Our post on economies seemed to imply that calculus shouldn’t be used for economics.
Is this really a justified criticism?
The sad reality is that economics has taken science off its rails, and the result is so obscure that we can’t determine how science should proceed. Strangest of all, those who are very good at mathematics can be the worst judges of the nature of mathematics. It is actually a situation similar to that of evolutionary theory: there again ‘smart’ people are often unable to see the problem with darwinism (with or without its mathematical versions).
Take someone like Krugman, a mathematical economics whiz from his teens, yet is he a judge of economic fundamentals, i.e. as a science? Doubtful.
We have thus no way to proceed with economics because theory and ideology are entangled. It is a problem that Marx came across in the era of Ricardo. The whole game was fishy.
One solution is to keep mathematical economics on the sidelines and rewrite the subject with the simplest (i.e. positivistically transparent) concepts and/or specific models based possibly on some forms of measurable data. But here again the equations of metereology that make weather models work don’t exist in economics which can’t explain or predict much of anything.
In any case, it is important to declare yourself liberated from economic theories. Here marxists tend to skewer mainstream economics and then champion Marx’s theories. Marx had a fairly good batting average here, but that’s still not science. We need a looser non-theoretical approach. This could change, as computerized systems produce approximate solutions of various kinds. But the basic point, that a differential equation using calculus, let alone the weird tricks of marginalism, can apply to an economic situation.
The suspected conclusion is that economics has so far never produced a theory that has the status of physics. Ironically it is the use of differential equations that seems to make that clear.
The key point is that mathematical economics has not produced a foundational legitimation of capitalist systems.