Logical Foundations of Probability By Rudolf Carnap Pp xvii + 607 (London: Routledge and Kegan Paul, Ltd, 1951) 42s net

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Logical Foundations of Probability

In Defence of Objective Bayesianism

Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods with values of objective chances or relative frequencies. The best known version of a direct inference principle is David Lewis’s Principal Principle. Certain kinds of statements undermine direct inferences. Lewis calls such statements inadmissible. We show that on any Bayesian account of direct inference several kinds of intuitively innocent statements turn out to be inadmissible. This may pose a significant challenge to Bayesian accounts of direct inference. We suggest some ways in which these challenges may be addressed.

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Admissibility Troubles for Bayesian Direct Inference Principles

This paper highlights the role of Lewis’ Principal Principle and certain auxiliary conditions on admissibility as serving to explicate normal informal standards of what is reasonable. These considerations motivate the presuppositions of the argument that the Principal Principle implies the Principle of Indifference, put forward by Hawthorne et al. (British Journal for the Philosophy of Science, 68, 123–131, 2017). They also suggest a line of response to recent criticisms of that argument, due to Pettigrew (British Journal for the Philosophy of Science, 71, 605–619, 2020) and Titelbaum and Hart (British Journal for the Philosophy of Science, 71(2), 621–632, 2020). The paper also shows that related concerns of Hart and Titelbaum (Thought: A Journal of Philosophy, 4(4), 252–262, 2015) do not undermine the argument of Hawthorne et al. (2017).

/pdf/the-principal-principle-admissibility-and-normal-informal-487ptp147z.pdf

The Principal Principle, admissibility, and normal informal standards of what is reasonable

This paper poses a problem for Lewis’ Principal Principle in a subjective Bayesian framework: we show that, where chances inform degrees of belief, subjective Bayesianism fails to validate normal informal standards of what is reasonable. This problem points to a tension between the Principal Principle and the claim that conditional degrees of belief are conditional probabilities. However, one version of objective Bayesianism has a straightforward resolution to this problem, because it avoids this latter claim. The problem, then, offers some support to this version of objective Bayesianism.

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The Principal Principle and subjective Bayesianism

Intuitive Dilation?: Intuitive Dilation?

Roger White ([2010]) argued for a principle of indifference. Hart and Titelbaum ([2015]) showed that White’s argument relied on an intuition about conditioning on biconditionals that, while...

The Principal Principle Does Not Imply the Principle of Indifference, Because Conditioning on Biconditionals Is Counterintuitive

Impermissivists hold that an agent with a given body of evidence has at most one rationally permitted attitude that she should adopt towards any particular proposition. Permissivists deny this, often motivating permissivism by describing scenarios that pump our intuitions that the agent could reasonably take one of several attitudes toward some proposition. We criticize the following impermissivist response: while it seems like any of that range of attitudes is permissible, what is actually required is the single broad attitude that encompasses all of these single attitudes. While this might seem like an easy way to win over permissivists, we argue that this impermissivist response leads to an indefensible epistemology; permissive intuitions are not so easily co-opted.

Casey Hart

Papers

Intuitive Dilation?: Intuitive Dilation?

The Principal Principle Does Not Imply the Principle of Indifference, Because Conditioning on Biconditionals Is Counterintuitive

The imprecise impermissivist’s dilemma