Re: Epistemology 201: The Science of Science

From: Wolf Kirchmeir (wwolfkir_at_sympatico.ca)
Date: 03/20/05 

Date: Sun, 20 Mar 2005 12:58:43 -0500

Allan C Cybulskie wrote:
> "Wolf Kirchmeir" <wwolfkir@sympatico.ca> wrote in message
> news:mf4%d.78350$Jd2.1832783@news20.bellglobal.com...
>
>>Allan C Cybulskie wrote:
>>[...]
>>
>>>But cardinality is NOT the default meaning of "number of elements"
>>> EXCEPT
>>>among mathematicians who hold that it just IS the number of elements. I
>>>guarantee you that most people who do not hold that axiom who are asked
>>> if
>>>there are more integers than even integers will agree that there are
>>> more
>>>integers -- as I have attempted to show by appealing to our intuitions
>>> about counting.
>>
>>[...]
>>
>>So what? What most people hold is irrelevant. This isn't a discussion
>>about dictionary meanings, but about mathematics. If you want to talk
>>about what people think they mean when they use some word or other,
>>that's a whole different game. Try sci.lang.
>
>
> Um, who SAYS this is about mathematics? The group I'm in is
> sci.philosophy.meta. There is no assumption that any term I or others use
> here is the mathematical.

Not the NG I subscribe to.

[...]

You are purporting to prove that a mathematical argument or proof makes
no sense, so you are talking mathematics. You can't drag
non-mathematical, common-language meanings into the argument - if you
do, you are actually taking psycho-linguistics, not math, and not
philosophy. If you want to discuss the different meanings of a term in
different contexts, say so. That might be interesting, even.

Nobody disagrees that the common parlance meaning of infinity doesn't
work as Cantor's precise definition of it works. So what?

If you want to talk philosophy, be explicit: but in that case I fail to
see any problem, since it's obvious that a term can have different
meanings in different contexts, and there is no point in arguing that
any of these meanings is universally correct.

I know Lester for one wants to find the "real" or "universal" meanings
of terms, and he believes he knows what they are. But it's a mug's game,
looking for the "real" meaning of a word. An hour or two reading the OED
or any other etymological dictionary will show the futility of this
quest. (BTW, I've never understood why so many people think the
dictionary tells what a word "really" means. All a dictionary can do is
tell what meanings people use words for, and the very nature of language
guarantees that a dictionary is out of date even before it's published,
and becomes more so as time goes by.)

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