Lexicon of Arguments

 

Thiel I 73
Theory/Mathematics/Thiel: The term "meta mathematics" had already appeared in a different meaning in the 19th century, reformulated by Hilbert.
Hilbert had proved that in Euclid not all of the properties used in the geometric propositions are really developed from the basic properties recorded in the axioms. So it was incomplete.
>Axioms, >Axioms/Hilbert.
After Cantor's work at the end of the 19th century, it looked as if one could actually find a complete axiom system. Admittedly, no meta mathematics would have been necessary for this.
>Completeness, >Incompleteness.
I 75
Meta mathematics makes a difference between the proof that a statement A cannot be refuted (the proof that its opposite is not justifiable) and a "positive" justification of A. The first is a rebuttal of ~A thus a proof of ~~A, the second a proof of A.
I 76
New: in meta mathematics the existential statements are interpreted more strictly. Anyone who now claims the existence of evidence must also indicate a verifiable way of constructing such evidence. Def "effective" or "constructive" assertion of existence.
>Proofs, >Provability, >Syntax.