Teddy Seidenfeld (CMU) gives a talk in the talk series "MCMP & Statistics Department" titled "Three contrasts between two senses of coherence" (Joint work with M. J. Schervish and J. B. Kadane – Statistics, CMU). Abstract: B. de Finetti defended two senses of coherence in providing foundations for his theory of subjective probabilities. Coherence 1 requires that when a decision maker announces fair prices for random variables these are immune to a uniform sure-loss - no Book is possible using finitely many fair contracts! Coherence 2 requires that when a decision maker's forecasts for a finite set of random variables are evaluated by Brier Score - squared error loss - there is no rival set of forecasts that dominate with a uniformly better score for sure. De Finetti established these two concepts are equivalent: fair prices are coherent 1 if and only if they constitute a coherent 2 set of forecasts if and only if they are the expected values for the variables under some common (finitely additive) personal probability.

I report three additional contrasts between these two senses of coherence. One contrast (relating to finitely additive probabilities) favors coherence 2. One contrast (relating to decisions with moral hazard) favors coherence 1. The third contrast relates to the challenge of state-dependent utilities.

Teddy Seidenfeld (CMU) gives a talk in the talk series "MCMP & Statistics Department" titled "Three contrasts between two senses of coherence" (Joint work with M. J. Schervish and J. B. Kadane – Statistics, CMU). Abstract: B. de Finetti defended two senses of coherence in providing foundations for his theory of subjective probabilities. Coherence 1 requires that when a decision maker announces fair prices for random variables these are immune to a uniform sure-loss - no Book is possible using finitely many fair contracts! Coherence 2 requires that when a decision maker's forecasts for a finite set of random variables are evaluated by Brier Score - squared error loss - there is no rival set of forecasts that dominate with a uniformly better score for sure. De Finetti established these two concepts are equivalent: fair prices are coherent 1 if and only if they constitute a coherent 2 set of forecasts if and only if they are the expected values for the variables under some common (finitely additive) personal probability. I report three additional contrasts between these two senses of coherence. One contrast (relating to finitely additive probabilities) favors coherence 2. One contrast (relating to decisions with moral hazard) favors coherence 1. The third contrast relates to the challenge of state-dependent utilities.

Teddy Seidenfeld (CMU) gives a talk in the talk series "MCMP &amp; Statistics Department" titled "Three contrasts between two senses of coherence" (Joint work with M. J. Schervish and J. B. Kadane – Statistics, CMU). Abstract: B. de Finetti defended two senses of coherence in providing foundations for his theory of subjective probabilities. Coherence 1 requires that when a decision maker announces fair prices for random variables these are immune to a uniform sure-loss - no Book is possible using finitely many fair contracts! Coherence 2 requires that when a decision maker's forecasts for a finite set of random variables are evaluated by Brier Score - squared error loss - there is no rival set of forecasts that dominate with a uniformly better score for sure. De Finetti established these two concepts are equivalent: fair prices are coherent 1 if and only if they constitute a coherent 2 set of forecasts if and only if they are the expected values for the variables under some common (finitely additive) personal probability.

I report three additional contrasts between these two senses of coherence. One contrast (relating to finitely additive probabilities) favors coherence 2. One contrast (relating to decisions with moral hazard) favors coherence 1. The third contrast relates to the challenge of state-dependent utilities.

Three contrasts between two senses of coherence

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.
The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.
Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists. The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws. Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

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Three contrasts between two senses of coherence

Three contrasts between two senses of coherence

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