## Philosophy Lexicon of Arguments | |||

Classes: identity of classes provided by same elements (extension) - identity of properties by the same predicates (intension). | |||

Author | Item | Excerpt | Meta data |
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Russell, Bertrand Books on Amazon: Bertrand Russell |
Classes | I XIV Classes/concepts/Gödel: can, however, 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. I XVIII Set/Gödel: realistic: classes exist, circle fault no fault, not even if constructivistically construed. But Gödel non-constructivist - Russell: classes 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/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^ (j z) - - E.g. if j x is an equation, z^ (j z) will be the class of its roots - Example if j x means: "x has two legs and no feathers", z^ (j z) will be the class of the humans. I 120 Class/Principia Mathematica/Russell: incomplete symbol - 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^ (j z) = y ! z^" is not a value of "x = y" - because classes are incomplete symbols. III 117 Classes/sets/things/objects/Russell/Flor: sets must not be construed as things - otherwise, we would always have also 2^n 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 - ((s)> Quine: Class Abstraction). |
R I B. Russell/A.N. Whitehead Principia Mathematica Frankfurt 1986 R II B. Russell Das ABC der Relativitätstheorie Frankfurt 1989 R IV B. Russell Probleme der Philosophie Frankfurt 1967 R VI B. Russell Die Philosophie des logischen Atomismus InEigennamen, U. Wolf (Hg), Frankfurt 1993 R VII B. Russell Wahrheit und Falschheit InWahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996 |

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Ed. Martin Schulz, access date 2017-03-25