Re: Epistemology 201: The Science of Science

From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 03/23/05 

Date: Wed, 23 Mar 2005 19:05:34 GMT

On 23 Mar 2005 08:55:46 -0800, stevendaryl3016@yahoo.com (Daryl
McCullough) in comp.ai.philosophy wrote:

>Albert Wagner says...
>
>>I tried to warn you not to attempt this, Bob. But you had to try
>>anyway, didn't you? Infinite cannot be defined as an infinite
>>property of anything.
>>
>>In _MIND AND NATURE: A Necessary Unity_ Gregory Bateson describes
>>this faulty logic:
>>---------------------------------------
>>A common form of empty explanation is the appeal to what I have
>>called "dormitive principles", borrowing the word dormitive from
>>Molière. There is a coda in dog Latin to Molière’s Le Malade
>>Imaginaire, and in this coda, we see on the stage a medieval oral
>>doctoral examination. The examiners ask the candidate why opium
>>puts people to sleep. The candidate triumphantly answers,
>>"Because, learned doctors, it contains a dormitive principle."
>
>The definition of "infinite" has nothing in common with
>what Bateson is talking about. There is nothing circular
>about saying
>
> A set S is infinite if there exists a bijection between
> S and a proper subset of S.
>
>Bijection is defined without any mention of infinity. Proper
>subset is defined without any mention of infinity. Therefore,
>defining defining "infinite" in terms of "bijection" and "proper
>subset" is not circular.

It's not so much circular, Daryl, as not a definition. It's just a
list of consequences for infinity when applied to set operations.
It's more an illustration of what infinity means in a particular
instance by list of ostensible consequences.

Regards - Lester

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