## Abstract

I derive a sufficient condition for a belief set to be representable by a probability function: if at least one comparative confidence ordering of a certain type satisfies Scott’s axiom, then the belief set used to induce that ordering is representable. This provides support for Kenny Easwaran’s project of analyzing doxastic states in terms of belief sets rather than credences.

## Keywords

Formal epistemology Representation theorem Belief Credence Scott’s axiom## Notes

### Acknowledgements

Many thanks to Laura Callahan, Sam Carter, Kevin Dorst, Kenny Easwaran, Frankie Egan, Adam Elga, Danny Forman, Jimmy Goodrich, James Hawthorne, Nevin Johnson, Barry Loewer, Jonathan Schaffer, an anonymous reviewer, and the audience at NASSLLI 2017 for helpful comments. Special thanks are due to Branden Fitelson for all his help, guidance, and support.

## References

- 1.de Finetti, B. (1974).
*Theory of probability (Vol. 1)*. New York: Wiley.Google Scholar - 2.Easwaran, K. (2016). Dr. Truthlove or: how I learned to stop worrying and love Bayesian probabilities.
*Noûs*,*50*(4), 816–853.CrossRefGoogle Scholar - 3.Fitelson, B., & McCarthy, D. (2015).
*New foundations for comparative probability*. [Powerpoint slides]. Retrieved from http://fitelson.org/eut_handout.pdf. - 4.Foley, R. (1992). The epistemology of belief and the epistemology of degrees of belief.
*American Philosophical Quarterly*,*29*(2), 111–124.Google Scholar - 5.Hawthorne, J. (2009). The Lockean thesis and the logic of belief In F. Huber, & C. Schmidt-Petri (Eds.),
*Degrees of belief. Synthese Library*(pp. 49–74). Dordrecht: Springer.Google Scholar - 6.Leitgeb, H. (2013). Reducing belief simpliciter to degrees of belief.
*Annals of Pure and Applied Logic*,*164*, 1338–1389.CrossRefGoogle Scholar - 7.Leitgeb, H., & Pettigrew, R. (2010). An objective justification of Bayesianism I: measuring inaccuracy.
*Philosophy of Science*,*77*, 201–235.CrossRefGoogle Scholar - 8.
- 9.Savage, L. J. (1954).
*The foundations of statistics*. New York: Wiley.Google Scholar - 10.Scott, D. (1964). Measurement structures and linear inequalities.
*Journal of Mathematical Psychology*,*1*, 233–247.CrossRefGoogle Scholar - 11.Teller, P. (1973). Conditionalization and observation.
*Synthese*,*26*(2), 218–258.CrossRefGoogle Scholar - 12.van Eijck, J., & Renne, B. (2014). Belief as willingness to bet. Retrieved from 1412.5090.

## Copyright information

© Springer Science+Business Media B.V. 2017