Paul C. writes:
> Question to Gil
> ---------------
>
> What is the algebraic difference between an equality operator
> and an equivalence operator, and in consequence between and
> equality set and an equivalence set?
Let me answer in the language of sets rather than algebra. Think of
the relevant operators as rules for assigning entities to sets. An
equivalence operator assigns entities to a set based on their
possession of a *particular* characteristic or set of characteristics.
Two entities are *equal* iff they are equivalent in all dimensions or
characteristics allowed by the relevant axiom set.
In terms of algebra, here's an example: for any integer x, 2x and 4x are
equivalent in being even numbers, but they are not equal.
In effect, although it's not so obvious, Marx is saying that two integers are
equal because they're both even.
> An observation on price lists
> -----------------------------
>
> If we assume that Marx's examples are drawn from a price list,
> we should in consequence assume that when he talks of relative
> exchange values he does not assume barter exchange. It seems
> that Gils argument at times assumes barter. Is Gils argument
> still valid if we assume that the equivalence is assured by
> means of a set of money prices at a given instant of time.
In fact, my argument is easier to make with reference to money
prices. The fact that a set of goods are all exchanged for a
particular money price establishes a relationship of equivalence, not
equality. To say otherwise is to suggest that a parcel of
unimproved land is *necessarily* equal to, say, x bootpolish, if it
exchanges for the same money price (no matter whether Marx means to
exclude such things as unimproved land from the discussion in Ch. 1).
Gil Skillman