Abstract
Carl Hempel (1965) argued that probabilistic hypotheses are limited in what they can explain. He contended that a hypothesis cannot explain why E is true if the hypothesis says that E has a probability less than 0.5. Wesley Salmon (1971, 1984, 1990, 1998) and Richard Jeffrey (1969) argued to the contrary, contending that P can explain why E is true even when P says that E’s probability is very low. This debate concerned noncontrastive explananda. Here, a view of contrastive causal explanation is described and defended. It provides a new limit on what probabilistic hypotheses can explain; the limitation is that P cannot explain why E is true rather than A if P assign E a probability that is less than or equal to the probability that P assigns to A. The view entails that a true deterministic theory and a true probabilistic theory that apply to the same explanandum partition are such that the deterministic theory explains all the true contrastive propositions constructable from that partition, whereas the probabilistic theory often fails to do so.
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Notes
There is a second contrastive thesis about explanation; it concerns the explanans, not the explanandum: Is the question of whether hypothesis H explains why E is true rather than A incomplete until H is contrasted with an alternative hypothesis? I’m inclined to think that the answer is no, but will not discuss this issue here.
Existence claims are exceptions; the question of why there are some tigers rather than none at all is well-posed (Sober 1986).
Lipton’s example is inspired by Scriven’s (1959) introduction of paresis and syphilis into philosophical discussion of explanation. Only a minority of people with tertiary syphilis develop paresis, but only those suffering from tertiary syphilis can develop paresis. Scriven does not discuss the contrastive task of explaining why E is true rather than A.
Whenever I use a probability function, the arguments of that function should be understood as elements of an algebra on some exhaustive set of possibilities, and all conditional probabilities are calculated via the ratio formula.
There are nontrivial probability distributions on which “PrB(E | X & (EvA)) ≠ PrB(E | (EvA))” and PrB(E | X & (EvAvF)) ≠ Pr(E | EvAvF)” have different truth values. My thanks to William Roche for finding examples on Mathematica.
Here I disagree with the claim made in Sober (1986, p. 144) that the disjunction EvA is “insertable” into an explanation of why is E true rather than A, where “insertable” is a term of permission, not obligation. I think there is no such blanket permission.
I bring this up even though Hitchcock does not reference Strawson and says that his ideas on presupposition are broadly consonant with those of Stalnaker (1973) and Lewis (1983). Hitchcock also says that his ideas about presupposition are neutral on the question of whether presupposition is a semantic or a pragmatic concept. Indeed he seems to like both approaches; he talks about what a question presupposes and also about what a person presupposes when he or she asks a question. However, the work that Hitchcock does with the concept of presupposition is resolutely centered on the semantics. His theory describes what a why-question presupposes, and he proposes a test for whether a given proposition answers a why-question.
This principle holds for nonStrawsonian accounts of presupposition, provided that they say that S presupposes P precisely when something “bad” happens to S if P is false. It is up to a theory of presupposition to say what that bad outcome is; one option is to say that “bad” means that S is false; another is to say that “bad” means that S is nonsensical.
Here I write “Prx(E)” rather than “Pr(E|X)” because the standard definition of conditional probability says that Pr(E|X) = Pr(E&X)/Pr(X) if Pr(X) > 0. I want to be able to talk about the probabilities that hypotheses confer on explanandum propositions without having to assign probabilities to the hypotheses themselves. The subscript notation is used by Royall (1997) for the same reason.
Strictly speaking, causation is a relationship between events (or facts), not between propositions, so my talk of causation as a relationship between propositions should be understood to indicate a causal relationship between the events (or facts) described by those propositions.
And since CON will soon be applied to a true deterministic theory and to a true probabilistic theory that address the same explanandum partition, I’m assuming that objective probabilities that are strictly between 0 and 1 are compatible with an underlying determinism. See Sober (2011, Section 5.3) for discussion.
Philosophers disagree about what a causal explanation is; for example, see Lewis (1986), Sober (1983, 2011), Skow (2014), Elgin and Sober (2015), Lange and Rosenberg (2011), and Lange (2017). Some of the insights from this literature may require CON to be fine-tuned. I hope those insights won’t upset the apple-cart that I am pushing here.
In order not to multiply notations beyond necessity, I will usually treat X, E, and A as propositions, but sometimes I’ll treat them as events or states of a variable. I could introduce lower-case, x, e, and a for events (or states) and reserve capital letters X, E, A for the proposition that this or that event (or state) has occurred (or is instantiated), but that seems to me to be unnecessary since context indicates which of these I am talking about.
A lot of current philosophical discussion of causation focuses on causal variables, and authors who think along those lines sometimes see no point in distinguishing events that causally promote from events that tend to causally prevent. It’s interesting that contrastive explanations force one to consider distinct states of a single effect variable; variable-talk is not enough.
These claims about the two coins, if true, show why X’s raising the probability of E and lowering the probability of A isn’t sufficient for X to explain why E is true rather than A. Suppose you toss a fair coin and it lands heads. Suppose, further, that if you hadn’t tossed a fair coin, you would have tossed a coin that is biased in favor of tails. This means that tossing the fair coin raised the probability of heads (and lowered the probability of tails), but the fact remains that your tossing the fair coin doesn’t explain why it landed heads rather than tails.
For those who are reluctant to include “additional” propositions in the explanandum partition to which probabilistic theory P assigns zero probability, I note that depriving the partition of those propositions further reduces the contrastive explanatory power of the probabilistic theory, and thus strengthens the main thesis of this paper.
A partition that theory T says is exclusive and exhaustive can be expanded ad infinitum by adding new members to which T assigns zero probability. In doing so, T seems to achieve a degree of contrastive explanatoriness that approaches infinity, and that may seem to be an objection to the argument advanced here. My reply is that I never defined a measure of the absolute explanatoriness a theory. My exclusive focus was on comparing the contrastive explanatoriness of two theories, relative to a shared finite partition.
Glymour (2015) criticizes these measures for the Bayesian framework they adopt.
If the literature on measuring degree of Bayesian confirmation is any guide, there are many other measures of contrastive explanatory power to consider as well.
References
Ay, N., & Polani, D. (2008). Information Flows In Causal Networks. Advances in Complex Systems (ACS), 11(01), 17–41.
Bromberger, S. (1966). Why-questions. In R. Colodny (Ed.), Mind and cosmos (pp. 86–108). Pittsburgh: University of Pittsburgh Press.
Cheng, P. (1997). From Covariation to causation - a causal power theory. Psychological Review, 104(2), 367–405.
Clatterbuck H. (forthcoming). “A Defense of Low Probability Scientific Explanations,” Philosophy of Science.
Crupi, V., & Tentori, K. (2012). A second look at the logic of explanatory power (with two novel representation theorems). Philosophy of Science, 79, 365–385.
Dretske, F. (1972). Contrastive statements. Philosophical Review, 81, 411–437.
Elgin, M., & Sober, E. (2015). Causal, A Priori true, and explanatory − a reply to Lange and Rosenberg. Australasian Journal of Philosophy, 93, 167–171.
Fitelson, B., & Hitchcock, C. (2011). Probabilistic measures of causal strength. In P. McKay-Illari, F. Russo, & J. Williamson (Eds.), Causality in the Sciences (pp. 600–628). Oxford.
Garfinkel, A. (1981). Forms of explanation − rethinking the questions of social theory. New Haven: Yale University Press.
Gerstenberg, T., Goodman, N., Lagnado, D., & Tenenbaum, J. (2015). “How, whether, why - causal judgments as counterfactual contrasts.” Proceedings of the 37th Annual Conference of the Cognitive Science Society, Austin, pp. 782–787.
Glymour, C. (2015). Probability and the explanatory virtues. The British Journal for the Philosophy of Science, 66, 591–604.
Hacking, I. (1965). The logic of statistical inference. Cambridge: Cambridge University Press.
Hempel, C. (1965). “Aspects of scientific explanation.” In Aspects of Scientific Explanation and Other Essays in Philosophy of Science. Basic Books.
Hitchcock, C. (1999). Contrastive explanation and the demons of determinism. British Journal for the Philosophy of Science, 50, 585–612.
Humphreys, P. (1989). The chances of explanation. Princeton: Princeton University Press.
Jackson, F., & Pettit, P. (1992). In defense of explanatory ecumenism. Economics and Philosophy, 8(1), 1–21.
Janzing, D., Balduzzi, D., Grosse-Wentrup, M., & Schölkopf, B. (2013). Quantifying causal influences. Annals of Statistics, 41(5), 2324–2358.
Jeffrey, R. (1969). Statistical Explanation vs. Statistical Inference. In N. Rescher (Ed.), Essays in Honor of Carl G. Hempel (pp. 104–113). Dordrecht: D. Reidel.
Korb, K., Nyberg, E., & Hope, L. (2011). A new causal power theory. In P. McKay-Illari, F. Russo, & J. Williamson (Eds.), Causality in the Sciences (pp. 628–653). Oxford.
Lange, M. (2017). Because without cause − non-causal explanations in science and mathematics. Oxford: Oxford University Press.
Lange, M., & Rosenberg, A. (2011). Can there be A Priori causal models of natural selection? Australasian Journal of Philosophy, 89(4), 591–599.
Lewis, D. (1983). Keeping score in a language game. In Philosophical papers − volume I (pp. 243–249). Oxford: Oxford University Press.
Lewis, D. (1986). Causal Explanation. In Philosophical papers − volume 2 (pp. 214–240). Oxford: Oxford University Press.
Lipton, P. (1993). Inference to the best explanation. London: Routledge.
Putnam, H. (1975). Philosophy and our mental life. In Mind, Language, and Realty. Cambridge University Press.
Railton, P. (1981). Probability, explanation, and information. Synthese, 48, 233–256.
Royall, R. (1997). Statistical evidence – A likelihood paradigm. Boca Raton: Chapman and Hall.
Salmon, W. (1971). Statistical explanation. In I. W. Salmon (Ed.), Statistical explanation and statistical relevance (pp. 29–87). Pittsburgh: University of Pittsburgh Press.
Salmon, W. (1984). Scientific explanation and the causal structure of the world. Princeton: Princeton University Press.
Salmon, W. (1990). Four decades of scientific explanation. Pittsburgh: University of Pittsburgh Press.
Salmon, W. (1998). Causality and explanation. Oxford: Oxford University Press.
Schupbach, J., & Sprenger, J. (2011). The logic of explanatory power. Philosophy of Science, 78(1), 105–127.
Scriven, M. (1959). Explanation and prediction in evolutionary theory. Science, 130, 477–482.
Skow, R. (2014). Are there non-causal explanations (of particular events)? British Journal for the Philosophy of Science, 65, 445–467.
Sober, E. (1983). Equilibrium Explanation. Philosophical Studies, 43, 201–210.
Sober, E. (1986). Explanatory presupposition. Australasian Journal of Philosophy, 64, 143–149.
Sober, E. (1999). The multiple Realizability argument against reductionism. Philosophy of Science, 66, 542–564.
Sober, E. (2011). Did Darwin write the origin backwards? Amherst, New York: Prometheus Books.
Sober, E. (2015). Ockham’s razors – A User’s manual. Cambridge: Cambridge University Press.
Sprenger, J. (2018). Foundations of a probabilistic theory of causal strength. Philosophical Review, 27(3), 371–398.
Stalnaker, R. (1973). Presuppositions. Journal of Philosophical Logic, 2, 447–457.
Strawson, P. (1952). Introduction to logical theory. London: Methuen.
Strevens, M. (2000). Do large probabilities explain better? Philosophy of Science, 67, 366–390.
Strevens, M. (2008). Depth − an account of scientific explanation. Cambridge: Harvard University Press.
Van Fraassen, B. (1980). The scientific image. Oxford: Oxford University Press.
Woodward, J. (2003). Making Things Happen. Oxford: Oxford University Press.
Ylikoski, P. (2001). Indeterminism and the Contrastive Theory of Explanation. In M. Kiikeri & P. Ylikoski (Eds.), Explanatory Connections – Electronic Essays Dedicated to Matti Sintonen url = http://www.helsinki.fi/tint/matti/.
Ylikoski, P., & Kuorikoski, J. (2010). Dissecting explanatory power. Philosophical Studies, 148, 201–219.
Acknowledgments
I thank Hayley Clatterbuck, Daniel Hausman, Christopher Hitchcock, Stephanie Hoffmann, John MacKay, William Roche, David Hillel Ruben, Alan Sidelle, Dennis Stampe, and anonymous referees for useful discussion. My first exposure to the idea of contrastive contexts came from Fred Dretske, right after I started teaching at University of Wisconsin−Madison in 1974. Fred was a great mentor, a true friend, and an inspiring philosopher. This paper is dedicated to him.
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Sober, E. A theory of contrastive causal explanation and its implications concerning the explanatoriness of deterministic and probabilistic hypotheses. Euro Jnl Phil Sci 10, 34 (2020). https://doi.org/10.1007/s13194-020-00299-5
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DOI: https://doi.org/10.1007/s13194-020-00299-5