|Modalities: modalities are in modal logic possibility, necessity and contingency._____________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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Modality/Field: many people believe there can be a simple exchange between modality and ontology: one simply avoids an enrichment of the ontology by modal statements.
Modalization/Mathematics/Physics/Field: "Possible Mathematics":
1. Does not allow to preserve platonic physics
2. Advantage: This avoids the indispensability argument
3. False: "It is possible that mathematics is true" - but correct: Conservativity of modality. ((s) Mathematics does not change the content of physical statements).
4. For Platonic physics one still needs to use unmodalized mathematics.
5. Field: but we can formulate physics based neither on mathematics nor on modality : (See above) comparative predicates instead of numeric functors. - (257 +)
Modal translation/mathematics/Putnam/Field: the idea is that in the modal translation acceptable sentences become true modal statements and unacceptable sentences false modal statements.
Field: then there are two ways of looking at the translations: 1. as true equivalences: then the modal translation shows the truth of the Platonic theorems. (Truth preservation).
Or 2nd we can regard the modal translation as true truths: then the Platonic propositions are literally false. ((S) symmetry/asymmetry).
N.B.: it does not make any difference which view is accepted. They only differ verbally in the use of the word "true".
Truth/mathematical entities/mE/Field: if a modal translation is to be true, "true" must be considered non-disquotational in order to avoid mathematical entities. - True: can then only mean: it turns out to be disquotational true in the modal translation, otherwise the existence of mathematical entities would be implied. - ((s) "Non-disquotational": = "turns out as disquotational.") (No circle)._____________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