Lexicon of Arguments

 

I 220
Axiom/Field: a required law can easily be proven by adding it as an axiom - Vs: but then you need for each pair of distinct predicates an axiom that says that the first one and the second does not, e.g. "The distance between x and y is r times that between z and w".
Everything that substantivalism or heavy-duty Platonism may introduce as derived theorems, relationism must introduce as axioms ("no empty space").
>Substantivalism
>Relationism
That leads to no correct theory.
Problem of quantities.
The axioms used would precisely be connectable if also non-moderate characterizations are possible. The modal circumstances are adequate precisely then when they are not needed.
I 249ff
Axiom/Mathematics/Necessity/Field: axioms are not logically necessary, otherwise we would only need logic and no mathematics.
I 275
Axioms/Field: we then only accept those that have disquotationally true modal translations. - Because of conservativism.
>Conservativity.
Conservatism: is a holistic property, not property of the individual axioms.
Acceptability: of the axioms: depends on the context.
Another theory (with the same Axiom) might not be conservative.
Disquotational truth: can be better explained for individual axioms, though.
>Disquotationalism.
I 276
E.g. Set theory plus continuum hypothesis and set theory without continuum hypothesis can each be true for their representatives. - They can attribute different truth conditions. - This is only non-objective for Platonism.
>Platonism.
The two representatives can reinterpret the opposing view, so that it follows from their own view.
>Kurt Gödel, relative consistency.
- - -
II 142
Axiom/(s): not part of the object language.
Scheme formula: can be part of the object language.
Field: The scheme formula captures the notion of truth better.
>Truth/Field.