*Jan Sprenger and Stephan Hartmann*

- Published in print:
- 2019
- Published Online:
- October 2019
- ISBN:
- 9780199672110
- eISBN:
- 9780191881671
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199672110.003.0014
- Subject:
- Philosophy, Philosophy of Science

This chapter sets the stage for what follows, introducing the reader to the philosophical principles and the mathematical formalism behind Bayesian inference and its scientific applications. We ...
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This chapter sets the stage for what follows, introducing the reader to the philosophical principles and the mathematical formalism behind Bayesian inference and its scientific applications. We explain and motivate the representation of graded epistemic attitudes (“degrees of belief”) by means of specific mathematical structures: probabilities. Then we show how these attitudes are supposed to change upon learning new evidence (“Bayesian Conditionalization”), and how all this relates to theory evaluation, action and decision-making. After sketching the different varieties of Bayesian inference, we present Causal Bayesian Networks as an intuitive graphical tool for making Bayesian inference and we give an overview over the contents of the book.Less

This chapter sets the stage for what follows, introducing the reader to the philosophical principles and the mathematical formalism behind Bayesian inference and its scientific applications. We explain and motivate the representation of graded epistemic attitudes (“degrees of belief”) by means of specific mathematical structures: probabilities. Then we show how these attitudes are supposed to change upon learning new evidence (“Bayesian Conditionalization”), and how all this relates to theory evaluation, action and decision-making. After sketching the different varieties of Bayesian inference, we present Causal Bayesian Networks as an intuitive graphical tool for making Bayesian inference and we give an overview over the contents of the book.

*Andrew Bacon*

- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198712060
- eISBN:
- 9780191780264
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198712060.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology

Hartry Field has recently suggested that a non-standard probability calculus better represents our beliefs about vague matters. His theory has two notable features: (i) that your attitude to P when ...
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Hartry Field has recently suggested that a non-standard probability calculus better represents our beliefs about vague matters. His theory has two notable features: (i) that your attitude to P when you are certain that P is higher-order borderline ought to be the same as your attitude when you are certain that P is simply borderline, and (ii) that when you are certain that P is borderline you should have no credence in P and no credence in ~. This chapter rejects both elements of this view and advocates instead for the view that when you are in possession of all the possible evidence, and it is borderline whether P is borderline, it is borderline whether you should believe P. Secondly, it argues for probabilism: the view that your credences ought to conform to the probability calculus. To get a handle on these issues, the chapter looks at Dutch book arguments and comparative axiomatizations of probability theory.Less

Hartry Field has recently suggested that a non-standard probability calculus better represents our beliefs about vague matters. His theory has two notable features: (i) that your attitude to P when you are certain that P is higher-order borderline ought to be the same as your attitude when you are certain that P is simply borderline, and (ii) that when you are certain that P is borderline you should have no credence in P and no credence in ~. This chapter rejects both elements of this view and advocates instead for the view that when you are in possession of all the possible evidence, and it is borderline whether P is borderline, it is borderline whether you should believe P. Secondly, it argues for probabilism: the view that your credences ought to conform to the probability calculus. To get a handle on these issues, the chapter looks at Dutch book arguments and comparative axiomatizations of probability theory.

*Ralph Wedgwood*

- Published in print:
- 2017
- Published Online:
- September 2017
- ISBN:
- 9780198802693
- eISBN:
- 9780191841972
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198802693.003.0009
- Subject:
- Philosophy, Metaphysics/Epistemology

Internalism implies that rationality requires nothing more than what in the broadest sense counts as ‘coherence’. The earlier chapters of this book argue that rationality is in a strong sense ...
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Internalism implies that rationality requires nothing more than what in the broadest sense counts as ‘coherence’. The earlier chapters of this book argue that rationality is in a strong sense normative. But why does coherence matter? The interpretation of this question is clarified. An answer to the question would involve a general characterization of rationality that makes it intuitively less puzzling why rationality is in this strong sense normative. Various approaches to this question are explored: a deflationary approach, the appeal to ‘Dutch book’ theorems, the idea that rationality is constitutive of the nature of mental states. It is argued that none of these approaches solves the problem. An adequate solution will have to appeal to some value that depends partly on how things are in the external world—in effect, an external goal—and some normatively significant connection between internal rationality and this external goal.Less

Internalism implies that rationality requires nothing more than what in the broadest sense counts as ‘coherence’. The earlier chapters of this book argue that rationality is in a strong sense normative. But why does coherence matter? The interpretation of this question is clarified. An answer to the question would involve a general characterization of rationality that makes it intuitively less puzzling why rationality is in this strong sense normative. Various approaches to this question are explored: a deflationary approach, the appeal to ‘Dutch book’ theorems, the idea that rationality is constitutive of the nature of mental states. It is argued that none of these approaches solves the problem. An adequate solution will have to appeal to some value that depends partly on how things are in the external world—in effect, an external goal—and some normatively significant connection between internal rationality and this external goal.

*Jon Williamson*

- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780199666478
- eISBN:
- 9780191749292
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666478.003.0009
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

Chapter 9 presents a formal justification of the objective Bayesian approach. The norms of objective Bayesianism are justified on the grounds that they must hold if one is to avoid certain avoidable ...
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Chapter 9 presents a formal justification of the objective Bayesian approach. The norms of objective Bayesianism are justified on the grounds that they must hold if one is to avoid certain avoidable losses. In particular, they must hold if one is to avoid avoidable sure loss and worst-case expected loss. This line of justification is shown to be robust with respect to various ways in which the underlying assumptions might be relaxed.Less

Chapter 9 presents a formal justification of the objective Bayesian approach. The norms of objective Bayesianism are justified on the grounds that they must hold if one is to avoid certain avoidable losses. In particular, they must hold if one is to avoid avoidable sure loss and worst-case expected loss. This line of justification is shown to be robust with respect to various ways in which the underlying assumptions might be relaxed.