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50とはずがたり:2018/11/15(木) 14:21:55
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Truth and probability
Ramsy, F.
Foundations of Mathematics
and other Logical Essays, Ch. VII, p.156-198
https://core.ac.uk/download/pdf/7048428.pdf

Truth and probability
Keynes in his A Treatise on Probability (1921) argued against the subjective approach in epistemic probabilities. For Keynes, subjectivity of probabilities doesn't matter as much, as for him there is an objective relationship between knowledge and probabilities, as knowledge is disembodied and not personal.

Ramsey in his article disagrees with Keynes's approach as for him there is a difference between the notions of probability in physics and in logic. For Ramsey probability is not related to a disembodied body of knowledge but is related to the knowledge that each individual possesses alone. Thus personal beliefs that are formulated by this individual knowledge govern probabilities, leading to the notions of subjective probability and Bayesian probability. Consequently, subjective probabilities can be inferred by observing actions that reflect individuals' personal beliefs. Ramsey argued that the degree of probability that an individual attaches to a particular outcome can be measured by finding what odds the individual would accept when betting on that outcome.

Ramsey suggested a way of deriving a consistent theory of choice under uncertainty that could isolate beliefs from preferences while still maintaining subjective probabilities.

Despite the fact that Ramsey's work on probabilities was of great importance again no one paid any attention to it until the publication of Theory of Games and Economic Behavior of John von Neumann and Oskar Morgenstern in 1944 (1947 2nd ed.)


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