*Juan Comesaña*

- Published in print:
- 2020
- Published Online:
- April 2020
- ISBN:
- 9780198847717
- eISBN:
- 9780191882388
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198847717.003.0002
- Subject:
- Philosophy, Metaphysics/Epistemology

This chapter introduces the mathematics of probability and decision theory. The probability calculus is introduced in both a set-theoretic and a propositional context. Probability is also related to ...
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This chapter introduces the mathematics of probability and decision theory. The probability calculus is introduced in both a set-theoretic and a propositional context. Probability is also related to measure theory, and stochastic truth-tables are presented. Problems with conditional probability are examined. Two interpretations of the probability calculus are introduced: physical and normative probabilities. The problem of logical omniscience for normative probabilities is discussed. Dutch Book arguments and accuracy-based arguments for Probabilism (the claim that our credences must satisfy the probability axioms) are examined and rejected. Different interpretations of the “idealization” reply to the problem of logical omniscience are considered, and one of them is tentatively endorsed. The expected utility maximization conception of decision theory is introduced, and representation arguments are considered (and rejected) as another reply to the problem of logical omniscience.Less

This chapter introduces the mathematics of probability and decision theory. The probability calculus is introduced in both a set-theoretic and a propositional context. Probability is also related to measure theory, and stochastic truth-tables are presented. Problems with conditional probability are examined. Two interpretations of the probability calculus are introduced: physical and normative probabilities. The problem of logical omniscience for normative probabilities is discussed. Dutch Book arguments and accuracy-based arguments for Probabilism (the claim that our credences must satisfy the probability axioms) are examined and rejected. Different interpretations of the “idealization” reply to the problem of logical omniscience are considered, and one of them is tentatively endorsed. The expected utility maximization conception of decision theory is introduced, and representation arguments are considered (and rejected) as another reply to the problem of logical omniscience.

*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.