Philosophy Lexicon of Arguments

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Classes: identity of classes provided by same elements (extension) - identity of properties by the same predicates (intension).
 
Author Item Excerpt Meta data
Russell, Bertrand
 
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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
In
Eigennamen, U. Wolf (Hg), Frankfurt 1993

R VII
B. Russell
Wahrheit und Falschheit
In
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996


> Counter arguments against Russell
> Counter arguments in relation to Classes



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Ed. Martin Schulz, access date 2017-04-25