Abstract
In this paper, I consider the relationship between Inference to the Best Explanation (IBE) and Bayesianism, both of which are well-known accounts of the nature of scientific inference. In Sect. 2, I give a brief overview of Bayesianism and IBE. In Sect. 3, I argue that IBE in its most prominently defended forms is difficult to reconcile with Bayesianism because not all of the items that feature on popular lists of “explanatory virtues”—by means of which IBE ranks competing explanations—have confirmational import. Rather, some of the items that feature on these lists are “informational virtues”—properties that do not make a hypothesis \(\hbox {H}_{1}\) more probable than some competitor \(\hbox {H}_{2}\) given evidence E, but that, roughly-speaking, give that hypothesis greater informative content. In Sect. 4, I consider as a response to my argument a recent version of compatibilism which argues that IBE can provide further normative constraints on the objectively correct probability function. I argue that this response does not succeed, owing to the difficulty of defending with any generality such further normative constraints. Lastly, in Sect. 5, I propose that IBE should be regarded, not as a theory of scientific inference, but rather as a theory of when we ought to “accept” H, where the acceptability of H is fixed by the goals of science and concerns whether H is worthy of commitment as research program. In this way, IBE and Bayesianism, as I will show, can be made compatible, and thus the Bayesian and the proponent of IBE can be friends.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Traditionally, defenders of scientific realism who rely on the so-called “No-Miracles Argument” formulate their defense of realism as an IBE, e.g. Putnam (1975), Boyd (1983), Psillos (1999). Moreover, appeals to explanatory virtues such as simplicity are often made as a kind of tie-breaker in cases in which theory is under-determined by data. See, for instance, Kukla (1994) for a critical discussion of the appeal to “non-empirical” virtues as a possible solution to the under-determination problem.
Credences are tracked by and for some Bayesians conceptually identified with betting behavior. For instance, if the agent believes with certainty, i.e. with a credence of 1, that some proposition A is true, then she would be willing to purchase a bet that pays $1 if A is true at a price \(\le \$1\), if she has a credence of 1/2 that A is true, then she would be willing to purchase a bet that pays $1 if A is true at a price \(\le \$0.5\), etc., if she has a credence of 1/4, then she would be willing to purchase such a bet at a price \(\le \$0.25\), etc.
Formally, the agent’s personal credences can be represented as a function from a set of propositions S to the set of real numbers R, such that for each proposition \(\hbox {A} \in \hbox {S}\), A satisfies the three axioms of probability theory: (1) \(\hbox {Pr(A)} \ge 0\) (Non-Negativity), (2) If A is a tautology, then Pr(A) = 1 (Normality), and (3) If A is incompatible with some proposition \(\hbox {B} \in \hbox {S}\), then Pr(A v B) \(=\) Pr(A) + Pr(B) (Finite Additivity). Additionally the conditional probability of A given B, i.e. \(\hbox {Pr}(\hbox {A} {\vert } \hbox {B})\) satisfies, and for some Bayesians is defined by, the “Ratio Formula”: \( \textit{Pr}(A|B)=\frac{\textit{Pr}\left( {A \& B} \right) }{Pr\left( B \right) }\).
Subjective conditionalization assumes that when some piece of evidence E is learned, Pr(E) \(=\) 1. In cases in which the agent increases her credence in E to some value x, where \(\hbox {x} < 1\), then the agent may update by a more general rule, called “Jeffrey conditionalization”: \(\hbox {P}_{\mathrm{j}}(\hbox {H}) = \hbox {P}_{\mathrm{i}} (\hbox {H}{\vert } \hbox {E}) \hbox {P}_{\mathrm{j}} (\hbox {E}) + \hbox {P}_{\mathrm{i}} (\hbox {H} {\vert }\,{\sim }\hbox {E}) \hbox {P}_{\mathrm{j}}({\sim }\hbox {E})\). See Jeffrey (1983). Henceforth, I will neglect the issue of uncertain evidence and assume that whenever E is learned, Pr(E) \(=\) 1.
For a finite partition of hypotheses \(\hbox {H}_{1}, \hbox {H}_{2}, \ldots \hbox {H}_{\mathrm{n}}\), Bayes’ theorem can be generalized as: \(\hbox {Pr}\left( H_i |E\right) = \frac{\hbox {Pr} \left( {\hbox {H}_{\mathrm{i}}} \right) \hbox {Pr} (\hbox {E}|\hbox {H}_{\mathrm{i}})}{{\sum } \hbox { j Pr}\left( {\hbox {H}_{\mathrm{j}}} \right) \hbox {Pr}\left( \hbox {E}|\hbox {H}_{\mathrm{j}}\right) }\).
As an account of the nature of scientific inference, Bayesianism also includes some quantitative measure of how much E confirms H. There are many options on offer. One example which is not without its problems is the “Difference Measure” (Carnap 1962, pp. 21–22), according to which the degree to which E confirms H is given by \(\hbox {Pr} (\hbox {H} {\vert }\hbox {E}) - \hbox {Pr}(\hbox {H})\). A full account of scientific inference would include a quantitative measure as well, but we need not take any stand on this question here. See Fitelson (1999) for a discussion of the plurality of measures.
As Harman (1965, pp. 88–89) notes, something like IBE often goes by many names one of which is “abduction”, a term coined by C.S. Peirce. But despite some similarities between Peirce’s abduction and IBE, it has been argued that viewing abduction as the intellectual forbearer of IBE is not historically accurate, e.g. Minnameier (2004), Campos (2009). One key difference between Peirce’s abduction and IBE is that the former belongs to the context of discovery, while the latter belongs to the context of justification. For Peirce, it seems abduction is just the way one invents a new hypothesis, and so it is not warrant-conferring. For instance, Peirce (1934) writes: “[a]bduction is the process of forming explanatory hypotheses. It is the only logical operation which introduces any new idea” (CP 5.172).
See Salmon (1989) for an important critical survey of analyses of the concept of explanation in the twentieth century.
In a direct response, Lipton (2001, p. 100) resists this criticism, arguing that our grasp of the concept of an explanation is good enough, even in the absence of a widely agreed-upon philosophical account. It should be noted, Salmon (2001b, p. 122) concedes this point in a further response to Lipton.
That is to say, if the agent adopts IBE as a rule of updating, then there exists a series of bets, each of which the agent will individually sanction as fair, but which together logically guarantee a loss. See Roche and Sober (2013) who take themselves to be making a similar argument against IBE, although one that does not rely on pragmatic features.
Here, I will pass over those discussions of the relationship between IBE and Bayesianism that explicitly reject the key assumptions of Bayesianism, e.g. Betz (2013, p. 3555), along with those that propose or defend versions of IBE that are straightforwardly incompatible with Bayesianism, e.g. Douven and Wenmackers (2015), Douven and Schupbach (2015).
Hitchcock (2007) is an exception, rightly noting that a full reconciliation between Bayesianism and IBE “can only be achieved (if at all) in a piecemeal fashion, through the identification of factors that contribute to explanatory loveliness, and an exploration of the ways in which these factors might plausibly influence the probability assignments of a Bayesian agent” (p. 439). As I argue below, the prospects for fulfilling this project look grim.
Salmon also claims that some of Kuhn’s criteria are “economic” virtues—which concern how useful it is to employ the theory. While some of the virtues put forth by IBE-ists may be economic, I will not address this issue further.
For a more extensive and technical treatment of this idea, see Myrvold (2003) who also agrees that “the ability of a theory to unify phenomena consists in its ability to render what, on prior grounds, appear to be independent phenomena informationally relevant to each other” (p. 400). See Lange (2004) for a critique of this approach to explicating unification and Schupbach (2005) for a reply.
Of course, conceptually identifying explanatory power with likelihoods is problematic because it’s always the case that \(\hbox {Pr} (\hbox {E} {\vert } \hbox {E}) = 1 \ge \hbox {Pr}(\hbox {E})\). Just because some hypothesis entails the phenomena, it does not follow that the hypothesis explains the phenomena.
Sometimes “explanatory power” is used as a catch-all term to refer to how well a hypothesis does with respect to all the virtues (e.g. Thagard 1993; Psillos 1999; Mackonis 2013). But it is also common to use “explanatory power” to designate one virtue in particular (e.g. Okasha 2000; McGrew 2003; Glymour 2015).
Lipton (2004) seems aware of this (p. 116), but not that it is in tension with his view of IBE as theory of confirmation (p. 62), nor with his claim that his version of IBE can be reconciled with Bayesianism (pp. 103–120).
This is true only if we ignore the small corrections to the laws of Galileo and Kepler that Newton’s theory makes.
One case that Henderson (2014, pp. 703–711) focuses on is the preference for Copernicus’ theory over Ptolemy’s theory.
It should be noted that although Psillos (2007, p. 447) claims that IBE and Bayesianism are incompatible, he expresses sympathy toward a marriage between IBE and Objective Bayesianism. Lipton (2007, p. 458) too expresses sympathy with the Objective Bayesian approach, holding out hope that there is a “normatively privileged way of assigning priors and likelihoods” that will vindicate the explanatory virtues of IBE.
This is in contrast to other versions of compatibilism, endorsed by Okasha (2000), McGrew (2003), and Lipton (2004) which attempt to reconcile IBE from within the subjective Bayesian framework. This brand of compatibilism argues that explanatory factors can be used as a kind of heuristic approximation to Bayesian inference, at which we are by our nature psychologically deficient. In my view, the position that IBE simply provides a kind of heuristic aid, which we might use instead of performing a Bayesian inference directly, robs IBE of much of its philosophical interest. See Douven (2005), Weisberg (2009), and Henderson (2014) for extensive criticisms of this version of compatibilism.
It should be noted that Williamson (2010) defends a version of Objective Bayesianism, but rejects Bayesian conditionalization, relying instead on the principle of maximum entropy as an updating rule.
This second suggestion of Weisberg’s is similar to Jeffreys’ “Simplicity Postulate” (1931), according to which given a set of competing hypotheses, the simpler hypotheses ought to be assigned a higher prior probability. One way Jeffreys applies this idea is to interpret simplicity in terms of the degree of a polynomial equation relating two variables to each other (e.g. temperature and pressure) and to distribute priors in the following way: the simplest hypothesis \(\hbox {H}_{1}\) of some partition is to be assigned a prior of 1/2 , the next simplest \(\hbox {H}_{2}\) a prior of 1/4, \(\hbox {H}_{3}\) a prior of 1/8, and so on, where \(\hbox {H}_{\mathrm{n}}\) receives a prior of \((1/2)^{\mathrm{n}}\). Thus, for instance, the model that posits a linear relationship receives a prior probability of 1/2, that which posits a quadratic relationship a prior probability of 1/4, that which posits a cubic relationship a prior probability of 1/8, etc. See Sober (2015, pp. 87–93) for a critical discussion of the Simplicity Postulate.
While Poston may be right that there is no exhaustive analysis of simplicity that covers every plausible case, certain instances of simplicity can be given a deeper justification. See, for example, Forster and Sober (1994).
Interestingly, Salmon (1990), despite being a critic of IBE, offers this track-record defense of virtues such as simplicity and unification. According to Salmon (1990, p. 187), we can give the prior probabilities that feature in Bayes’ theorem an objective interpretation by understanding them “as our best estimates of the frequencies with which certain kinds of hypotheses succeed”.
One might object, as Lycan (2002) does, that the track-record defense is in principle impossible because to argue, for instance, that simplicity has a successful track-record assumes that we can verify which hypotheses are true independently of our appeals to simplicity. But this is false. It is not as though we have access to all the true hypotheses and from there we can check to see that a high proportion of them have the virtue of simplicity. On the contrary, we believe that our hypotheses are true on the basis of simplicity. To respond to this worry, one might argue that, while we can’t inspect all the true theories from the view from nowhere and then see what proportion are simple, we can in principle investigate those theories which have been predictively successful and resisted disconfirmation for a long time and see what proportion of those theories have been simple, unifying, precise, etc. If we have reason to believe that mature, predictively successful theories are true, and those theories are also simple, unifying, precise etc. then we would in principle be able to defend the track-record argument for the truth-conduciveness of the explanatory virtues.
Some philosophers accept this deflationary view of IBE. For example, Ben-Menahem (1990, p. 324) equates explanatory merit with high probability, and happily admits that this trivializes IBE. See also, Cartwright (1983, p. 6), who remarks: “no inference to best explanation; only inference to most likely cause.”
The views of Dawes (2013) and Nyrup (2015), both of whom sketch a deflated view of IBE, are similar to the one that I advocate below, although differing in the details. My approach, however, is unique in that I propose reconceiving the nature of IBE as a solution to the problem of sorting out IBE’s relationship to Bayesianism.
On Kaplan’s view, “You count as believing P just if, were your sole aim to assert the truth (as it pertains to P), and your only options were to assert that P, assert that \(\sim \)P, or make neither assertion, you would prefer to assert that P” (1996, p. 109). On this view, as Kaplan notes (1996, p. 111), it is possible to have very little confidence in P and still believe P.
One might wish to assert the stronger principle that it is rational to believe that P if and only if \( \hbox { Pr} (\hbox {P}) > 0.5\); however, while this principle seems prima facie plausible, the lottery paradox (Kyburg 1961) shows that imposing the threshold \(\hbox {Pr} (\hbox {P}) > 0.5\) (or any threshold aside from 1) as necessary and sufficient for its being rational to believe that P, and assuming some plausible rational constraints on binary beliefs, leads to objectionable results.
In accordance with E&W’s broad account of acceptance, one might accept for predictive purposes a theory that one knows to be false, one which, for example, contains obviously false idealizations. But if one of the goals of science is truth, then a theory without such idealizations is ultimately desirable.
Of course, van Fraassen thinks that we should never believe T is true if T makes claims about unobservables.
This increasingly popular terminological choice of using “acceptance” in a way that is severed from belief, which I admittedly perpetuate, is in some ways unfortunate. For instance, Laudan (1977, pp. 108–114) articulates a distinction similar to the one that I am urging here in the context of IBE, distinguishing between the “context of acceptance” and the “context of pursuit”, where by “acceptability”, he means, as in ordinary English, “worthy of belief” (p. 110). My use of “acceptance” most closely matches Laudan’s use of “pursuit” and its cognates. So, where Laudan would say, “scientists can have good reasons for working on theories they would not accept” (p. 110), I would say, “scientists can have good reasons for accepting theories they would not believe.” Similarly, where Laudan would say, “we cannot be accused of inconsistency or irrationality if we pursue (without accepting) some highly progressive research tradition” (p. 112), I would say, “we cannot be accused of inconsistency or irrationality if we accept (without believing) some theory with a high degree of explanatory content.” As I discuss below, I take Laudan’s concerns about fecundity seriously by including fecundity as one of the IBE-ist informational virtues. Unlike Laudan, however, I urge that for a theory to be acceptable (or worthy of pursuit for Laudan) it must have some degree of plausibility. Still, on my view, we are justified in committing to (or pursuing for Laudan) theories that we would be irrational to believe, a point that Laudan takes pains to emphasize.
At present one of the most well-known pairs of well-confirmed, though inconsistent theories, is the theory of general relativity and quantum mechanics. See the contributions in the edited volume of Callender and Huggett (2001) for contemporary approaches to reconciling general relativity and quantum mechanics.
It should be noted, valuing informative content is not an aesthetic idiosyncrasy on the part of scientists; rather, we assume, and with good reason, that whatever the truth is, that truth is a substantive truth.
This approach is similar to the epistemic utility theory of Levi (1967), according to which theory choice is a pragmatic, decision-theoretic problem mediated by the two distinct and competing goals of truth and informative content. Others who advocate a similar view, whereby truth and content combine to fix what it is that we ought to believe, include Hintikka and Pietarinen (1966), Maher (1993), and Huber (2007). One could locate IBE in this framework as well, but this involves radically re-thinking the connection between full belief and degrees of belief, as full belief would no longer be solely determined by degrees of belief, but would be partly determined by pragmatic factors.
I owe this objection to an anonymous reviewer.
References
Ben-Menahem, Y. (1990). The inference to the best explanation. Erkenntnis, 33(3), 319–344.
Betz, G. (2013). Justifying inference to the best explanation as a practical meta-syllogism on dialectical structures. Synthese, 190, 3553–3578.
Boyd, R. (1983). On the current status of scientific realism. Erkenntnis, 19(3), 45–90.
Bratman, M. (1999). Faces of intention. Cambridge: Cambridge University Press.
Brown, M. (2013). Values in science beyond underdetermination and inductive risk. Philosophy of Science, 80(5), 829–839.
Callender, C., & Huggett, N. (2001). Introduction. In C. Callender & N. Huggett (Eds.), Physics meets philosophy at the Planck scale: Contemporary theories in quantum gravity. Cambridge: Cambridge University Press.
Campos, D. (2009). On the distinction between Peirce’s abduction and Lipton’s inference to the best explanation. Synthese, 180(3), 419–442.
Carnap, R. (1962). Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.
Cartwright, N. (1983). How the laws of physics lie. Oxford: Oxford University Press.
Cohen, J. (1992). An essay on belief and acceptance. New York: Oxford University Press.
Darwin, C. (1962). On the origin of species. New York: Collier.
Dawes, G. (2013). Belief is not the issue: A defence of inference to the best explanation. Ratio, 26(1), 62–78.
Douglas, H. (2000). Inductive risk and values in science. Philosophy of Science, 67(4), 559–579.
Douglas, H. (2009). Science, policy, and the value-free ideal. Pittsburgh: University of Pittsburgh Press.
Douven, I. (2005). Wouldn’t it be lovely: Explanation and scientific realism. Metascience, 14, 338–343.
Douven, I., & Schupbach, J. (2015). Probabilistic alternatives to Bayesianism: The case of explanationism. Frontiers in Psychology, 6, 459. doi:10.3389/fpsyg.2015.00459.
Douven, I., & Wenmackers, S. (2015). Inference to the best explanation versus Bayes’s rule in a social setting. British Journal for the Philosophy of Science. doi:10.1093/bjps/axv025.
Elliott, K. (2011). Direct and indirect roles for values in science. Philosophy of Science, 78, 303–328.
Elliott, K. C., & McKaughan, D. J. (2014). Non-epistemic values and the multiple goals of science. Philosophy of Science, 81(1), 1–21.
Elliott, K. C., & Willmes, D. (2013). Cognitive attitudes and values in science. Philosophy of Science, 80(5), 807–817.
Fitelson, B. (1999). The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philosophy of Science, 66, S362–S378.
Forster, M., & Sober, E. (1994). How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions. British Journal for the Philosophy of Science, 45(1), 1–35.
Friedman, M. (1974). Explanation and scientific understanding. The Journal of Philosophy, 71(1), 5–19.
Glymour, C. (2015). Probability and the explanatory virtues. British Journal for the Philosophy of Science, 66(3), 591–604.
Goldman, A. (1986). Epistemology and cognition. Cambridge, MA: Harvard University Press.
Goodman, N. (1954). Fact, fiction, and forecast. Cambridge, MA: Harvard University Press.
Harman, G. (1965). The inference to the best explanation. Philosophical Review, 74, 88–95.
Hempel, C., & Oppenheim, P. (1948). Studies in the logic of explanation. Philosophy of Science, 15, 135–175.
Henderson, L. (2014). Bayesianism and inference to the best explanation. British Journal for the Philosophy of Science, 65(4), 687–715.
Hintikka, J., & Pietarinen, J. (1966). Semantic information and inductive logic. In J. Hintikka & P. Suppes (Eds.), Aspects of inductive logic (pp. 96–112). Amsterdam: North-Holland.
Hitchcock, C. (2007). The lovely and the probable. Philosophy and Phenomenological Research, 74(2), 433–440.
Huber, F. (2007). Hempel’s logic of confirmation. Philosophical Studies, 139(2), 181–189.
Huemer, M. (2009). Explanationist aid for the theory of inductive logic. British Journal for the Philosophy of Science, 60, 345–375.
Janssen, M. (2002). COI stories: Explanation and evidence from Copernicus to Hockney. Perspectives on Science, 10, 457–522.
Jeffrey, R. (1983). The logic of decision (2nd ed.). Chicago: University of Chicago Press.
Jeffreys, H. (1931). Scientific inference. London: Macmillan.
Kaplan, M. (1996). Decision theory as philosophy. Cambridge: Cambridge University Press.
Kelvin, L. (1862). Physical considerations regarding the possible age of the Sun’s heat. Philosophical Magazine and Journal of Science, 23(4), 158–160.
Kitcher, P. (1989). Explanatory unification and the causal structure of the world. In P. Kitcher & W. Salmon (Eds.), Scientific explanation (Vol. 13, pp. 410–505)., Minnesota Studiesin the Philosophy of Science Minneapolis: University of Minnesota Press.
Kourany, J. A. (2003). A philosophy of science for the twenty-first century. Philosophy of Science, 70(1), 1–14.
Kuhn, T. (1962). The structure of scientific revolutions (1st ed.). Chicago: University of Chicago Press (2nd ed. 1970).
Kuhn, T. (1977). The essential tension (pp. 320–339). Chicago: University of Chicago Press.
Kukla, A. (1994). Non-empirical theoretical virtues and the argument from underdetermination. Erkenntnis, 41(2), 157–170.
Kyburg, H. (1961). Probability and the logic of rational belief. Middletown: Wesleyan University Press.
Lacey, H. (1999). Is science value-free? Values and scientific understanding. London: Routledge.
Lange, M. (2004). Bayesianism and unification: A reply to Wayne Myrvold. Philosophy of Science, 71(2), 205–215.
Laudan, L. (1977). Progress and its problems: Toward a theory of scientific growth. Berkeley, CA: University of California Press.
Levi, I. (1960). Must the scientist make value judgments? Journal of Philosophy, 57, 345–357.
Levi, I. (1967). Gambling with truth: An essay on induction and the aims of science. Cambridge, MA: MIT Press.
Lewis, D. (1973). Counterfactuals. Cambridge, MA: Harvard University Press.
Lewis, D. (1981). A subjectivist’s guide to objective chance. The University of Western Ontario Series in Philosophy of Science, 15, 267–297.
Lipton, P. (2001). Is explanation a guide to inference? A reply to Wesley C. Salmon. In G. Hon & S. S. Rakover (Eds.), Explanation: Theoretical approaches and applications (pp. 93–120). Dordrecht: Kluwer.
Lipton, P. (2004). Inference to the best explanation (2nd ed.). New York: Routledge.
Lipton, P. (2007). Replies. Philosophy and Phenomenological Research, 74(2), 433–440.
Longino, H. (1996). Cognitive and non-cognitive values in science: Rethinking the dichotomy. In L. H. Nelson & J. Nelson (Eds.), Feminism, science, and the philosophy of science (pp. 39–58). Dordrecht: Kluwer.
Lycan, W. G. (1988). Judgement and justification. Cambridge: Cambridge University Press.
Lycan, W. G. (2002). Explanation and epistemology. In P. Moser (Ed.), Oxford handbook of epistemology (pp. 408–433). Oxford: Oxford University Press.
Machamer, P., Darden, L., & Craver, C. (2000). Thinking about mechanisms. Philosophy of Science, 67, 1–25.
Mackonis, A. (2013). Inference to the best explanation, coherence and other explanatory virtues. Synthese, 190(6), 975–995.
Maher, P. (1993). Betting on theories. Cambridge: Cambridge University Press.
McGrew, T. (2003). Confirmation, heuristics, and explanatory reasoning. British Journal for the Philosophy of Science, 54(4), 553–567.
McMullin, E. (1983). Values in science. In P. Asquith & T. Nickles (Eds.), Proceedings of the 1982 biennial meeting of the philosophy of science association (Vol. 2, pp. 3–28). East Lansing: Philosophy of Science Association.
Minnameier, G. (2004). Peirce-suit of truth: Why inference to the best explanation and abduction ought not to be confused. Erkenntnis, 60(1), 75–105.
Myrvold, W. (2003). A Bayesian account of the virtue of unification. Philosophy of Science, 70, 399–423.
Myrvold, W. (2015). On the evidential import of unification. Unpublished MS. http://philsci-archive.pitt.edu/11670/.
Nyrup, R. (2015). How explanatory reasoning justifies pursuit: A Peircean view of IBE. Philosophy of Science, 82(5), 749–760.
Okasha, S. (2000). Van Fraassen’s critique of inference to the best explanation. Studies in the History and Philosophy of Science, 31, 691–710.
Peirce, C. S. (1934). The collected papers of Charles Sanders Peirce. Cambridge, MA: Harvard University Press.
Popper, K. (1980). The logic of scientific discovery. London: Routledge.
Poston, T. (2014). Reason & explanation: A defense of explanatory coherentism. New York: Palgrave-MacMillan.
Psillos, S. (1999). Scientific realism: How science tracks the truth. London: Routledge.
Psillos, S. (2002). Simply the best: A case for abduction. In A. C. Kakas & F. Sadri (Eds.), Computational logic: Logic programming and beyond (pp. 605–626). Berlin: Springer.
Psillos, S. (2004). Inference to the best explanation and Bayesianism. In F. Stadler (Ed.), Induction and deduction in the sciences (pp. 83–91). Dordrecht: Kluwer.
Psillos, S. (2007). The fine structure of inference to the best explanation. Philosophy and Phenomenological Research, 74(2), 441–448.
Putnam, H. (1975). What is mathematical truth? In H. Putnam (Ed.), Mathematics, matter and method: Philosophical papers (pp. 60–78). Cambridge: Cambridge University Press.
Quine, W. V. O., & Ullian, J. (1978). The web of belief. New York: Random House.
Roche, W., & Sober, E. (2013). Explanatoriness is evidentially irrelevant, or inference to the best explanation meets Bayesian confirmation theory. Analysis, 73, 659–668.
Rooney, P. (1992). On values in science: Is the epistemic/non-epistemic distinction useful? In D. Hull, M. Forbes, & K. Okruhlik (Eds.), Proceedings of the 1992 biennial meeting of the philosophy of science association (pp. 3–28). East Lansing, MI: Philosophy of Science Association.
Rudner, R. (1953). The scientist qua scientist makes value judgments. Philosophy of Science, 20(1), 1–6.
Salmon, W. (1971). Statistical explanation. In 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. (1989). Four decades of scientific explanation. Minneapolis: University of Minnesota Press.
Salmon, W. (1990). Rationality and objectivity in science or Tom Kuhn meets Tom Bayes. In C. Wade Savage (Ed.), Scientific theories (pp. 175–204). Minneapolis: University of Minnesota Press.
Salmon, W. (2001a). Explanation and confirmation: A Bayesian critique of inference to the best explanation. In G. Hon & S. S. Rakover (Eds.), Explanation: Theoretical approaches and applications (pp. 61–91). Dordrecht: Kluwer.
Salmon, W. (2001b). Reflections of a bashful Bayesian: A reply to Peter Lipton. In G. Hon & S. S. Rakover (Eds.), Explanation: Theoretical approaches and applications (pp. 121–136). Dordrecht: Kluwer.
Schupbach, J. (2005). On a Bayesian analysis of the virtue of unification. Philosophy of Science, 72(4), 594–607.
Sider, T. (2013). Against parthood. In K. Bennett & D. Zimmerman (Eds.), Oxford studies in metaphysics (Vol. 8, pp. 237–293). Oxford: Oxford University Press.
Sober, E. (1990). Explanation in biology: Let’s Razor Ockham’s Razor. Royal Institute of Philosophy Supplement, 27, 73–93.
Sober, E. (2001). Venetian sea levels, British bread prices, and the principle of the common cause. British Journal for the Philosophy of Science, 52(2), 331–346.
Sober, E. (2002). Bayesianism–its scope and limits. In R. Swinburne (Ed.), Bayes’ theorem, Proceedings of the British Academy Press (Vol. 113, pp. 21–38). Oxford: Oxford University Press.
Sober, E. (2015). Ockham’s Razors: A user’s manual. Cambridge: Cambridge University Press.
Thagard, P. (1978). The best explanation: Criteria for theory choice. The Journal of Philosophy, 75(2), 76–92.
Thagard, P. (1993). Computational philosophy of science. Cambridge, MA: MIT Press.
van Fraassen, B. C. (1980). The scientific image. Oxford: Oxford University Press.
van Fraassen, B. C. (1989). Laws and symmetry. Oxford: Oxford University Press.
Weisberg, J. (2009). Locating IBE in the Bayesian framework. Synthese, 167, 125–143.
Whewell, W. (1968). In R. Butts (Ed.), William Whewell’s theory of scientific method. Pittsburgh, PA: University of Pittsburgh Press.
White, R. (2005). Explanation as a guide to induction. Philosophers’ Imprint, 5(2), 1–29.
Williamson, J. (2010). In defence of objective Bayesianism. Oxford: Oxford University Press.
Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford: Oxford University Press.
Acknowledgments
I am grateful to Elliott Sober as well as the anonymous reviewers at Synthese for many helpful comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cabrera, F. Can there be a Bayesian explanationism? On the prospects of a productive partnership. Synthese 194, 1245–1272 (2017). https://doi.org/10.1007/s11229-015-0990-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-015-0990-z