Bertrand S Paradox And The Principle Of Indifference

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Bertrand's Paradox and the Principle of Indifference

Nicholas Shackel
Bertrand s Paradox and the Principle of Indifference Book PDF

Author : Nicholas Shackel
Publisher : Unknown
Page : 0 pages
File Size : 46,9 Mb
Release : 2024
Category : Logic, Symbolic and mathematical
ISBN : 1032597984

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Bertrand's Paradox and the Principle of Indifference by Nicholas Shackel Pdf

"Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand's 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 Bertrand's 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 author's proposed solution-a solution in the spirit of Bertrand's, 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. Bertrand's Paradox and the Principle of Indifference will appeal to scholars and advanced students working in the philosophy of mathematics, epistemology, philosophy of science, probability theory, and mathematical physics"--

Bertrand’s Paradox and the Principle of Indifference

Nicholas Shackel
Bertrand s Paradox and the Principle of Indifference Book PDF

Author : Nicholas Shackel
Publisher : Taylor & Francis
Page : 390 pages
File Size : 52,7 Mb
Release : 2024-02-29
Category : Philosophy
ISBN : 9781003813354

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Bertrand’s Paradox and the Principle of Indifference by Nicholas Shackel Pdf

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s 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 Bertrand’s 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 author’s proposed solution—a solution in the spirit of Bertrand’s, 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. Bertrand's Paradox and the Principle of Indifference will appeal to scholars and advanced students working in the philosophy of mathematics, epistemology, philosophy of science, probability theory and mathematical physics.

Paradoxes from A to Z

Michael Clark
Paradoxes from A to Z Book PDF

Author : Michael Clark
Publisher : Psychology Press
Page : 234 pages
File Size : 45,7 Mb
Release : 2002
Category : Paradox
ISBN : 0415228085

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Paradoxes from A to Z by Michael Clark Pdf

'This sentence is false'. Is it? If a hotel with an infinite number of rooms is fully occupied, can it still accommodate a new guest? How can we have emotional responses to fiction, when we know that the objects of our emotions do not exist?

Recent Developments in the Philosophy of Science: EPSA13 Helsinki

Uskali Mäki,Ioannis Votsis,Stéphanie Ruphy,Gerhard Schurz
Recent Developments in the Philosophy of Science EPSA13 Helsinki Book PDF

Author : Uskali Mäki,Ioannis Votsis,Stéphanie Ruphy,Gerhard Schurz
Publisher : Springer
Page : 391 pages
File Size : 46,6 Mb
Release : 2015-09-09
Category : Science
ISBN : 9783319230153

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Recent Developments in the Philosophy of Science: EPSA13 Helsinki by Uskali Mäki,Ioannis Votsis,Stéphanie Ruphy,Gerhard Schurz Pdf

This volume showcases the best of recent research in the philosophy of science. A compilation of papers presented at the EPSA 13, it explores a broad distribution of topics such as causation, truthlikeness, scientific representation, gender-specific medicine, laws of nature, science funding and the wisdom of crowds. Papers are organised into headings which form the structure of the book. Readers will find that it covers several major fields within the philosophy of science, from general philosophy of science to the more specific philosophy of physics, philosophy of chemistry, philosophy of the life sciences, philosophy of psychology, and philosophy of the social sciences and humanities, amongst others. This volume provides an excellent overview of the state of the art in the philosophy of science, as practiced in different European countries and beyond. ​It will appeal to researchers with an interest in the philosophical underpinnings of their own discipline, and to philosophers who wish to explore the latest work on the themes explored.

E.T. Jaynes

Edwin T. Jaynes
E T Jaynes Book PDF

Author : Edwin T. Jaynes
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 40,8 Mb
Release : 1989-04-30
Category : Mathematics
ISBN : 0792302133

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E.T. Jaynes by Edwin T. Jaynes Pdf

The first six chapters of this volume present the author's 'predictive' or information theoretic' approach to statistical mechanics, in which the basic probability distributions over microstates are obtained as distributions of maximum entropy (Le. , as distributions that are most non-committal with regard to missing information among all those satisfying the macroscopically given constraints). There is then no need to make additional assumptions of ergodicity or metric transitivity; the theory proceeds entirely by inference from macroscopic measurements and the underlying dynamical assumptions. Moreover, the method of maximizing the entropy is completely general and applies, in particular, to irreversible processes as well as to reversible ones. The next three chapters provide a broader framework - at once Bayesian and objective - for maximum entropy inference. The basic principles of inference, including the usual axioms of probability, are seen to rest on nothing more than requirements of consistency, above all, the requirement that in two problems where we have the same information we must assign the same probabilities. Thus, statistical mechanics is viewed as a branch of a general theory of inference, and the latter as an extension of the ordinary logic of consistency. Those who are familiar with the literature of statistics and statistical mechanics will recognize in both of these steps a genuine 'scientific revolution' - a complete reversal of earlier conceptions - and one of no small significance.

Probability Theory

E. T. Jaynes
Probability Theory Book PDF

Author : E. T. Jaynes
Publisher : Cambridge University Press
Page : 764 pages
File Size : 55,5 Mb
Release : 2003-04-10
Category : Mathematics
ISBN : 0521592712

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Probability Theory by E. T. Jaynes Pdf

Index.

Paradoxes from A to Z

Michael Clark
Paradoxes from A to Z Book PDF

Author : Michael Clark
Publisher : Routledge
Page : 298 pages
File Size : 40,8 Mb
Release : 2012-11-12
Category : Philosophy
ISBN : 9781136218040

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Paradoxes from A to Z by Michael Clark Pdf

Paradoxes from A to Z, Third edition is the essential guide to paradoxes, and takes the reader on a lively tour of puzzles that have taxed thinkers from Zeno to Galileo, and Lewis Carroll to Bertrand Russell. Michael Clark uncovers an array of conundrums, such as Achilles and the Tortoise, Theseus’ Ship, and the Prisoner’s Dilemma, taking in subjects as diverse as knowledge, science, art and politics. Clark discusses each paradox in non-technical terms, considering its significance and looking at likely solutions. This third edition is revised throughout, and adds nine new paradoxes that have important bearings in areas such as law, logic, ethics and probability. Paradoxes from A to Z, Third edition is an ideal starting point for those interested not just in philosophical puzzles and conundrums, but anyone seeking to hone their thinking skills.

E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics

R.D. Rosenkrantz
E T Jaynes Papers on Probability Statistics and Statistical Physics Book PDF

Author : R.D. Rosenkrantz
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400965812

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E. T. Jaynes: Papers on Probability, Statistics and Statistical Physics by R.D. Rosenkrantz Pdf

The first six chapters of this volume present the author's 'predictive' or information theoretic' approach to statistical mechanics, in which the basic probability distributions over microstates are obtained as distributions of maximum entropy (Le. , as distributions that are most non-committal with regard to missing information among all those satisfying the macroscopically given constraints). There is then no need to make additional assumptions of ergodicity or metric transitivity; the theory proceeds entirely by inference from macroscopic measurements and the underlying dynamical assumptions. Moreover, the method of maximizing the entropy is completely general and applies, in particular, to irreversible processes as well as to reversible ones. The next three chapters provide a broader framework - at once Bayesian and objective - for maximum entropy inference. The basic principles of inference, including the usual axioms of probability, are seen to rest on nothing more than requirements of consistency, above all, the requirement that in two problems where we have the same information we must assign the same probabilities. Thus, statistical mechanics is viewed as a branch of a general theory of inference, and the latter as an extension of the ordinary logic of consistency. Those who are familiar with the literature of statistics and statistical mechanics will recognize in both of these steps a genuine 'scientific revolution' - a complete reversal of earlier conceptions - and one of no small significance.

Classic Topics on the History of Modern Mathematical Statistics

Prakash Gorroochurn
Classic Topics on the History of Modern Mathematical Statistics Book PDF

Author : Prakash Gorroochurn
Publisher : John Wiley & Sons
Page : 776 pages
File Size : 49,8 Mb
Release : 2016-03-29
Category : Mathematics
ISBN : 9781119127932

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Classic Topics on the History of Modern Mathematical Statistics by Prakash Gorroochurn Pdf

"There is nothing like it on the market...no others are as encyclopedic...the writing is exemplary: simple, direct, and competent." —George W. Cobb, Professor Emeritus of Mathematics and Statistics, Mount Holyoke College Written in a direct and clear manner, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times presents a comprehensive guide to the history of mathematical statistics and details the major results and crucial developments over a 200-year period. Presented in chronological order, the book features an account of the classical and modern works that are essential to understanding the applications of mathematical statistics. Divided into three parts, the book begins with extensive coverage of the probabilistic works of Laplace, who laid much of the foundations of later developments in statistical theory. Subsequently, the second part introduces 20th century statistical developments including work from Karl Pearson, Student, Fisher, and Neyman. Lastly, the author addresses post-Fisherian developments. Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times also features: A detailed account of Galton's discovery of regression and correlation as well as the subsequent development of Karl Pearson's X2 and Student's t A comprehensive treatment of the permeating influence of Fisher in all aspects of modern statistics beginning with his work in 1912 Significant coverage of Neyman–Pearson theory, which includes a discussion of the differences to Fisher’s works Discussions on key historical developments as well as the various disagreements, contrasting information, and alternative theories in the history of modern mathematical statistics in an effort to provide a thorough historical treatment Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times is an excellent reference for academicians with a mathematical background who are teaching or studying the history or philosophical controversies of mathematics and statistics. The book is also a useful guide for readers with a general interest in statistical inference.

Tychomancy

Michael Strevens
Tychomancy Book PDF

Author : Michael Strevens
Publisher : Harvard University Press
Page : 260 pages
File Size : 53,6 Mb
Release : 2013-06-03
Category : Science
ISBN : 9780674076020

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Tychomancy by Michael Strevens Pdf

Tychomancy—meaning “the divination of chances”—presents a set of rules for inferring the physical probabilities of outcomes from the causal or dynamic properties of the systems that produce them. Probabilities revealed by the rules are wide-ranging: they include the probability of getting a 5 on a die roll, the probability distributions found in statistical physics, and the probabilities that underlie many prima facie judgments about fitness in evolutionary biology. Michael Strevens makes three claims about the rules. First, they are reliable. Second, they are known, though not fully consciously, to all human beings: they constitute a key part of the physical intuition that allows us to navigate around the world safely in the absence of formal scientific knowledge. Third, they have played a crucial but unrecognized role in several major scientific innovations. A large part of Tychomancy is devoted to this historical role for probability inference rules. Strevens first analyzes James Clerk Maxwell’s extraordinary, apparently a priori, deduction of the molecular velocity distribution in gases, which launched statistical physics. Maxwell did not derive his distribution from logic alone, Strevens proposes, but rather from probabilistic knowledge common to all human beings, even infants as young as six months old. Strevens then turns to Darwin’s theory of natural selection, the statistics of measurement, and the creation of models of complex systems, contending in each case that these elements of science could not have emerged when or how they did without the ability to “eyeball” the values of physical probabilities.

Paradoxes from A to Z

Head of German Dictionaries Michael Clark,Michael Clark
Paradoxes from A to Z Book PDF

Author : Head of German Dictionaries Michael Clark,Michael Clark
Publisher : Routledge
Page : 268 pages
File Size : 47,8 Mb
Release : 2007-04-13
Category : Philosophy
ISBN : 9781134104062

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Paradoxes from A to Z by Head of German Dictionaries Michael Clark,Michael Clark Pdf

This updated second edition is the essential guide to paradoxes and takes the reader on a lively tour of puzzles that have taxed thinkers from Zeno to Galileo and Lewis Carroll to Bertrand Russell. Michael Clark uncovers an array of conundrums, such as Achilles and the Tortoise, Theseus' Ship and the Prisoners' Dilemma, taking in subjects as diverse as knowledge, ethics, science, art and politics. Clark discusses each paradox in non-technical terms, considering its significance and looking at likely solutions. Including a full glossary, Paradoxes from A to Z is a refreshing alternative to traditional philosophical introductions.

Philosophy and Probability

Timothy Childers
Philosophy and Probability Book PDF

Author : Timothy Childers
Publisher : OUP Oxford
Page : 214 pages
File Size : 49,8 Mb
Release : 2013-05-31
Category : Philosophy
ISBN : 9780191668029

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Philosophy and Probability by Timothy Childers Pdf

Probability is increasingly important for our understanding of the world. What is probability? How do we model it, and how do we use it? Timothy Childers presents a lively introduction to the foundations of probability and to philosophical issues it raises. He keeps technicalities to a minimum, and assumes no prior knowledge of the subject. He explains the main interpretations of probability-frequentist, propensity, classical, Bayesian, and objective Bayesian-and uses stimulating examples to bring the subject to life. All students of philosophy will benefit from an understanding of probability, and this is the book to provide it.

Paradox Lost

Michael Huemer
Paradox Lost Book PDF

Author : Michael Huemer
Publisher : Springer
Page : 260 pages
File Size : 43,6 Mb
Release : 2018-06-28
Category : Philosophy
ISBN : 9783319904900

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Paradox Lost by Michael Huemer Pdf

Paradox Lost covers ten of philosophy’s most fascinating paradoxes, in which seemingly compelling reasoning leads to absurd conclusions. The following paradoxes are included: The Liar Paradox, in which a sentence says of itself that it is false. Is the sentence true or false? The Sorites Paradox, in which we imagine removing grains of sand one at a time from a heap of sand. Is there a particular grain whose removal converts the heap to a non-heap? The Puzzle of the Self-Torturer, in which a series of seemingly rational choices has us accepting a life of excruciating pain, in exchange for millions of dollars. Newcomb’s Problem, in which we seemingly maximize our expected profit by taking an unknown sum of money, rather than taking the same sum plus $1000. The Surprise Quiz Paradox, in which a professor finds that it is impossible to give a surprise quiz on any particular day of the week . . . but also that if this is so, then a surprise quiz can be given on any day. The Two Envelope Paradox, in which we are asked to choose between two indistinguishable envelopes, and it is seemingly shown that each envelope is preferable to the other. The Ravens Paradox, in which observing a purple shoe provides evidence that all ravens are black. The Shooting Room Paradox, in which a deadly game kills 90% of all who play, yet each individual’s survival turns on the flip of a fair coin. Each paradox is clearly described, common mistakes are explored, and a clear, logical solution offered. Paradox Lost will appeal to professional philosophers, students of philosophy, and all who love intellectual puzzles.

Philosophy of Probability and Statistical Modelling

Mauricio Suárez
Philosophy of Probability and Statistical Modelling Book PDF

Author : Mauricio Suárez
Publisher : Cambridge University Press
Page : 128 pages
File Size : 48,7 Mb
Release : 2021-01-21
Category : Philosophy
ISBN : 9781108983846

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Philosophy of Probability and Statistical Modelling by Mauricio Suárez Pdf

This Element has two main aims. The first one (sections 1-7) is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim (sections 8-13) focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and a novel methodological study of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the 'complex nexus of chance'.

Universal Measurements: How To Free Three Birds In One Move

De Bianchi Massimiliano Sassoli,Aerts Diederik
Universal Measurements How To Free Three Birds In One Move Book PDF

Author : De Bianchi Massimiliano Sassoli,Aerts Diederik
Publisher : World Scientific
Page : 148 pages
File Size : 48,9 Mb
Release : 2017-03-22
Category : Science
ISBN : 9789813220188

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Universal Measurements: How To Free Three Birds In One Move by De Bianchi Massimiliano Sassoli,Aerts Diederik Pdf

This is a book presenting to a wide audience of readers, ranging from fans of science to professional researchers, some of the authors' recent discoveries in three distinct, but intimately related domains: probability theory (Bertrand's paradox), observation in physics (the measurement problem) and the modeling of experiments in psychology (quantum cognition). In all three of these domains of investigation, and the associated problems, the authors explain how to advantageously use the key notion of universal measurement, which constitutes the fil rouge of the whole text.