Venn Diagrams for Plurative Syllogisms
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:
U: Most S is P
W: Most S is not P
U′ (not-U): Half-or-more S is not P
W′ (not-W): Half-or-more S is P.
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- 1.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 ).Google Scholar
- 2.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.Google Scholar
- 3.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.Google Scholar