Formal analysis

Keynes is rather dismissive of what he calls ‘“mathematical” economics’. The following passage is from chapter 21 of The General Theory:

The object of our analysis is, not to provide a machine, or method of blind manipulation, which will furnish an infallible answer, but to provide ourselves with an organised and orderly method of thinking out particular problems; and, after we have reached a provisional conclusion by isolating the complicating factors one by one, we then have to go back on ourselves and allow, as well as we can, for the probable interactions of the factors amongst themselves. This is the nature of economic thinking. Any other way of applying our formal principles of thought (without which, however, we shall be lost in the wood) will lead us into error. It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis, such as we shall set down in section vi of this chapter, that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep “at the back of our heads” the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials “at the back” of several pages of algebra which assume that they all vanish. Too large a proportion of recent “mathematical” economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.

There is much truth in the above, I think, and it is truth that applies not only to “economic thinking” but to any kind of thinking that relies on formalization. Statistical analysis is plagued with this kind of problems. Keynes does lay too much stress on the matter of interaction between factors. The problem with formal methods is not particularly with neglecting various effects – it is that they simply are false in various ways (neglecting various effects is only one of the sources of falsehoods). Informal methods have the same problem, of course – and in addition have problems associated with informality.

A short mathematical description of Keynes’s general theory