Lexicon of Arguments

 

I 96
Def Strong Consistency/strong consistent/Field: a mathematical theory M is strong consistent, if it causes that the conjunction with a consistent non-mathematical theory T is still consistent. - T + M = consistent.
Punch line: although strong consistency does not follow from truth, it follows from necessary truth. - However strong consistency is weaker than necessary truth because strongly consistent theories need not be true.
Purely mathematical theories (without mathematical entities): for them consistency involves strong consistency.
>Mathematical entities.
Non-pure: E.g. set theory with basic elements.
Urelement: Element of the lowest level, e.g. real numbers.
I 240
Consistency/consistent/Mathematics/FieldVs: consistency is untenable as a condition for the quality of mathematics: a consistent mathematical theory can be largely inadequate. - Consistent (without contradiction) here means semantically consistent, i.e. satisfiable.
>Satisfaction, >Satisfiability.