Philosophy Lexicon of Arguments

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Subsets, set theory: subsets are not to be confused with elements of sets which are not themselves sets. Individual sets can be formed from individual elements if additional assumptions are introduced. On the other hand, subsets may consist of 0 or more elements. Subsets are in each case related to a set whose subset they are. The cardinality of a set results from the counting of its elements and not from the counting of its subsets, since these can overlap. The set of all subsets of a set is called a power set. The empty set {0} is a subset of each set, but not an element of it. See also set theory, sets, power set, element relation.

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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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Books on Amazon
I 53
Two-Classes-Theory/GeachVs: is even worse than the Two-Names-Theory: the assumption that the general term "philosopher" denotes the "class of philosophers". - Socrates would then only be a part of the class. Vs: the element-relation is quite different from the subclass-relation: E.g. a parliamentary committee is not a member of Parliament. - But: "Is a philosopher" means exactly the same in both applications. - copula: fallacy of separation: as if there were two varieties of "is": one for "is a philosopher" and one for "is an element of the class of philosophers" - Geach: equivalent sentences must not be divided into equivalent partial sentences. - "Every logician" is not equivalent to "class of logicians".


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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.

Gea I
P.T. Geach
Logic Matters Oxford 1972


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Ed. Martin Schulz, access date 2017-10-21