# Keynes, John Maynard (1883–1946)

# KEYNES, JOHN MAYNARD

*(1883–1946)*

The English economist John Maynard Keynes, the son of a distinguished Cambridge logician and economist, was one of the most brilliant and influential men of the twentieth century. His role as the architect and chief negotiator of Britain's external economic policies in two world wars was only one side of his public life. During his own lifetime, his economic views, contained primarily in two great works, *A Treatise on Money* (London, 1930) and *The General Theory of Employment, Interest and Money* (London, 1936), revolutionized the economic practice, and to a lesser extent, the economic theory, of Western governments.

Keynes wrote only one philosophical work, *A Treatise on Probability* (London, 1921), but it is a philosophical classic. The following account of the book's leading ideas adheres to its own main divisions.

## Philosophy of Probability

Keynes's philosophy of probability is contained chiefly in Parts I and II. For Keynes, only a proposition can be probable or improbable. A proposition has probability only in relation to some other proposition(s) taken as premise(s). Hence a proposition may have different probabilities on different premises. Nevertheless, the probability that *p* does have, given *q* (which Keynes writes as *p/q*, is perfectly objective. Some probabilities are known to us indirectly—for example, as a result of applying the theorems of the probability calculus; but first, of course, some probabilities must be known directly. Where a probability is known to us directly, it is known to us in the way that the validity of a syllogistic argument is known, whatever that way is. The probability relation is not an empirical one. If it is true that *p/q* > *r/s*, or that *p/q* > 1/3, or that *r/s* = 1/2, then it is true a priori, and not in virtue of any matter of fact. In particular, the truth of such statements is independent of the factual truth of *p, q, r*, and *s*. Finally, *p/q* = 0 if *p* is inconsistent with *q*, and *p/q* = 1 if *q* entails *p*.

Keynes's fundamental thesis, of which the above statements are developments, is that there are inferences in which the premises do not entail the conclusion but are nevertheless, just by themselves, objectively more or less good reason for believing it. This thesis seems to require the existence of different degrees of implication. Such degrees are Keynes's probabilities. Thus, for Keynes the study of probability coincides exactly with the study of inference, demonstrative and nondemonstrative. He developed, though somewhat obscurely, a general theory of inference in Chapter X. However, from the axioms and definitions from which he derived the accepted theorems of the probability calculus, he also derived many theorems of demonstrative inference, for example, "if *a/h* = 0 then *ab/h* = 0."

It would be hard to exaggerate the importance of Keynes's fundamental thesis. Classical probability theory of the eighteenth and nineteenth centuries must have presupposed some such thesis. Recent theory on degrees of confirmation presupposes it. To Keynes, as to Pierre Simon de Laplace and Rudolf Carnap, this thesis appeared to be necessary as a means of avoiding skepticism about induction. But David Hume would presumably have rejected it outright, and it is by no means free from difficulty.

There are two negative theses that distinguish Keynes's philosophy of probability from most earlier or later formulations. One is that probabilities simply do not have a numerical value, except in certain exceptional circumstances, and never in normal inductive contexts. The other is that there are noncomparable probabilities, that is, probabilities that are neither equal to nor greater nor less than one another. For obvious reasons, these theses have contributed to the neglect of Keynes by statistical writers.

## Induction

In Part III, Keynes discussed induction. The most important arguments of those that are rational but not conclusive belong to the class of inductions whose conclusions are universal generalizations and whose premises are about instances of the generalization.

Keynes, like John Stuart Mill, regarded all scientific induction as essentially eliminative induction. His account of the circumstances in which we regard an inductive argument as strong is, in essentials (although not otherwise), a development in detail of Mill's method of agreement.

The mere number of confirmations of a hypothesis in itself is of no evidential weight. The important thing is the variety of the instances, in respects other than those that constitute the instances' confirming ones. We regard inductions as being of greatest weight when the evidence approaches the ideal case in which the confirming instances are known to be not all alike in every respect. Various ways in which our evidence can fall short of this ideal are discussed in Chapter XIX. Keynes thought that the extent to which the evidence, by its variety, eliminates alternative hypotheses is the only important factor—not only when our hypothesis is empirical, but when it is, for instance, mathematical or metaphysical.

Keynes very clearly distinguished between the task of analyzing those inductive arguments that we regard as strong and the task of justifying the fact that we regard them as strong.

The latter task, he appears to have assumed, requires a proof of the proposition that relative to instantial evidence, the probability of a universal hypothesis can approach certainty as a limit. It will do so, he purported to prove, if (and one must assume only if) the probability of the instantial evidence supposing the hypothesis to be false can be made small in comparison with the probability of the hypothesis prior to the instantial evidence (its "a priori" probability). To reduce the former probability is the object of "varying the circumstances." The required disparity between the two probabilities will exist, Keynes argued, if (and one must assume only if), inter alia, the hypothesis has finite a priori probability. This requires that it be a member of a finite disjunction of exhaustive alternatives.

When the universal hypothesis is an empirical one, this amounts to the assumption that there exists in nature the materials for only a finite number of generalizations linking empirical properties. In other words, the number of the logically independent properties of empirical objects, which a priori might have been constantly conjoined, is finite. This is the famous principle of limited independent variety (Chapter XX). Hence, the fact that the probability of any empirical universal generalization should approach certainty as a limit requires the assumption of this principle. Or rather, Keynes thought, all that is required for this principle is finite a priori probability, since experience can and does noncircularly support the principle, provided it does have this initial probability.

It does so, Keynes appears to have argued, because we have a direct apprehension of the truth of the principle, just as, he thought, we have an apprehension (not independent of experience, yet not inductively inferred) of the truth of the statement, "Color cannot exist without extension."

## Statistical Inference

The main subject of Part V is those inductive inferences whose premises include a statement of the frequency of a property *B* in an observed series of *A* 's, and whose conclusions concern *B* 's frequency in the population of *A* 's as a whole, or in a further series of *A* 's, or the probability of the next *A* being a *B*.

The theory of statistical inference had been dominated by two methods of making such inferences, both due to Laplace. One is the "rule of succession," according to which the probability of the next *A* being *B* is

if *m* out of *m* + *n* observed *A* 's have been *B*. The other is the "inversion" of the great-numbers theorem of Bernoulli. This theorem permits us—under an important restriction—to infer what frequency of *B* is most probable among observed *A* 's, given its frequency among *A* 's as a whole. Laplace purported to supply a theorem that would guide our inferences in the reverse, inductive direction, that is, from observed *A* 's to *A* 's as a whole.

Keynes regarded both methods as "mathematical charlatanry." His many criticisms of them cannot be weighed here. Apart from these criticisms, however, he considered it absurd to imagine that we could have exact measures of the probability of statistical conclusions. Statistical induction is subject to all the difficulties that beset inductions with universal conclusions, and to others beside. Moreover, the only evidence taken into account by all methods like Laplace's is numerical. The vital requirement of variety in the instances is neglected. In statistical contexts, the variety of the positive "instances" takes the form of the stability of the observed frequency when the observed series is considered as divided into subseries according to many different principles of division.

Keynes did think that, under a number of extremely stringent conditions, an inversion of Bernoulli's theorem is legitimate. But even to license these inductive inferences, as Keynes interpreted them, the principle of limited independent variety is required.

## Bibliography

Keynes's only philosophical work is *A Treatise on Probability* (London: Macmillan, 1921). On Keynes's life, see R. F. Harrod, *The Life of John Maynard Keynes* (London: Macmillan, 1951).

Valuable critical material on Keynes's theories of probability and induction may be found in the following: Jean Nicod, *Foundations of Geometry and Induction* (London: Kegan Paul Trench and Trubner, 1930); F. P. Ramsey, *Foundations of Mathematics* (London: Kegan Paul Trench and Trubner, 1931); G. H. von Wright, *The Logical Problem of Induction* (Helsingfors, 1941); G. H. von Wright, *A Treatise on Induction and Probability* (London: Routledge and Kegan Paul, 1951); Bertrand Russell, *Human Knowledge, Its Scope and Limits* (London: Allen and Unwin, 1948); and Arthur Pap, *An Introduction to the Philosophy of Science* (New York: Free Press of Glencoe, 1962). Joan Robinson, *Economic Philosophy* (London: Watts, 1962), Ch. 4, is a highly readable brief account of Keynes's place in economic theory.

For another facet of Keynes's many-sided career, see *Essays and Sketches in Biography* (New York, 1956), a varied collection of Keynes's writings on economists, politicians, acquaintances, and himself.

### other recommended works

Davis, John Bryan. *Keynes's Philosophical Development*. New York: Cambridge University Press, 1994.

Keynes, John Maynard. *The Collected Writings of John Maynard Keynes*. London: Macmillan; New York: St. Martin's Press, for the Royal Economic Society, 1971–1989.

Keynes, John Maynard. *The John Maynard Keynes Papers, King's College, Cambridge*. Cambridge, U.K.: Chadwyck-Healey, 1993.

Moggridge, D. E. *Maynard Keynes: An Economist's Biography*. New York: Routledge, 1992.

O'Donnell, R. M. *Keynes: Philosophy, Economics, and Politics: The Philosophical Foundations of Keynes's Thought and Their Influence on His Economics and Politics*. New York: St. Martin's, 1989.

Skidelsky, Robert Jacob Alexander. *John Maynard Keynes: Vol. 1, Hopes Betrayed 1883–1920: A Biography*. London: Macmillan, 1983.

Wittgenstein, Ludwig. *Letters to Russell, Keynes, and Moore*. Oxford: Basil Blackwell, 1974.

*D. Stove (1967)*

*Bibliography updated by Michael J. Farmer (2005)*

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