Skip to main content
SpringerLink
Log in

Competing accounts of contrastive coherence

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

The proposition that Tweety is a bird coheres better with the proposition that Tweety has wings than with the proposition that Tweety cannot fly. This relationship of contrastive coherence is the focus of the present paper. Based on recent work in formal epistemology we consider various possibilities to model this relationship by means of probability theory. In a second step we consider different applications of these models. Among others, we offer a coherentist interpretation of the conjunction fallacy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. A different example is given by Bovens and Hartmann in their Tokyo murder case (cf. Bovens and Hartmann 2003, p. 39f.).

  2. An analysis of the coherence measures to be introduced in the next section shows disagreement with respect to this test case (proof omitted).

  3. In a recent anthology, Martin Blauw even speaks of a “contrastivist movement” in philosophy (Blauw 2013, p. 1).

  4. For a survey see Schippers (2014, 2015).

  5. Note that the case for the pair \(((\dagger _d),(\dagger _J))\) is so far unsettled.

  6. \((\dagger _l)\) satisfies (QD) provided that division by zero is equated with infinity. Alternatively, an ordinally equivalent measure put forward by Kemeny and Oppenheim (1952) can be used.

  7. This constraint is know as the law of likelihood (cf. Royal 1997; Fitelson 2007).

  8. Condition (D3) is similar to the Bovens–Olsson condition that is well-known in the literature on measuring coherence (cf. Bovens and Olsson 2000, p. 688). In contrast to (D3), the Bovens–Olsson condition considers one pair of propositions with respect to two different probability distributions where (D3) only pertains to cases where two different pairs of propositions are assessed with respect to one probability distribution. For an assessment of (a generalized form of) the Bovens–Olsson condition with respect to probabilistic measures of coherence see Schippers (2015). (D3) itself is discussed by Glass (2007) as a condition for ranking different explanations.

  9. There is a small caveat in this observation: so far the case of \((\dagger )_z\) is unsettled, i.e. I have neither been able to prove that it does satisfy (D3) nor have I been able to find a counterexample using Branden Fitelson’s PrSAT (see Fitelson 2008).

  10. Based on the close relationship between the concepts of coherence and explanation, Siebel even argues in these papers for the impossibility of probabilistically measuring coherence. Starting from the observation that the concept of explanation cannot be reduced to probability, Siebel concludes that “if probabilistic accounts cannot cope with explanation, they will hardly be able to deal with coherence because, as BonJour (1985) and many others have pointed out, coherence is a function of explanation.” For a rebuttal see Roche and Schippers (2013).

  11. Note that this inequality is the common core of various measures of explanatory power (Good 1960; McGrew 2003; Schupbach and Sprenger 2011; Crupi and Tentori 2012), that is, each of these measures \({\mathscr {E}}_{\Pr }(e,h)\) that quantify the degree of explanatory power that h provides for e (given \(\Pr \)) satisfies the following principle for any contingent \(e,h_1,h_2\) and any regular probability \(\Pr \) (cf. Crupi and Tentori 2012):

    $$\begin{aligned} {\mathscr {E}}_{\Pr }(e,h_1)\gtreqless {\mathscr {E}}_{\Pr }(e,h_2) \quad \text { iff}\quad \Pr (e|h_1)\gtreqless \Pr (e|h_2) \end{aligned}$$

  12. More precisely, this relationship holds for all probabilistic confirmation measures that satisfy the “weak law of likelihood” (cf. Joyce 2004; Fitelson 2007).

  13. Measures that satisfy \((\ddagger )\) are (among others) d, l, r, z, ku, Shogenji’s justification measure J and Kemeny and Oppenheim’s (1952) measure k.

  14. Another interpretation of the conjunction fallacy is given by Shogenji (2012). There, Shogenji shows that conditions (3) and (4) also imply that the conjunctive hypothesis \(b\wedge f\) is more justified by e than b, as measured by his justification measure J. Given that J also satisfies \((\ddagger )\), we also know that the degree justification-based coherence as measured by \({\mathscr {C}}_J\) is higher for the conjunctive hypothesis.

References

  • Blauw, M. (Ed.). (2013). Contrastivism in philosophy. New York: Routledge.

    Google Scholar 

  • BonJour, L. (1985). The structure of empirical knowledge. Cambridge: Harvard University Press.

    Google Scholar 

  • Bovens, L., & Hartmann, S. (2003). Bayesian epistemology. Oxford: Oxford University Press.

  • Bovens, L., & Olsson, E. J. (2000). Coherentism, reliability and Bayesian networks. Mind, 109, 685–719.

    Article  Google Scholar 

  • Brössel, P. (2013). The problem of measure sensitivity redux. Philosophy of Science, 80, 378–397.

    Article  Google Scholar 

  • Chandler, J. (2007). Solving the tacking problem with contrast classes. British Journal for the Philosophy of Science, 58, 489–502.

    Article  Google Scholar 

  • Chandler, J. (2013). Contrastive confirmation: Some competing accounts. Synthese, 190, 129–138.

    Article  Google Scholar 

  • Chart, D. (2001). Inference to the best explanation, Bayesianism, and feminist bank tellers. Online-paper. http://philsci-archice.pitt.edu/documents/disk0/00/00/03/22/.

  • Crupi, V., Festa, R., & Buttasi, C. (2010). Towards a grammar of Bayesian confirmation. In M. Surez, M. Dorato, & M. Rdei (Eds.), Epistemology and methodology of science (pp. 73–93). Berlin: Springer.

    Google Scholar 

  • Crupi, V., Fitelson, B., & Tentori, K. (2008). Probability, confirmation, and the conjunction fallacy. Thinking and Reasoning, 14, 182–199.

    Article  Google Scholar 

  • Crupi, V., & Tentori, K. (2012). A second look at the logic of explanatory power (with two new representation theorems). Philosophy of Science, 79, 365–385.

    Article  Google Scholar 

  • Crupi, V., Tentori, K., & Gonzalez, M. (2007). On Bayesian measures of evidential support: Theoretical and empirical issues. Philosophy of Science, 74, 229–252.

    Article  Google Scholar 

  • de Finetti, B. ([1937] 1980). Foresight: Its logical laws, its subjective sources. In H. E. Kyburg, Jr. & H. E. Smokler (Eds.), Studies in subjective probability (2nd ed., pp. 53–118). Huntington, NY: Robert E. Krieger.

  • Douven, I., & Meijs, W. (2007). Measuring coherence. Synthese, 156, 405–425.

    Article  Google Scholar 

  • Eells, E., & Fitelson, B. (2000). Measuring confirmation and evidence. Journal of Philosophy, 97, 663–672.

    Article  Google Scholar 

  • Fitelson, B. (1999). The plurality of Bayesian measures of confirmation and the problem of measure sensitivity. Philosophy of Science, 66, 362–378.

    Article  Google Scholar 

  • Fitelson, B. (2003). A probabilistic theory of coherence. Analysis, 63, 194–199.

    Google Scholar 

  • Fitelson, B. (2007). Likelihoodism, Bayesianism, and relational confirmation. Synthese, 156, 473–489.

    Article  Google Scholar 

  • Fitelson, B. (2008). A decision procedure for probability calculus with applications. The Review of Symbolic Logic, 1, 111–125.

    Article  Google Scholar 

  • Gigerenzer, G. (1994). Why the distinction between single-event probabilities and frequencies is important for psychology (and vice versa). In G. Wright & P. Ayton (Eds.), Subjective probability (pp. 129–161). New York: Wiley.

    Google Scholar 

  • Gigerenzer, G. (1996). On narrow norms and vague heuristics: A rebuttal to Kahneman and Tversky. Psychological Review, 103, 592–596.

    Article  Google Scholar 

  • Gigerenzer, G. (2001). Content-blind norms, no norms, or good norms? A reply to Vranas. Cognition, 81, 93–103.

    Article  Google Scholar 

  • Glass, D. H. (2002). Coherence, explanation, and Bayesian networks. In M. ONeill, et al. (Eds.), Artificial intelligence and cognitive science (pp. 177–182). Berlin: Springer.

  • Glass, D. H. (2007). Coherence measures and inference to the best explanation. Synthese, 157, 275–296.

    Article  Google Scholar 

  • Good, I. J. (1960). Weight of evidence, corroboration, explanatory power, information and the utility of experiments. Journal of the Royal Statistical Society (Series B), 22, 319–331.

    Google Scholar 

  • Grice, H. P. (1975). Logic and conversation. Studies in the way of words (pp. 22–40). Cambridge, MA: Harvard University Press.

  • Hertwig, R., & Chase, V. M. (1998). Many reasons or just one: How response mode affects reasoning in the conjunction problem. Thinking and Reasoning, 4, 319–352.

    Article  Google Scholar 

  • Hertwig, R., & Gigerenzer, G. (1999). The ‘conjunction fallacy’ revisited: How intelligent inferences look like reasoning errors. Journal of Behavioral Decision Making, 12, 275–305.

    Article  Google Scholar 

  • Hitchcock, C. R. (1996). The role of contrast in causal and explanatory claims. Synthese, 107, 395–419.

    Article  Google Scholar 

  • Hitchcock, C. D. (1999). Contrastive explanation and the demons of determinism. British Journal for the Philosophy of Science, 50, 585–612.

    Article  Google Scholar 

  • Joyce, J. (2004). Bayes’s theorem. In E. N. Zalta (Ed.). The Stanford encyclopedia of philosophy (Summer 2004 ed.). http://plato.stanford.edu/archives/sum2004/entries/bayes-theorem/.

  • Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases. Cambridge: Cambridge University Press.

    Google Scholar 

  • Kemeny, J., & Oppenheim, P. (1952). Degrees of factual support. Philosophy of Science, 19, 307–324.

    Article  Google Scholar 

  • Lipton, P. (1990). Contrastive explanation. In D. Knowles (Ed.), Explanation and its limits (pp. 247–266). Cambridge: Cambridge University Press.

    Google Scholar 

  • McGrew, T. (2003). Confirmation, heuristics, and explanatory reasoning. British Journal for the Philosophy of Science, 54, 553–567.

    Article  Google Scholar 

  • Mellers, A., Hertwig, R., & Kahneman, D. (2001). Do frequency representations eliminate conjunction effects? An exercise in adversarial collaboration. Psychological Science, 12, 269–275.

    Article  Google Scholar 

  • Olsson, E. J. (2002). What is the problem of coherence and truth? The Journal of Philosophy, 99, 246–272.

    Article  Google Scholar 

  • Ramsey, F. P. (1926). Truth and probability. In H. E. Kyburg Jr & H. E. Smokler (Eds.), Studies in subjective probability (2nd ed., pp. 23–52). Huntington, NY: R. E. Krieger. 1980.

  • Reichenbach, H. (1949). The theory of probability. Berkeley: University of California Press.

    Google Scholar 

  • Roche, W., & Schippers, M. (2013). Coherence, probability and explanation. Erkenntnis, 79, 821–828.

    Article  Google Scholar 

  • Royal, R. (1997). Statistical evidence: A likelihood paradigm. London: Chapman and Hall.

    Google Scholar 

  • Schippers, M. (2014). Probabilistic measures of coherence. From adequacy constraints towards pluralism. Synthese, 191, 3821–3845.

    Google Scholar 

  • Schippers, M. (2015). The grammar of Bayesian coherentism. Studia Logica, 103, 955–984.

    Article  Google Scholar 

  • Schupbach, J. N., & Sprenger, J. (2011). The logic of explanatory power. Philosophy of Science, 78, 105–127.

    Article  Google Scholar 

  • Shafir, E., Smith, E., & Osherson, D. (1990). Typicality and reasoning fallacies. Memory and Cognition, 18, 229–239.

    Article  Google Scholar 

  • Shogenji, T. (1999). Is coherence truth conducive? Analysis, 59, 338–345.

    Article  Google Scholar 

  • Shogenji, T. (2012). The degree of epistemic justification and the conjunction fallacy. Synthese, 184, 29–48.

  • Sides, A., Osherson, D., Bonini, N., & Viale, R. (2002). On the reality of the conjunction fallacy. Memory and Cognition, 30, 191–198.

    Article  Google Scholar 

  • Siebel, M. (2003). There’s something about Linda: Probability, coherence and rationality. Unpublished manuscript.

  • Siebel, M. (2005). Against probabilistic measures of coherence. Erkenntnis, 63, 335–360.

    Article  Google Scholar 

  • Siebel, M. (2011). Why explanation and thus coherence cannot be reduced to probability. Analysis, 71, 264–266.

    Article  Google Scholar 

  • Tentori, K., & Crupi, V. (2012). On the conjunction fallacy and the meaning of and yet again: A reply to Hertwig, Benz, and Krauss (2008). Cognition, 122, 123–134.

    Article  Google Scholar 

  • Tversky, A., & Kahneman, D. (1982). Judgments of and by representativeness. In D. Kahneman, P. Slovic, & A. Tversky (Eds.), Judgment under uncertainty: Heuristics and biases (pp. 84–98). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • von Mises, R. (1957). Probability, statistics and truth. New York: Macmillan.

    Google Scholar 

Download references

Acknowledgments

This work was supported by Grant SI 1731/1-1 to Mark Siebel from the Deutsche Forschungsgemeinschaft (DFG) as part of the priority program “New Frameworks of Rationality” (SPP 1516).

Author information

Authors and Affiliations

  1. University of Oldenburg, 26111, Oldenburg, Germany

    Michael Schippers

Authors
  1. Michael Schippers
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Schippers.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Schippers, M. Competing accounts of contrastive coherence. Synthese 193, 3383–3395 (2016). https://doi.org/10.1007/s11229-015-0937-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-015-0937-4

Keywords

Search

Navigation