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I've Eliminated 'irrational' numbers

r norman rsn_ at _comcast.net
Thu Apr 22 12:29:36 EST 2004

On Thu, 22 Apr 2004 16:48:06 GMT, "Glen M. Sizemore"
<gmsizemore2 at yahoo.com> wrote:

>Norman: You might as well also question the existence of "learned mental
>constructs" as honor, integrity, loyalty, etc. We humans live in an
>intellectual world of ideas which transcend the physical reality of
>the spatial/material/energy world our bodies inhabit.
>GS: OK. "Learned mental constructs" exist only in the sense that the
>behavior they are said to explain "exists" or, at least, occurs. What exists
>is operant stimulus control and the inter-related processes of
>discrimination and generalization. These behavioral processes are, no doubt,
>mediated by physiology, but in as yet unknown ways. So, it would be more
>correct to say that what exists is a physiology that results in what we call
>behavioral processes that are modulated by exposure to past and current
>environments. "Constructs" exist "in" behavior, not in the brain or alleged
>mind. Another way of saying this is that "mental constructs" is a
>scientifically useless term.
>Needless to say, I'm not endorsing anything Ken says.

I was actually referring to an even fuzzier concept of "existence".
These concepts exist as ideas that can be argued, discussed, analyzed,
and explored.  They do not necessarily have to have physical
representations in behavior, except in the trivial sense that the act
of discussing "honor" is itself a form of behavior. That is perhaps
the same sense that lets us talk about the "existence" of an
infinite-dimensional vector space of functions or of the set of
Mersenne primes.  We humans in possession of language and a shared
level of experience can define the notions and describe their
properties, even prove theorems about them.  Or, to open another and
even larger can of worms, discuss the existence of God.

Mathematicians have long argued about the nature of mathematical
constructs and the relation (or lack thereof) between mathematics and
physical reality (whatever that may be).

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