Jerry writes:
>Consider the following equation:
>
>1 U.S. dollar bill = 100 pennies
>
>Can we infer from the above "equation" that a penny is in all respects
>merely 1/100th of a dollar?
>
>If this were quite literally true than we should be able to divide a
>dollar bill into 100 pieces and each part would then = 1 penny.
>
>Yet, this is not the case! Thus we must reject the "equation" of pennies
>with dollars!
>
>Or should we?
>
>Perhaps an alternative explanation might be that there is no necessary
>suggestion that 100 pennies and 1 dollar are in all respects equal simply
>because there is an equation and an "=" sign.
Yes, this is an excellent illustration of the point Steve and I have been
making, and I thank Jerry for introducing it. I've acknowledged all along
that equivalence relations establish "a kind of equality", which is to say,
the equation of sets **with respect to the dimension defined by the
original relation**. Thus I could go further than Jerry and say with
respect to the relation "same monetary value as" that the following items
are equal: 4 quarters, ten dimes, 100 pennies, 2 half-dollars, dollar bill.
The point of my argument is that one cannot infer from this equality
defined with respect to a given dimension, a commonality along any other
dimension, as Marx's argument requires. Thus, as Jerry says, one cannot
infer from "100 pennies = 1 dollar" that both entities are made of copper
or zinc. Similarly, Marx can't legitimately infer from the "equation" of 1
quarter of corn and x cwt of iron that "a common element of identical
magnitude exists in [the] two different things.."
Gil