Abstract
By a ‘plurative syllogism’ we understand a two-premiss argument in which, in addition to the familiar categorical propositions of the types A, E, I, and O, there may also figure plurative propositions 1 of these four types:
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U: Most S is P
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W: Most S is not P
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U′ (not-U): Half-or-more S is not P
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W′ (not-W): Half-or-more S is P.
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References
We owe this term to correspondence with P. T. Geach. The treatment of such propositions goes back to the Middle Ages at least, and some discussion of the matter can be found, for example, in Averroes’ Quaesita in libros logicae Aristotelis, in Aristotelis opera cum Averrois commentaries, Vol. I (Venice, 1562; photoreprinted, Frankfurt am Main, 1962 ).
Formal Logic (La Salle, Ill., Open Court, 1926), Chap. VIII. Compare also Henry A. Finch, ‘Validity Rules for Proportionally Quantified Syllogisms’, Philosophy of Science 24 (1957) 1–18.
This chapter presents details of a finding previously announced by the author in an abstract entitled ‘Plurality Quantification’, The Journal of Symbolic Logic 27 (1962) 372–374. It was originally published as a joint paper with Neil A. Gallagher in Philosophical Studies 16 (1965) 49–55. Its authors take pleasure in acknowledging helpful suggestions by Nuel D. Belnap, Jr.
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Rescher, N. (1968). Venn Diagrams for Plurative Syllogisms. In: Topics in Philosophical Logic. Synthese Library, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3546-9_7
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