Re: Is equality evil?

["Fred E.J. Linton" <fejlinton@usa.net>]

Toby Bartels <toby+categories@ugcs.caltech.edu> wrote in part:
  
> The point is that one can recognise that two syntactic expressions,
> such as x and x, are the same, ...

Sorry, Toby, when I see "such as x and x" I have to struggle to
treat the expression between "as" and "and" as anything other than
different from the expression following the "and" -- for, if they
were really the same, there would be but one expression, not two,
it would be in one of those positions only, not both (I'm put in mind 
of the good old "Cheech and Chong"-ism, "How can you be in two places 
at once, if you're not anywhere at all?"), and you'd have used not 
the plural verb form "are" but the singular "is".

An illustration from another realm: each time the clerk behind the deli 
counter finishes with one customer and shouts "Next!" so as to bring up 
another one, the expression the clerk shouts refers to an entirely 
different customer than it did the time just before.

> ... or even that one reduces to another,
> such as fst(x,y) and x (where fst: A x B -> A is the usual projection),

Again I'm puzzled: what can fst(x,y) (where fst: A x B -> A is as you say)
possibly have to do with x (as in A x B, presumably -- or did you mean
as in fst(x,y), which could be problematic for void B)?

Sorry to be so obtuse, but ...; cheers, -- Fred



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]