Ramsey on Keynes’ Treatise
F. P. Ramsey Mr Keynes on Probability Brit. J. Phil. Sci. 40 (1989), 219-222
Review (1922) of: A Treatise on Probability by J. M. Keynes.
Ramsey here seems to take a commonsense view of probability, and to be concerned about the foundations of the theory. Ramsey argues that:
[T]here is no such probability as the probability that ‘my carpet is blue’ given only that ‘Napoleon was a great general’, and there is therefore no question of assigning a numerical value.
Thus both Ramsey and Keynes seem to agree that some probabilities can be assigned a numerical value. The difference seems to be that Keynes considers a broader, problematic, range of cases and thus deals with things that Ramsey does not consider to be ‘real’ probabilities.
Ramsey supposes that:
[W]e are concerned with the relation which actually holds between two propositions; the faculty of perceiving this relation, accurately or otherwise, we call insight, perfect or imperfect.
Thus, in distinction to his later view, he seems to suppose that there is some actual ‘objective’ probability relation that we are trying to assess. Keynes is seeking a much broader theory.
In considering Keynes notion that probability is relative to evidence, Ramsey notes:
In everything, it might be urged, owing to the possibility that there is evidence to which we have no access, we are only justified in saying not ‘p’ but ‘We have reason to suppose p’. The logical conclusion of this view is that we are not justified in saying anything at all; for our evidence about human reason might also be fragmentary. We cannot therefore reasonably say ‘We have reason to suppose the probability is a’, but only ‘We have reason to suppose that we have reason to suppose the probability is a’, and so on ad Infinitum—on the lines of a celebrated argument in Dr Moore’s Ethics.
It seems to me that when I say ‘p’ I usually mean that ‘I have an adequate reason, in the context, to say p’, which would normally imply that I ‘supposed’ p. I also habitually interpret other’s utterances in this way. This thinking of mine has its ancestry in Keynes, so I tend to agree with Ramsey that this is a reasonable interpretation of Keynes’ Treatise. Thus a claim about probabilities would be based on experience and only ‘good’ for ‘the foreseeable future’, for as long as the context lasted.
Ramsey’s objection to this seems to me largely technical and entirely unappealing. It is quite true that my appreciation of ‘human reasoning’ is empirical and hence my notion of ‘good reasoning’ is uncertain. But I can make my own ‘best effort in the circumstances’ and rest on that without recursion. Certainly I tend not to suppose that others are reasoning to any particular standard, but only that their mode reasoning is ‘reasonable’ with regard to their culture and the circumstances.
With Keynes and Good in mind, we might be more specific: when we say ‘p’ we at least mean that p appears to us to be consistent with what we know and that there are no ‘significantly different’ alternatives that we have thought of and which seem to us reasonable to take account of. For example, if – in the morning – my partner says that our car has a full tank of fuel, I do not assume that she has kept guard over it all night to prevent anyone from syphoning off the fuel. Thus Ramsey’s objection seems not to apply in practice. Ramsey does make some other valid technical points, but they do not affect ‘the big picture’ of the Treatise, which is that probability cannot always be treated as a number, that there are some ‘work-arounds’, and even if not it can pay to be aware of when one is in a complex situation.
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djmarsay 
Dave,
I like this article and it bought to mind that Donald Gillies has argued (I recall) that Keynes adopted an “intersubjective” position on probability, where as Ramsey took a subjective position. (Intersubjectivity is associated with (at least) two people coming to a consensus on an object and is a cornerstone of Pragmatic thinking). Ramsey makes frequent references to Pragmatists, notably Pierce, in his article and this has left me thinking if you read Ramsey from a Pragmatic perspective is it as far from Keynes and as close to Savage as people (like the Post-Keynesians) believe?
Closeness is in the eye of the beholder. Ramsey and Savage mostly seem to focus on justifying what we now think of as the Bayesian approach, and many people focus on how they do that. But my interest is in how we know when it is reasonable to apply their conclusions.
Ramsey and Savage invite an interpretation in which probability is derived from people’s behaviours, so probability is an element in a model of human decision making and is fair game for criticism by behavioural economists. Probability understood in this sense is not ‘pure’ mathematics. Keynes at least attempts to give us a mathematical account of probability, and in this sense is distant from the other two. It cannot be touched by behavioural economists, but instead can be used to critique their work.
In financial mathematics it is sometimes assumed that the law of large numbers applies. It obviously applies to any Bayes/Markov model, but how about a real financial time series? Keynes discusses this. As far as I know the others do not. Prior to 2007 many in finance thought it ‘pragmatic’ to assume this law. I wish they hadn’t. It seems to me that pragmatism is reasonable when one has a reasonable view of the potential consequences of one’s models. But if one’s horizon is limited then a blinkered pragmatism is very dangerous, and not to be emulated.
It seems to me that Keynes, Ramsey and Savage all had narrow experiences bases when they did their work, but that Keynes’ Treatise benefitted from a partial revision following his experience in the war and at Versailles. I only wish he had done a more thorough and accessible job.