Re: "Number" of elements; was: Distinct linear orderings on Z

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

Date: Thu, 24 Mar 2005 13:41:10 -0600

Daryl McCullough wrote:
> Albert Wagner says...
>
>
>>This is *not* a definition of 'red': A car is red, if there
>>exists on it's surface a coat of red paint.
>
>
> As I said in another thread, whether something counts as an
> adequate definition of a concept depends on what concepts are
> *already* understood by the person asking for a definition.
> If I already know what the operation "+" means, then I can
> define the successor function as follows:
>
> successor(x) = x+1
>
> If I don't know what "+" means, then that is of course a useless
> definition.
>
> If you don't know what "red" means, then of course saying
>
> A car is red, if there exists on its surface a coat of red paint
>
> doesn't tell me anything about the concept "red".
>
> However, if I already know what "red paint" means, then saying
>
> A car is red, if there exists on its surface a coat of red paint
>
> *does* define what it means for a *car* to be red. This definition
> tells me that it isn't necessary for the *tires* to be red, and it
> isn't necessary for *hubcaps* to be red, in order for it to be considered
> a red car. It is sufficient that the car have red paint on its surface.
>
> Saying
>
> A set is infinite if there exists a bijection between that set and a
> proper subset.
>
> is a perfectly adequate definition of what it means for a set to be
> infinite, assuming that you already understand what "bijection" and
> "proper subset" mean.

You're absolutely hopeless, Daryl. 

-- 
"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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