Abstract
Conditional constructions – constructs of the form If A, then B – have for over a century been subject to intense study in a wide variety of philosophical areas, as well as outside of philosophy. One important reason is that such constructs allow one to encode connections and dependencies, be they causal, epistemic, conceptual, or metaphysical. This chapter briefly outlines some of the main formal models that have been employed to analyze such constructs, as well as their philosophical motivation.
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Notes
- 1.
The field is far too wide to enable an exhaustive survey in these few pages and so the present overview largely reflects the author’s own interests and prejudices. Many important issues are ignored or treated only in passing and countless important contributions will not be credited. References given reflect (but by no means exhaust) works of seminal importance, works that give a more thorough overview of the issues, as well as work that may point towards interesting new developments.
- 2.
Arló-Costa [3] presents a thorough overview of the logic of conditionals and how they relate to structural conditions.
- 3.
Reflexivity: v ≤u v. Transitivity: If v ≤u w and w ≤u z, then v ≤u z. Completeness: Either v ≤u w or w ≤u v.
- 4.
The limit assumption is not, strictly speaking, necessary, but if one omits this constraint the semantic clause becomes more complex.
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- 6.
- 7.
Some have argued that counterfactual conditionals can be given an epistemic interpretation, but this is a matter of considerable controversy.
- 8.
A probability measure is, as is standard, here taken to be a real-valued function P that take sentences as their arguments and satisfies (a) 0 ≤P(A) ≤ 1, (b) P(¬A) = 1 −P(A), and (c) P(A ∨ B) = P(A) + P(B) −P(A ∧ B).
- 9.
Conditionalisation only covers the case when P(A) > 0; to deal with the case when P(A) = 0 one can use Popper-measures or let P ∗ A be a non-standard measure that assigns probability 1 (or 0) to all sentences.
- 10.
* Indicates recommended reading.
References
* Indicates recommended reading.
Adams, E. W. (1975). The logic of conditionals. Dordrecht: Reidel.
Adams, E. W. (1998). A primer of probability logic. Stanford: CSLI.
*Arló-Costa, H. (2009). The logic of conditionals. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy (Spring 2009 ed.).
*Bennett, J. F. (2003). A philosophical guide to conditionals. Oxford: Oxford University press.
*Bradley, R. (2002). Indicative conditionals. Erkenntnis, 56, 345–378.
Bradley, R. (2007). A defence of the Ramsey test. Mind, 116(461), 1–21.
Cantwell, J. (2008). Indicative conditionals: Factual or epistemic? Studia Logica, 88, 157–194.
Cantwell, J., Lindström, S., & Rabinowicz W. (2017). McGee’s counterexample to the Ramsey test. Theoria, 83(2), 154–168.
*Edgington, D. (1995). On conditionals. Mind, 104, 235–329.
Evans, J., & Over, D. (2004). If. Oxford: Oxford University Press.
Gärdenfors, P. (1986). Belief revision and the Ramsey test for conditionals. Philosophical Review, 95, 81–93.
*Grice, H. P. (1989). Indicative conditionals. In Studies in the way of words (pp. 58–87). Cambridge, MA: Harvard University Press.
Jackson, F. (1979). On assertion and indicative conditionals. Philosophical Review, 88, 565–589.
Kratzer, A. (1977). What ‘must’ and ‘can’ must and can mean. Linguistics and Philosophy, 1(3), 337–356.
Kratzer, A. (1979). Conditional necessity and possibility. In R. Bäuerle, U. Egli & A. von Stechow (Eds.), Semantics from different points of view (pp. 117–147). Berlin: Springer.
*Kratzer, A. (2012). Modals and conditionals: New and revised perspectives. Oxford: Oxford University Press.
Leitgeb, H. (2012). A probabilistic semantics for counterfactuals. The Review of Symbolic Logic, 5, 26–84.
Levi, I. (1996). For the sake of the argument. Cambridge: Cambridge University Press.
*Lewis, D. (1973). Counterfactuals. Cambridge: Harvard University Press.
*Lewis, D. (1976). Probabilities of conditionals and conditional probabilities. Philosophical Review, 85, 297–315.
Lewis, D. (1979). Counterfactual dependence and Time’s arrow. Nous, 13, 455–476.
Lewis, D. (1986). Probabilities of conditionals and conditional probabilities II. Philosophical Review, 95, 581–589.
McDermott, M. (1996). On the truth conditions of certain ‘If’-sentences. Philosophical Review, 105, 1–37.
*McGee, V. (1989). Conditional probabilities and compounds of conditionals. Philosophical Review, 98, 485–542.
McGee, V. (2000). To tell the truth about conditionals. Analysis, 60, 107–111.
Morton, A. (2004). Against the Ramsey test. Analysis, 64(4), 294–299.
Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge: Cambridge University Press.
Ramsey, F. P. (1931). Foundations of mathematics and other essays. New York: Routledge and Kegan Paul.
Stalnaker, R. (1968). A theory of conditionals. In Studies in logical theory (No. 2 in American philosophical quarterly monograph series). Oxford: Blackwell.
Stalnaker, R. (1975). Indicative conditionals. Philosophia, 5, 269–286. Reprinted in Ifs, ed. W. L. Harper, R. Stalnaker & G. Pearce 1976 by Reidel.
Stalnaker, R. (1984). Inquiry. Cambridge, MA: The MIT press.
Strevens, M. (2003). Against Lewis’s new theory of causation: A story with three morals. Pacific Philosophical Quarterly, 84(4), 398–412.
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Cantwell, J. (2018). Conditionals. In: Hansson, S., Hendricks, V. (eds) Introduction to Formal Philosophy. Springer Undergraduate Texts in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-77434-3_6
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