`Das Kapital opens with a disastrous argument, to the effect that if two commodities exchange against each other their ‘exchange-value’ must be ‘the mode of expression, the phenomenal form, of something contained in [them], yet distinguishable from them’. The remark, phrased already in the tendentious idiom of ‘classical German philosophy’, is justified by an important fallacy:
Let us take two commodities, e.g., corn and iron. The proportions in which they are exchangeable, whatever those proportions may be, can always be represented by an equation in which a given quantity of corn is equated to some quantity of iron: e.g., 1 quarter corn = x cwt. iron. What does this equation tell us? It tells us that in two different things – in 1 quarter of corn and x cwt. of iron, there exists in equal quantities something common to both. The two things must therefore be equal to a third, which in itself is neither the one nor the other. Each of them, so far as it is exchange value, must therefore be reducible to this third. [ref]'
Scruton continues
Now the only logical conclusion to be drawn from the fact that two commodities exchange at a given rate is that they exchange at that rate. If a money value is assigned to the given equation then this is simply another fact of the same kind. The value of any commodity can be seen as an ‘equivalence class’. Just as a geometer would define the direction of a line as the set of all lines that are identically directed, and just as Frege and Russell defined the number of a class as the class of all classes that are equinumerous with it, so might the economist define the value of a commodity as the class of all commodities that exchange equally against it. The assumption of a ghostly ‘third’ item, in terms of which this equivalence is to be defined, is strictly redundant – a purely metaphysical commentary upon facts that provide no independent support for it. [Page 121]
As it is assumed in reading every book, I was reading it `in good will' and given the confidence of Scruton in `Marx’s fallacy' took this a real objection. The other night, I took advantage of mania's insomnia to reflect on this `fallacy'. Scruton claims that this is simply an equivalence class: all commodities with price $x. It is true that this is an equivalence class --which I shall not explain here, see Wikipedia--, but it does not tell us what a dollar is, which is what Marx is trying to find out.
