Lexicon of Arguments

 

I 86
Logically possible/possibility/diamond/KripkeVsField: "it is possible that" is not a logical truth.
FieldVsKripke: yes it is, this is only due to Kripke's model-theoretical definition. - It should not be read "mathematically" or "metaphysically possible".
>Logical truth, >Metaphysical possibility.
---
I 87
E.g. Carnap: "He is bachelor and married": is logically wrong.
>Meaning postulates.
FieldVsCarnap: Meaning relations between predicates should not count to logic. - Then the sentence is logically consistent.
Consistency operator/Field:
MEx (x is red & x is round)
should not only be true, but logically true. - ((s) Also without meaning postulates.)
((s) Meaning postulate/(s): here it is about the extent of the logic.)
---
I 203
Geometric Possibility/Field: instead of logical possibility: there are different geometries.
>Geometry.
Precondition: there are empirical axioms which differentiate the possibility from impossibility. However, the existential quantifier must be within the range of the modal operator.
>Existential quantification, >Modal operator, >Scope.
---
I 218
Problem of Quantities/mathematical entities/me/Field: For example, it is possible that the distance between x and y is twice as long as the one between x and w, even if the actual distance is more than twice as long.
Problem: extensional adequacy does not guarantee that the defined expression is true in every non-actual situation - that is, that we must either presuppose the substantivalism or the heavy duty Platonism. That is what we do in practice.
I 192
Heavy Duty Platonism/Field: assumes size relationships between objects and numbers.
>Substantivalism.