Julio Huato wrote:
As I said, this conception of "preferences"
assumes that, to the extent required by the
argument, the identities of the related
entities (the "variables") remain unchanged
with changes in their relations. This is
explained in the Whitehead passage. Where
this isn't true, i.e. where relations are
"internal" in a relevant way, the hypothesis
"breaks down." This is true independent of
how abstract you make the "variables."
With all due respect to Whitehead, if the "internal change" of
variable X invalidates its use in a given reasoning, then how come the
"internal change" of your term "internal change" doesn't invalidate
your statements? I mean, your term "internal change" changed
internally from the time you began to type it to the time you ended
typing it. How seriously should I take your terms then?
Don't you realize that your (or Whitehead's?) argument would make all
discursive (not only all mathematical) logic impossible, since the
content of *all* terms is subject to "internal change" as a result of
their relations with other terms? Or are your terms only externally
related to your overall argument?
This is another straw man.
As both the passage to which you're responding and the Whitehead
passage point out, though (on the assumption that relations are
"internal") "complete self-identity can never be preserved in any
advance to novelty," the change in self-identity only invalidates the
reasoning if it's relevant to it. The idea doesn't have the absurd
implication that language or arithmetic or algebra are useless.
"The baby in the cradle, and the grown man in middle age, are in some
senses identical and in other senses diverse. Is the train of
argument in its conclusions substantiated by the identity or vitiated
by the diversity?"
So "mathematical abstractions" are limited in their applicability by
"internal relations," the degree of limitation depending on the
degree to which "internal relations" are relevant,.
Ted
