Philosophy Lexicon of Arguments

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I 104
Universe/Classes/Sets/Model/"all"/Field: as the universe of all classes is too large to form a countable model, it is too big to form a class and therefore too large, to form any (over-countable) model.
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II 335
Universe/Standard-Platonism/Field: (thesis: "There's only one universe") - Problem: /PutnamVsPlatonism: How can we make it at all possible to pick out the "full" (universal) universe and to make it face a partial universe, and accordingly the standard-element-relation in contrast to a non-standard-element-relation? (Putnam 1980) - Putnam: Thesis: we cannot do that - i.e. that the "incomplete content" of the concepts "quantity" and "element of" is not sufficient to determine the truth value of all set theoretical theorems.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980


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Ed. Martin Schulz, access date 2017-05-24