The Problem of Context-Sensitivity for the Formal Theories of Belief-Credence Interaction

Thème : OLOFOS

Résumé

In the past decade or so, new work in formal epistemology has provided novel and precise coherence principles between categorical beliefs and numerical credences (e.g., Lin and Kelly 2012, 2021; Leitgeb 2013, 2014, 2017). The characteristic of this work is to combine logical norms on belief and probabilistic norms on credence into a plausible theory of how belief and credence should hang together. Focusing on Leitgeb’s theory, this paper discusses a well-recognized problem of context sensitivity for such formal approaches. On these theories, you may rationally believe X if you are concerned with this proposition only; but if you want to consider X together withsome other proposition(s), then believing X may no longer be rational. As Titelbaum (2020, 11) has put it: “… when an agent’s evidence remains constant, Leitgeb allows her beliefs to crumble in the face of partitional change.” This paper aims to go beyond the simple context-sensitivity of such formal theoriesand provide a richer setting that allows us to articulate a more context-invariant and stable conception of belief. This setting is developed within the framework of Bayesian networks.

My proposal is motivated by one of the central functions of rational categorial belief: its role in simplifying and supporting reliable reasoning. Following Foley (2009), Lin and Kelly (2012), and Staffel (2019), I take it that rational beliefconsiderably simplifies reasoning compared to probabilistic reasoning. But this simplification comes with a price. As pointed out by Foley (2009), when we reason with a large set of propositions that are not strongly theoretically intertwined, such reasoning is often unreliable: the joint probability of a relatively large set of premises – where each premise is required for an inference – may not be high and can be very low. These ideas will be used to motivate the thesis that contexts relevant to whether an agent believes X are the contexts that represent the causal or evidential structure of the agent’s evidence concerning X. I will precisify and defend the thesis by using the tools from Bayesian network theory (Bovens and Hartmann 2003; Fenton and Neil 2019). In conclusion, I’ll discuss the implications of the defended view for the lottery and preface paradoxes, and suggesta unified solution.

References:

[1] Fenton, N., & Neil, M. (2018). Risk assessment and decision analysis with Bayesian networks. Crc Press.

[2] Foley, R. (2009). Beliefs, Degrees of Belief, and the Lockean Thesis. In Degrees of Delief (pp. 37-47). Dordrecht: Springer.

[3] Leitgeb, H. (2013). Reducing Belief Simpliciter to Degrees of Belief. Annals of Pure and Applied Logic, 164(12)., 1338-1389.

[4] Leitgeb, H. (2014). The Stability Theory of Belief. Philosophical Review 123.2, 131-71.

[5] Leitgeb, H. (2017). The Stability of Belief. How Rational Belief Coheres with Probability. Oxford: Oxford University Press.

[6] Lin, H., & Kelly, K. T. (2012). Propositional Reasoning that Tracks Probabilistic Reasoning. Journal of philosophical logic 41.6, 957-981.

[7] Lin, H., & Kelly, K. T. (2021). Beliefs, Probabilities, and their Coherent Correspondence. In I Douven (Ed.), Lotteries, knowledge and Rational Belief: Essays on the Lottery Paradox (pp. 185-222). Cambridge University Press.

[8] Staffel, J. (2018). How do Beliefs Simplify Reasoning? Noûs. 937-962.

[9] Titelbaum, M. G. (2020). The Stability of Belief: How Rational Belief Coheres with Probability, by Hannes Leitgeb. Mind.

Organisation

Peter Verdée (peter.verdee@uclouvain.be)