However, if we proceed from the conception of rationality adopted by Keynes and developed by the Post Keynesian economists, it is quite easy to show that this is not the case. There are two reasons for this. The first is that any complete analysis of Keynes's theory cannot ignore the two different notions of rationality that he took the pains to distinguish: instrumental rationality, which characterizes the adaptation of available means to desired objectives, and cognitive rationality, which adjusts the uncertainty concerning the environment to the available information.

The conception of instrumental rationality that Keynes proposes is hardly original with respect to traditional theory. Indeed, even in the context of strong uncertainty, such as proposed in the 1937 article in the Quarterly Journal of Economics, agents are not assumed to act in a purely random or irrational fashion: 'the necessity for action and for decision compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability, waiting to be summed' (Keynes, 1973e [1937], p. 114). This leads to the interpretation that Keynes in GT had deliberately accepted the traditional approach of instrumental rationality in order to ease the acceptance of his ideas. As a result, there can be little dispute over the notion of instrumental rationality, and it should not be necessary to point out that Keynes's theory does not imply the assumption of instrumental irrationality. On the other hand, Keynes stresses the originality of his approach to the idea of cognitive rationality and gives it an important role in GT.

The second reason for the mistaken interpretation of rational behaviour in the face of an uncertain environment is that the majority of economies have never taken the time and effort to follow Keynes's explicit references linking the concept of 'animal spirits' to his TP. It is in this context that the relation between the tools of probability and the analysis of uncertainty is of importance. A number of Post Keynesian authors have dealt with this question and we can rely on this work to supplement TP (see Kregel, 1987; Davidson, 1987).

The point of distinction is Keynes's very conception of probability. We have already noted that Keynes did not embrace the frequency theory of probability. Further, as well as being more subtle,^{6} Keynes's approach to subjective probability was also critical:

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, and not merely with the actual beliefs of particular individuals, which may or may not be rational.

(TP, p. 4)

On the contrary, in opposition to the usual 'frequency' theory of probability, Keynes viewed probability as a logical relationship between propositions rather than between event states of the world. Keynes is concerned with 'logical probability' or the 'degree of confirmation' or the 'degree of rational belief' defined as follows: 'Let our premisses consist of any set of propositions h, and our conclusion consist of any set of propositions a, then, if a knowledge of h justifies a rational belief in a of degree a, we say that there is a probability-relation of degree a between a and h' (TP, p. 4).^{7} The problem that Keynes seeks to resolve is the manner in which individuals determine their 'rational beliefs' concerning a proposition when their knowledge of a proposition is not certain.

Keynes considers two ways in which rational belief about a proposition may be reached when knowledge is uncertain. The first is based on the formulation of a probability reached on the basis of uncertain information or of 'doubtful arguments' (TP, p. 3). In the second it is impossible to determine a rational belief, so that it is rational to allow 'animal spirits' to determine actions. It is precisely these two types of uncertainty that traditional theory excludes by assuming that individuals have full or certain knowledge of what Keynes calls a 'primary proposition' (the relation that one seeks to validate, written as p = ah in TP (p. 11).

Criticism of any use of the frequency theory of probability has tended to combine, and sometimes confuse, these two separate forms of uncertainty. For example, as noted above, Shackle considers the investment decision as a 'crucial' decision that cannot be repeated. Thus, the facts of experience (or the 'premises' in 'h' as defined in TP) cannot contain any repetitions of the event. As a result, there is no reason for the probabilities to sum to 1. It is in this context that Shackle's rejection of the applicability of statistical probabilities should be understood. It is undeniable that the majority of investment decisions refer to situations in which the degree of rational belief or the 'secondary propositions' (TP, p. 11), ph exhibit uncertainty in the first sense defined by Keynes, that is, when the probability associated with the secondary proposition is less than one (p|h < 1).

However, even in this case it is possible to calculate a probability by formulating a secondary proposition concerning the primary proposition that, say, an investment in a particular project will produce a particular return given the information contained in 'h'. In situations of this first type of uncertainty, the approach suggested by Keynes does not imply that the behaviour adopted will be 'irrational'. In fact, every entrepreneur confronting the same situation (and with the same mental capacity) should have the same degree of rational belief and should act on this in exactly the same way. A difference in behaviour could arise only from subjective differences associated with each individual entrepreneur, including differences in their evaluation of the information in 'h'.

This definition of 'rationality' clearly differs from that employed by Shackle. Although the situation examined above is characterized by an inability to calculate a statistical probability based on a frequency distribution, in contrast to Shackle, who considers such decisions as 'irrational', Keynes could classify it as a decision based on a degree of rational belief that is less than perfectly certain. It is not a question of subjective 'caprice' or of any kind of 'irrationality'. This highlights an importance consequence of the distinction between the analysis of risk and Knight-Keynes uncertainty in an analogous divergence between Keynes's notion of rationality and the traditional concept underlying rational expectations.

It should first be noted that rational expectations theory shares Keynes's opinion that the theory of probability should refer not to the occurrence of events but to the assertions of individuals concerning the occurrence of events. As Kregel points out, 'rational expectations might thus be described as a theory concerning the formulation of secondary propositions containing primary propositions that are statistical probabilities of events generated on the basis of an economic model and which have probability approaching certainty as the observations of the events occurring over time included in h become large' (Kregel, 1987, p. 524). In the case of the analysis of the theory of rational expectations, the certainty of rational belief is linked to the hypothesis that the distribution of the subjective probability of the variable under consideration in h of the secondary proposition ph can be assimilated to the objective distribution that actually produces the current values of the variable. But, as pointed out above, this is possible only if the process that determines the events that are the object of expectations is ergodic. Kregel's analysis thus completes the Post Keynesian critique of the theory of rational expectations initiated by Davidson (see, in particular, Davidson, 1982-83). According to Kregel 'the term "rational", as used by traditional theory, can only refer to the limited conditions of certainty of rational belief in a world governed by ergodic stochastic processes; the possibility of decision or choice in uncertain conditions is thus excluded, or classified as "non rational"' (Kregel, 1987, p. 524). In opposition, Post Keynesian analysis develops a theory of the formation of expectations applicable to situations in which the degree of rational belief is less than certain.

It should not be overlooked, however, that Keynes identifies a second type of uncertainly, which precludes the determination of any kind of rational belief. This second form of uncertainty in fact covers two types of uncertainty, which it is necessary to keep analytically separate. The first case corresponds to the possibility of the non-comparability of the probabilities associated with the secondary propositions. The primary reason for this is that the facts of experience that are incorporated in 'h' can be extremely heterogeneous or even non-existent. This provides the basis for Keynes's affirmation that 'our knowledge of the factors which will govern the yield of an investment some years hence is usually very slight and often negligible. If we speak frankly, we have to admit that our basis of knowledge for estimating the yield ten years hence [of an investment] amounts to little and sometimes to nothing' (GT, pp. 149-50). In other terms, it will often be the case that it will be impossible to place an ordinal measure on the probability in question. In these conditions, the principle of 'insufficient reason' or the principle of indifference (which states that, if there is no reason to prefer a possible solution to another, each should have equal probability) must be rejected (see Keynes, TP, p. 45).

It thus becomes necessary, following Hicks, to reformulate the axiom of the comparability of probabilities in the following manner: starting from a certain set of information, it is possible to say of two propositions, A and B, that A is more probable than B, or that B is more probable than A, or that they are equally probable, or that they are not comparable.^{8} It should also be noted that, contrary to certain interpretations of Keynes's analysis (for example, Lawson, 1985) that limit uncertainty to only those cases where the determination of probability is impossible, the author of

TP considered the non-calculability and the non-comparability to be equivalent as expressions of uncertainty.

However, if the non-comparability of probability implies uncertainty, it will be impossible for agents to formulate rational beliefs. To deal with this question Keynes introduces another essential element in his theory of logical probability: the weight of the argument. It is this factor that comes to dominate the decision to act:

It seems that there may be another aspect in which some kind of quantitative comparison between arguments is possible. This comparison turns upon a balance, not between the favourable and the unfavourable evidence, but between the absolute amounts of relevant knowledge and of relevant ignorance respectively ... As the relevant evidence at our disposal increases, the magnitude of the probability of the argument may either decrease or increase, according as the new knowledge strengthens the unfavourable or the unfavourable evidence; but something seems to have increased in either case, — we have a more substantial base upon which to rest our conclusion. I express this by saying that an accession of new evidence increases the weight of the argument.