Abstract
The central problem of epistemology is often taken to be that of explaining how we can know what we do, but the content of this problem changes from age to age with the scope of what we take ourselves to know; and philosophers who are impressed with this flux sometimes set themselves the problem of explaining how we can get along, knowing as little as we do. For knowledge is sure, and there seems to be little we can be sure of outside logic and mathematics and truths related immediately to experience. It is as if there were some propositions – that this paper is white, that two and two are four – on which we have a firm grip, while the rest, including most of the theses of science, are slippery or insubstantial or somehow inaccessible to us. Outside the realm of what we are sure of lies the puzzling region of probable knowledge – puzzling in part because the sense of the noun seems to be cancelled by that of the adjective. The obvious move is to deny that the notion of knowledge has the importance generally attributed to it, and to try to make the concept of belief do the work that philosophers have generally assigned the grander concept. I shall argue that this is the right move.
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Notes
- 1.
Frank P. Ramsey, ‘Truth and probability’, in The Foundations of Mathematics and Other Logical Essays, R. B. Braithwaite, ed., London and New York, 1931, p. 171.
- 2.
‘Truth and probability’, F. P. Ramsey, op. cit.
- 3.
See Richard C. Jeffrey, The Logic of Decision, McGraw-Hill, 1965, the mathematical basis for which can be found in Ethan Bolker, Functions Resembling Quotients of Measures, Ph. D. Dissertation, Harvard University, 1965, and Trans. Am. Math. Soc., 124, 1966, pp. 293–312.
- 4.
Jeffrey, op. cit., chs. 6, 8.
- 5.
Jeffrey, op. cit., pp. 145–150.
- 6.
G. E. M. Anscombe, Intention, § 8, Oxford, 1957; 2nd ed., Ithaca, N.Y., 1963.
- 7.
See, e.g., J. L. Austin, Sense and Sensibilia, Oxford, 1962.
- 8.
Austin, op. cit., ch. 10
- 9.
C. I. Lewis, An Analysis of Knowledge and Valuation, La Salle, Illinois, 1946, p. 186.
- 10.
Jeffrey, op. cit., ch. 11.
- 11.
Problem 13 of Frederick Mosteller, Fifty Challenging Problems in Probability, Reading, Mass., Palo Alto, and London, 1965.
- 12.
K. R. Popper, The Logic of Scientific Discovery, London, 1959, p. 105.
- 13.
Popper, op. cit., p. 106.
- 14.
This is a simplified version of ‘the paradox of ideal evidence’, Popper, op. cit., pp. 407–409.
- 15.
Jeffrey, op. cit., pp. 57–59.
- 16.
Support of U.S. Air Force Office of Scientific Research is acknowledged, under Grant AF–AFOSR–529–65.
- 17.
In the problem as reported by Mosteller, it might be reasonable to take \( \beta ={\frac{1}{2}} \). In that case, let us note, \( {\pi}_b=1/\left(1+{\frac{1}{2}}\right)={\frac{2}{3}} \) (not \( {\frac{1}{2}} \) as suggested in the statement of the problem!) and also \( {\pi}_c=1/\left(2-\beta \right)=1/\left(2-{\frac{1}{2}}\right)={\frac{2}{3}} \). Hence (for \( \beta ={ \frac{1}{2}} \)) a was wrong to expect the probabilities to change. But, on the other hand, the warden’s reply would give him no additional information.
- 18.
Or suppose, that β = 1 (and a knows this). Then if a hears the warden tell him that c is one of the persons to be released, he will have good reason to feel happy. For when β = 1, the warden will tell a about having selected c only if the selected pair was AC. On the other hand, still with β = 1, if the warden says that b is one of the persons to be released, this means (with equal probabilities) that either AB or BC has been chosen, but not AC. Hence, with the latter piece of information, a will be justifiably less optimistic about his chances of release. (With β close to one, a similar situation prevails.)
- 19.
In the sense of the mathematical expectation of a random variable.
- 20.
See footnote 22 on the next page.
- 21.
‘On the average’ expresses the fact that the decision is made on the basis of mathematical expectation. It need not imply a frequency interpretation of probabilities.
- 22.
When utilities are non-linear with respect to probabilities of release, the prospect of additional information may be helpful or harmful.
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Jeffrey, R.C. (2016). Probable Knowledge. In: Arló-Costa, H., Hendricks, V., van Benthem, J. (eds) Readings in Formal Epistemology. Springer Graduate Texts in Philosophy, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-20451-2_4
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