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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".
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.)
Geometric Possibility/Field: instead of logical possibility: there are different geometries. - Precondition: there are empirical axioms which differentiate the possibility from impossibility. - However, the existence quantifier must be within the range of the modal operator.
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.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980