|Counterfactual conditional: the counterfactual conditional is equivalent to unreal conditional sentences. Conditionals, in which a fact is mentioned in the antecedent, which is not expressly the case. If A were the case, B would have been the case.|
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Counterfactual Conditional/Co.Co./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: 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"). - These 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/Co.Co./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.
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