2 Probability and knowledge

If Russell and Wittgenstein prompted Ramsey’s work on mathematics, Keynes prompted his work on economics and probability. The latter was provoked especially by Keynes’ A Treatise on Probability (1921), which extends the deductive logic of conclusive inference to an inductive logic of inconclusive inference by postulating a relation of ‘partial entailment’, knowable a priori. This, when measurable, enables a probability measure of the strength of an inference from one proposition to another. But in ‘Truth and Probability’ (1926) Ramsey attacked the idea of an a priori inductive logic so effectively that Keynes abandoned it, although it was later revived (see Carnap; Probability, interpretations of).

Ramsey’s main achievement in ‘Truth and Probability’ is his probability measure of the strength (degree) of a belief. This starts from ‘the old-established way of measuring a person’s belief, [that is,] to propose a bet, and see what are the lowest odds which he will accept’ (1990a: 68). Refining this by invoking ‘the theory that we act in the way we think most likely to realise the objects of our desires’ (1990a: 69), Ramsey derives measures both of desires (subjective utilities) and of beliefs (subjective probabilities), thereby founding the now standard use of these concepts (see Decision and game theory).

Ramsey himself uses his theory to extend ‘the lesser logic … of consistency’ (1990a: 82) from full to partial beliefs. Thus to the injunction not to believe both p and not-p he adds, for example, that anyone who believes p to degree 1/3 must believe not-p to degree 2/3. Otherwise what these beliefs will make him do ‘would depend on the precise form in which the options were offered him, which would be absurd’: that is, they would make him bet at different odds on p and against not-p, so that ‘he could have a book made against him by a cunning better and would then stand to lose in any event’ (1990a: 78).

Ramsey also uses his theory to develop ‘the larger logic … of discovery’, applied (following Peirce) to belief-forming ‘habits of inference … observation and memory’ (1990a: 92). He shows why such a habit is good or bad ‘as the degree of belief it produces is near or far from the actual proportion in which the habit leads to truth’, and hence why the fact that ‘the world is so constituted that inductive arguments lead on the whole to true opinions’ makes our inductive habits reasonable (1990a: 93).

Hence also Ramsey’s claim in ‘Knowledge’ (1929) that ‘a belief [is] knowledge if it is (i) true, (ii) certain [that is, a full belief], (iii) obtained by a reliable process … [that is, one] that can be more or less relied on to give true beliefs’ (1990a: 110). This claim anticipates later accounts of knowledge (see Internalism and externalism in epistemology; Reliabilism), showing amongst other things how we can know things we do not know we know. This in particular enables Ramsey to evade several well-known objections to knowledge, conceived of as true belief that the believer could justify, which need to assume that I can only know something if I know I know it (Sahlin 1991).

In ‘Truth and Probability’ Ramsey does not apply his subjective reading of probability to physics. Unfortunately he later, in ‘Chance’ (1928), anticipates de Finetti (1937) by taking even physical chances to be only ‘in another sense objective, in that everyone agrees about them’ (1990a: 106). To this we may reply by adding to his objection to Keynes, that determining the right probabilities ‘in molecular mechanics … is a matter of physics rather than pure logic’ (1990a: 85), that it takes more than mass psychology to explain (for example) the random decay of radioactive atoms.

Fortunately Ramsey does not make all his successors’ mistakes. In particular, unlike many later decision theorists (for example, Jeffrey 1983), he never prescribes acting ‘in the way we think most likely to realise the objects of our desires’. He claims only that the theory that we do so is ‘a useful approximation to the truth … like Newtonian mechanics’ (1990a: 69). Here he is right: for even when I in fact do something because ‘it seemed a good idea at the time’, this fact about my action does not suffice to make it rational.