2.1. Ontological uncertainty, nonergodicity and probabilities in an economy subject to change

6As noted above, Keynes drew a sharp distinction between the analysis of decision-making in traditional theory and the conditions faced by decisionmakers in the real world. For Keynes, the characteristic feature of a relevant theory of decision-making under uncertainty is the recognition of the importance of distinguishing between risk and uncertainty. To understand this theory, it may be useful to recall the distinction he makes in the 1937 Quarterly Journal of Economics article between events that are uncertain and events that are only probable: “By ‘uncertain' knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty... The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention... About these matters, there is no scientific basis on which to form any calculable probability whatever. We simply do not know”. (Keynes [1973c] [1937], p. 113-14)

7Keynes even denies the possibility of describing the game of roulette as being uncertain even though it is the most common example of uncertainty cited by traditional theory. The crucial point for Keynes is the inadequacy of statistical quantification in the form of a probability for the analysis of uncertainty since “human decisions affecting the future, whether personal or political or economic, cannot depend on strict mathematical expectation, since the basis for making such calculations does not exist” (GT, p. 162-3). Keynes clearly stated his view on this fundamental limitation of orthodox (i.e. “classical”) economic theory in an exchange with Townshend [1]: “I think there is a great deal to be said for your view that the classical theory is not valid on any assumptions, and that you have put your finger on the spot in saying that they are trying to describe a world in which risk exists without uncertainty”. (Keynes [1979] [1937], p. 258)

8Keynes thus considered “classical” economic theory as having reduced the analysis of behavior under uncertainty to the special case of risk in which there exists a well-defined probability distribution with a complete set of possible future outcomes and associated relative frequencies. He sought to develop an original approach aiming at encompass the theory of decision-making under conditions of risk within a more general theory that allowed for a broader conception of uncertainty. The interest – and the difficulties sometimes encountered by commentators – in interpreting the uncertainty in the sense of Keynes is that it has both an ontological and an epistemic dimension [2].

9The ontological dimension relates to the nature of the real causal structure with which the choice situation is concerned. Uncertainty stems from the complex and unstable configuration of the universe itself. This dimension is emphasized by Keynes throughout his work. In the Treatise on Probability (Keynes ( [1973a], [1921]), hereafter TP), he highlighted the fact that “states of the universe, identical in every particular, may never recur” (TP, p. 286), or that “although nature has her habits, due to the recurrence of causes, they are general, not invariable” because “the possible contingencies are too numerous” (TP p. 420). Likewise, in the General Theory, he takes up this idea by pointing out that “the outstanding fact is the extreme precariousness of the basis of knowledge on which our estimates of prospective yield have to be made.” (TG, p. 165). Similarly, when considering the investment, Keynes points out that “there is not one of the above factors which is not liable to change without much warning, and sometimes substantially. Hence the extreme complexity of the actual course of events.” (TG, p. 254).

10This form of uncertainty has been the subject of much work by economists whom Coddington [1976] described as “Fundamentalist Keynesians”, including so-called “Post-Keynesian economists” as Joan Robinson, George Shackle, Paul Davidson or Jan Kregel. They have adopted the terms “true” or “fundamental” uncertainty to identify the definition of uncertainty originally formulated by Keynes. They have sought to characterize the conditions of its existence by referring to notions such as “historical time” and “crucial decision-making”.

11Thus “Post-Keynesian theory... is concerned primarily with the depiction of an economic system expanding over time in the context of history” (Eichner and Kregel [1975], p. 1294, emphasis in the original) so that time is “a realworld device which prevents everything from happening at once” (Davidson [1980], p. 158). In fact, since the basic economic decisions concerning production and investment are processes that take time and are essentially irreversible, they are said to take place in historical or calendar time. Decisions that lead to actions that cannot be reversed or repeated to produce more desirable outcomes are called “crucial” decisions. In the “neoclassical” approach, in contrast, either time takes the form of a logical and thus a reversible process, or agents are simply discovering an already known future; their actions cannot determine the future. Consequently, when these issues are treated in the traditional perspective, it is in terms of probabilistic risk, since true uncertainty as defined by Keynes is not considered.

12Shackle was the first to note that historical time implied what he called “crucial” decisions: an agent faces a crucial decision when he “cannot exclude from his mind the possibility that the very act of performing the experiment may destroy forever the circumstances in which it is performed… Crucialness is the real and important source of uniqueness in any occasion of choosing” (Shackle [1955], p. 6 and 63). In other words, crucial decisions describe situations in which the act of taking a decision destroys the existing distribution functions so that a crucial decision that cannot be repeated [3].

13Among Post Keynesians Davidson [1982-83, 1991] has argued that these two characteristic features of uncertainty in the “real world”—historical time and crucial decisions—imply that the stochastic process that generates real world events is “non-ergodic”. An ergodic process is one for which time and space averages are equal; what happens at points in time for different initial states coincides with what happens over time for a given initial state. This suggests that over time economic processes follow averages that can be discovered by rational agents, thus implying the possibility of rational expectations. In contrast, Davidson argues that agents would be truly uncertain in conditions of non-ergodicity.

14The identification of Keynesian uncertainty to a world characterized by non-ergodicity of economic time series generally leads fundamentalist Keynesian economists to reject the relevance of the rational expectations hypothesis. Indeed, under non-ergodicity conditions, sampling from the past in the manner implied by the rational expectations theorists is not rational since, even if agents have the possibility to assemble and process all the relevant information pertaining to past and present outcomes, the future course of events will still not reveal itself.

15Moreover, the rejection of the hypothesis of rational expectations is often accompanied by an outright rejection of probabilistic reasoning for studying economic decisions. In particular, Davidson considers that, “when agents make crucial decisions they necessarily destroy any stochastic processes that may have existed at the point of time of the decision” ( [1982-83], p. 192). This implies that in conditions of non-ergodicity “objective probability structures do not even fleetingly exist, and a distribution function of probabilities cannot be defined” (Davidson [1991], p. 132). In other words, for Davidson, uncertainty is seen as opposed to probability and probabilities represent knowledge for when probabilities are available, uncertainty disappears: only probabilistic knowledge exists, never probabilistic uncertainty: “In the ergodic circumstances of objective probability distribution, probability is knowledge, not uncertainty!” (Davidson [1991], p. 132) [4]. In the same vein, Shackle underlined that the representation of uncertainty by means of probability is problematic because, on one hand, it may not be feasible to portray the set of future possible realizations (Shackle [1972], p. 23) and on the other hand, the decision to invest is a crucial decision that cannot be repeated. The distant future is “essentially a void” (Shackle [1974], p. 36) and investments are subject to large and sudden revisions in profit expectations, and market valuations of assets (bonds and shares) are subject to violent shifts in market sentiment far beyond the reach of probabilistic calculation. Each reasoner has a distinct subjective framework, a “personal intellect background, temperamental constitution, educational history” (Shackle [1972], p. 389) and so on. He preferred to view investment decisions as “irrational... or -non-rational” (Shackle [1967], p. 130).

16These conclusions have often led a large number of economists to identify Keynesian uncertainty with radical subjectivism, and the associated scientific and theoretical nihilism. This is clearly the interpretation of Keynes adopted by Lucas, who writes that “in cases of uncertainty, economic reasoning will be of no value” (Lucas [1981], p. 224). The most widespread opinion on the question is well summed up by Walliser ( [1985], p. 17), who writes that Keynes’s ideas on uncertainty have “remained at the pre-formal stage, they do not seem to have had any general “cultural” influence on economic thinking except as complications or useless subtleties”. As a result, in the contemporary literature Keynes’s analysis is either criticized or credited as an approach to macroeconomics that is incompatible with the traditional concept of individual behavior based on the assumption of economic rationality. The widely shared position within contemporary mainstream approaches, whether classical or Keynesian in inspiration [5], is (1) that individuals’ decisions must be analyzed in an environment of probabilistic risk and (2) that this environment is the only one that can guarantee a relevant analysis of the individual rationality embodied by the rational expectations hypothesis.

2.2. Epistemic uncertainty, logical probability and rational choices in a complex decision-making environment

17Contrary to the limitations and criticisms presented above, we believe that a careful rereading of Keynes’ work shows that the existence of true uncertainty and a non-ergodic environment are not synonymous with irrationality or theoretical nihilism. In Keynes’ approach, the complexity of the decision-making environment of an economy “subject to change” is compatible with an original and coherent theory of individual rationality. This approach is based on a specific theory of probability which relies on an “epistemic” conception of uncertainty. The epistemic dimension relates to the decisionmaker’s knowledge and understanding of the real causal structure with which the choice situation is concerned. This theory is based both on the notion of logical probability he developed in his TP and on the specific form of rationality studied in the GT and to which he refers in his 1937 Quarterly Journal of Economics article.

18We thus believe that there is a real coherence and continuity on this subject in Keynes’ work, which to some extent links our work to the “continuityor-change?” debate on the unified and coherent nature of the author’s approach. Some researchers (Bateman [1987], Davis [2009]; Gillies [2003]) argue that there is radical discontinuity between the Keynes of the TP and the author of the GT. One Keynes would praise the rational reasoning in terms of probability and the other Keynes would praise the irrationality of subjectivity and psychology. Our position is closer to that of authors like O’Donnell [1989, 1990], Carabelli [1988], Gerrard [1994] or Runde [1994] who argue that there is continuity in the development of Keynes’ analysis of rational behavior from his early work on probability and rational belief in the TP to his analysis of economic choices under uncertainty in the GT. In other words, the positions considering on the one hand that there is theoretical discontinuity between the TP and the GT and that on the other hand the behaviors described in the GT are purely subjective or irrational don’t seem relevant to us.

19To show this, it is useful to re-examine, the very nature of probabilities that can – according to Keynes – be used in a relevant way for studying individual decisions. We have already noted that Keynes did not embrace the frequency theory of probability. Further, as well as being more subtle, Keynes’s approach to subjective probability was also critical.

20In contrast 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”. The problem that Keynes tries to solve is the manner in which individuals determine their “rational beliefs” concerning a proposition when their knowledge of a proposition is not certain; thus in the TP, Keynes noted that “in as much as it is always assumed that we can sometimes judge directly that a conclusion follows from a premiss, it is no great extension of this assumption to suppose that we can sometimes recognise that a conclusion partially follows from, or stands in a relation of probability to a premiss.” (TP, p. 56).

21This line of thought suggests that there might be a logical theory of partial entailment generalising the usual theory of full entailment which is found in deductive logic: “Let our premises 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 ?, we say that there is a probability-relation of degree ? between a and h. This will be written a/h = ?.” (TP, p. 4).

22So a probability is always associated to a degree of a partial entailment. Keynes further makes the assumption that if h partially entails a to degree ?, then, given h, it is rational to believe a to degree ?. For Keynes probability is a degree of rational belief not simply a degree of belief.

23The original conception of probability proposed by Keynes in the TP is particularly adapted to the analysis of economic decisions under uncertainty within an economy subject to change. Indeed, he defines a classification linking different kinds of decision-making environments – and their respective degree of uncertainty – to specific forms of rationality characterizing each of these degrees of uncertainty. This classification is based on the identification of three main forms/degrees of uncertainty.

24The first form of uncertainty refers to situations in which the probability, that is the degree of rational belief a/h is less than one (? < 1). For Keynes, 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.

25In situations of this first type of uncertainty, every economic agent 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 behavior could arise only from subjective differences associated with each individual, including differences in their evaluation of the information in h. Although such a situation is characterized by an inability to calculate a statistical probability based on a frequency distribution, Keynes classifies 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. Although in one sense the probability-relation is objective and any person operating from the same knowledge base will arrive at the same secondary proposition, in another sense it is subjective because knowledge/evidence varies across individuals and over time, and the rationally justifiable degrees of belief in a given conclusion will change accordingly. Probabilistic knowledge cannot be defined in terms of absolutes. Just as our estimates of probability are relative to our knowledge of other propositions, they are also relative to our capacity for logical insight (TP, 18-19).

26This first form of uncertainty for which it is possible to construct a rational degree of belief based on experience and knowledge clearly refers to the analytical framework of short-term anticipations in the General Theory. Indeed, learning by experience requires enough repetitiveness to allow agents to observe and understand phenomena. It also requires that the degree of complexity of the experience itself be not excessive lest agents will not understand the nature of the experiment and draw its lessons. The short-term expectations framework perfectly meets these conditions since: “[T] he process of revision of short-term expectations is a gradual and continuous one, carried on largely in the light of realized results” (GT, p. 50). Experience guides these expectations because “[i] t would be too complicated to work out the expectations de novo whenever a productive process was being started; and it would, moreover, be a waste of time, since a large part of the circumstances usually continue substantially unchanged from one to the next” (GT, p. 51). The missing premises in the case of production decisions are not, under normal conditions, impossible to visualize with some assurance: “For production decisions, the premises are safer, formal logic can dominate expectations formation, and the possibility of induction is preserved” (de Carvalho [1988], p. 79).

27Keynes identifies a second type of uncertainty. This situation 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, p. 149-50). In other words, it will often be the case that it will be impossible to place an ordinal measure on the probability in question.

28To deal with the uncertainty induced by the non-comparability of probability, Keynes introduces another essential element in his theory of logical probability: the weight of the argument, exposed in Chapters 6 and 26 of the TP. The weight of an argument is a measure of the amount of evidence, h, on which a proposition is based. It provides a measure of the well-foundedness of non-conclusive arguments. Arguments of high weight are based on much information, are well-founded and hence merit high degree of confidence, regardless of whether their probability is high or low [6].

29The notion of weight of argument is crucial to differentiate Keynes’ decision theory from that of classical theories, whether they are objectivist à la Morgenstern and Von Neumann or subjectivist à la Savage. The latter are in fact valid only when we reason with a weight of argument equal to one, i.e. at its maximum level, which corresponds to simple situations of risk or to what Vercelli [2001, 2016] calls situations of “weak uncertainty”. In this decision-making environment, the only forecasting errors of decisionmakers are due to stochastic errors that are by nature unpredictable, while expected systematic errors are excluded from the field of possibilities [7]. On the contrary, the possibility highlighted by Keynes of situations where the weight is between 0 and 1, between the two extremes – the simple stochastic risk and the situation of complete relevant ignorance – makes it possible to take into account and analyze learning behaviors aimed at increasing the weight of argument in order to decrease the level of ignorance and reduce the expected systematic errors.

30The nature of the rationality adopted by economic agents in front of this type of uncertainty can also be enlightened referring to the approach proposed by O’Donnell [1990]. He emphasizes that the TP is constituted by two distinct domains of analysis. The first domain is called the “determinate domain”. In this case, economic agents have a “strong rationality”. Within this domain, determinate answers are available to the questions posed, and human reason is strong in the sense that it can provide such answers. Examples of determinacy are the following: probabilities are known because “agents have sufficient logical insight; probabilities are comparable because they belong to the same series; the weights of arguments are comparable; and probable values may be ordinally ranked because agents can form judgments combining nonnumerical probabilities with (possibly) nonnumerical values” (O’ Donnell [1990], p. 257).

31The determinate domain of the TP thus encompasses both short term expectations of the GT and also long-term expectations with relatively high weight. In all these cases, “human rationality is patent because it generates definitive answers, which lay claim, in Keynes’s scheme, to objectivity and truth” (ibid., p. 257).

32This kind of rationality can be found in Chapter 12 of the GT. Indeed, when Keynes evokes the role of confidence in the decision to undertake an investment, it is precisely the “weight of the argument” that he has in mind (GT, p. 148-49). Thus, when probabilities cannot be compared and it is impossible to formulate a rational belief, it is the weight of the argument which becomes the determining factor, that is, which allows the evaluation of investment alternatives that produces a final decision to act. The subjectivity that resides in the evaluation of different individuals may then become dominant, since it is individual experience that will determine the weight that will be assigned to new information. As Kregel pointed out ( [1987], p. 526), it is only at this point that the idea of “animal sprits” enters into the decision-making framework of the GT. Animal spirits will be the final determinant of the moment at which the weight of the argument attached to a proposition is sufficient to make it dominant over all other possible propositions. They thus represent, in Keynes’s words, the “spontaneous urge to action rather than inaction”. It is important to note at this point that Keynes insists that this “spontaneous urge to action” does not depend on “waves of irrational psychology” (GT, p. 162), but rather that this type of decision is securely founded in “rational spirits” (Kregel [1987], p. 526), by “our rational selves choosing between the alternatives as best we are able, calculating where we can, but often falling back for our motive or whim or sentiment or chance” (GT, p. 163).

33Another interesting and more contemporary application of the rationality used within the determinate domain is provided by the approach of Hyman P. Minsky, whose ideas were brought to the forefront during the financial crisis of 2007. Although rarely emphasized by commentators [8], the theory of financial instability he develops is based on a form of rationality strongly inspired by the concepts of and methodology present in the TP. This is not surprising inasmuch as Minsky’s references to TP are present in his work from the 1970s. For him, there is undeniably a very strong influence of TP on GT: “In interpreting The General Theory it should be kept in mind that Keynes was first the author of a Treatise on Probability” (Minsky [1975], p. 67) and TP provides relevant tools for the analysis of decisions in situations of uncertainty: “Keynes held that there was no way of replacing this uncertainty with certainty equivalents, and furthermore that the relevant probabilistic propositions and the weight attached to such propositions change, not in a random or unpredictable manner, but in a consistent manner in response to events” (Minsky [1975], p. 66) [9].

34It is on the basis of this theoretical background that Minsky analyses the behavior of banks. Minsky’s bankers will typically seek to assign a degree of rational belief to a primary proposition (conclusion) as of the type: “the borrower is a good credit risk”. Included in the information set, h, will be the credit history of the borrowers. Here we clearly find the influence of the TP where the determination of the logical probability – that is to say of the degree of rational belief assigned to a proposition – is a function of the objective data drawn from experience.

35To this objective factor influencing the formation of banks’ expectations, there is an added subjective component. It implies that realized outcomes (for example, the quantity of loans that has been repaid) can induce banks to modify their decisions as to the amount of credit to be granted, independently of how these outcomes fit in with their expectations. This means that, even if results merely confirm the banks’ expectations, it is likely that, encouraged by increased confidence in their forecasting methods, they will make more loans. Accordingly, the longer the period during which the debt to equity ratio of the economy remains at a certain level without provoking a financial crisis, the more banks are likely to raise their estimates of the maximum level of indebtedness (in proportion to the value of assets both they and potential borrowers hold) to which it is prudent to agree. In Minskyan terms, this means an erosion of the “margins of safety” required by banks.

36Here again, the reference to the concepts of weight of the argument of the TP and state of confidence of the GT is striking. More precisely, as a period of expansion goes on, the amount of positive information in h increases and in doing so increases the weight of the argument in favor of accepting the conclusion a as a correct assessment of borrowers’ creditworthiness. But, as the expansion goes on, there are more and more “good credits” who represent acceptable margins of safety. In periods of boom, these margins may thus be set at levels that are too low to effectively protect the balance sheet because investors and financial institutions believe that risks are in reality low.

37Thus, the banker become more confident, without any necessity for euphoria or excessive optimism. All these behaviors are neither irrational nor myopic. As banks have to take their decisions in a situation of true uncertainty, they are led to adopt behaviors that are rational in this type of environment, i.e. behaviors similar to the ones described by Keynes in the TP and the GT. In the determinate domain, it consists in mixing an objective part, linked to experience and objective observations, and a more subjective, but equally rational part, linked to the weight of argument/state of confidence. It is in this context that financial fragility highlighted by Minsky builds up endogenously and rationally in the expansionary phase of a business cycle.

38Finally, Keynes highlights a third situation of uncertainty. This appears when the weight of argument is very weak, or even non-existent, which involves the impossibility of obtaining a cardinal measure of the probability. Far from being rare, Keynes considered this the most likely case whenever expectations were formed over the long period. This point of view appears very clearly in the TP, which contains successive warmings against what Keynes calls “numerical expression” (TP, p. 21-22). Notably, he points out that:

39[i] t has been assumed hitherto as a matter of course that probability is, in the full and literal sense of the word, measurable. I shall have to limit, not extend, the popular doctrine... The calculus of probability has received far more attention than its logic, and mathematicians, under no compulsion to deal with the whole of the subject, have naturally confined their attention to those special cases... where algebraical representation is possible (ibid.).

40Keynes thus considered that the possibility of obtaining a numerical (cardinal) measure of the degree of probability as only occasionally possible: “A rule can be given for numerical measurement when the conclusion is one of a number of equiprobable, exclusive, and exhaustive alternatives, but not otherwise” (TP, p. 122).

41Now, in most situations concerning decisions with long period consequences, this is far from realized. It then becomes very difficult to endogenize the process of expectations formation and, as Keynes notes, “the state of long term expectation [...] cannot be inferred from the given factors” (Keynes [1973d] ( [1934], p. 480) so that these decisions must be considered as being taken outside the “realm of the formally exact” (GT, p. 2).

42Economic agents have now to face a new decision-making environment corresponding to what O’Donnell calls the second or “indeterminate” domain of the TP where “probabilities are unknown for want of reasoning power; it is theoretically impossible to compare probabilities; weights are also non-comparable; and agents are unable to combine probabilities and values where either or both are non-numerical” (O’Donnell [1990], p. 257). For O’Donnell, the existence of an indeterminate domain was already recognized by Keynes in the TP, even though it was relegated to a subordinate position and its implications never explored in detail. But after the TP, however, Keynes’s priorities changed, with increased significance being given to this non-determinate region.

43Of course, in this situation strong rationality is impotent. However, for Keynes, the inability to apply strong rationality in certain circumstances does not imply the adoption of irrational behavior. Economic agents will follow a form of “weak rationality” consisting in developing strategies and responses different from those adopted in the determinate domain.

44More precisely, Keynes suggests that the optimal behavior to be adopted by decision makers is to fall back on their common sense as reflected in “the actual observation of markets and business psychology” (GT, p. 149) rather than on the calculus of probability. Thus, entrepreneurs will first consider their past experience, and may presume that “the most recently realized results will continue, except in so far as there are definite reasons for expecting a change” (GT, p. 51.) This initial response comes to the same thing as adopting an extrapolative behavior that gives the present and the recent past an equivalent role to that which they play in the short period. In the second place, conscious of the lack of information and of the reliability of their individual judgements, entrepreneurs may adopt a conventional attitude: by doing so, they will “fall back on the judgement of the rest of the world which is perhaps better informed in such a way that behavior permanently conforms to that of the majority or the average and the psychology of a society of individuals each of whom is endeavoring to copy the others leads to what we may strictly term a conventional judgement” (Keynes [1973c] [1937], p. 114). It is against this background that Keynes’s remark that “in practice we have tacitly agreed, as a rule, to fall back on what is, in truth, a convention” (GT, p. 152) should be interpreted. Finally, entrepreneurs may admit that the “existing state of opinion” as expressed by the evaluation of the market is the only one that should be considered the “correct summing up of future prospects” for investment (Keynes [1973c] [1937], p. 114). But included in this market evaluation will be “all sorts of considerations... which are in no way relevant to the prospective yield” (GT, p. 152). In fact, in these conditions the calculations of agents count for less than their “nerves and hysteria, and even digestions and reactions to the weather” (GT, p. 162). It thus becomes easier to understand why long-run expectations, and thus the marginal efficiency of capital, can be considered as being subject to sudden, sometimes violent, changes, marked by waves of optimism and pessimism.

45Nevertheless, it is important to point out that although Keynes agreed that markets actually adopt conventional expectations, he never accepted them as a general rule. In particular, for Carabelli and De Vecchi [2001], even in situations of strong uncertainty, economic agents can form what the authors call “reasonable expectations” which they distinguish from “conventional expectations”. According to them, Keynes considered conventions as an artificial means by which economic agents rationalize uncertainty only in cases of total ignorance. On the other hand, the existence of a limited knowledge, however small it may be makes it possible to use an autonomous reasonable judgement that guides action. Within this context, “reasonable expectations are not grounded on rules, but on logical probabilities, i.e. upon ‘real', limited knowledge or upon reasons in which we ‘really believe'” (Carabelli and De Vecchi [2001], p. 280) [10]. In other words, the “reasonable” economic agent, when able of doing so, should base his expectations on his own personal judgement independently of traditional judgements and conventions. He can do this by taking advantage of all the limited “real” knowledge available to him.

46Interestingly, conventional and reasonable expectations coexist in Chapters 12 and 13 of the GT where Keynes describes actual markets, with agents characterized by different degrees of limited knowledge. Some agents are ignorant, i.e. they lack judgement or even limited knowledge, or they are operating in situations where logical probability is intrinsically inapplicable. Others are “skilled” agents, i.e. they are “expert professionals” who possess “judgement and knowledge” (Keynes [1936], p. 154, 156): they are the short-term speculators and the long-term investors (entrepreneurs). [11] In the GT, the speculative motive is defined as “the object of securing profit from knowing better than the market what the future will bring forth” (Keynes [1936], p. 170). Speculators do not follow conventions but are concerned with “foreseeing changes in the conventional basis of valuation a short time ahead of the general public” (Keynes [1936], p. 154). In other words, speculators follow “probable” knowledge in trying to anticipate market conventions: the continuity of the GT with the TP is apparent.

47Thus, in Keynes’ approach, even in the most extreme conditions of uncertainty, behaviors based on a probabilistic analysis are quite possible and will be rationally adopted by the most skilled agents. The foundations of this analysis are mainly developed in chapters 3, 15, 17 and 26 of the TP as well as in the correspondence he had with Hugh Townshend between 1936 and 1938. In the Chapter 26 of TP dealing with the “Application of probability to conduct”, Keynes proposes a theory of “non-numerical” or “numerically undetermined” probabilities. More precisely, he seeks to establish a numerical measure of a relation of probability through the method of “numerical approximation” allowing to link non-numerical probabilities to numerical ones: “Many probabilities, which are incapable of numerical measurement, can be placed nevertheless between numerical limits. And by taking particular ‘non-numerical' probabilities as standards a great number of numerical comparison or appropriate measurements become possible” (TP, p. 176). As pointed out by Zappia, “In uncertain settings Keynesian agents are not forced to rely on ‘conventions' or ‘useful mental habits' as if complete ignorance would represent the entire spectrum of economic activity. […] In trying to focus on a positive analysis of decision-making under uncertainty, therefore, one is simply adhering to Keynes’s long-standing commitment to interpret reasonable judgement in a, surely unconventional, probabilistic set-up” (Zappia [2016], p. 855).

48This relatively understudied aspect of Keynes’s theory is fundamental in more than one respect. On the one hand, it marks a clear differentiation with certain fundamentalist interpretations recalled above which exclude any recourse to probabilistic reasoning in situations of strong uncertainty. On the other hand, it offers an original analytical framework for the study of decisions in an uncertain environment, the use of non-numerical probabilities and the possibility of inexact numerical comparison making this approach very different from the strict Bayesian approach of subjectivists à la de Finetti and Savage [12].

49This first part enabled us to present and clarify the impact of considering a truly uncertain economic environment on the methodology used by Keynes. For him, the complexity and non-ergodicity of the real world are not synonymous with the irrationality of economic agents and do not induce any theoretical nihilism. On the contrary, it is the integration of true uncertainty as a central element of his approach that allows him to develop a theory of economic decisions that is both original and coherent. As we have pointed out, the main originality of this theory rests on a well-argued classification of the different forms of uncertainty and the way in which they determine the specific forms of rationality associated with them: the highlighting of greater or lesser degrees of uncertainty goes hand in hand with the definition of more or less strong forms of rationality. In this framework, when uncertainty is at its highest level, and even when an ordinal or cardinal measure of probability is impossible, Keynes provides a coherent set of tools for analyzing economic decisions. Even if a measurable degree of rational belief cannot be obtained, the choices of economic agents will be rationally governed by conventional attitudes or animal spirits but also, often, by a reasoning based on the limited but real knowledge available to economic agents and even by non-numerical probabilities.

3.1. Keynes, economic behaviour and philosophy

53This other conception of Keynes’s works is not based on economics mainly interpreted as a language. It contrasts with “classical” and modern mainstream which assume in common a closed and self-contained conception of economics based on given and exogeneous “fundamentals” (preferences, techniques and distribution norms and rules) a priori attributed to each atomistic and specific individual agent. Quite the contrary, it is based on the complete set of social sciences and on philosophical foundations. Therefore it is not a priori self-contained but open.

54First of all, for the defenders of the traditional view of Keynes’s economics based on a closed system, the scientific nature of our discipline is strictly connected to its strict autonomy with regard to other social sciences or to philosophy; thus any assumed form of dependence between economics and these sciences or philosophy – even limited – would indeed imply that economic “fundamentals” are no longer self-contained and do no longer exist without the help of other social sciences; therefore the so-called “microeconomic foundations” of rational choice would lose their basic importance or even disappear.

55Secondly, we stressed earlier that Keynes’s insistence on the necessity of a realistic economics implied a major difference between Keynes’s and the traditional approaches of decisions in a context of uncertainty: actually the notion of uncertainty makes no sense in this second approach; the traditional view indeed refers to a world in which the concept of computable risk is the only one which remains (see what we noted in part 1 concerning Lucas).

56Thirdly, a careful read back of Keynes’s writings would contradict the very coherence of the traditional approach; if economics is supposed independent from philosophy in these writings, it would indeed be necessary to find the real intellectual meaning of such a broad space devoted by Keynes to philosophy and not to ignore and cancel it.

57Conversely, the “classical” and the modern mainstream Keynes’s interpretations cannot be accepted when they ignore the relation of economics and philosophy even if the contents of this relation varies from one interpretation to the next. This is one of the major conclusions of part 2. For instance we could here refer to Carabelli [1988], de Carvalho [1988], Gerrard [1994], O’Donnell [1989, 1990], Minsky [1975] or Zappia [2015] who all contested the theory of rational choice with uncertainty based on a closed system. They replaced it by various interpretations of Keynes’s theory of decision making; but these different interpretations could not have been built if they had not in common the definition of economics as an open science requiring specific societal or philosophical foundations of economic behavior and the choice of empirical observations allowing a characterization of the “real world”.

58To a large extent this opposition between both interpretations of Keynes’s intellectual construction reflects the fundamental meaning of the philosophical and methodological foundations of his writings.

59As we know (see Davis [2009]), Keynes’s youth was first and strongly influenced by the philosophical debates which took place in Cambridge since 1820 when the Apostles Society was created by George Tomlinson. Now, concerning the relations of economics and philosophy, this Society allowed discussions and mutual exchanges inside or outside of it between Keynes and four major Cambridge philosophers of the XXth century who shared a part of their common academic life: G.E. Moore, B. Russell, A.N. Whitehead and L. Wittgenstein. Keynes was also aware of the contributions of H. Sidgwick, A. Marshall, and of his own father John Neville who belonged to another previous generation, which did not accept to include economics among pure natural sciences and agreed on the fact that economic science had to be built on induction, defined as an empirical generalization of well-established facts and therefore on a given and preliminary view of the “real world”.

60Keynes took this view into account but was more influenced by Moore and by some members of the Bloomsbury Group as R. Fry or L. Strachey for instance. He had important philosophical intellectual and constructive exchanges with them on art, science, philosophy and society.

61At last, one of the differences between Keynes and Moore is related to the relation between universal and individual assertions and judgements and we will start here from it. In his 1904-1911 manuscripts, Keynes indeed criticized Moore’s conceptions. In these writings, Keynes discussed in particular four Moore’s issues: (i) has individual behavior to be conform to general rules?; (ii) how can we characterize the individual evaluation of a given probability?; (iii) what is the importance of the individual capacity to make judgements? and (iv) what is the difference between individual egoism and utilitarianism?

63This reference and the other ones show that since the first decade (in relation with Moore) to the last one of Keynes’s life, the core of his approach was never a set of macro-magnitudes as such (he never used the word “macroeconomics” in his writings) but a specific open conception of individuals different from the self-contained one developed by what Keynes called “orthodoxy” in the GT.; this crucial characteristic obviously exclude a conception of “macroeconomics” based on aggregation and opened the way to a conception based on interaction between agents and including the concept of complexity. Why this difference? We noted earlier that Keynes “took into account” the idea expressed by the generation (including his own father) which preceded him, i.e., the fact that economic science had to be built on logic but also on induction seen as a simple empirical generalization of well-established facts. Now this view and its reference to the “real world” exclude formal aggregation and requires the use of interactive agents and complex relations.

64In line with part 2 it is now time to be analytically more specific, mentioning the concept of probability and the way individuals try to connect it with economic reality: “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 it 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: .4)

65This quotation of the TP is crucial to understand the way which is used by individuals – according to Keynes – when they try to predict the future of the economic system and of its components. First it excludes the assumption of subjectivism as the theoretical foundation of individuals as it was promoted by the Austrian and the “neo-classical” traditions. For Keynes the “real world” is not determined by each individual according to his personal view and his opinion. Probability cannot be the only result of individual imagination. It is “concerned with the degree of belief which it 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: 4).

66However, this assertion does not mean that expectations are optimal or rational as it is the case in traditional analysis. Keynes speaks of probabilities as being fixed objectively, but he is not using here the concept of objectivity to refer to things in the material world. In compliance with his view of the relation between economics and philosophy and by contrast with the “orthodox” one, he means objective in the Platonic sense, referring to the element of a supposed Platonic world of abstract ideas. This world obviously supposes the existence of an approach which explains how we may obtain knowledge about this logical relation of probability. Keynes’s answer is that we get to know at least some probability relations by direct acquaintance or immediate logical intuition. As Keynes says “we pass from a knowledge of the proposition to a knowledge about the proposition by perceiving a logical relation between them. With this logical relation we have direct acquaintance.” (TP: 13).

67This “logical” and “objective” conception implied a debate between Keynes and Ramsey in which the former changed partially his view but however maintained: (i) his opposition to Ramsey’s theory of subjective probabilities; (ii) the role given by Keynes to the “weight of arguments” as it was developed in the TP. This is why this role continued to be present after the TP.

68As we noted earlier, Keynes then used weight both as an absolute and a relative concept. According to the former, weight is measured by the absolute amount of relevant evidence. But the latter also introduces a notion of relevant ignorance. After referring to probability as depending on the balance of favourable and unfavourable evidence, Keynes introduced actually the concept of weight as an additional respect in which arguments may be compared: “This comparison turns on a balance, not between the favourable and the unfavourable evidence, but between the absolute amounts of relevant knowledge and of relevant ignorance respectively” (TP, p. 77). Therefore, Keynes opened the way to the concept of confidence but also, as underlined earlier, to a weak form of rationality. According to O’Donnell, this last type of rationality refers to modes of behavior as the “acceptance of social conventions, customs, moral duties and rules of thumb, the following of better informed opinion, and even allowing arbitrary procedures such as pure caprice or coin tossing to decide issues” (O’Donnell [1990], p. 257-58).

69Therefore this weak form of rationality is central because: (i) it reveals the existence of a “real world” which could not have been introduced at all in the formalist traditional approach; (ii) it introduces a concept which could not have been introduced in the traditional approach since this approach neglects any possible help of philosophy; (iii) it defines a concept which is both logical and psychological (iv) it is both absent from the Austrian as well as the traditional approach.

70In line with these arguments, in “Ramsey as a philosopher”, Keynes wrote about his colleague:

71In attempting to distinguish “rational” degrees of belief from belief in general he was not yet, I think, quite successful. It is not getting to the bottom of the principle of induction merely to say that it is a useful mental habit. Yet in attempting to distinguish a “human” logic from formal logic on the one hand and descriptive psychology on the other, Ramsey may have been pointing the way to the next field of study when formal logic has been put into good order and its highly limited scope properly defined. ( [1972], [1931], p. 338-39).

72Therefore, for Keynes, induction remains something more than a “useful mental habit”: it is also an element of logic. This is why contrary to some of his Cambridge colleagues, he always preferred to use the expression “logical intuition” to the simple expression “intuition” used by the philosophers of the period of his father in a more empiricist way.

73To precise the concepts of “logical intuition” and “real world”, let us come back again to Keynes’s example of individual decision making. Why did he consider that this example is crucial? The answer is to be found in the role attributed by Keynes to uncertainty which is central if we try understanding individual economic actions. As soon as the TP, Keynes indeed tried to show that uncertainty is always present when we refer to time and therefore to economic dynamics. In the TP, he criticized the law of large numbers and the frequentist approach to probabilities since for him economics was not a natural but a moral science in connection with the Cambridge tradition. In a letter to Harrod written on the 4^th July of 1938, he noted that this moral science copes essentially with introspection, values but also with motivations, expectations and psychological uncertainties. Now to understand these psychological elements, we need modelling but also a careful observation of the working of the real world, mixing statistical data, intuition, imagination and researcher common sense: now the real world is never static or repetitive. It is always moving, and unstable. Keynes therefore refers here at least implicitly to the notion of emergence and consequently of complexity: Economics is a science of thinking in terms of models joined to the art of choosing models which are relevant to the contemporary world. It is compelled to be this, because, unlike the typical natural science, the material to which it is applied is, in too many respects, not homogeneous through time. The object of a model is to segregate the semi-permanent or relatively constant factors from those which are transitory or fluctuating so as to develop a logical way of thinking about the latter, and of understanding the time sequences to which they give rise in particular cases (…). In the second place, as against Robbins, economics is essentially a moral science and not a natural science. That is to say, it employs introspection and judgments of value (Keynes, J.M. ( [1973c], [1938], p. 296).

74We know the various fields considered by Keynes in the GT in which the example of the theory of decision making could be applied as the determinants of effective demand; the “objective” and the “subjective factors” of the propensity to consume; the “psychological and business incentives to liquidity”; or the working of financial markets. These fields would show the fundamental role played by this theory in the GT. The conclusions would be analogous to those of the first part our paper. According to Keynes, one of the major limits he attributed to what he called “orthodoxy” was indeed related to its choice of defining it as a self-contained conception of economics which excluded the help of the contribution of other social sciences as psychology instance. Therefore if we insisted in this section on the relations between economics and philosophy, in the last section of our paper our remarks may be extended to other social sciences as psychology for instance.

75This is also why Keynes’s self-contained conception opens the way to usual macroeconomics based on a very specific definition of rationality and individuals which excludes the analysis of real and complex economic instability. The acceptance of closed fundamentals indeed leads to both an optimal general equilibrium in microeconomics and to an aggregation procedure in macroeconomics. Then the combination of these two approaches generates a form of dynamics which distinguishes balanced growth related to equilibrium and business cycles which are the result of exogenous and stochastic disturbances excluding endogenous instability as well as structural change.

76Moreover, from a more methodological point of view, in the traditional approach, individual rationality is reduced to optimization while Keynes’s one cannot be limited to it. According to Keynes, the prevalence of uncertainty excludes this reduction and obliges economists to combine two determinants through “logical intuition”. The first refers to logic and explains why modelling has its space in the objective aspect of probability. The second requires intuition namely the observation of the real world and of the causes and forms of its instability. Therefore Keynes’s view of instability is fundamentally endogenous and complex; it cannot be eliminated or reduced to equilibrium, balanced growth or exogenous business cycles.

77This crucial emphasis on complexity in Keynes’s works has been very precisely and convincingly generalized, stressed and analyzed by authors as Marchionatti [2010] and Carabelli ( [1988] and [2012]). First, “complexity and incommensurability (which Keynes often treats as synonymous) of magnitudes is absolutely crucial in Keynes’s way of reasoning in economics and in his philosophy of measurement (see Carabelli [1992, 1994, 1995]). His works are literally full of references to various complex and incommensurable magnitudes” (Carabelli [2012]: .87).

78Secondly, in contrast with “classical” approach, Keynes’s complexity excludes various “fallacies” as for instance the “fallacy of independence (when reductionism is applied to a complex economic material)”,” the fallacy of composition (when conclusions about a whole are arrived at by analyzing parts of it in isolation; partial equilibrium analysis, in Keynes’s view, suffers from this fallacy)”, (…) “the fallacy of homogeneity (when treating heterogeneous magnitudes as if they were homogeneous)” and “false analogies (such as those related to the use of statistical inference in econometrics, or the shaping of conventional expectations on the market – “market idola”).” (Carabelli [2012]: 82).

79Thirdly, Carabelli’s emphasis on complexity also allows to avoid the risk of reductionism in the non-traditional interpretation of Keynes’s view of economic decisions. Let us take the example of Keynes’s crucial concept of “reasonableness”: “Reasonableness is based on a non-demonstrative logic and on intuition versus psychology and behaviourism. But reasonableness must not be confused with following habits, rules and market conventions: Keynes defends partial knowledge against mere experience. This is why Keynes’s suggestion differs from Marshall’s and Hayek’s “follow rules, routines and conventions”. Only in a situation of uncertainty (radical ignorance, very low weight of argument or confidence) and of incommensurability of magnitudes, rules, routines and market conventions may play a role and be reasonably justified.” (Carabelli, ibid, 91; see also Zappia [2015] on this theme).

80Another example can also be found in Keynes’s various contributions dedicated to probability measurement and comparison. Again, Carabelli [1994] dedicated an excellent paper and a convincing argumentation to this theme, insisting on Keynes’s “philosophy of measure” (ibid. 21) and on the absolute necessity of relating economics and philosophy to understand the meaning of Keynes’s fundamental contribution.

81Let us now consider more carefully another inter-disciplinary dimension based on Keynes’s view of psychology to see whether it reinforces our first reinterpretation of Keynes’s approach.

3.2. Keynes, economic behaviour and psychology

82The previous section of our paper highlighted the importance of the role of logic and philosophy in the context of Keynes’s process of individual decision making. In spite of the differences between his social philosophy and those of Moore and Russell, Keynes was certainly influenced by both of them with regard to the fundamental contribution of logic to philosophy.

83As we already noted, Keynes however never reduced the issue of decision to a purely logical problem as the traditional economic analysis did. As we also argued, being a “moral science” for him, it also coped with “motives, expectations, psychological uncertainties” (Keynes [1973c]: 300). Now, we already stressed that for him these motives, expectations and psychological aspects provide the source of uncertainty as well as permanent change and instability. This is the meaning of Keynes’s remark according to which to explain the origin of this change and this instability, the economist must mainly try to “segregate the semi-permanent or relatively constant factors from those which are transitory or fluctuating” (Keynes, ibid.: 296-7). The origin of this distinction between two types of “factors” is not technical or mainly based on optimization. It is primarily psychological: “In ethical calculation each individual’s momentary state of mind is our sole unit. In so far as a state of mind has parts, to this extent I admit the principle of organic unities [as Moore did it – RA and EN]: it is the excellence of the state as a whole with which we are concerned. But beyond each individual the organic principle cannot reach” (Moore’s “organic principle is here contested in line with Keynes’s definition of individuals – RA and EN – extract of unpublished “Miscellanea Ethica”).

84Among the “parts” of the “state of mind”, some are therefore constant as logical calculus or judgements and other ones – being psychological or sometimes inter-psychological – are permanently changing and contributed to the explanation of economic changes and economic instability. Both these concepts are related to individuals or to inter-individual interactions – as various types of expectations (related to demand for money, investment and production); wage partial rigidity; animal spirits; money illusion; conventions; or the state of confidence for instance. They provide the psychological illustrations and foundations of Keynes’s economic analysis. They fundamentally differ from the formal assumptions of “neoclassical economics”. It is indeed obvious that the imposition of optimizing rationality as the decisive criterion, i.e., obeying some specific axioms, does not conform for Keynes to how people actually behave in the real world: these assumptions indeed exclude any help of the contributions of psychology.

85Therefore, as we already noted, the reasons why Keynes left such a large space to psychology and rejected the traditional analysis are also related to the issue of economic dynamics. On one side, Keynes never accepted the introduction of simple extrapolative or adaptive expectations, apart in the cases of certainty or very short periods. This type of expectations is indeed incompatible with an economic analysis which attributes a major importance to future and expected economic change, in the short as well as the long period: “Although output and employment are determined by the producer’s short-term expectations and not by past results, the most recent result usually plays a predominant part in determining what these expectations are. It would be too complicated to work out the expectations de novo whenever a productive process was being started; and it would, moreover, be a waste of time since a large part of the circumstances usually continues substantially unchanged from one day to the next”. (GT: 51).

86This is why mental habits and psychological factors cannot be neglected in a changing world: “It would be foolish, in forming our expectations, to attach great weight to matters which are very uncertain. It is reasonable, therefore, to be guided to a considerable degree by the facts about which we feel somewhat confident, even though they may be less decisively relevant to the issue than other factors about which our knowledge is vague and scanty. (…) our usual practice being to take the existing situation and to project it into the future, modified only to the extent that we have more or less definite reasons for expecting a change.” (ibid: 148).

87As it is the case for logic, another social science is therefore necessary here for Keynes to help economics to explain decision making in the real world. This conclusion is not so surprising too since it also reveals the limits of traditional theory concerning dynamics and uncertainty.

88What kind of psychology, by the way, can be used by economists if we focus on Keynes’s approach? The first is certainly cognitive psychology in which Keynes included logical intuition (see Mini [1994]; Almeida and Curado [2019]). The second is social psychology and focuses on social interactions as conventions, herd behavior or emotional contagion, for instance (see Barnett [2013]; Koutsobinas [2004]). The third is Freudian psychology (see for instance Winslow [1986]; Dostaler and Maris [2009] or King [2010]).

89To-day however the situation is somewhat different. Besides the optimizing behavior of modern “neo-classical” approaches, traditional behavioral psychology and behavioral game theory gave birth to behavioral economics and the issue of the relation between this new form of economics and Keynes’s thought became present in modern literature. Why is it the case?

90First because optimizing behavior is still present as a benchmark in behavioral economics (BE) after having played a crucial role in traditional analysis even if this role is very different. Many contemporary economists are to-day satisfied to be able to use renewed and more realistic microeconomics without being compelled to forsake individual optimization. Secondly because with time BE is becoming more and more interdisciplinary attributing a specific and more precise role to psychology. Thirdly because BE acquired a growing propensity to be more open than traditional analysis to economic dynamics. These are the reasons why more and more papers to-day are dedicated to the relation between behavioral economics and the economics of Keynes (see for instance Baddeley [2013]; Davidson [2011]; Fung [2006], [2010] and [2011]; Pech and Milan [2009]; Schettkat [2018]). We will not investigate here in detail this literature which is still in progress and under ongoing discussion to understand if BE provides a possible renewal of standard economics or a possible emergence of a new form of economics.

91What we will argue is only to briefly mention some of the psychological developments utilized by BE to try to provide some significant analytical foundations of Keynes’s economic analysis. These developments are mainly related to the GT: “useful mental habits”; fundamental uncertainty; status quo bias; overconfidence; conventional behavior; the role of animal spirits in carrying out investment plans; herding behavior; conformity; use of heuristics in decision making; marginal efficiency of capital; existence of nominal rigidities; money illusion; financial instability; recurrent unemployment; cyclical fluctuations; speculative spurts; irrational waste of resources. They play a major role in the GT and cover a considerable part of the book. A very well-done presentation of these developments with BE is to-day available in contributions as Davis [2009], Muchlinski [1998], Pech and Milan [2009] or Runde and Mizuhara [2003].

92These developments were also mentioned by Akerlof who noted when he connected BE to Keynes’s approach presenting his project as an initial “dream”:

93“That dream was the development of a behavioral macroeconomics in the original spirit of John Maynard Keynes’ General Theory [1936]. Macroeconomics would then no longer suffer from the “ad hockery” of the neoclassical synthesis, which had overridden the emphasis in The General Theory on the role of psychological and sociological factors, such as cognitive bias, reciprocity, fairness, herding, and social status. My dream was to strengthen macroeconomic theory by incorporating assumptions honed to the observation of such behavior.” (Akerlof [2002]: 411)

94We can see now at the end of section 3 that logic and psychology provided a strong help to build Keynes’s intellectual construction. History, political science and sociology might also have been investigated and would have reinforced the conclusion that Keynes’s point of view is fundamentally interdisciplinary and excludes a closed view of economics. This conclusion is crucial. For us it provides the main foundations of the opposition between traditional and Keynes’ economic approaches even if it started from the particular case of decision-making process.

95(i) We indeed noted that “classical” and modern mainstream analysis indeed supposed that economic science is closed or self-contained, namely based on axiomatic “fundamentals” and this is true in general economic equilibrium (GEE) research program as well as in standard simultaneous game theory. Pareto and Schumpeter strongly contributed to popularize this view. To be more precise, for Schumpeter, Walras founded the most rigorous form of traditional economic analysis when he built his GEE model (see Arena [2005] and [2014]). Therefore, according to Schumpeter, the existence of a “causal relation” between “fundamentals” and Walrasian unknown quantities and prices establishes economics as a science in its own right. Thus, after Walras, economists could legitimately claim that economic analysis is a perfectly self-contained and consistent science that does not require any analytical or methodological support from other social sciences. This characterization of a self-contained economics can be applied to the GEE research program from Léon Walras to the end of the XXth century. It can also be applied to standard and simultaneous game theory till the beginning of the XXIst century. It only began to be contested later with the emergence of a new microeconomics based on dynamic game theory and of BE.

96(ii) If we consider now Keynes’s various interpretations we presented in part 1 of this paper, we can distinguish four groups. The first group includes the traditional reinterpretations which saw in Keynes’s economic theory a pure macroeconomic analysis which could allow the construction of a Keynesian/Neo-classical synthesis but was methodologically analogous to traditional theory. The second group corresponds to models which tried to find microeconomic foundations for a macroeconomic representation explaining disequilibria through ad hoc rigidity (of prices, wages…) assumptions. The third group also accepts the notion of microeconomic foundations but maintains usual rationality assumptions and introduces asymmetric information. The fourth group includes all the Cambridge and Post-Keynesian economists and introduces various assumptions concerning money supply, expectations, marginal efficiency of capital and labour market. Maybe apart from the last group (see for instance, Arena, Dow and Klaes [2009]), psychology, history and sociology do not play a major role in these various approaches and as far as it is concerned, inter-disciplinarity occupies a rather limited methodological space.

97The previous remarks and our paper confirm the methodological opposition between both our types of economic approaches. This opposition has still to be investigated to-day since the debates related to it are far to be ended. Keynes indeed never dedicated his writings to strictly methodological developments and to-day Keynes’s ideas still more remain an inspiration in various fields and not a finished and complete construction.