Richard Swinburne
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780199271672
- eISBN:
- 9780191709357
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199271672.003.0004
- Subject:
- Philosophy, Philosophy of Religion
An explanatory hypothesis (whether of the personal or scientific kind) is probable in so far as it makes probable the occurrence of many observed phenomena, the occurrence of which is not probable ...
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An explanatory hypothesis (whether of the personal or scientific kind) is probable in so far as it makes probable the occurrence of many observed phenomena, the occurrence of which is not probable otherwise; and in so far as it is simple, and fits with background knowledge. This account of the probability of hypothesis is given precise form by Bayes's Theorem.Less
An explanatory hypothesis (whether of the personal or scientific kind) is probable in so far as it makes probable the occurrence of many observed phenomena, the occurrence of which is not probable otherwise; and in so far as it is simple, and fits with background knowledge. This account of the probability of hypothesis is given precise form by Bayes's Theorem.
Richard Swinburne
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199243792
- eISBN:
- 9780191598524
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199243794.003.0005
- Subject:
- Philosophy, Metaphysics/Epistemology
The logical probability of a proposition on another proposition is the true measure of how probable the latter makes the former. The central case of this concerns how likely some evidence makes some ...
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The logical probability of a proposition on another proposition is the true measure of how probable the latter makes the former. The central case of this concerns how likely some evidence makes some hypothesis postulated to explain it. This depends on how probable it is, given the hypothesis that we would find the observed evidence, whether the hypothesis fits with background evidence, how simple it is, and how narrow is its scope. (The scope of a hypothesis depends on how many big and detailed claims it makes.) The latter two a priori criteria give to every proposition an intrinsic probability (a probability on no evidence). These criteria are captured by Bayes's Theorem. A detailed analysis is provided of what it is for a hypothesis to be simple. This account of the probability of a hypothesis on evidence is extended to deal generally with the probability of one proposition on another; and in particular with our grounds for believing testimony.Less
The logical probability of a proposition on another proposition is the true measure of how probable the latter makes the former. The central case of this concerns how likely some evidence makes some hypothesis postulated to explain it. This depends on how probable it is, given the hypothesis that we would find the observed evidence, whether the hypothesis fits with background evidence, how simple it is, and how narrow is its scope. (The scope of a hypothesis depends on how many big and detailed claims it makes.) The latter two a priori criteria give to every proposition an intrinsic probability (a probability on no evidence). These criteria are captured by Bayes's Theorem. A detailed analysis is provided of what it is for a hypothesis to be simple. This account of the probability of a hypothesis on evidence is extended to deal generally with the probability of one proposition on another; and in particular with our grounds for believing testimony.
Colin Howson
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198250371
- eISBN:
- 9780191597749
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250371.003.0009
- Subject:
- Philosophy, Philosophy of Science
Applies the results of Ch. 7 to scientific methodology and shows that they give a logical interpretation of the subjective Bayesian theory of inductive inference. This theory is therefore no more ...
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Applies the results of Ch. 7 to scientific methodology and shows that they give a logical interpretation of the subjective Bayesian theory of inductive inference. This theory is therefore no more necessarily subjective than deductive logic, consisting as both do of objective logical rules for proceeding from premises to conclusion. In the Bayesian case, the premises are prior probability assignments. It is shown that familiar rules of scientific method are endorsed, and, in particular, the rule that unless there is prior support for a hypothesis, its overall probability will be very small however good the fit with current evidence.Less
Applies the results of Ch. 7 to scientific methodology and shows that they give a logical interpretation of the subjective Bayesian theory of inductive inference. This theory is therefore no more necessarily subjective than deductive logic, consisting as both do of objective logical rules for proceeding from premises to conclusion. In the Bayesian case, the premises are prior probability assignments. It is shown that familiar rules of scientific method are endorsed, and, in particular, the rule that unless there is prior support for a hypothesis, its overall probability will be very small however good the fit with current evidence.
Steven J. Osterlind
- Published in print:
- 2019
- Published Online:
- January 2019
- ISBN:
- 9780198831600
- eISBN:
- 9780191869532
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198831600.003.0006
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter discusses evidence and probability data with particular attention on Bayesian estimation. The Protestant ethic slowed probability developments in the United States, but the idea of ...
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This chapter discusses evidence and probability data with particular attention on Bayesian estimation. The Protestant ethic slowed probability developments in the United States, but the idea of quantification continued apace in England and on the Continent. In particular, Thomas Bayes invented a simple but profound mathematical means to connect outcomes with causes with conditional probabilities and Bayesian estimation. The chapter explains conditional probabilities and Bayesian logic, giving several examples, including incidence of accurate cancer diagnosis with inexact diagnostics. The chapter also introduces Bayes’s magnum opus An Essay Toward Solving a Problem in the Doctrine of Chances and gives his example of rolling billiard balls on a billiard table to show Bayes’s theorem.Less
This chapter discusses evidence and probability data with particular attention on Bayesian estimation. The Protestant ethic slowed probability developments in the United States, but the idea of quantification continued apace in England and on the Continent. In particular, Thomas Bayes invented a simple but profound mathematical means to connect outcomes with causes with conditional probabilities and Bayesian estimation. The chapter explains conditional probabilities and Bayesian logic, giving several examples, including incidence of accurate cancer diagnosis with inexact diagnostics. The chapter also introduces Bayes’s magnum opus An Essay Toward Solving a Problem in the Doctrine of Chances and gives his example of rolling billiard balls on a billiard table to show Bayes’s theorem.
Richard Swinburne
- Published in print:
- 2003
- Published Online:
- November 2003
- ISBN:
- 9780199257461
- eISBN:
- 9780191598616
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199257469.003.0014
- Subject:
- Philosophy, Philosophy of Religion
Summarizes the argument of the book. Given only a moderate amount of evidence from natural theology in favour of the existence of God and his having reason to become incarnate among humans, there is ...
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Summarizes the argument of the book. Given only a moderate amount of evidence from natural theology in favour of the existence of God and his having reason to become incarnate among humans, there is far more evidence that Jesus led the sort of life that God Incarnate would lead, and that that life was culminated by a super‐miracle, than there is for any other prophet in human history. In consequence, the overall balance of evidence in favour of the Resurrection having occurred is very strong. This is elucidated in the formalism of the probability calculus by Bayes's theorem.Less
Summarizes the argument of the book. Given only a moderate amount of evidence from natural theology in favour of the existence of God and his having reason to become incarnate among humans, there is far more evidence that Jesus led the sort of life that God Incarnate would lead, and that that life was culminated by a super‐miracle, than there is for any other prophet in human history. In consequence, the overall balance of evidence in favour of the Resurrection having occurred is very strong. This is elucidated in the formalism of the probability calculus by Bayes's theorem.
Brian D. Haig
- Published in print:
- 2018
- Published Online:
- January 2018
- ISBN:
- 9780190222055
- eISBN:
- 9780190871734
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190222055.003.0004
- Subject:
- Psychology, Social Psychology
Chapter 4 focuses on Bayesian confirmation theory, a formal theory of reasoning based on probability theory. It deals with important, and related, general ideas, such as rationality, confirmation, ...
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Chapter 4 focuses on Bayesian confirmation theory, a formal theory of reasoning based on probability theory. It deals with important, and related, general ideas, such as rationality, confirmation, and inductive inference, including statistical inference. The chapter also provides a selective discussion of Bayesian statistics. The chapter traces some of the broad contours of Bayesian confirmation theory and then presents an evaluation of a philosophy of Bayesian statistical practice. Psychology’s attitudes to Bayesianism are briefly discussed. Considered is the question of whether Bayesianism provides an illuminating account of the approach to theory evaluation known as inference to the best explanation. The chapter offers some broad recommendations for research practice.Less
Chapter 4 focuses on Bayesian confirmation theory, a formal theory of reasoning based on probability theory. It deals with important, and related, general ideas, such as rationality, confirmation, and inductive inference, including statistical inference. The chapter also provides a selective discussion of Bayesian statistics. The chapter traces some of the broad contours of Bayesian confirmation theory and then presents an evaluation of a philosophy of Bayesian statistical practice. Psychology’s attitudes to Bayesianism are briefly discussed. Considered is the question of whether Bayesianism provides an illuminating account of the approach to theory evaluation known as inference to the best explanation. The chapter offers some broad recommendations for research practice.
Bas C. van Fraassen
- Published in print:
- 1989
- Published Online:
- November 2003
- ISBN:
- 9780198248606
- eISBN:
- 9780191597459
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198248601.003.0013
- Subject:
- Philosophy, Philosophy of Science
While it was argued earlier in the book that no rule‐governed notion of rational opinion change could be adequate, there are certainly patterns of normal opinion change (updating in response to new ...
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While it was argued earlier in the book that no rule‐governed notion of rational opinion change could be adequate, there are certainly patterns of normal opinion change (updating in response to new data or new constraints accepted in response to experience), which have a rule‐following form. The basic example is Simple Conditionalization (often characterized as the application of Bayes's rule or Bayes's theorem, sometimes called Bayesian Conditionalization, and sometimes accepted as the sole admissible form of opinion change), but more advanced patterns (beginning with Jeffrey Conditionalization) have been described in the literature, as well as challenged there, e.g. by Isaac Levi. The question of what can justify such rules is addressed using symmetry arguments, and the (hidden or explicit) premises of such arguments analysed. Probability kinematics, as formulated initially by Richard Jeffrey, is the general theory of rules for changing a (‘prior’) probability function, subject to given or imposed constraints, into a new (‘updated’, ‘posterior’) function. Such constraints can take various forms, and the rules offered for them can be limited by symmetry considerations but may not be uniquely determined.Less
While it was argued earlier in the book that no rule‐governed notion of rational opinion change could be adequate, there are certainly patterns of normal opinion change (updating in response to new data or new constraints accepted in response to experience), which have a rule‐following form. The basic example is Simple Conditionalization (often characterized as the application of Bayes's rule or Bayes's theorem, sometimes called Bayesian Conditionalization, and sometimes accepted as the sole admissible form of opinion change), but more advanced patterns (beginning with Jeffrey Conditionalization) have been described in the literature, as well as challenged there, e.g. by Isaac Levi. The question of what can justify such rules is addressed using symmetry arguments, and the (hidden or explicit) premises of such arguments analysed. Probability kinematics, as formulated initially by Richard Jeffrey, is the general theory of rules for changing a (‘prior’) probability function, subject to given or imposed constraints, into a new (‘updated’, ‘posterior’) function. Such constraints can take various forms, and the rules offered for them can be limited by symmetry considerations but may not be uniquely determined.
Colin Howson
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198250371
- eISBN:
- 9780191597749
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250371.003.0010
- Subject:
- Philosophy, Philosophy of Science
Considers the nature of chance and its role in statistical hypotheses. It is argued that the best way to understand chance is as tendency, naturally measured by the frequency in repeated trials of ...
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Considers the nature of chance and its role in statistical hypotheses. It is argued that the best way to understand chance is as tendency, naturally measured by the frequency in repeated trials of the occurrence of the event in question. The relationship with von Mises's theory is briefly examined. It is shown how, via Bayes's Theorem, statistical data can support or undermine chance hypotheses even though there is no deductive relation between the hypotheses and the data.Less
Considers the nature of chance and its role in statistical hypotheses. It is argued that the best way to understand chance is as tendency, naturally measured by the frequency in repeated trials of the occurrence of the event in question. The relationship with von Mises's theory is briefly examined. It is shown how, via Bayes's Theorem, statistical data can support or undermine chance hypotheses even though there is no deductive relation between the hypotheses and the data.
Richard Swinburne
- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239635
- eISBN:
- 9780191598609
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239637.003.0004
- Subject:
- Philosophy, Philosophy of Religion
An explanatory hypothesis (whether of the personal or scientific kind) is probable insofar as it makes probable the occurrence of many observed phenomena, the occurrence of which is not probable ...
More
An explanatory hypothesis (whether of the personal or scientific kind) is probable insofar as it makes probable the occurrence of many observed phenomena, the occurrence of which is not probable otherwise and insofar as it is simple and fits with background knowledge. This account of the probability of hypothesis is given precise form by Bayes's Theorem.Less
An explanatory hypothesis (whether of the personal or scientific kind) is probable insofar as it makes probable the occurrence of many observed phenomena, the occurrence of which is not probable otherwise and insofar as it is simple and fits with background knowledge. This account of the probability of hypothesis is given precise form by Bayes's Theorem.
Colin Howson
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198250371
- eISBN:
- 9780191597749
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250371.003.0012
- Subject:
- Philosophy, Philosophy of Science
The coda discusses Hume's famous account of miracles in the Enquiry, and his criterion for belief in miracles, and shows that it amounts to a simple argument in the probability calculus.
The coda discusses Hume's famous account of miracles in the Enquiry, and his criterion for belief in miracles, and shows that it amounts to a simple argument in the probability calculus.
Gregory J Morgan
- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780199738625
- eISBN:
- 9780199894642
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199738625.003.0012
- Subject:
- Philosophy, Philosophy of Science
In his Particles and Waves, Peter Achinstein gives a precise probabilistic version of theoretical coherence inspired by William Whewell's somewhat vague notion of coherence. Whewell believed that as ...
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In his Particles and Waves, Peter Achinstein gives a precise probabilistic version of theoretical coherence inspired by William Whewell's somewhat vague notion of coherence. Whewell believed that as theoretical science proceeds, it becomes more coherent and rejects false incoherent theories. Achinstein offers a challenge: try to make Whewell's idea more precise while maintaining the properties that Whewell claimed coherence to have. This chapter argues (1) that Achinstein's probabilistic rendition of coherence fails to capture Whewell's notion since the probabilistic rendition of coherence is not an a priori sign of truth and (2) that Achinstein's approach is better seen as a critique of Whewell's central methodological claims than as an interpretation of Whewell's ideas.Less
In his Particles and Waves, Peter Achinstein gives a precise probabilistic version of theoretical coherence inspired by William Whewell's somewhat vague notion of coherence. Whewell believed that as theoretical science proceeds, it becomes more coherent and rejects false incoherent theories. Achinstein offers a challenge: try to make Whewell's idea more precise while maintaining the properties that Whewell claimed coherence to have. This chapter argues (1) that Achinstein's probabilistic rendition of coherence fails to capture Whewell's notion since the probabilistic rendition of coherence is not an a priori sign of truth and (2) that Achinstein's approach is better seen as a critique of Whewell's central methodological claims than as an interpretation of Whewell's ideas.
Andrew C. A. Elliott
- Published in print:
- 2021
- Published Online:
- September 2021
- ISBN:
- 9780198869023
- eISBN:
- 9780191905490
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198869023.003.0014
- Subject:
- Mathematics, Applied Mathematics, Probability / Statistics
Courts of law must weigh evidence to determine the likelihood of competing interpretations of past events, and different legal contexts require different standards of proof, but this falls short of a ...
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Courts of law must weigh evidence to determine the likelihood of competing interpretations of past events, and different legal contexts require different standards of proof, but this falls short of a quantification of probability. Bayes’s theorem and the associated formula provide a way of combining multiple elements of evidence and using them to refine prior assessments of probability. The prosecutor’s fallacy involves an incorrect reversal of the logic of evidence. The ecological fallacy involves incorrectly attributing proportions derived from large groups to smaller groups or individuals.Less
Courts of law must weigh evidence to determine the likelihood of competing interpretations of past events, and different legal contexts require different standards of proof, but this falls short of a quantification of probability. Bayes’s theorem and the associated formula provide a way of combining multiple elements of evidence and using them to refine prior assessments of probability. The prosecutor’s fallacy involves an incorrect reversal of the logic of evidence. The ecological fallacy involves incorrectly attributing proportions derived from large groups to smaller groups or individuals.
Peter Achinstein
- Published in print:
- 2018
- Published Online:
- December 2018
- ISBN:
- 9780190615055
- eISBN:
- 9780190615086
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190615055.003.0002
- Subject:
- Philosophy, Philosophy of Science, General
Both Newton and Einstein claim that nature is simple and that simplicity is an epistemic guide to truth. This chapter examines various arguments for these claims, including that, historically, ...
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Both Newton and Einstein claim that nature is simple and that simplicity is an epistemic guide to truth. This chapter examines various arguments for these claims, including that, historically, simpler theories have been more empirically successful than complex ones; that the epistemic value of simplicity can be demonstrated by appeal to Bayes’s probability theorem; and that simpler strategies for changing one’s beliefs in the light of new evidence can be shown to be more successful than complex ones. It is concluded that none of these arguments shows that nature is simple or that simplicity is an epistemic virtue.Less
Both Newton and Einstein claim that nature is simple and that simplicity is an epistemic guide to truth. This chapter examines various arguments for these claims, including that, historically, simpler theories have been more empirically successful than complex ones; that the epistemic value of simplicity can be demonstrated by appeal to Bayes’s probability theorem; and that simpler strategies for changing one’s beliefs in the light of new evidence can be shown to be more successful than complex ones. It is concluded that none of these arguments shows that nature is simple or that simplicity is an epistemic virtue.
Timothy McGrew
- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780190842215
- eISBN:
- 9780190874445
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190842215.003.0021
- Subject:
- Religion, Theology
The mid-20th century consensus regarding Hume’s critique of reported miracles has broken down dramatically in recent years thanks to the application of probabilistic analysis to the issue and the ...
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The mid-20th century consensus regarding Hume’s critique of reported miracles has broken down dramatically in recent years thanks to the application of probabilistic analysis to the issue and the rediscovery of its history. Progress from this point forward is likely to be made along one or more of three fronts. There is wide room for interdisciplinary collaboration, work that will bring together scholars with expertise in religion, psychology, philosophy, and empirical science. There is a great deal of work still to be done in formal analysis, making use of the tools of modern probability theory to model questions about testimony and inference. And the recovery and study of earlier works on the subject—works that should never have been forgotten—can significantly enrich our understanding of the underlying issues.Less
The mid-20th century consensus regarding Hume’s critique of reported miracles has broken down dramatically in recent years thanks to the application of probabilistic analysis to the issue and the rediscovery of its history. Progress from this point forward is likely to be made along one or more of three fronts. There is wide room for interdisciplinary collaboration, work that will bring together scholars with expertise in religion, psychology, philosophy, and empirical science. There is a great deal of work still to be done in formal analysis, making use of the tools of modern probability theory to model questions about testimony and inference. And the recovery and study of earlier works on the subject—works that should never have been forgotten—can significantly enrich our understanding of the underlying issues.
Trent Dougherty and Justin P. McBrayer (eds)
- Published in print:
- 2014
- Published Online:
- August 2014
- ISBN:
- 9780199661183
- eISBN:
- 9780191785566
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199661183.001.0001
- Subject:
- Religion, Religious Studies, Philosophy of Religion
Given that we meet evils in every quarter of the world, could it be governed by an all-good and all-powerful deity? Some philosophers say no and claim that the problem of evil is good evidence for ...
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Given that we meet evils in every quarter of the world, could it be governed by an all-good and all-powerful deity? Some philosophers say no and claim that the problem of evil is good evidence for atheism. Other philosophers say yes and claim that all of the evils in our world can be explained as requirements for deeper goods. And still other philosophers say yes but demur on the task of explaining the role of evils in our world. Philosophers who believe in God and yet take this latter route are called “skeptical theists.” Such thinkers are skeptical about human abilities to determine whether the evils in our world could be justifiably allowed by a being such as God. Despite believing in God, these philosophers insist that humans are not cognitively equipped to discern many of the reasons that might be available to God. This collection of essays presents cutting-edge work on skeptical theistic responses to the problem of evil and the persistent objections that such responses invite. Part I investigates the epistemology of skepticism as it applies to evils and the nature of epistemic humility. Part II explores the tenability of a particular epistemic principle about the conditions of reasonable epistemic access (CORNEA). The remaining sections of the book address objections to sceptical theism, namely the objection that skeptical theism undermines the theistic life (Part III) and the objection that skeptical theism undermines the moral life (Part IV).Less
Given that we meet evils in every quarter of the world, could it be governed by an all-good and all-powerful deity? Some philosophers say no and claim that the problem of evil is good evidence for atheism. Other philosophers say yes and claim that all of the evils in our world can be explained as requirements for deeper goods. And still other philosophers say yes but demur on the task of explaining the role of evils in our world. Philosophers who believe in God and yet take this latter route are called “skeptical theists.” Such thinkers are skeptical about human abilities to determine whether the evils in our world could be justifiably allowed by a being such as God. Despite believing in God, these philosophers insist that humans are not cognitively equipped to discern many of the reasons that might be available to God. This collection of essays presents cutting-edge work on skeptical theistic responses to the problem of evil and the persistent objections that such responses invite. Part I investigates the epistemology of skepticism as it applies to evils and the nature of epistemic humility. Part II explores the tenability of a particular epistemic principle about the conditions of reasonable epistemic access (CORNEA). The remaining sections of the book address objections to sceptical theism, namely the objection that skeptical theism undermines the theistic life (Part III) and the objection that skeptical theism undermines the moral life (Part IV).
Amos Golan
- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780199349524
- eISBN:
- 9780199349555
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199349524.003.0004
- Subject:
- Economics and Finance, Econometrics
In this chapter I develop the essential maximum entropy procedure, which is an inversion procedure for inferring an unknown probability distribution function from incomplete information. The ...
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In this chapter I develop the essential maximum entropy procedure, which is an inversion procedure for inferring an unknown probability distribution function from incomplete information. The formulation here is the root of info-metrics and is grounded in the motivations provided in Chapter 2 and the metrics defined in Chapter 3. Once the basic maximum entropy problem is defined and the solution is derived via the method of Lagrange multipliers, I derive and discuss its dual formulation. I then define and discuss the concept of conjugate variables, which is related to the Lagrange multipliers. Throughout, the mathematical derivations are supported by graphical illustrations and supplemented with heuristic arguments and with numerous examples in ideal settings.Less
In this chapter I develop the essential maximum entropy procedure, which is an inversion procedure for inferring an unknown probability distribution function from incomplete information. The formulation here is the root of info-metrics and is grounded in the motivations provided in Chapter 2 and the metrics defined in Chapter 3. Once the basic maximum entropy problem is defined and the solution is derived via the method of Lagrange multipliers, I derive and discuss its dual formulation. I then define and discuss the concept of conjugate variables, which is related to the Lagrange multipliers. Throughout, the mathematical derivations are supported by graphical illustrations and supplemented with heuristic arguments and with numerous examples in ideal settings.
Timothy McGrew
- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780198746904
- eISBN:
- 9780191809125
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198746904.003.0015
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology
One of the central complaints about Bayesian probability is that it places no constraints on individual subjectivity in one’s initial probability assignments. Those sympathetic to Bayesian methods ...
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One of the central complaints about Bayesian probability is that it places no constraints on individual subjectivity in one’s initial probability assignments. Those sympathetic to Bayesian methods have responded by adding restrictions motivated by broader epistemic concerns about the possibility of changing one’s mind. This chapter explores some cases where, intuitively, a straightforward Bayesian model yields unreasonable results. Problems arise in these cases not because there is something wrong with the Bayesian formalism per se but because standard textbook illustrations teach us to represent our inferences in simplified ways that break down in extreme cases. It also explores some interesting limitations on the extent to which successive items of evidence ought to induce us to change our minds when certain screening conditions obtain.Less
One of the central complaints about Bayesian probability is that it places no constraints on individual subjectivity in one’s initial probability assignments. Those sympathetic to Bayesian methods have responded by adding restrictions motivated by broader epistemic concerns about the possibility of changing one’s mind. This chapter explores some cases where, intuitively, a straightforward Bayesian model yields unreasonable results. Problems arise in these cases not because there is something wrong with the Bayesian formalism per se but because standard textbook illustrations teach us to represent our inferences in simplified ways that break down in extreme cases. It also explores some interesting limitations on the extent to which successive items of evidence ought to induce us to change our minds when certain screening conditions obtain.
