Philosophy Dictionary of ArgumentsHome
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| Classes: In logic, a class is a collection of objects that share a common characteristic or property. Statements about classes can be expressed using logical symbols, such as "∈" for membership and "⊆" for subset. Identity of classes is provided by same elements (extension) - or identity of properties by the same predicates (intension). See also Sets, Set theory, Subsets, Element relation. - B. Classes in political theory refer to societal groups sharing economic interests, often defined by their relationship to production and resources. See also Society, Conflicts._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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B. Russell on Classes - Dictionary of Arguments
I XIV Classes/Concepts/Gödel: can be construed as real objects, namely as "multiplicities of things" and concepts as properties or relations of things that exist independently of our definitions and constructions - which is just as legitimate as the assumption of physical bodies - they are as necessary for mathematics as they are for physics. >Platonism, >Universals, >Mathematical entities, cf. >Hartry Field's Antiplatonism. I XVIII Set/Gödel: realistic: classes exist, circle fault no fault, not even if it is seen constructivistically. But Gödel is a non-constructivist. Russell: classes are only facon de parler, only class names, term, no real classes. I XVIII Class names/Russell: eliminate through translation rules. I XVIII Classes/Principia Mathematica(1)/PM/Russell/Gödel: Principia do without classes, but only if one assumes the existence of a concept whenever one wants to construct a class - E.g. "red" or "colder" must be regarded as real objects. I 37 Class/Principia Mathematica/Russell: The class formed by the function jx^ is to be represented by z^ (φ z) - E.g. if φ x is an equation, z^ (φ z) will be the class of its roots - Example if φ x means: "x has two legs and no feathers", z^ (φ z) will be the class of the humans. I 120 Class/Principia Mathematica/Russell: incomplete symbol. >Incomplete symbols. Function: Complete Symbol - therefore no transitivity when classes are inserted for variables - E.g. x = y . x = z . > . y = z (transitivity) is a propositional function which always applies. But not if we insert a class for x and functions for y and z. - E.g. "z^ (φ z) = y ! z^" is not a value of "x = y" - because classes are incomplete symbols. 1. Whitehead, A.N. and Russel, B. (1910). Principia Mathematica. Cambridge: Cambridge University Press. - - - Flor III 117 Classes/sets/things/objects/Russell/Flor: sets must not be seen as things - otherwise, we would always have also 2n things at n things (combinations - i.e. we would have more things than we already have - Solution: Eliminate class symbols from expressions - instead designations for propositional functions. >Quine: Class Abstraction._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Russell I B. Russell/A.N. Whitehead Principia Mathematica Frankfurt 1986 Russell II B. Russell The ABC of Relativity, London 1958, 1969 German Edition: Das ABC der Relativitätstheorie Frankfurt 1989 Russell IV B. Russell The Problems of Philosophy, Oxford 1912 German Edition: Probleme der Philosophie Frankfurt 1967 Russell VI B. Russell "The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202 German Edition: Die Philosophie des logischen Atomismus In Eigennamen, U. Wolf (Hg), Frankfurt 1993 Russell VII B. Russell On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit" In Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996 Flor I Jan Riis Flor "Gilbert Ryle: Bewusstseinsphilosophie" In Philosophie im 20. Jahrhundert, A. Hügli/P. Lübcke, Reinbek 1993 Flor II Jan Riis Flor "Karl Raimund Popper: Kritischer Rationalismus" In Philosophie im 20. Jahrhundert, A.Hügli/P.Lübcke, Reinbek 1993 Flor III J.R. Flor "Bertrand Russell: Politisches Engagement und logische Analyse" In Philosophie im 20. Jahrhundert, A. Hügli/P.Lübcke (Hg), Reinbek 1993 Flor IV Jan Riis Flor "Thomas S. Kuhn. Entwicklung durch Revolution" In Philosophie im 20. Jahrhundert, A. Hügli/P. Lübcke, Reinbek 1993 |
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Ed. Martin Schulz, access date 2024-04-19