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