Abstract
Producing a properly philosophical theory of capitalism as an open axiomatic system requires adding intensive multiplicities to the mathematical account of set theory, which allows only extensive multiplicities. Doing so enables us to understand pricing as a process of transforming intensive quantities into metric quantities, and thereby develop a diagram of the dynamics of axiomatisation and of the market as the two-sided and asymmetrical recording surface of the capitalist socius whose slope represents the infinite debt owed to finance capital. The capitalist market axiomatises four kinds of flows – flows of liquid capital and abstract labour, of course, but also flows of raw materials and energy and of human populations. At the same time that axiomatisation conjugates these flows in denumerable sets to extract surplus-value, it connects flows in minor, non-denumerable sets that escape axiomatisation and may become revolutionary. Such minor connections would constitute the fabric of a post-capitalist axiomatics.
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