Abstract
This chapter is a reprint of Frank P. Ramsey’s seminal paper “Truth and Probability” written in 1926 and first published posthumous in the 1931 The Foundations of Mathematics and other Logical Essays, ed. R.B. Braithwaite, London: Routledge & Kegan Paul Ltd.
The paper lays the foundations for the modern theory of subjective probability. Ramsey argues that degrees of beliefs may be measured by the acceptability of odds on bets, and provides a set of decision theoretic axioms, which jointly imply the laws of probability.
Frank P. Ramsey was deceased at the time of publication.
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Notes
- 1.
J.M. Keynes, A Treatise on Probability (1921).
- 2.
p. 32, his italics.
- 3.
“Logical Constants”, Mind, 1927.
- 4.
See N. Campbell, Physics The Elements (1920), p.277.
- 5.
Ibid., p.271.
- 6.
I assume here Wittgenstein’s theory of propositions; it would probably be possible to give an equivalent definition in terms of any other theory.
- 7.
α and β must be supposed so far undefined as to be compatible with both p and not-p.
- 8.
Here β must include the truth of p, γ its falsity; p need no longer be ethically neutral. But we have to assume that there is a wolrd with any assigned value in which p is true, and one in which p is false.
- 9.
A. D. Ritchie, “Induction and Probability.” Mind, 1926. p. 318. ‘The conclusion of the foregoing discussion may be simply put. If the problem of induction be stated to be “How can inductive generalizations acquire a large numerical probability?” then this is a pseudo-problem, because the answer is “They cannot”. This answer is not, however, a denial of the validity of induction but is a direct consequence of the nature of probability. It still leaves untouched the real problem of induction which is “How can the probability of an induction be increased?” and it leaves standing the whole of Keynes’ discussion on this point.’
- 10.
C.S. Peirce Change Love and Logic, p. 92.
- 11.
It appears in Mr Keynes’ system as if the principal axioms -- the laws of addition and multiplication -- were nothing but definitions. This is merely a logical mistake; his definitions are formally invalid unless corresponding axioms are presupposed. Thus his definition of multiplication presupposes the law that if the probability of a given bh is equal to that of c given dh, and the probability of b given h is equal to that of d given h, then will the probabilities of ab given h and of cd given h be equal.
- 12.
Cf. Kant: ‘Denn obgleich eine Erkenntnis der logischen Form völlig gemäss sein möchte, dass ist sich selbst nicht widerspräche, so kann sie doch noch immer dem Gegenstande widersprechen.’ Kritik der reinen Vernunft, First Edition. p. 59.
- 13.
[Earlier draft of matter of preceding paragraph in some ways better. – F.P.R.
What is meant by saying that a degree of belief is reasonable? First and often that it is what I should entertain if I had the opinions of the person in question at the time but was otherwise as I am now, e.g. not drunk. But sometimes we go beyond this and ask: ‘Am I reasonable?’ This may mean, do I conform to certain enumerable standards which we call scientific method, and which we value on account of those who practise them and the success they achieve. In this sense to be reasonable means to think like a scientist, or to be guided only by ratiocination and induction or something of the sort (i.e. reasonable means reflective). Thirdly, we may go to the root of why we admire the scientist and criticize not primarily an individual opinion but a mental habit as being conducive or otherwise to the discovery of truth or to entertaining such degrees of belief as will be most useful. (To include habits of doubt or partial belief.) Then we can criticize an opinion according to the habit which produced it. This is clearly right because it all depends on this habit; it would not be reasonable to get the right conclusion to a syllogism by remembering vaguely that you leave out a term which is common to both premisses.
We use reasonable in sense 1 when we say of an argument of a scientist this does not seem to me reasonable; in sense 2 when we contrast reason and superstition or instinct; in sense 3 when we estimate the value of new methods of thought such as soothsaying.].
- 14.
What follows to the end of the section is almost entirely based on the writings of C. S. Peirce. [Especially his “Illustrations of the Logic of Science”, Popular Science Monthly, 1877 and 1878, reprinted in Chance Love and Logic (1923).].
- 15.
‘Likely’ here simply means that I am not sure of this, but only have a certain degree of belief in it.
- 16.
Cf. also the account of ‘general rules’ in the Chapter ‘Of Unphilosophical Probability’ in Hume’s Treatise.
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Ramsey, F.P. (2016). Truth and Probability. 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_3
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