Re: Epistemology 201: The Science of Science

From: Albert Wagner (albertwagner_at_cox.net)
Date: 03/23/05 

Date: Wed, 23 Mar 2005 12:41:25 -0600

Daryl McCullough 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.

<sigh> Please read my signature. 

-- 
"I know that most men, including those at ease with
problems of the greatest complexity, can seldom
accept even the simplest and most obvious truth
if it be such as would oblige them to admit the falsity
of conclusions which they have delighted in explaining
to colleagues, which they have proudly taught to others,
and which they have woven, thread by thread,
into the fabric of their lives." -
	-- Tolstoy

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