Braithwaite on Models
Why scientists (and economists) should exercise 'eternal vigilance'
The late Robert Solow (1924-2023) was one of the few genuine ‘wise men’ of modern economics. Not only did he create a model that actually works (insofar as it reconciles the data in a way that yields genuine insight), he also had a humane and reflective mind. This meant he had interesting things to say about the nature of economics as a scientific practice. Take, for example, the following passage from his excellent essay ‘How did Economics get that way & what way did it get?’ (1997):
Modern mainstream economics is not all that formal. What the outsider really sees is model-building, which is an altogether different sort of activity. In college classrooms in the 1940s, whole semesters could go by without anyone talking about building or testing a model. Today, if you ask a mainstream economist a question about almost any aspect of economic life, the response will be: suppose we model that situation and see what happens. It is important, then, to understand what a model is and what it is not.
Robert M Solow, ‘How did economics get that way & what way did it get?’, Daedalus (winter, 1997)
There is a strong professional prejudice against philosophy among economists. Solow himself is partly shaped by it. As he says in the same essay only a ‘small fringe’ of economists bother with questions about the conceptual underpinnings of their work. Most want to get on with making and testing models, even if they do not have any settled beliefs about what models really are. And so what? After all, ‘philosophical tendencies may come and go’. It is enough to know how to construct a model that meets professional standards, and to be familiar with its internal structure and typical behaviour. Looking for anything deeper is a distraction from the more pressing work of getting the model to fit its data.
For those economists wary of this ‘loose fitting positivism’ (Solow’s words), a good place to look for a more rigorous and philosophically robust account of models is R B Braithwaite’s Scientific Explanation: A Study of the Function of Theory, Probability, and Law in Science (1953). The book is one of the gems of the analytical tradition in the philosophy of science, full of suggestive ideas, especially for economists with a philosophical turn of mind, who would probably find themselves reading and re-reading chapter 4 on 'Models for scientific theories; their use and misuse'. To give a full account of Braithwaite's theory of models would require a summary of the first half of the book so for our purposes I will go straight on to how Braithwaite thought models should be used, and how they could, if used improperly, lead to philosophical and scientific nonsense.
Braithwaite has a high ideal of science that would mark him out as odd today. As he puts it the aim of scientific theory is to assemble a deductive system of propositions arranged 'in such a way that from some of the hypotheses as premises all the other hypotheses logically follow'. Achieving logical consistency in a system of scientific propositions is no small task, and there is a perpetual risk that the requirement of total coherence at every level of the system, and at every moment of its construction, may cause a sort of arrest or paralysis. For the scientist, this is where the model comes in:
'…there are great advantages in thinking about a scientific theory through the medium of thinking about a model for it; to do this avoids the complications and difficulties involved in having to think explicitly about the language or other form of symbolism by which the theory is represented. The use of models allows of a philosophically unsophisticated approach to an understanding of the structure of a scientific deductive system'
R B Braithwaite, Scientific Explanation (1953), p 92
Max Black, another philosopher, puts it well; a model for Braithwaite is a legitimate 'substitute for the available alternative of taking the scientific theory "straight"'. It gives the scientist room to breathe - or to be less of a logician, and more of a researcher. Elsewhere Black describes the model as a ‘short cut’. However, this temporary relaxation of the strict canons imposed by the high ideal of science is bought at the cost of two closely related 'dangers'. Here is (to my mind) the most important section of the whole chapter - on what for Braithwaite is the first danger of using models:
'The first danger is that the theory will be identified with a model for it, so that the objects with which the models is concerned… will be supposed actually to be the same as the theoretical concepts of the theory […] Thinking of scientific theories by means of models is always as-if thinking; hydrogen atoms behave (in certain respects) as if they were solar systems each with an electronic planet revolving round a protonic sun. But hydrogen atoms are not solar systems; it is only useful to think of them as if they were such systems if one remembers all the time that they are not. The price of the employment of models is eternal vigilance.'
R B Braithwaite (1953), p. 93
The second danger also arises from our tendency to identify model and theory - which is to say two structures with different canons of rigor - and is in many ways a derivative of the first danger:
'There is a second danger inherent in the use of models, a danger which is more subtle than that of projecting on to the concepts of the theory some of the empirical features of the objects of the model. This danger is that of transferring the logical necessity of some of the features of the chosen model on to the theory, and thus of supposing, wrongly, that the theory, or parts of the theory, have a logical necessity which is in fact fictitious'
R B Braithwaite (1953), p. 94
Braithwaite's antidote for the second danger is to refer the reader to a line from Heinrich Hertz (a paragon of the scientist for Braithwaite) to the effect that we must always distinguish three things in a scientific system - 'what arises from necessity in thought, what from experience, and what from our arbitrary choice'. The model can smuggle in much by way of arbitrary choice, which would ultimately fall apart for the purposes of building a genuine theoretical structure. As Solow himself said in a famous 1957 paper ‘it takes something more than the usual “willing suspension of disbelief” to talk seriously about aggregate production functions’. Frustratingly, Braithwaite says surprisingly little about how to train a mind so that it can sustain an 'eternal vigilance' in the use of models.
I do not have the space to say much about this. But Braithwaite's insistence that a hydrogen atom is a solar system in miniature but also is emphatically not such a system reminds me of a very interesting book by the philosopher Paul Ricoeur called The Rule of Metaphor (1975). Metaphor, according to Ricoeur, always involves a tension between 'identity and difference in the interplay of resemblance'. He builds a magnificent theory of metaphor around this central idea. To say more would take us far away from Braithwaite and this blog. But, as you can probably tell, in my rather clumsy way, I want to argue that at least insofar as he/she is a user of models the scientist (and the economist) may want to look first to philosophy of science and then possibly even (oh the horror!) to the humanities, not so much to learn how to construct models, but rather make sure that in using them he/she is still making sense.