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On Probability and Induction

Published online by Cambridge University Press:  14 March 2022

Hans Reichenbach
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Extract

In a review of my book “Wahrscheinlichkeitslehre”, Dr. Ernest Nagel has recently criticized some of my ideas on probability and induction. His review includes a good exposition of my ideas, and I have to thank him for his serious attempts to do justice to my results. He attacks, however, some very essential points of my theory. I may be allowed, therefore, to answer him as frankly and thoroughly as he attacks me.

Type
Research Article
Information
Philosophy of Science , Volume 5 , Issue 1 , January 1938 , pp. 21 - 45
Copyright
Copyright © Philosophy of Science Association 1938

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References

Notes

1 Leiden, 1935, Sijthoff.

2 Mind XLV, No. 180, p. 501.

3 I use here the terms introduced by Carnap and Tarski. Object language is the ordinary language, concerning things; syntactic language concerns symbols and relations between symbols; semantic language concerns, jointly, symbols and ordinary objects, i.e. qualities of symbols in relation to facts, such as truth. The transition from a symbol to the designation of a symbol is indicated by quotation marks.

4 cf. Wahrschcinlichkeitslehre, p. 375.

5 This is made clear on p. 376 where I call the probability statement an analogue of tatements of the form “a is true”.

6 Axiomatik der Wahrscheinlichkeitsrechnung, Math. Zeitschr. 34, 1932, p. 572 cf. also the new paper in Erkenntnis VII, 1937, quoted above.

7 To avoid misunderstandings: it is, of course, verifiable whether there is the relation of syntactic certainty between two formulas. But the question whether the events demand the introduction of syntactic certainty or that of extensional certainty, is not verifiable.

8 Philos. Review, Vol. XLV, 6, p. 625.

9 Cf. Wahrscheinlichkeitslehre p. 386.

10 Cf. the report on the discussion of the congress of Prague 1934, in Erkenntnis V, 1935. p. 174.

11 A. Tarski in the discussion of the Congress of Prague 1934; cf. the report in Erkenntnis V, 1935, p. 174, and my answer p. 177. J. Hosiasson, Actes du Congrès international de Philosophie scientifique, Paris 1936, IV, p. 58; my answer to this is given in my new paper quoted above, appearing in Erkenntnis 7, 1937.

12 In this formula, “(ai)” is not a propositional series, but the designation of a prepositional series.

13 American Journal of Mathematics, XLIII, 1921, p. 182.

14 According to my remark above I drop the quotation marks.

15 Actes du Congrès de Philosophie Scientifique 1935, Paris 1936, IV 26.

16 I put here the quotation marks beside the terms “proposition” and “fact” because Dr. Nagel does so; I think it however more correct to drop them. We say e.g.: “attraction is a relation between a magnet and a piece of iron”; and not: “attraction is a relation between ‘a magnet’ and ‘a piece of iron’ “.

17 Annalen d. Physik 79, 1926, p. 509.

18 I have used these terms already in a discussion on the Congress of Prague 1934; cf. Erkenntnis V, 1935, p. 172.

19 I have given some examples of this kind at another place, cf. Actes du Congrès International de Philosophie scientifique Paris 1935, IV, 6 and 28.

20 A. A. Michelson, Astrophys. Journ. 65, 1, 1927.

21 Cf. the author's Wahrscheinlichkeitslehre, p. 226.

22 This remark needs some qualification. We could eliminate the numerical width of the constant by passing to a statement about a limit occurring for intervals of a width converging towards zero, and might interpret this as a statement about an absolute constant. As the formulation of this statement, however, presupposes other statements admitting a numerical width of the constant, and as statements of this kind suffice for all purposes of physics, we content ourselves here with a statement of this type.

23 In Erkenntnis 5, 1935, p. 275. I have used for this the term “Wahrscheinlichkeit erster Form”. I must refer to this paper for an explanation of the different types of probabilities occurring for theories.

24 Experience and Prediction. Chicago University Press, 1937.

25 By differential diagnosis the physicians understand a case where the observed symptoms of illness indicate several diseases as their possible origin, but do not permit a decision among the members of this group unless certain new symptoms can be observed.