|Consistency, philosophy, logic: within a system, consistency may be demonstrated, but not beyond the boundaries of this system, since the use of the symbols and the set of possible objects are only defined for this system.|
Within mathematics, and only there applies that the mathematical objects, which are mentioned in consistent formulas, exist (Hilbert, Über das Unendliche, 1926). See also falsification, verification, existence, well-formed.
_____________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.
Books on Amazon
Consistency / existence / Frege: from c. does not follow existence -_____________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.
Die Grundlagen der Arithmetik Stuttgart 1987
Funktion, Begriff, Bedeutung Göttingen 1994
Logische Untersuchungen Göttingen 1993