Conclusion
It has been argued that the attempt to meet indispensability arguments for realism in mathematics, by appeal to counterfactual statements, presupposes a view of mathematical modality according to which even though mathematical entities do not exist, they might have existed. But I have sought to defend this controversial view of mathematical modality from various objections derived from the fact that the existence or nonexistence of mathematical objects makes no difference to the arrangement of concrete objects. This defense of the controversial view of mathematical modality obviously falls far short of a full endorsement of the counterfactual approach, but I hope my remarks may serve to help keep such an approach a live option.
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References
Benacerraf, Paul, 1973, ‘Mathematical truth’,Journal of Philosophy, 19, 661–679.
Creath, Richard, 1980a. ‘Nominalism by Theft’,American Philosophical Quarterly, 17, 311–318.
Creath, Richard, 1980b, ‘Benacerraf and mathematical truth’,Philosophical Studies, 37, 335–340.
Field, Hartry, 1974, ‘Quine and the correspondence theory’,Philosophical Review, 83, 200–228.
Field, Hartry, 1980,Science without Numbers: A Defense of Nominalism, Princeton: Princeton University Press.
Field, Hartry, 1984, ‘Is mathematical knowledge just logical knowledge?’, in Field 1989.
Field, Hartry, 1988, ‘Realism, Mathematics and Modality’, in Field 1989.
Field, Hartry, 1989,Realism, Mathematics and Modality, Oxford: Basil Blackwell.
Goodman, Nelson, 1979,Fact, Fiction and Forecast, Indianapolis: Hacket Publishing Co.
Hale, Bob, 1987,Abstract Objects, Oxford: Blackwell.
Hellman, Geoffrey. 1989,Mathematics without Numbers: Towards a Modal-Structural Interpretation, Oxford: Clarendon Press.
Horgan, Terence, 1984, ‘Science nominalized’,Philosophy of Science, 51, 529–549.
Horgan, Terence, 1987, ‘Science Nominalized Properly’,Philosophy of Science, 54, 281–283.
Kitcher, Philip, 1980, ‘Arithmetic for the Millian’,Philosophical Studies, 37, 215–236.
Lear, Jonathan, 1977, ‘Sets and Semantics’,Journal of Philosophy, 74, 86–102.
Lewis, David, 1973,Counterfactuals, Cambridge, Mass.: Harvard University Press.
Lewis, David, 1986,On the Plurality of Worlds, Oxford: Basil Blackwell.
Reichenbach, Hans, 1958,The Philosophy of Space and Time, New York: Dover.
Resnik, Michael, and Hale, Susan, 1987, ‘Science Nominalized?’,Philosophy of Science, 54, 277–280.
Suppes, Patrick, 1972, ‘Finite equal-interval measurement structures’,Theoria, 38, 44–63.
Tichy, Pavel, 1984, ‘Subjunctive Conditionals: two parameters vs. three’,Philosophical Studies, 45, 147–179.
White, N. P., 1974, ‘What numbers are’,Synthese, 27, 111–124.
Wright, Crispin, 1988, ‘Why numbers can believably be: a reply to Hartry Field’,Revue Internationale de Philosophie, 42, 425–473.
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Cornwell, S. Counterfactuals and the applications of mathematics. Philos Stud 66, 73–87 (1992). https://doi.org/10.1007/BF00668396
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DOI: https://doi.org/10.1007/BF00668396