Abstract
Adopting a central feature of Stoic epistemology, Descartes treated belief as action that might be undertaken wisely or rashly, and enunciated a method for avoiding false belief, a discipline of the will “to include nothing more in my judgments than what presented itself to my mind with such clarity and distinctness that I would have no occasion to put it in doubt”.1 He called such acts of the will “affirmations”, i.e., acts of accepting sentences or propositions as true.
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Notes
Discourse on the method…, part 2.
As probabilities p range over the unit interval [0,1], the corresponding odds o = p/(1-p) range over the extended non-negativereals [0, 00], enhancing resolution high in the scale. Thus, probabilities 99%, 99.9%, 99.99% correspond to odds 99, 999, 9999. But at the low end, where odds p/(1-p) are practically equal to probabilities p, there is no such increase in resolution. Logarithms of odds, increasingly positive above p=.5 and symmetrically negative below, yield the same resolution at both ends. (Odds of 99, 999, 9999 become log odds of approximately 2, 3, 4, and at the low end, probabilities of.01,.001.0001 become log odds of approximately -2, -3, -4.)
See Richard Jeffrey, The Logic of Decision, McGraw-Hill, 1965; University of Chicago Press, 1983, 1990.
Blindsight, a Case Study and Implications, by L. Weiskrantz, Oxford: Clarendon Press, 1986, pp.3–6, 24, and 168–169. See also Patricia Smith Churchland, Neurophilosophy, Cambridge, Mass.: MIT Press, 1986, pp.224–228.
W.V. Quine, The Pursuit of Truth, Cambridge, Mass.: Harvard University Press, 1990, p.2.
Allen Hobson, The Dreaming Brain, New York: Basic Books, 1988, pp.110–112.
Given an old probability distribution, P, and a new one, Q, it is an open question whether, among the sentences D in your language for which your conditional probabilities are the same relative to Q as they are relative to P, there are any for which your new probability Q(D) is 1. If so, and only then, Q can be viewed as coming from P by conditioning.
Such uses of Bayes factors were promoted by I.J. Good in chapter 6 of his book Probability and the Weighing of Evidence, London: Charles Griffin, 1950. See also Alan Turing: the Enigma, by Andrew Hodges, New York: Simon and Schuster, 1983, pp.196–197. Good promotes logarithms of odds (“plausibilities”) and of Bayes factors (“weights of evidence”) as intelligence amplifiers which played a role in cracking the German “enigma” code during the Second World War.
Proposed by Schwartz, W.B., Wolfe, H.J., and Pauker, S.G., “Pathology and probabilities: a new approach to interpreting and reporting biopsies”, The New England Journal of Medicine 305, 1981, pp.917–923.
See Richard Jeffrey and Michael Hendrickson, “Probabilizing pathology”, Proceedings of the Aristotelian Society, v. 89, part 3, 1988/8, p.217, odds kinematics.
In general, elicitation is a process of drawing forth. Here, authenticity does not require the elicited Bayes factors to have been present in the pathologist’s mind before the process began; the process may well be one in which she is induced to form a judgment, making up her mind probabilistically.
An Analysis of Knowledge a nd Valuation, La Salle, Ill.: Open Court, 1946, pp.182–183. (Lewis’s emphasis).
The first sentences of “On medical experience”, translated by Richard Walzer, in Three Treatises on the Nature of Science, Indianapolis: Hackett, 1985, p.49.
Like “experience”, “reason” has a different sense (comprehending theory) in Galen’s formula from what it has in C.I. Lewis’s; see pp.xx-xxxi of Michael Frede’s introduction to the Galen book (note 10).
For Carnap’s program, see his essays in Studies in Inductive Logic and Probability, Berkeley, Los Angeles and London: University of California Press, volume 1, Rudolf Carnap and Richard Jeffrey (eds.), 1971, volume 2, Richard Jeffrey (ed.), 1980.
In meteorology, radically probabilistic methods of assessing and improving the quality of probabilistic judgment have been in use since the 1950’s, but such techniques remain largely unknown in medicine and other areas. For an account of such methods, see Morris H. DeGroot and Stephen E. Fienberg, “Assessing probability assessors: calibration and refinement.” In Statistical Decision Theory and Related Topics, vol. 3. New York: Academic Press, 1982.
The practical framework of Bayesian decision analysis is the native ground of such probabilizing. See, e.g., Clinical Decision Analysis by Milton C. Weinstein, Harvey V. Fineberg, Philadelphia, London, Toronto, Mexico City, Rio de Janeiro, Sydney, and Tokyo: W.B. Saunders Co., 1980.
The relevance quotient Q(A)/P(A) plays the same role in updating probabilities that the Bayes factor plays in updating odds. Where Q comes from P by conditioning on a data proposition, Q(A)/P(A) = P(A i data)/P(A) = P(data l A)/P(data).
But here Carnap’s notion of confirmation is not yet definitely probabilistic.
This paper is adapted from the introductory essay in Richard Jeffrey, Probability and the Art of Judgment, Cambridge: Cambridge University Press, 1992.
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Jeffrey, R. (1993). From Logical Empiricism to Radical Probabilism. In: Stadler, F. (eds) Scientific Philosophy: Origins and Developments. Vienna Circle Institute Yearbook [1993], vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2964-2_8
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