|Axiom: principle or rule for linking elements of a theory that is not proven within the theory. It is assumed that axioms are true and evident. Adding or eliminating axioms turns a system into another system. Accordingly, more or less statements can be constructed or derived in the new system. See also axiom systems, systems, strength of theories, proofs, provability._____________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. |
|Thiel I 341
Axioms/Zermelo/Thiel: Zermelo himself has emphasized that the question of the origin and validity domain of his set theoretical axioms remains philosophically excluded.
It will be at most possible to say that logicism has survived in the axiomatic set theory insofar as cardinal numbers are defined there as definite sets and a cardinal number arithmetic is created with them._____________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. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Philosophie und Mathematik Darmstadt 1995