On ignorance priors and the principle of indifference

ABSTRACTThis book symposium on Accuracy and the Laws of Credence consists of an overview of the book’s argument by the author, Richard Pettigrew, together with four commentaries on different aspects of that argument. Ben Levinstein challenges the characterisation of the legitimate measures of inaccuracy that plays a central role in the arguments of the book. Julia Staffel asks whether the arguments of the book are compatible with an ontology of doxastic states that includes full beliefs as well as credences. Fabrizio Cariani raises concerns about the argument offered in the book for various chance-credence principles. And Sophie Horowitz questions the assumptions at play in the book’s argument for the Principle of Indifference, as well as asking how the various laws of credence considered in the book relate to one another.

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Two Non-senses of “Probability”

Beyond Chance and Credence ◽

10.1093/oso/9780198865094.003.0003 ◽

2021 ◽

pp. 47-76

Author(s):

Wayne C. Myrvold

Keyword(s):

Relative Frequency ◽

The Other ◽

Objective Probability ◽

Sequence Of Events ◽

Principle Of Indifference ◽

Long Run ◽

Eighteenth And Nineteenth Centuries

This chapter engages in some ground-clearing. Two concepts have been proposed to play the role of objective probability. One is associated with the idea that probability involves mere counting of possibilities (often wrongly attributed to Laplace). The other is frequentism, the idea that probability can be defined as long-run relative frequency in some actual or hypothetical sequence of events. Associated with the idea that probability is merely a matter of counting of possibilities is a temptation to believe that there is a principle, called the Principle of Indifference, which can generate probabilities out of ignorance. In this chapter the reasons that neither of these approaches can achieve its goal are rehearsed, with reference to historical discussions in the eighteenth and nineteenth centuries. It includes some of the prehistory of discussions of what has come to be known, misleadingly, as Bertrand’s paradox.

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12. Inverse probability: you can’t be indifferent about it!

Logic: A Very Short Introduction ◽

10.1093/actrade/9780198811701.003.0012 ◽

2017 ◽

pp. 84-91

Author(s):

Graham Priest

Keyword(s):

Intuitive Reasoning ◽

Relevant Difference ◽

Inverse Probability ◽

Principle Of Indifference ◽

The Relationship ◽

The Way

People often confuse probabilities with their inverses. Many inductive arguments require us to reason about inverse probabilities. ‘Inverse probability: you can’t be indifferent about it!’ looks at the relationship between inverse probabilities, illustrating it with the Argument to Design, which asks: does not the fact that the physical cosmos is ordered in the way that it is give us reason to believe in the existence of a god of a certain kind? Logicians use the term Principle of Indifference to describe an important part of intuitive reasoning about probability: given a number of possibilities, with no relevant difference between them, they all have the same probability.

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