Skip to main content Accessibility help
×
Home
Hostname: page-component-5c569c448b-phmbd Total loading time: 0.227 Render date: 2022-07-02T21:43:02.657Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

TOWARDS THE INEVITABILITY OF NON-CLASSICAL PROBABILITY

Published online by Cambridge University Press:  21 February 2022

GIACOMO MOLINARI*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BRISTOLBRISTOL BS8 1TH, UK

Abstract

This paper generalises an argument for probabilism due to Lindley [9]. I extend the argument to a number of non-classical logical settings whose truth-values, seen here as ideal aims for belief, are in the set $\{0,1\}$ , and where logical consequence $\models $ is given the “no-drop” characterization. First I will show that, in each of these settings, an agent’s credence can only avoid accuracy-domination if its canonical transform is a (possibly non-classical) probability function. In other words, if an agent values accuracy as the fundamental epistemic virtue, it is a necessary requirement for rationality that her credence have some probabilistic structure. Then I show that for a certain class of reasonable measures of inaccuracy, having such a probabilistic structure is sufficient to avoid accuracy-domination in these non-classical settings.

Type
Research Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Carr, J. R. (2017). Epistemic utility theory and the aim of belief. Philosophy and Phenomenological Research, 95(3), 511534.CrossRefGoogle Scholar
De Finetti, B. (1974). Theory of Probability: A Critical Introductory Treatment. New York: Wiley.Google Scholar
Di Nola, A., Georgescu, G., & Lettieri, A. (1999). Conditional states in finite-valued logics. In Dubois, D., Prade, H., & Klement, E. P., editors, Fuzzy Sets, Logics and Reasoning about Knowledge. Dordrecht: Kluwer Academic, pp. 161174.CrossRefGoogle Scholar
Easwaran, K. (2011). The varieties of conditional probability. In Bandyopadhyay, P. S., & Forster, M. R., editors, Handbook of the Philosophy of Science, Philosophy of Statistics, Vol. 7. Amsterdam: North-Holland, pp. 137148.Google Scholar
Hájek, A. (2003). What conditional probability could not be. Synthese, 137(3), 273323.CrossRefGoogle Scholar
Joyce, J. M. (1998). A nonpragmatic vindication of probabilism. Philosophy of Science, 65(4), 575603.CrossRefGoogle Scholar
Joyce, J. M. (2009). Accuracy and coherence: Prospects for an alethic epistemology of partial belief. In Degrees of Belief. New York: Springer, pp. 263297.CrossRefGoogle Scholar
Joyce, J. M. (2015). The value of truth: a reply to Howson. Analysis, 75(3), 413424.CrossRefGoogle Scholar
Lindley, D. V. (1982). Scoring rules and the inevitability of probability. International Statistical Review/Revue Internationale de Statistique, 50(1), 111.Google Scholar
Maher, P. (2002). Joyce’s argument for probabilism. Philosophy of Science, 69(1), 7381.CrossRefGoogle Scholar
Mundici, D. (2006). Bookmaking over infinite-valued events. International Journal of Approximate Reasoning, 43(3), 223240.CrossRefGoogle Scholar
Paris, J. B. (2001). A note on the Dutch book method. In De Cooman, G., Fine, T., & Seidenfeld, T., editors, Proceedings of the Second International Symposium onImprecise Probabilities and their Applications, ISIPTA 2001. Ithaca: Shaker Publishing Company, pp. 301306.Google Scholar
Pettigrew, R. (2011). Epistemic utility arguments for probabilism. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy (Winter 2019 Edition. https://plato.stanford.edu/archives/win2019/entries/epistemic-utility/.Google Scholar
Pettigrew, R. (2016). Accuracy and the Laws of Credence. Oxford: Oxford University Press.Google Scholar
Predd, J. B., Seiringer, R., Lieb, E. H., Osherson, D. N., Poor, H. V., & Kulkarni, S. R. (2009). Probabilistic coherence and proper scoring rules. IEEE Transactions on Information Theory, 55(10), 47864792.Google Scholar
Staffel, J. (2020). Unsettled Thoughts: A Theory of Degrees of Rationality. Oxford: Oxford University Press.Google Scholar
Titelbaum, M. (2015). Fundamentals of Bayesian epistemology. Unpublished manuscript.Google Scholar
Weatherson, B. (2003). From classical to intuitionistic probability. Notre Dame Journal of Formal Logic, 44(2), 111123.CrossRefGoogle Scholar
Williams, J. R. G. (2012a). Generalized probabilism: Dutch books and accuracy domination. Journal of Philosophical Logic, 41(5), 811840.CrossRefGoogle Scholar
Williams, J. R. G. (2012b). Gradational accuracy and nonclassical semantics. The Review of Symbolic Logic, 5(4), 513537.CrossRefGoogle Scholar
Williams, J. R. G. (2016). Probability and nonclassical logic. In The Oxford Handbook of Probability and Philosophy. Oxford: Oxford University Press, pp. 248276.Google Scholar

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

TOWARDS THE INEVITABILITY OF NON-CLASSICAL PROBABILITY
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

TOWARDS THE INEVITABILITY OF NON-CLASSICAL PROBABILITY
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

TOWARDS THE INEVITABILITY OF NON-CLASSICAL PROBABILITY
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *