Normative Models of Rational Agency: The Theoretical Disutility of Certain Approaches

Much of cognitive science seeks to provide principled descriptions of various kinds and aspects of rational behaviour, especially in beings like us or AI simulacra of beings like us. For the most part, these investigators presuppose an unarticulated common sense appreciation of the rationality that such behaviour consists in. On those occasions when they undertake to bring the relevant norms to the surface and to give an account of that to which they owe their legitimacy, these investigators tend to favour one or other of three approaches to the normativity question. They are (1) the analyticity or truth-in-a-model approach; (2) the pluralism approach; and (3) the reflective equilibrium approach. All three of these approaches to the normativity question are seriously flawed, never mind that the first two have some substantial (and often tacit) provenance among logicians and the third has enjoyed a flourishing philosophical career. Against these views, we propose a strong version of what might be called normatively immanent descriptivism. We attempt to elucidate its virtues and to deal with what appears to be its most central vulnerability, embodied in the plain fact that actual human behaviour is sometimes irrational. A great deal of modern economics is based on the accommodations of the discipline to the demand of mathematics. Models based on dynamic disequilibrium or nonlinearity ... are intractable to mathematical formulation. Without the postulate of general equilibrium there is no solution to the system of simultaneous equations which economics needs to prove that markets allocate resources efficiently. That is why economics has been uncomfortable with attempts to model economies as sequences of events occurring in historical time — which is what they are. There is a nice irony here. The more “formal” economics becomes, the more it has to treat reality as a purely logical construction. When it looks on the market system and finds it good, its admiring gaze is actually directed at its own handiwork. Robert Skidelsky, New York Review, 8 March, 2001. 597 L. J. of the IGPL, Vol. 11 No. 6, pp. 597–613 c ©Oxford University Press 2003, all rights reserved 598 Normative Models of Rational Agency 1 A Brief Word on Modelling Given its rapid absorption by mathematics, it is hardly surprising that modern mainstream logic has turned to mathematics for its working notion of model. Indeed it could be said that logic’s model of the model was the mathematical model. Such in turn was the choice of the natural sciences, certainly of those of them for the expression of whose laws mathematics is indispensable. The more complex of the natural sciences fared less well in capturing its essential insights in mathematical formalisms. This, too, is not surprising, given the comparative messiness and lack of generality of, say, the life sciences. Biology is an interesting test case for the would-be practical logician. There is a use of the word ‘theory’ in which a scientific accounts theoretical component is that which falls beyond the ambit of observation. In many cases, a theory is little more than a mechanical device that computes or predicts output from a system’s inputs. In biology, perhaps the classic example is theoretical populations and evolutionary genetics. Here all the basic processes are quite well known. These include the operations of inheritance, the facts of mutation, migration, and the mechanisms of natural selection under varying conditions of survival and fertility. Thus Theoretical evolutionary genetics assembles all these phenomena into a formal mathematical structure that predicts changes in the genetic composition of populations and species over time as a function of the numerical values of these elementary processes. [21, p. 40] Here the formalisation works. It works because the underlying mechanisms are known. There are lots of cases in which this is not so. The formal modelist has, apart from desistance, no option but to fly high. For here, in its pure form, the mechanical formalities are posited without any direct connection to underlying material data. This makes the theorist’s formal model an empirically unsupported place-holder for the actual dynamical details once they become known. An especially extreme, and failed, example of this theoretical high-flying was the Rashevsky school of mathematical biophysics, which operated in the late 1930s at the University of Chicago. Within three decades the movement was dead, made so by the extreme over-idealisation of his physical models, so radical as to make them empirically useless. The Rashevsky collapse teaches an important lesson. It is that certain biological processes may not admit of accurate mathematical expression. There are still other cases in which postulated mathematical expressions of biological processes turn out to be right, but a good deal less than optimal even so. This we see in the case of Turing’s conjecture that early embryonic development could be understood as the result of different concentrations of (observationally undetermined) molecules, distributed differentially within the embryo. This is right as far as it goes. But developmental genetics owes nothing to Turing’s model. What it achieves in accuracy it pays for in over-simplification. These are lessons for the practical logician to take to heart. For one thing, the behaviour of human animals exceeds in complexity any grasp we have of the fruit fly, no matter how exhaustive. Apart from that, there is the vexing problem of own below, which is where much of a practical agent’s cognitive agenda is transacted. The republic of down below is ringed by unwelcoming borders. Not only is much of what goes on there inaccessible to introspection, but experimental probes are heavily constrained by the ethical requirement to do no harm.1 1Even so, there are clear experimentally derived intuitions about how things go down below, not only in the case of reasoning, but also in the case of vision; concerning which, see [30]. 2. LOGIC AND MISTAKES OF REASONING 599 2 Logic and Mistakes of Reasoning Everyone makes mistakes, of course. Not every instance of a mistake, even of an avoidable mistake, is a failure of rationality, but we may take it that when rationality does fail it does so because mistakes have been made of a nature and on a scale and with a frequency of requisite gravity. There are all kinds of mistakes, needless to say. You might mistake Hortense for Sarah or an utterance of “the cross I’d bear” for an utterance of “the cross-eyed bear”. You might misremember Carol’s birthday as the 16th of March. Or you might detach a proposition Φ on the strength of a pair of propositions pIf Φ then Ψq and Ψ. It is widely believed that this latter is a mistake of reasoning and that rationality fails when mistakes of this kind are made. We have it, then, that a theory of rationality or rational agency must contain a theory of mistakes of such a kind. For a very long time it has been taken for granted that, for reasoning of a suitably rigorous nature, a theory of mistakes of reasoning is furnished by a logic of an appropriate design. Thus, for reasoning that might answer to the standards of strict proof, there is deductive logic, and for reasoning that is characteristic of science, there is inductive and abductive logic. Approached in this way, a mistake of reasoning is reasoning which disconforms to a logical rule or principle or norm. It would follow from this that one of the tasks of the logician is to privilege those propositions, standards or rules disconformity to which constitutes a mistake. Our task in this note is to press the following question: How does the logician know what proposition, standard or rule to privilege in this way? A common answer is that the logician constructs normative models of reasoning.