Abstract
Experience does not tell us anything but what occurred and was observed in the past; nothing else can be logically inferred from all that: nothing, in particular, concerning the future.
Reprinted from Synthase 20 (1969) 2–16.
The reader’s attention is called to Professor de Finetti’s articles on the foundations of probability in Contemporary Philosophy, vol. I (ed. by R. Klibansky), La Nuova Italia Editrice, Florence 1968, in Philosophy in Mid-Century, vol. I (ed. by R. Klibansky), La Nuova Italia Editrice, Florence, 1958, and in the International Encyclopedia of the Social Sciences, The Macmillan Company, New York 1967.
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References
Why I use the phrase ‘random number’, or ‘random quantity’, instead of ‘random variable’, is explained in H. E. Kyburg and H. E. Smokier (eds.), Studies in Subjective Probability, New York and London. 1964, pp. 95–96 (Translator’s note’ to my lectures at l’lnstitut Henri Poincaré, Paris 1935).
(Added in proof.) Good’s position, as I gathered it from his talk at the Salzburg Colloquium, is less radical than I supposed. According to it, ‘adhockeries’ ought not to be rejected outright; their use may sometimes be an acceptable substitute for a more systematic approach. I can agree with this only if - and in so far as - such a method is justifiable as an approximate version of the correct (i.e. Bayesian) approach. (Then it is no longer a mere ‘adhockery’.)
The following is a necessary and sufficient condition for the possibility of continuation: the ω h ( N ) (in the example: probabilities that M=h, h = 0, …, N) must be mixtures of ( N h ) ξh(1−ξ)N- ngiven by some distribution F(ξ), 0 ⩽ ξ ⩽ 1) for endless continuation, mixtures of an(i),i=0, …, N+ 1, with a n (i) =1 − (1/(N+1)) if h = i, an(i)= 1/(N+1) if h=i − 1, and an(i) = 0 otherwise, for one step continuation (to N+1), and so on. The same criticism applies, with some more complications of a technical nature, to the case of random numbers ‘equally distributed, with unknown distribution, and independent conditionally on the knowledge of the distribution’; they need only to be defined as exchangeable by a straightforward extension of the notion.
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© 1970 D. Reidel Publishing Company, Dordrecht-Holland
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De Finetti, B. (1970). Initial Probabilities: A Prerequisite for any Valid Induction. In: Weingartner, P., Zecha, G. (eds) Induction, Physics and Ethics. Synthese Library, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-3305-3_1
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