|Possibility, philosophy: something is possible if it cannot be excluded. This has to be distinguished from the concept of contingency that expresses that something could have been different._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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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._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
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