From: Wade T. Smith (email@example.com)
Date: Wed 28 May 2003 - 22:26:17 GMT
> It is logically inconsistent to on the one hand, acknowledge
> that a set (thoughts) reside in the mind, and on the other hand, that a
> subset of that set (communicable thoughts) do not reside there.
n : the branch of pure mathematics that deals with the nature
and relations of sets
<mathematics> A mathematical formalisation of the theory of
"sets" (aggregates or collections) of objects ("elements" or
"members"). Many mathematicians use set theory as the basis
for all other mathematics.
Mathematicians began to realise towards the end of the 19th
century that just doing "the obvious thing" with sets led to
embarrassing paradoxes, the most famous being Russell's
Paradox. As a result, they acknowledged the need for a
suitable axiomatisation for talking about sets. Numerous
such axiomatisations exist; the most popular among ordinary
mathematicians is Zermelo Fränkel set theory.*
- As I understand, pure mathematics is just that. Applying set theory
to any _process_ or aggregate of processes is, perhaps, a bit specious,
if not downright irrelevent. It is not a calculus.
I do know I can describe the bricks in the sidewalk outside my
apartment building in terms of all kinds of sets- the set of bricks
with the manufacturing mark up, the set with the mark down, the set of
chipped bricks, the set of loose bricks, the subset of loose bricks
with the mark down, the subset of chipped bricks with the mark up, the
subset of loose and chipped bricks, etc.
But, nothing about set theory will tell me a thing about the process of
laying bricks, or making bricks, or why bricks are here, or how
slippery they are when wet, and yet, there they are, and they got there
somehow. Furthermore, I doubt any application of set theory will
explain any facet of behavior, at all. Set theory is not a description
of physical processes, it's a math of after-the-fact relational
And, nothing about set theory will tell us a thing about cognition, or
effectively elucidate consciousness, not as a process.
Prove to us all that set theory is applicable to consciousness. What
rationale is there to demand that set theory is relevant to
understanding the cognitive process, or even the structure of thought
or the system of mind?
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