Plausible reasoning under fundamental uncertainty
Emphasis on the cognitive dimension of rationality enhances the domain in which the plausibility of reasoning criteria can be assessed and compared. In other words, moving beyond the circumscribed assumptions of 'standard' rational choice theory does not lend (by itself ) to relaxation of general rationality conditions, such as the propensity to deliberately draw conclusions from premises, to follow any given chain of reasoning step by step, and to identify on that basis connections among seemingly disjointed objects or ideas. It is fully consistent with the recognition that problem spaces are to a large extent a product of the constructive work of the human mind, and that assessment of that work presupposes careful consideration of situation and context (see also note 1, and Marzetti Dall'Aste Brandolini, Chapter 12, this volume). However, under conditions of fundamental uncertainty, classical rules for inductive inference (such as the Humean multiplication of instances) may be replaced by a strategy in which inductive arguments are associated with the identification of stochastic regularities for relatively independent sets of objects or agents. This approach calls attention to the possibility of representing any given set of heterogeneous objects or agents as a universe of agent types, in which each type would be associated with a specific collection of attributes (see Costantini and Garibaldi, Chapter 8, this volume).
Under fundamental uncertainty, rational choices are guided by 'the degree of belief that it is rational to entertain in given conditions' (Keynes, 1973 , p. 4). This means that guesswork is fundamental to rational understanding and acting. Keynes carefully argued this point when he wrote: '[g]iven the body of direct knowledge which constitutes our ultimate premises, [...] further rational beliefs, certain or probable, can be derived by valid argument from our direct knowledge' (Keynes, 1973 , p. 4). The close intertwining of subjective perceptions and objective (intersubjective) relations is outlined by Keynes in the passage that immediately follows the previous quotation:
[t]his involves purely logical relations between the propositions which embody our direct knowledge and the propositions about which we seek indirect knowledge. What particular propositions we select as the premises of our argument naturally depends on subjective factors peculiar to ourselves; but the relations, in which other propositions stand to these, and which entitle us to probable beliefs, are objective and logical.
(Keynes, 1973 , p. 4)
Plausible reasoning under fundamental uncertainty gives prominence to the identification of what 'given conditions' (in Keynes's sense) are, and the identification of those conditions becomes increasingly important as one moves away from known circumstances to largely unknown sets of possibilities. Fundamental uncertainty is likely to be associated with event fluctuations around the mean that are not self-averaging, that is, they do not tend to 0 as the model size n tends to infinity (see Aoki,
Chapter 9, section 9.1, this volume). Once fundamental uncertainty is acknowledged, the constraints associated with a cognitive frame become relevant and may be central for the utilization of available and relevant knowledge in choice situations. In short, fundamental uncertainty is bound to 'twist' our attention towards the ontological and epistemic premises for rational arguments, but does not make rationality constraints redundant. Indeed, there are grounds for believing that those constraints may become increasingly important when the 'imprecision' of possibility spaces does not allow unambiguous identification of what may be likely (or unlikely). For in this case rationality constraints narrow down the epistemic source of uncertainty and reduce the set of possibilities that it is reasonable to conceive of. The above argument entails that, under conditions of fundamental uncertainty, rationality may have a twofold role to play. On the one hand, the guesswork needed in identifying suitable problem spaces must be grounded in reasons: cognitive agents should be suitably equipped to sort out relevant information and to construct an effective representation of the world.6 On the other hand, that preliminary guesswork is often conducive to rationality constraints circumscribing the range of options to be considered for any such representation. It may be interesting to note that the twofold role of rationality in cognition has an equivalent in the domain of reasons for acting. For in this case, too, reasons for accepting a certain view of the world are often associated with reasons inducing us to act upon that particular representation of the world. Conditions of fundamental uncertainty strengthen the relationship between knowing and acting because of the greater freedom acquired by the constructive power of the human mind. Again, we owe to Keynes an effective picture of that relationship: '[t]o believe one thing in preference of another, as distinct from believing the first true or more probable and the second false or less probable, must have reference to action and must be a loose way of expressing the propriety of acting on one hypothesis rather than another' (1973 , p. 339).
The above argument calls attention to the relationship between situational judgement and rationality standards (see Marzetti Dall'Aste Brandolini, Chapter 12, this volume). When probability distributions are unknown and even the space of possible events is not fully explored, agents are likely to fall back on judgements of likeness in their search for a suitable representation of problem space and an effective set of epistemic criteria. It is primarily the type of rationality called forth in judgements of similarity rather than in processes of inference. Indeed, the connection between judgements of similarity and judgements of probability had been recognized long ago. Joseph Butler noted that it is a distinctive feature of reasoning under uncertainty: 'when we determine a thing to be probably true, suppose that an event has or will come to pass, it is from the mind's remarking in it a likeness to some other event, which we have observed has come to pass' (Butler, 1834 , p. 2). In this connection, however, the objective (or intersubjective) character of rational judgement might be questioned. As noted by Arthur Cecil Pigou, 'it seems paradoxical to speak of its being rational for me to perceive something, which, from the constitution of my mind, it is impossible for me to perceive' (Pigou, 1921, p. 507). Fundamental uncertainty enhances the dependence of similarity recognition on human judgement (see above). At the same time, the active role of judgement in similarity assessment calls attention to criteria and constraints that make judgement reasonable in any given situation.
The language used for describing uncertain situations also deserves attention, since situations may be described in different ways according to the language used. In this connection, Lotfi A. Zadeh (Chapter 6, section 6.1, this volume) highlights the fact that 'more often than not uncertain knowledge is described in a natural language'. This condition introduces a constraint on the range of descriptions that are feasible for any given language and highlights the need to distinguish between possibility and probability, as well as between 'probabilistic uncertainty and possibilistic uncertainty' (Zadeh, ibid.). In particular, it is emphasized that, since standard probability theory is based on the belief that information is statistical in nature, when information is expressed in a 'natural language', considered as propositions or a system of propositions, uncertainty cannot be dealt with by standard theory. This point of view suggests a generalized theory of uncertainty based on nonbivalent (fuzzy) logic and indicates that different patterns of rational behaviour may coexist within the same social universe due to a variety of linguistic constraints.7