If the theory is valid we would have two hundred years of statistical evidence showing the vector of profit rates headed to zero. There is no such evidence.
Capital accumulation is doing fine. The evidence that it's on its last
legs exists nowhere.
I doubt whether there would be such evidence. The evidence that I would look for is the kind of evidence that I am seeing: primitive accummulation and plunder, crumbling infrastructure in the principal capitalist country, endemic war and failed states, destruction of nature, creation of billions of surplus people/labour, desperate invention of ever more sophisticated financial instruments, whose workings threaten the entire financial system. Why should all of these things happen in a capitalist world if profits are more or less guaranteed by operation of the system? There are profits within all this, yes, but how much of this is due to the mythical 'pure capitalist system' (which exists in one country, has only two classes, etc.) and how much of it is to do with unsustainable looting on a worldwide scale?
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