Williamson, Jon (2024) Where do we stand on maximal entropy? [Preprint]

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Abstract

Edwin Jaynes’ principle of maximum entropy holds that one should use the probability distribution with maximum entropy, from all those that fit the evidence, to draw inferences, because that is the distribution that is maximally non-committal with respect to propositions that are underdetermined by the evidence. The principle was widely applied in the years following its introduction in 1957, and in 1978 Jaynes took stock, writing the paper ‘Where do we stand on maximum entropy?’ to present his view of the state of the art. Jaynes’ principle needs to be generalised to a principle of maximal entropy if it is to be
applied to first-order inductive logic, where there may be no unique maximum entropy function. The development of this objective Bayesian inductive logic has also been very fertile and it is the task of this chapter to take stock. The chapter provides an introduction to the logic and its motivation, explaining how it overcomes some problems with Carnap’s approach to inductive logic and with the subjective Bayesian approach. It also describes a range of recent
results that shed light on features of the logic, its robustness and its decidability, as well as methods for performing inference in the logic.

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Item Type:	Preprint
Creators:	Creators Email ORCID Williamson, Jon j.williamson@kent.ac.uk 0000-0003-0514-4209
Additional Information:	in press
Subjects:	Specific Sciences > Mathematics > Logic General Issues > Confirmation/Induction Specific Sciences > Probability/Statistics
Depositing User:	Prof Jon Williamson
Date Deposited:	06 Oct 2023 17:35
Last Modified:	06 Oct 2023 17:35
Item ID:	22626
Publisher:	Springer
Subjects:	Specific Sciences > Mathematics > Logic General Issues > Confirmation/Induction Specific Sciences > Probability/Statistics
Date:	2024
URI:	https://philsci-archive.pitt.edu/id/eprint/22626

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