This paper discusses the question of whether all counterfactuals with necessarily false antecedents (counterpossibles) are vacuously true. The orthodox view of counterpossibles (vacuism) answers that question in the affirmative. This paper explains vacuism before turning to examples from science that seem to require us to reason non-trivially using counterpossibles, and it seems that the counterpossibles used in such cases can be true or false. This is a threat to vacuism. It is then argued that the same kind of reasoning which produces non-trivial counterpossibles in scientific cases can be extended to the case of counterpossibles in mathematics. Ordinary counterfactual reasoning relies on rejecting background assumptions in order to assume the truth of the antecedent. A failure to perform this process in the counterpossible case is what leads one to vacuism and it is explained how this process produces non-vacuous; counterfactuals, scientific counterpossibles, and mathematical counterpossibles.
Baron, S., Colyvan, M., Ripley, D. (2017). How Mathematics Can Make a Difference. Philosophers’ Imprint, 17(3), 1–19.
Berto, F., French, R., Priest, G., Ripley, D. (2018). Williamson on Counterpossibles. Journal of Philosophical Logic, 47(4), 693–713.
Brogaard, B., Salerno, J. (2013). Remarks on Counterpossibles. Synthese, 190(4), 639–660.
Emery, N., Hill, C. H. (2017). Impossible Worlds and Metaphysical Explanation: Comments on Kment’s Modality and Explanatory Reasoning. Analysis, 77(1), 134–148.
Grice, H. P. (1975). Logic and Conversation. In P. Cole, J. Morgan (Eds.), Syntax and Semantics, Volume 3: Speech Acts (pp. 41–58). New York: Academic Press.
Jenny, M. (2018). Counterpossibles in Science: The Case of Relative Computability. Noȗs, 52(3), 530–560.
Lange, M. (2017). Because Without Cause. Oxford: OUP.
Leng, M. (2010). Mathematics and Reality. Oxford: OUP.
Lewis, D. (1973). Counterfactuals. Hoboken: Blackwell.
McLoone, B. (2020). Calculus and Counterpossibles in Science. Synthese, 198(12), 12153–12174.
Putnam H. (1969) Is Logic Empirical? In R. S. Cohen, M. W. Wartofsky (Eds.), Boston Studies in the Philosophy of Science (vol. 5, pp. 216–241). Springer: Dordrecht. doi:10.1007/978-94-010-3381-7_5
Reutlinger, A., Colyvan, M., Krzyżanowska, K. (2020). The Prospects for a Monist Theory of Non-Causal Explanation in Science and Mathematics. Erkenntnis. doi:10.1007/s10670-020-00273-w
Sendłak, M. (2021). Counterpossibles, Story Prefix and Trivialism. Synthese, 199, 7283–7301. doi:10.1007/s11229-021-03114-7
Stalnaker, R. C. (1968). A Theory of Conditionals. In W. Harper, R. Stalnaker, G. Pearce (Eds.), Ifs (pp. 41–55). Dordrecht: D. Reidel Publishing Company.
Tan, P. (2019). Counterpossible Non-Vacuity in Scientific Practice. Journal of Philosophy, 116(1), 32–60.
Williamson, T. (2007). The Philosophy of Philosophy. Oxford: Blackwell.
Williamson, T. (2018). Counterpossibles. Topoi, 37(3), 357–368.
Williamson, T. (2020). Suppose and Tell: The Semantics and Heuristics of Conditionals. Oxford: OUP.
Wilson, A. (2021). Counterpossible Reasoning in Physics. Philosophy of Science, 88(5). doi:10.1086/714706
Yagisawa, T. (2010). Worlds and Individuals, Possible and Otherwise. Oxford: OUP.
Yli-Vakkuri, J., Hawthorne, J. (2020). The Necessity of Mathematics. Noȗs, 54(3), 549–577.