By Grover Maxwell, Robert Anderson
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Extra resources for Induction, Probability and Confirmation (Minnesota Studies in Philosophy of Science)
Ed. (Berkeley and Los Angeles: University of California Press, 1949), p. 348. 50 BAYESIAN METHODS actually used in scientific contexts. Just as the justification for assigning a numerical mass to the unobservable electron is found in the verifiable consequences of this assignment, so the justification for assigning a probability value to a hypothesis prior to evidence is to be found in the agreement or disagreement of the consequences of this assignment with the posterior probabilities of hypotheses which are implicit in our attitudes of acceptance or rejection of these hypotheses on the basis of evidence.
The number associated with the arrow from e(t) to h indicates the portion of the full luminosity of e(t) which the net transmits to h. As t increases, some parts of the net increase in brightness while others dim. There is a point to the image of the twinkling, luminous net. One can see that different nodes have different brightnesses at time r, even though the luminosities represent someone else's beliefs. Dropping the metaphor, this "seeing" is a matter of knowing the fellow's preference ranking at time t: If he would rather have h be true than have h' be true, then his preference at time t is for h over h', and we write hPth'.
But my own uncertain sense of plausibility leads me off on a different tack. REFERENCES Bolker, E. (1967). "A Simultaneous Axiomatization of Utility and Subjective Probability," Philosophy of Science, vol. 34, pp. 333-40. Carnap, R. (1968). "Inductive Logic and Inductive Intuition," in I. Lakatos, ed. The Problem of Inductive Logic. Amsterdam: North Holland. , and R. Jeffrey, eds. (1971). Studies in Inductive Logic and Probability, vol. 1. Berkeley, Los Angeles, and London: University of California Press.