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Causality, Meaningful Complexity and Embodied Cognition pp 231–246Cite as

Epistemic Complexity from an Objective Bayesian Perspective

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Part of the book series: Theory and Decision Library A: ((TDLA,volume 46))

Abstract

Evidence can be complex in various ways: e.g., it may exhibit structural complexity, containing information about causal, hierarchical or logical structure as well as empirical data, or it may exhibit combinatorial complexity, containing a complex combination of kinds of information. This paper examines evidential complexity from the point of view of Bayesian epistemology, asking: how should complex evidence impact on an agent’s degrees of belief? The paper presents a high-level overview of an objective Bayesian answer: it presents the objective Bayesian norms concerning the relation between evidence and degrees of belief, and goes on to show how evidence of causal, hierarchical and logical structure lead to natural constraints on degrees of belief. The objective Bayesian network formalism is presented, and it is shown how this formalism can be used to handle both kinds of evidential complexity – structural complexity combinatorial complexity.

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Notes

  1. 1.

    This norm is typically justified by an appeal to a Dutch book argument or Cox’s theorem – see, e.g., Paris (1994, Chapter 3).

  2. 2.

    This norm is typically justified on the grounds that degrees of belief are used to make predictions, and calibrated degrees of belief lead to optimal predictions in the long run (Howson and Urbach, 1989, §13.e). Strictly speaking \({P}_{\mathcal{E}}\) depends on \(\mathcal{L}\) as well as \(\mathcal{E}\); we will write \({P}_{\mathcal{E}}^{\mathcal{L}}\) where we need to emphasise this dependence, but drop reference to \(\mathcal{L}\) and \(\mathcal{E}\) where the context permits. Williamson (2005, Chapter 12) discusses language change in the context of objective Bayesianism.

  3. 3.

    This norm may be justified on the grounds that degrees of belief are used as a basis for action, extreme degrees of belief lead to riskier actions, and one should only take on risk to the extent that evidence demands – see Williamson (2007).

  4. 4.

    Ontological or semantic evidence may be understood in terms of influence relations, just as can causal, hierarchical and logical evidence – see Williamson (2005, §11.4).

References

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Acknowledgment

This research was carried out as a part of the project progicnet: Probabilistic logic and probabilistic networks, supported by the Leverhulme Trust.

Author information

Authors and Affiliations

  1. Department of Philosophy and Centre for Reasoning, University of Kent, Kent, U.K.

    Jon Williamson

Authors
  1. Jon Williamson
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Correspondence to Jon Williamson .

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Editors and Affiliations

  1. Facoltà di Lettere e Filosofia, Università di Roma - Tor Vergata, Via Columbia 1, Roma, 00133, Italy

    A. Carsetti

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Williamson, J. (2010). Epistemic Complexity from an Objective Bayesian Perspective. In: Carsetti, A. (eds) Causality, Meaningful Complexity and Embodied Cognition. Theory and Decision Library A:, vol 46. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3529-5_13

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