|Universe, logic, philosophy: the universe contains all the objects to which a theory, a model or a discourse intends to refer. See also discourse universe, outer/ inner, self-reference, paradoxes, domains, range, totality, whole, levels, description levels._____________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. |
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.
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 a nd 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._____________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.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980