In my reading, Gil sees Marx's argument as having the following structure. Marx defines a kind of equality (congruence) between commodities which purports to prove the existence, underlying this relational structure, of a quantity (value) which is different from the quantity defined by the exchange relationship itself.
This argument doesn't work for him because "there is no evident sense in which exchange establishes an 'equation' in a sense sufficient to support Marx's inference that 'a common element of identical magnitude exists in two different exchanged things'. Now, one could [...] *define* exchange [...] to establish a sort of equality, in which Marx's inferences follow as a simple tautology." [OPE-L: 627]. But (if I read Gil right) this would still be unsatisfactory as a justification for Marx's Chapter 1 argument, because under this interpretation Marx would only find in his inferences the result he had pre-determined in his premises (the axiomatic presentation of exchange).
This leads Gil to pose for his opponents a dilemma. Did Marx presuppose labour as the content of value (in which case his Chapter 1 argument is irrelevant) or is the Chapter 1 argument supposed to allow us to infer labour as the content of value from properties of exchange (in which case it only appears to do so because this conclusion has been smuggled into the premises of the analysis of exchange)?
I see my own position as embracing both horns of this dilemma.
I think Marx pre-supposed labour as the content of value. I think that this pre-supposition determines the choices that Marx made in Chapter 1, viz. to focus on the commodity (rather than "exchange", which he put off to Chapter 2), and to focus on the "forms of value" rather than concrete exchanges. Nevertheless, I think that the Chapter 1 argument does allow Marx to show that exchange only brings to light a quantity (value) associated with the commodities, which is equal in both commodities, and different from the use-values of either commodity. Marx goes on, in Chapter 2, to discuss exchange. Here his argument takes a more conventional form, since the form of exposition matches the direction of the implication: from value determined in production to price in exchange (whereas in Chapter 1 the argument was inverted with respect to the implication that Marx wanted to show).
My justification is as follows.
Taking Marx's characterisation of the properties of exchangeability as valid, we can show that they entail certain properties of the exchangeability relation: reflexivity, symmetry, transitivity and composition. This means that they define a kind of equality. What kind?
The properties of exchange assign to each commodity a positive integral number (of units of the universal equivalent commodity) that is conserved when commodities are aggregated. In this sense the price behaves just like the mass of physical objects, as if it was a scalar physical property of commodities. This is the basis for fetishism. But, unlike mass, the assigned property is equal in two exchangeable commodities. This evident close link between exchange and value leads to the fallacy that exchange determines value. But Marx's analysis allows him to disprove this.
If you look at the properties of the commodity that Marx uses to characterise the value forms, you can see that he ignores at all times the concrete use-values or actual prices of any commodity. This means that, given his analysis, the properties of exchange that define the "equality" (or "congruence" or whatever) do not include use-value or price. This implies that the "scalar quantity embodying" property of exchange would apply equally well to a set of commodities embodying *any* use-values, and exchanging with *any* vector of prices.
This means that the definite price vector of commodities in real life can *not* have been determined by the exchange relation and hence *must* have come from outside it, from production. He achieves a neat trick: he shows that exchange defines the necessity of a definite positive scalar quantity associated with each commodity *without* defining what the value of that quantity is.
Then the fact of definite prices shows that prices formed in exchange are the form of expression of something else, i.e. not just that the values are formed elsewhere, but that prices formed in exchange express them.
Because the actual use-values of commodities have also been ignored, Marx can show that no use-value can be the source of the common property that allows two commodities to exchange. What is left but their common existence as produced things, i.e. products of human labour? Nothing.
At the risk of being long-winded here, I'd like to suggest an analogous form of argument. Consider the theory that the marginal productivity of factors of production determines the income shares of the classes of factor owners. It's well known that this theoretical construct is circular: the measure of capital goods depends on the profit rate and hence on the income shares of the classes which it purports to explain. Hence, even if the various assumptions required for the theory to work were valid, it could not serve as an *explanation* of the income shares: if the income shares were changed, the marginal productivity of the factors would also change. The theory could still be true as description, but false as explanation. To pursue the analogy, Marx's Chapter 1 argument shows that the exchange relation defines a vector of prices that necessarily describes values without explaining them.
Now I can return to Gil Skillman's dilemma: Marx can presuppose and also infer the labour content of value because he shows that the exchangeability of two commodities demands a "third thing" (a scalar quantity associated with each commodity which is conserved in exchange and aggregation) and also fails to explain it.
Now for the relevance of Marx's restriction of his analysis to the commodity, the product of labour. This allows him to avoid the distinction between the "definite prices" of Chapter 1 on one hand and values on the other, which comes into play later in his analysis of capitalist relations. In this sense, the Chapter 1 argument presupposes the determination of values by labour time.
Brendan