universal set

<logic> The set of all things. Cantor's theorem (that the power set of a given set has a greater cardinality than the given set) implies that there is no largest set or all-inclusive set, at least if every set has a power set. Hence as "the set of all things", the universal set is not recognized in standard set theory. Sometimes the set of all things under consideration in the context; the universe of discourse. The complement of the null set. Notation: 1 (numeral one), or V.

See power set, universe of discourse

[Glossary of First-Order Logic]

<2001-03-16>

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Nearby terms: universalisability « universal proposition « universal quantifier « universal set » universals problem of » univocal - equivocal » ursache

universals problem of

<philosophy of science, metaphysics>, <controversy about universals, metaphysics, scholasticism> <realism, nominalism, ockhamism, formalism, logic> <conceptualism> universals are features (e.g., redness or tallness) shared by many individuals, each of which is said to instantiate or exemplify the universal. Although it began with dispute over the status of Platonic Forms, the problem of universals became a central concern during the middle ages. The metaphysical issue is whether or not these features exist independently of the particular things that have them: realists hold that they do; nominalists hold that they do not; conceptualists hold that they do so only mentally. Recommended Reading: Properties, ed. by D. H. Mellor and Alex Oliver (Oxford, 1997); Richard Ithamar Aaron, Our Knowledge of Universals (Haskell, 1975); The Problem of Universals, ed. by Andrew B. Schoedinger (Humanity, 1991); Five Texts on the Mediaeval Problem of Universals, ed. by Paul Vincent Spade (Hackett, 1994); and D. M. Armstrong, Universals: An Opinionated Introduction (Westview, 1989).

[A Dictionary of Philosophical Terms and Names]

the properties or attributes expressed (or kinds denoted) by abstract or general words or predicates in speech (or concepts in thought). Just as the words (or concepts) apply to many things, properties corresponding to the words (or concepts) inhere in many individuals; in just those same individuals to which the word (or concept) can be truly applied. The relation between the universal corresponding to the word and the things to which the word is applied in speech (or the concept in thought) is supposed to explain the truth of that application. If the universal the word expresses does belong to the thing to which the word is applied then the application (an assertion, or affirmative judgment) is true; if the universal does not belong to the thing, then the application is false. "Grass is green" is true because grass has the property of being green; "Grass is carnivorous" is false because grass hasn't the property of being carnivorous; etc. See nominalism and realism above.

[Philosophical Glossary]

<2002-05-04>

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Nearby terms: universal proposition « universal quantifier « universal set « universals problem of » univocal - equivocal » ursache » urteil