From Deleuze to Badiou radical philosophy seems to have tired of dialectical contradiction, yet....
http://press.princeton.edu/titles/8386.html
How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics William Byers
From the point of view of strict logic, Byers argues, zero would never have been allowed to see the light of day because it is a contradictory concept--it is both something and nothing, both presence and absence, positive and negative, even though these ideas are mutually contradictory. Indeed the power of zero may be proportional, not to its properties of harmony and consistency, but "to the inner contradiction to which its gives form and by so doing resolves in some way". Combining strict logic and naive realism, the ancient Greeks simply were incapable of inventing the concept zero.
Implications for Marx of Byer's understanding of inner contradiction of which the concept zero is the leading example...
If Evald Ilyenkov is correct--I just finished Dialectics of the Abstract and Concrete in Marx's Capital which is on line, and I don't remember Ilyenkov is even being cited by Balibar in his excellent book The Philosophy of Marx-- then formal logic forces us to mistake the contradiction within commodity (the value it manifests in exchange which is mutually exclusive of the value it has in use) for its external form of appearance--the contradiction between the relative and equivalent form.
As Ilyenkov writes:
>The principle forbidding direct coincidence of mutually exclusive
>forms of being in one and the same thing and at one and the same
>time (and consequently in the theoretical expression of this thing)
>applies, it appears, to the external empirical form of manifestation
>of analysed reality (value, in this case) but is directly rejected
>with respect to the inner content of this reality, to the
>theoretical definitions of value as such.
>The inner nature of value is theoretically expressed only in the
>concept of value. The distinctive feature of the Marxian concept of
>value is that it is revealed through identity of mutually exclusive
>theoretical definitions.
>The value concept expresses the inner relation of the commodity form
>rather than the external relation of one commodity to another (in
>the latter the inner contradiction is not directly manifested but
>split into contradictions 'in different, relations': in one
>relation, in relation to the owner, the commodity appears as
>exchange value only; in another, in relation to the owner of the
>other commodity, it appears ,is use-value, although objectively
>there is one, not two relations, To put it differently, a commodity
>is here considered not in relation to another commodity but in
>relation to itself reflected through the relation to another
>commodity.
>This point contains the mystery of Marxian dialectics, and it is
>impossible to understand anything either in Capital or in its logic
>unless this point, this kernel of the logic of Capital, is properly
>understood.
But David Bakhurst and others have reasonable objections that there is no reason to put the principle of non-contradiction under suspicion in the understanding of the value form. It's enough to emphasize that while the classical economists saw simple identity in the equation x commodity A=y commodity B Marx saw a unity of opposites, i.e. he disclosed how the relative and equivalent forms are mutually exclusive.
Yet Marx did derive money from the inner contradictions of the commodity. He did not simply demystify money by saying that it is a commodity; rather he attempts to derive the celestial substance out of the contradictions of the earthly commodity. That is Marx's method after all--to develop from the actual relations of life the corresponding celestial forms of those relations; he is not content to 'discover' the earthly kernel of celestial forms. Marx is not like Ricardo in that he did not say that the kernel of money is that it is a commodity and that therefore its movement should answer directly to the requirements of the universal law of value.
With his method, Marx derives that money has or rather is the monopoly over the representation of abstract social labor time, that is money is the externalization of one pole of the contradictory unity latent within commodities.
Perhaps this monopoly does not depend on money remaining itself a commodity, given Marx's logic, even if Marx could not forsee pure fiat money?
Rakesh