The weight of argument in the General Theory
As is well known, the weight of argument is explicitly mentioned by Keynes in GT on two occasions (see footnotes on pp. 148 and 240). The importance of these references is confirmed in his correspondence (see, for example, the well-known letter to Townshend of December 1938; Keynes, 1979b , p. 293). Although explicit hints at the weight of argument are scarce, we contend that its role is important as it intervenes in the reasoning in a crucial way, although sometimes only implicitly. Its role looms wherever Keynes refers to uncertainty with a meaning different from that of classical economics and classical decision theory. Actually, as we have seen in section 7.3, uncertainty, as distinct from probability, implies a weight of argument lower than 1 and vice versa. Therefore, the weight of argument is potentially relevant in all the passages in GT where uncertainty, confidence and expectations play a crucial role. This is true in particular for the passages where expectations affect economic behaviour. In particular, sudden and discontinuous shifts of the weight of argument induced by variations in the macroeconomic and policy context of agents' decisions determine significant shifts also in the two crucial functions that determine aggregate income: liquidity preference and marginal efficiency of capital.
Before discussing the role of the weight of argument in GT we have to dispose of a preliminary objection. According to some interpreters,2 the references in GT to TP should not be taken too seriously since Keynes had changed his ideas on probability under the influence of Ramsey (Keynes, 1931). Extrapolating from a famous passage contained in Keynes's review (Keynes, 1931) of Ramsey's posthumous book (Ramsey, 1931), many interpreters claimed that Keynes accepted Ramsey's criticisms of TP and adhered from then on to his subjective approach to probability theory. If true, this assertion would destroy the continuity in Keynes's thought not only in the field of probability philosophy but also as between TP and GT, making meaningless his subsequent references to the weight of argument. O'Donnell rightly maintains that this crucial interpretive issue should be discussed in the light of all the relevant writings of Keynes before and after the alleged conversion around 1931 (O'Donnell, 1990). After an accurate analysis of this kind, he advances seven arguments in favour of the continuity thesis. Further arguments have been put forward by other interpreters (in particular Carabelli, 1988). On this occasion, I do not want to assess these arguments, which on the whole seem to me compelling, but only to complement them with some further considerations from the specific point of view of the weight of argument.
I observe first that both Keynes (1973a ) and Ramsey (1931) believe that the theory of probability is a normative discipline since its rules of inference are based on well-precise rationality requirements. However, according to Ramsey probability theory has to be seen as a branch of formal logic, whereas according to Keynes it has to be treated as an extension of logic to non-demonstrative inference. Before reading Ramsey's own version, Keynes rejected subjective probability theory because of its psychological and arbitrary nature:
in the sense important to logic, probability is not subjective. It is not, that is to say, subject to human caprice. A proposition is not probable because we think it so. When once the facts are given which determine our knowledge, what is probable or improbable in these circumstances has been fixed objectively, and is independent of our opinion. The theory of probability is logical, therefore, because it is concerned with the degree of belief which is rational to entertain in given conditions.
(TP, p. 4)
However, in his review of Ramsey's posthumous book he readily admits that 'Ramsey [...] succeeds in showing that the calculus of probabilities simply amounts to a set of rules for ensuring that the system of degrees of belief which we hold shall be a consistent system. Thus, the calculus of probabilities belongs to formal logic' (Keynes, 1972 ), pp. 338-9). According to Keynes, Ramsey's proof that the subjective theory may be conceived of as normative qualifies such a theory as an acceptable theory, but only in the case of demonstrative arguments where the inference may be understood as a logical implication; and the weight of argument is one. This, however, is an extreme case that applies only when probabilities are numerical. On this point Keynes did not change his mind, as explicitly confirmed in his correspondence with Townshend in 1938: 'a main point to which I would call your attention is that, on my theory of probability, the probabilities themselves are non-numerical' (Keynes, 1979a) , p. 289). This argument is sufficient to preclude a conversion of Keynes to subjective probability theory, with the only possible exception of the extreme case of numerical probabilities coupled with a weight of argument equal to 1. In any case, whenever the relevant knowledge is incomplete and the weight of argument is less than 1, the probability inference, to be distinguished from the classical probability calculus to which Ramsey referred, follows different rules from those that Keynes discussed in TP and tried to apply to economic decisions in GT. This is especially the case with induction, statistical inference (see Carabelli, 1988, chs. 4-7) and causal inference (see Vercelli, 1991; 2001).
The second issue discussed by Keynes in his alleged retreat is the nature of initial, or a priori, probabilities that provide the basis of the inference. Here Keynes declares that he yields to Ramsey, agreeing with him that '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 us merely by natural selection' (Keynes, 1931, pp. 338-39). This is not far from his previous point of view as expressed in TP (see Carabelli, 1988). It is, however, inconsistent with the assertion, often iterated in TP, that probability statements are 'objective' in the sense of logic (see the quotation above). This assertion was a source of countless misunderstandings with his readers since, as became evident with Ramsey's criticisms, many interpreters mainly focused on this specific point. With this assertion Keynes wanted to emphasize the irreconcilable distance between his theory and the pre-Ramsey subjective theory by emphasizing that the degree of probability is not to be taken as psychological or arbitrary belief but as the one 'which it is rational for us to entertain' (TP, p. 35). The word 'objective' does not aim to have deontological overtones but only to emphasize its non-arbitrary relation with rationality; and the word 'logic' does not refer to formal logic, or to the logic of implication, characterizing demonstrative arguments but the extension of logic to non-demonstrative arguments. The acceptance of Ramsey's assertion that initial probabilities are intersubjective rather than objective does not change Keynes's view of probabilistic inference. The crucial difference with Ramsey, before and after 1931, lies in a radically different view of the relationship between probability theory and rationality: 'in attempting to distinguish "rational" degrees of belief from beliefs in general he was not yet, I think, quite successful' (Keynes, 1972 ), pp. 338-9). In fact, in Ramsey the rationality requirements of probabilistic inference are too strong for a general theory of probability as they apply only to a very limited subset of probabilities when they can be expressed as numerical and the weight of argument is one. In contrast, the initial probabilities may be explained in terms of the logic of discovery, which in Ramsey has no clear-cut rationality requirements. In Keynes, on the other hand, the probabilistic inference continues to be conceived of as 'relative ... to the principles of human reason ... does not presume perfect logical insight, and ... is ... relative to human powers' (TP, p. 35). Ramsey's approach, as pursued in particular in his sketch of natural logic, induces Keynes to broaden the scope of non-demonstrative inference whose validity is now seen as relative not only to the premises and background knowledge but also to the pragmatic and semantic context. This may explain the growing attention given to social psychology in GT, particularly in the passages where Keynes attributes a crucial role to uncertainty, but this does not change the essential outlines of his theory of probability inference.
The new point of view adopted by Keynes blurs the clear demarcation put forward in TP between rational and non-rational choice based on 'objective' criteria. This stimulates Keynes to investigate in more depth the grey zone between rational choice in the TP sense and non-rational choices3 based, as in the real world, on the interaction between subjective beliefs and intersubjective beliefs (conventions). As we have seen in section 4, the practical role of the weight of argument refers exactly to this borderline zone of bounded rationality, so that its revival in GT is altogether appropriate and must be taken very seriously (Vercelli, 2005).
In GT the weight of argument plays a crucial role in the central argument of Keynes. In its absence it would be very difficult to demonstrate the inability of the market to regulate itself. In particular, Keynes does not deny that an excess supply of labour may bring about a reduction in money wages; this would reduce the money supply in real terms and this should reduce the rate of interest, so increasing investment and reabsorbing the involuntary unemployment. The reason why this virtuous interaction between real and monetary markets is unreliable is the increase in perceived uncertainty triggered by deflation, leading to a reduction in the weight of argument that shifts the liquidity preference schedule upwards and the marginal efficiency of capital downwards, offsetting the potentially positive effects of deflation.
If we assume soft uncertainty, as classical economics and DTU do, an increase in the perceived risk of a recession associated with wage deflation does not necessarily shift the two curves in a perverse direction since, at least in principle, the additional risk may be insured through hedging techniques or issuing 'Arrow securities' (see Arrow, 1964). In contrast, in the case of hard uncertainty the effects of a change in the weight of argument cannot be insured, so that uncertainty aversion (or second-order risk aversion) shifts the curves in the wrong direction, jeopardizing the process of market adjustment. From the analytic point of view a way out has been concocted by assuming that the liquidity preference curve becomes horizontal at a level of the rate of interest higher than the one that would assure full employment equilibrium (Modigliani, 1944). This way of giving foundations to Keynesian analysis and policy, promoted by the neoclassical synthesis, should be discarded as ad hoc from the point of view of theory and empirical evidence. In contrast, the approach based on the weight of argument provides the proper foundations for the central message of Keynes, namely, that the market may be unable to regulate itself so that full employment equilibrium can be restored and maintained only through judicious policies of intervention in the economy by the state.