# Probabilistic coherence measures: a psychological study of coherence assessment

- 263 Downloads
- 1 Citations

## Abstract

Over the years several non-equivalent probabilistic measures of coherence have been discussed in the philosophical literature. In this paper we examine these measures with respect to their empirical adequacy. Using test cases from the coherence literature as vignettes for psychological experiments we investigate whether the measures can predict the subjective coherence assessments of the participants. It turns out that the participants’ coherence assessments are best described by Roche’s (Insights from philosophy, jurisprudence and artificial intelligence, 2013) coherence measure based on Douven and Meijs’ (Synthese 156:405–425, 2007) average mutual support approach and the conditional probability.

## Keywords

Bayesian coherentism Probabilistic coherence measures Probabilistic support measures Test cases Experimental philosophy## Notes

### Acknowledgments

We would like to thank (in alphabetical order) Arndt Bröder, Andreas Glöckner, Björn Meder, Michael Schippers and Mark Siebel for their contributions. We would also like to thank the participants of the Operationalization Workshop 2013 in Freiburg for helpful comments. This work was supported by grant SI 1731/1-1 to Mark Siebel and grant GL 632/3-1 and BR 2130/8-1 to Andreas Glöckner and Arndt Bröder from the Deutsche Forschungsgemeinschaft (DFG) as part of the priority program “New Frameworks of Rationality” (SPP 1516).

## References

- Akiba, K. (2000). Shogenji’s probabilistic measure of coherence is incoherent.
*Analysis*,*60*, 356–359.CrossRefGoogle 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.Google Scholar - Carnap, R. (1950).
*Logical foundations of probability*. Chicago: University of Chicago Press.Google Scholar - Cheng, P. W. (1997). From covariation to causation: A causal power theory.
*Psychological Review*,*104*, 367–405.CrossRefGoogle Scholar - Cialdini, R. B., Trost, M. R., & Newsom, J. T. (1995). Preference for consistency: The development of a valid measure and the discovery of surprising behavioral implications.
*Journal of Personality and Social Psychology*,*69*, 318–328.CrossRefGoogle Scholar - Crupi, V., Tentori, K., & Gonzales, M. (2007). On Bayesian measures of evidential support: Theoretical and empirical issues.
*Philosophy of Science*,*74*, 229–252.CrossRefGoogle Scholar - Festa, R. (2012). For unto every one that hath shall be given. Matthew properties for incremental confirmation.
*Synthese*,*184*, 89–100.CrossRefGoogle Scholar - Finch, H. A. (1960). Confirming power of observations metricized for decisions among hypotheses.
*Philosophy of Science*,*27*, 293–307.CrossRefGoogle Scholar - Fitelson, B. (2004). Two technical corrections to my coherence measure. http://fitelson.org/coherence2.
- Fitelson, B. (2003). A probabilistic theory of coherence.
*Analysis*,*63*, 194–199.CrossRefGoogle Scholar - Frederick, S. (2005). Cognitive reflection and decision making.
*Journal of Economic Perspectives*,*19*, 25–42.CrossRefGoogle Scholar - Gaifman, H. (1979). Subjective probability, natural predicates and Hempel’s ravens.
*Erkenntnis*,*21*, 105–147.Google Scholar - Glass, D. H. (2002). Coherence, explanation, and Bayesian networks. In O’Neill, M., Sutcliffe, R. F. E., Ryan, C., Eaton, M., & Griffith, N. J. L. (Eds.),
*Artificial intelligence and cognitive science. 13th Irish conference, AICS 2002, Limerick, Ireland, September 2002*(pp. 177–182). Berlin: Springer.Google Scholar - Glass, D. H. (2005). Problems with priors in probabilistic measures of coherence.
*Erkenntnis*,*63*, 375–385.CrossRefGoogle Scholar - Good, I. J. (1984). The best explicatum for weight of evidence.
*Journal of Statistical Computation and Simulation*,*19*, 294–299.CrossRefGoogle Scholar - Greiner, B. (2004). An online recruitment system for economic experiments. In K. Kremer & V. Macho (Eds.),
*Forschung und wissenschaftliches Rechnen 2003, GWDG Bericht 63*(pp. 79–93). Goettingen: Ges. fuer Wiss. Datenverarbeitung.Google Scholar - Harris, A., & Hahn, U. (2009). Bayesian rationality in evaluating multiple testimonies: Incorporating the role of coherence.
*Journal of Experimental Psychology: Learning, Memory, and Cognition*,*35*(5), 1366–1373.Google Scholar - Jeffreys, H. (1961).
*Theory of probability*. Oxford: Oxford University Press.Google Scholar - Joyce, J. (2008). Bayes’ theorem. http://plato.stanford.edu/archives/fall2008/entries/bayes-theorem/.
- Kemeny, J., & Oppenheim, P. (1952). Degrees of factual support.
*Philosophy of Science*,*1952*, 307–324.CrossRefGoogle Scholar - Keynes, J. (1921).
*A treatise on probability*. London: Macmillan.Google Scholar - Kolmogorov, A. (1956).
*Foundations of the theory of probability*. New York: AMS Chelsea Publishing.Google Scholar - Koscholke, J. (2015). Evaluating test cases for probabilistic measures of coherence.
*Erkenntnis*. doi: 10.1007/s10670-015-9734-1. - Kuipers, T. A. F. (2000).
*From instrumentalism to constructive realism*. Dordrecht: Reidel.CrossRefGoogle Scholar - Levi, I. (1962). Corroboration and rules of acceptance.
*British Journal for the Philosophy of Science*,*13*, 307–313.Google Scholar - Meijs, W. (2005). Probabilistic measures of coherence. PhD thesis, Erasmus University, Rotterdam.Google Scholar
- Meijs, W. (2006). Coherence as generalized logical equivalence.
*Erkenntnis*,*64*, 231–252.CrossRefGoogle Scholar - Meijs, W., & Douven, I. (2007). On the alleged impossibility of coherence.
*Synthese*,*157*(3), 347–360.CrossRefGoogle Scholar - Mortimer, H. (1988).
*The logic of induction*. Paramus: Prentice Hall.Google Scholar - Nozick, R. (1981).
*Philosophical explanations*. Oxford: Clarendon.Google Scholar - Olsson, E. J. (2002). What is the problem of coherence and truth?
*The Journal of Philosophy*,*94*, 246–272.CrossRefGoogle Scholar - Olsson, E. J. (2005).
*Against coherence: Truth, probability and justification*. Oxford: Oxford University Press.CrossRefGoogle Scholar - Pfeiffer, P. (1990).
*Probability for applications*. New York: Springer.CrossRefGoogle Scholar - Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., & R Core Team (2013). nlme: Linear and nonlinear mixed effects models. http://CRAN.R-project.org/package=nlme.
- Popper, K. R. (1954). Degree of confirmation.
*British Journal for the Philosophy of Science*,*5*, 143–149.CrossRefGoogle Scholar - R Core Team (2015). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.Google Scholar
- Rescher, N. (1973).
*The coherence theory of truth*. Oxford: Oxford University Press.Google Scholar - Rips, L. J. (2001). Two kinds of reasoning.
*Psychological Science*,*12*, 129–134.CrossRefGoogle Scholar - Roche, W. (2013). Coherence and probability: A probabilistic account of coherence. In M. Araszkiewicz & J. Savelka (Eds.),
*Coherence: Insights from philosophy, jurisprudence and artificial intelligence*(pp. 59–91). Dordrecht: Springer.CrossRefGoogle Scholar - Schippers, M. (2014). Probabilistic measures of coherence: From adequacy constraints towards pluralism.
*Synthese*,*191*(16), 3821–3845.CrossRefGoogle Scholar - Schippers, M., & Siebel, M. (2015). Inconsistency as a touchstone for coherence measures.
*Theoria*,*30*, 11–41.CrossRefGoogle Scholar - Schupbach, J. N. (2011). New hope for Shogenji’s coherence measure.
*British Journal for the Philosophy of Science*,*62*(1), 125–142.CrossRefGoogle Scholar - Schwarz, G. (1978). Estimating the dimension of a model.
*The Annals of Statistics*,*6*(2), 461–464.CrossRefGoogle Scholar - Shogenji, T. (2012). The degree of epistemic justification and the conjunction fallacy.
*Synthese*,*184*, 29–48.CrossRefGoogle Scholar - Siebel, M., & Wolff, W. (2008). Equivalent testimonies as a touchstone of coherence measures.
*Synthese*,*161*, 167–182.CrossRefGoogle Scholar - Wagenmakers, E. J. (2007). A practical solution to the pervasive problems of \(p\) values.
*Psychonomic Bulletin & Review*,*14*, 779–804.CrossRefGoogle Scholar - Weller, J. A., Dieckmann, N. F., Tusler, M., Mertz, C. K., Burns, W. J., & Peters, E. (2013). Development and testing of an abbreviated numeracy scale: A Rasch analysis approach.
*Journal of Behavioral Decision Making*,*26*, 198–212.CrossRefGoogle Scholar