*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.

*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.