Re: Epistemology 201: The Science of Science

From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 03/24/05 

Date: Thu, 24 Mar 2005 19:04:00 GMT

On 24 Mar 2005 07:34:57 -0800, stevendaryl3016@yahoo.com (Daryl
McCullough) in comp.ai.philosophy wrote:

>Lester Zick says...
>>
>>On 23 Mar 2005 22:31:42 GMT, stephen@nomail.com in comp.ai.philosophy
>>wrote:
>
>>>The 5th definition is:
>>> 5. Math. a. not finite. b. (of a set) having elements
>>> that can be put into one-to-one correspondence with a subset
>>> that is not the given set
>>>
>>>This is the 1994 "Webster's New Universal Unabridged Dictionary"
>>
>>5a strikes a little close to home however unless you prefer to say
>>"infinite is not when something is finite because finite doesn't mean
>>defined so infinite can't mean undefined".
>
>That's an awkward way to put it, but yes---finite does not mean "defined"
>and infinite does not mean "undefined". sin(1/0) is undefined, but it isn't
>infinite.

Daryl, I addressed this early on. This is an awkward way to put it
because it isn't a definition. There are many predicates in a given
instance. In the case of set theory sets counting is one predicate.
The term infinite applies to counting wherein you have undefined
countability. This doesn't affect definition of other predicates but
does mean that certain contradictions are possible where counting is
the critical concept. And this makes it look like a concept defined in
other respects is defined when it may not actually be. What remain
defined are other aspects of the definition. I don't know how else to
say it.

Regards - Lester

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