Bertrand’s Paradox and the Principle of Indifference

Bertrand's chord paradox challenges the assumption that events with equal epistemic probabilities have equal epistemic probabilities. This book explores the paradox,its possible solutions,the philosophical errors made in attempting to solve it,and what it proves for the philosophy of probability. It proposes a solution in the spirit of Bertrands,where an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference.

Format: Hardback
Length: 376 pages
Publication date: 29 February 2024
Publisher: Taylor & Francis Ltd

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrands chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum-sized state spaces. Articulating the nature of such spaces involves some deep mathematics, and that is perhaps why the recent literature on Bertrands Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum-sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it, and what the paradox proves for the philosophy of probability. The book finishes with the authors proposed solution—a solution in the spirit of Bertrands, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference.

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities.

Bertrands chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum-sized state spaces.

Articulating the nature of such spaces involves some deep mathematics, and that is perhaps why the recent literature on Bertrands Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication.

At the same time, the philosophy of probability has been left out.

In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum-sized event spaces, and what these entail for rigour in developing the paradox itself.

This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it, and what the paradox proves for the philosophy of probability.

The book finishes with the authors proposed solution—a solution in the spirit of Bertrands, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference.

Weight: 880g
Dimension: 229 x 152 (mm)
ISBN-13: 9781032597935