I have been exploring Sraffa's correspondence after the publication of his book. Here is a letter dated June 18, 1962, from Mathur to Sraffa (D3/12/111: 298):
Dear Mr. Sraffa,
In Nuffield there is a senior research student Edmund Nell who is attached to the faculty of Literae Humaniores[?] and is researching into the significance of concepts in economics. He is highly interested in the type of analysis you have proposed, and has been trying to work his way through it. In Oxford there is no other person whom I have met or heard of who has made a more detailed study of your book.
He would very much like to meet you, to discuss some of his problems, and would be writing to you direct regarding it. In the meantime, he has asked me to introduce him to you. This letter is meant to perform that function, though imperfectly.
I shall be in Cambridge on 25th, 26th, 27th, and would like to see you sometime. I shall ring you up on arrival. I am leaving England on the 30th June.
With regards,
Yours sincerely
Gautam Mathur
Nell's 14 July 1962 letter (D3/12/111: 299-302) is the longest I have found in the archives so far:
Dear Mr. Sraffa,
I believe Gautam Mathur wrote to you about me recently. I had rather hoped that I might be able to see you in Cambridge before you left for the summer, but I'm afraid I just left it too late. Anyway, I don't know if I really have anything to say that would be of much interest to you (and perhaps I'm a little afraid I'm on the wrong track completely.) I was greatly impressed and excited by Production of Commodities, when it was brought to my attention last year by Luigi Pasinetti. Subsequently I have tried to use it in my own work, which is an attempt to criticise (what I take to be) the neo-classical theory of general equilibrium in production and exchange, which I think to be nonsense. (Roughly speaking, I cannot see either what utility functions and production functions are supposed to be predicated of, or how in general preference orderings and production possibilities could be defined independently of each other. Nor do I see what the neo-classical theorists mean when they talk of a (homogeneous) commodity. Indeed, it seems to me that the implications of the notion of an artefact are quite inconsistent with the neo-classical doctrine of "substitution" on both sides of the market.)
Perhaps I should give some background information. I came to Oxford from Princeton, where I studied Politics, as a Rhodes Scholar. I read PPE at Magdalen, received a First, and was elected to Nuffield, where I have been for the past three years. I am now working on a D.Phil. thesis which might be call something like, "Agent and Object in the Theory of Production and Exchange".
Let me sketch briefly the problem that worries me, what I take to be the solution of it, and the way I propose to support this solution.
The general question that troubles me is this: I do not see at all clearly what is meant when one uses a mathematical formula to represent social behavior. Are the actual, historical acts of particular persons supposed to be represented? Or is what is represented supposed to be the relations of various roles in institutions? Many further questions present themselves: How are the value-ranges of the variables defined? Are all the concepts that regulate role-behavior such as to "have number"? Is the relation of a particular act to the general concept of the action of which it is an instance the same as the relation of a value to the variable of which it is a value. And so on. These rather general worries take a much more particular and concrete form, however, when one comes to consider the neo-classical theory of general equilibrium. For example, one wants to know how the value-range of the variable standing for the quantity of some good demanded by an "individual" can be defined independently: a) of the quantity of any and all goods he supplies - whatever does he use the good for? And if what he uses it for is not fixed, then on what grounds does he "prefer" the good to others? To want something is to want it for something. b) of the quantities of other goods that he consumes. Goods are the goods they are because they have certain technological properties, which imply that they must be used in certain (relatively) fixed proportions with other goods; light bulbs require sockets, lampshades lamps.
Even more worrying, however, is the idea that the set of variable demands for each commodity by each individual can be defined independently of the set of variable supplies of each commodity by each firm. For instance it would seem that to make plausible the idea of substituting one good for another in demand, one must require that each good be carefully and minutely distinguished from each other good. But the more sharply we define a good, the more we specify its technological qualities, and therefore the more we determine both the kinds of things and the relative proportions of things that go into its make-up; hence the more plausible we make the idea of substitution in demand, the less plausible we make this same idea in supply. More generally, however, to say that a certain amount of any artefact exists, has been produced, is to imply that someone has been the producer of it; hence has acted in a role, has certain abilities, and has used up something in order to produce the artefact. Any production implies some consumption, and the qualities of the thing produced tell us what kinds of things have been consumed.
A further worry arises over the notion of "price". Even very elementary reflection suggests that exchange must take place between many holders of many different goods, and there seems no reason to assume at the outset that the price of a good can be adequately represented by a scalar variable1.
Finally, even supposing that these problems about the definitions of the value-ranges of the variables could be overcome, there remains the question of just what it is that has been represented: Have we represented here the behavior of actual persons, so that conclusions drawn from the theory could be used for prediction? Or have we represented the structure of institutions, so that conclusions drawn from the theory would serve to make explicit the way people ought to behave - and what the results of their doing of their duty must be? Even if the mathematical representation is valid, there remains the questions of exactly what has been represented, and what the representation can be used for.
These considerations may be summed up in four problems:
a) to discover and classify all the kinds of statements there are about agents acting upon, with, by, through, etc. to produce objects; that is, to analyze the agent-verb-object relation.
b) to see what differences there are in the way various forms of agent-verb-object are demonstrated; and also to see if any of these differ in the way they are demonstrated from the way propositions of the form φa and aRb are demonstrated. That is, what difference does the notion of "agency" make?
c) to see if statements of the agent-verb-object form are formally similar to (hence representable by) mathematical statements; and to see what are the conditions for this to be possible.
d) to see what limitations there are upon the use of a formal representation of statements of the agent-verb-object kind; in particular to see if these can be used for prediction. (My argument tentatively is that prediction and mathematical calculation are incompatible for purely logical reasons.)
So far I have just tried to give a very rough sketch of the problems that bother me and the general position I take on them. I don’t want to prolong this letter, so I won’t try to summarize my work on these four questions. Instead, I should like to mention briefly how I have drawn on Production of Commodities in my work, and indicate a problem that has arisen out of this.
Very shortly, I have tried to classify social actions according to the implications respectively about the agent and about the object(s) of a statement containing as verb the concept of the action. It seems that on the basis of such a study of verbs the concept of the action. It seems that on the basis of such a study of verbs one can make some general classification of institutions, and for each class, one can state the general form of the institutions in it, showing the logical relations of the elements of these institutions. The classes of institutions that stand out as particularly interesting I call "productions" and "performances". These involve, respectively, verbs of making and breaking, and verbs appropriate to what Austin has called "performative utterances". Now the connection with Production of Commodities comes in this way: a set of "productions" will do very nicely as an interpretation of the model there, but it seems more difficult to fit in performances (commands, orders, directives, advice, undertakings, making contracts, judging, passing sentence, etc.) since such roles do not produce any definite quantifiable product which can be shown both as output and as input. Yet a society is inconceivable without these institutions. How are these to be treated? They differ from non-basics in the fact that they are essential.
A second problem arises in that the "plus" sign is used to represent the relations of various commodities to each other in each industry. This seems harmless enough, but a verbal description would contain such prepositions as "on", "with", "by", "in", "through", "to", etc., each of which expresses quite a different relation. So long as neither substitution nor growth is contemplated, and the only point of the mathematical representation is to compute the ratios of exchange required for the possibility of reproduction, no harm seems done. I wonder about switches in methods of production, though.
I'm afraid this letter is very disorganized, and probably not at all clear. On the other hand, my purpose in writing it has been not so much to say something clearly, as to convey a general approach - to communicate an attitude rather than to make a statement. In short, I am writing in the hope that something I've said here may arouse your interest in one or more of my various muddles, and that we might correspond further.
Yours sincerely,
Edward J. Nell
1 That is, a variable whose value-range is a set of cardinal or ordinal numbers. To assume this is to assume away the possibility that a price of a good might change so as to be different but neither greater nor less. But this is exactly what would happen necessarily to at least the price of one good, if one carried out "substitution" of one good for another in an industry, in the system of equations in Section II of Production of Commodities - i.e assuming total proportions constant - hence that somewhere else the reverse substitution takes places. (But it is also the case if just one good is just increased in total amount.)
Sraffa wrote his response on 18 August 1962 (D3/12/111: 303):
Dear Mr. Nell
Thank you for your letter of 14 July which has reached me with delay as I have been moving about.
I greatly sympathise with your critical attitude to the neoclassical theory of equilibrium in production and exchange. On the other hand I have only partly understood what you say on particular points. This is probably due to your assumption that I am familiar with the language and technique of philosophy, which I am not.
I should very much like to discuss some of your criticisms, if we could meet sometime. My movements will be rather unpredictable next year, which will be a sabbatical for me. I am however likely to be in Cambridge during the latter part of September and in October, and if at that time you can get in touch by writing at Trinity perhaps we can arrange to a meeting.
Yours sincerely
P. S.
I have not included strikethroughs, handwritten emendations, and such-like above.
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