# Logic, Empiricism and Probability Structures

Henry E. Kyburg, Jr.

## Keynes's Treatise on Probability

### Logic and empiricism

One^{1} of the great and influential events of Keynes's youth was the publication of Whitehead and Russell's *Principia Mathematica* (Whitehead and Russell, 1910-1913). Keynes was enormously impressed by this work, and to some extent took it as the inspiration for *A Treatise on Probability (TP)* (Keynes, 1973 [1921]). To some extent only, because Keynes clearly rejected the atomism and some of the empiricism associated with Russell's philosophy of science. Nevertheless he never became a subjectivist with regard to probability.

In 1921, and certainly in 1907 when the first draft of the *Treatise* was completed (Carabelli, 1988), it was widely thought that the basic principles of logic had to be accepted on the basis of "intuition." Lewis Carroll/ John Dodgson wrote a cute spoof, "What the Tortoise Said to Achilles," whose point was that the validity of *modus ponens* (the inference by which, if *p* entails *q* and *p* can be stated, then also *q* can be stated) could not be demonstrated by *modus ponens* (Carroll, 1895). Many people thought that the "first principles" of logic had to be accepted on intuitive grounds. There was no semantic tradition that would have allowed us to "show" that standard logic is truth preserving.

It is important to note that in the philosophical world of the nineteenth century "intuition" did not carry overtones of arbitrariness or personal whimsy. It did not embody the sense of subjectivity that later gave rise to the doctrines of Ramsey (1931), de Finetti (1937; 1964) and Savage (1972). "Intuition" was what allowed us to *see* that *modus ponens *was a valid form of inference, as well as what allowed us to *see* that we were in the presence of a crow or a black patch.

"Empiricism" in probability, for Keynes, also had a specialized and narrow meaning. It referred to a doctrine, stated by Leslie Ellis (1844) and developed by John Venn (1866), according to which probability statements were nothing but statements about empirical relative frequencies.