Re: Distinct linear orderings on Z

From: Albert Wagner (albertwagner_at_cox.net)
Date: 03/24/05 

Date: Wed, 23 Mar 2005 21:44:11 -0600

Daryl McCullough wrote:
> Albert Wagner says...
>
>>Daryl McCullough wrote:
>
>
>>>Why? Infinite is a property of sets. If you have explained
>>>under what circumstances a property holds, then you have defined
>>>the property.
>>
>>No. You haven't.
>
>
> Yes, I have.
>
>
>>And 'infinite' is not a property of anything, much less sets.
>
>
> That's false.
>
>
>>I posted this earlier today but perhaps you
>>missed it:
>
>
> That passage doesn't support anything that you have said.
>
>
>>In _MIND AND NATURE: A Necessary Unity_ Gregory Bateson describes
>>this faulty logic:
>
>
>>Let's try a different approach.
>>
>>Your attempt at definition of 'infinite' is:
>>(1) A set S is said to be infinite if there exists a bijection
>>between S and a proper subset of S.
>>
>>Lets try this same form on another topic:
>>(2) A box of marbles is said to be empty if the count of marbles
>>in the box is zero.
>>
>>This is true, but it is not a definition of empty.
>
>
> Sure, it is.
>
>
>>It is only a prescription for determining if it is
>>appropriate to apply the qualifier 'empty' to a box
>>of marbles and thereby place that particular box under
>>the category of 'empty things'.
>
>
> That's what a definition is.
>

Well, then. *** you. 

-- 
"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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