|Counterfactual conditional: the counterfactual conditional is equivalent to unreal conditional sentences. Conditionals, in which a fact is mentioned in the antecedent, which is not the case. If A were the case, B would have been the case. Counterfactual conditionals are needed because of the indeterminacy of pointing. One cannot unequivocally single out a certain element of a situation. The counterfactual conditional tells us which element would have had to be different in order for a process under examination to have a different outcome._____________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. |
Counterfactual Conditional/FieldVsCounterfactual Conditional: It is too vague for physical theories or geometric concepts. - DummettVsCounterfactual Conditionals: they cannot be "barely true". - They need (without counterfactual conditionals) ascertainable facts as truth makers.
Substantivalism/Field: can guarantee that situations where distances differ also differ in non-counterfactual aspects.
FieldVsRelationism: it cannot.
FieldVsCounterfactual Conditionals: no theory about counterfactually defined relations works if these relations cannot be defined non-counterfactually as well. - (This is why they cannot be "barely true").
Counterfactual conditionals cannot be derived from counterfactual statements about points in the plane. - Therefore, we must take them as the naked truth. - That would be no problem if you only needed a few of them.
Counterfactual Conditional/explanation/Lewis: nothing can counterfactually depend on the non-contigent. - E.g. counterfactually depend on which mathematical entities there are. - Nothing sensible can be said about which of our opinions would be different if the number 17 did not exist. - Since mathematics consists of necessary truths, there can be no explanation problem here.
FieldVsLewis: not all facts in mathematics are necessary - e.g. number of planets._____________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