Bertrand's Paradox and the Maximum Entropy Principle

Nicholas SHACKEL; Darrell Patrick ROWBOTTOM

doi:10.1111/phpr.12596

Bertrand's Paradox and the Maximum Entropy Principle

Nicholas SHACKEL
, Darrell Patrick ROWBOTTOM

Department of Philosophy

Research output: Journal Publications › Journal Article (refereed) › peer-review

4 Citations (Scopus)

Abstract

An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand's chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, that is unique to the maximum entropy principle.

Original language	English
Pages (from-to)	505-523
Number of pages	19
Journal	Philosophy and Phenomenological Research
Volume	101
Issue number	3
Early online date	18 May 2019
DOIs	https://doi.org/10.1111/phpr.12596
Publication status	Published - Nov 2020

Bibliographical note

Author’s contributions: Shackel 90%, Rowbottom 10%. In memoriam Michael Clark 1940–2019, whoshared our delight in the philosophical problems posed by paradoxes.

Access to Document

10.1111/phpr.12596

https://orca.cardiff.ac.uk/id/eprint/121298/13/shackel%20bertrand%27s%20paradox%20and%20the%20mep%208%20PPR%20for%20ORCA.pdfLicence: Unspecified

Cite this

@article{3957d797e81941d68ad402232da3d730,

title = "Bertrand's Paradox and the Maximum Entropy Principle",

abstract = "An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand's chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, that is unique to the maximum entropy principle.",

author = "Nicholas SHACKEL and ROWBOTTOM, \{Darrell Patrick\}",

note = "Author{\textquoteright}s contributions: Shackel 90\%, Rowbottom 10\%. In memoriam Michael Clark 1940–2019, whoshared our delight in the philosophical problems posed by paradoxes.",

year = "2020",

month = nov,

doi = "10.1111/phpr.12596",

language = "English",

volume = "101",

pages = "505--523",

journal = "Philosophy and Phenomenological Research",

issn = "0031-8205",

publisher = "Wiley-Blackwell",

number = "3",

}

TY - JOUR

T1 - Bertrand's Paradox and the Maximum Entropy Principle

AU - SHACKEL, Nicholas

AU - ROWBOTTOM, Darrell Patrick

N1 - Author’s contributions: Shackel 90%, Rowbottom 10%. In memoriam Michael Clark 1940–2019, whoshared our delight in the philosophical problems posed by paradoxes.

PY - 2020/11

Y1 - 2020/11

N2 - An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand's chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, that is unique to the maximum entropy principle.

AB - An important suggestion of objective Bayesians is that the maximum entropy principle can replace a principle which is known to get into paradoxical difficulties: the principle of indifference. No one has previously determined whether the maximum entropy principle is better able to solve Bertrand's chord paradox than the principle of indifference. In this paper I show that it is not. Additionally, the course of the analysis brings to light a new paradox, a revenge paradox of the chords, that is unique to the maximum entropy principle.

UR - https://www.scopus.com/pages/publications/85066038510

U2 - 10.1111/phpr.12596

DO - 10.1111/phpr.12596

M3 - Journal Article (refereed)

SN - 0031-8205

VL - 101

SP - 505

EP - 523

JO - Philosophy and Phenomenological Research

JF - Philosophy and Phenomenological Research

IS - 3

ER -

Bertrand's Paradox and the Maximum Entropy Principle

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Probability

Bertrand's paradox revisited : why Bertrand's 'solutions' are all inapplicable

Bangu’s random thoughts on Bertrand’s paradox

Cite this