Keynes’ Ramsey as an Philosopher
JM Keynes ‘Logic’, New Statesman and Nation, vol. 2, 3 October 1931, 407; ‘Ramsey as an philosopher’, JMK 10, 336-9.
One of Keynes’ obituaries of his protégé, Ramsey.
[The] calculus of probabilities belong to formal logic. But the basis of our degrees of belief – or the a priori probabilities, as they used to be called – is part of our human outfit, perhaps given to us merely by human selection, analogous to our perceptions and our memories rather than to formal logic. So far I yield to Ramsey – I think he is right. But in attempting to distinguish ‘rational’ degrees of belief from belief in general he was not yet, I think, quite successful.
Consider an actual coin. P(Heads)=1/2 is a statement of formal logic. Keynes recognizes that our ground for believing it are subjective or possibly multi-subjective (common to most reasoning humans). Ramsey is right. But there is a distinction between this and a statement that P(Heads)=1/2 for an (idealised) fair coin, and – more generally – for Keynes and Good’s use of likelihood in assessing statistical hypotheses. Keynes does not think that Ramsey succeeded in making this distinction, and left many readers with the impression that all probabilities were subjective.
Note that for a real coin, Keynes can properly say P(Heads|This coin is fair)=1/2 or P(Heads|The principle of indifference holds)=1/2. This leaves us with wondering where such conditionals come from. My own view is that it is reasonable, and perhaps inevitable, that we will sometimes be left with such questions and do not attempt to represent them as a number.