Re: Epistemology 201: The Science of Science

From: Albert (albertwagner_at_cox.net)
Date: 02/24/05 

Date: Thu, 24 Feb 2005 03:15:34 -0600

stephen@nomail.com wrote:
> In sci.math Albert <albertwagner@cox.net> wrote:
> : stephen@nomail.com wrote:
> :> In sci.math Albert <albertwagner@cox.net> wrote:
> :> : stephen@nomail.com wrote:
> :> :> In sci.math Albert <albertwagner@cox.net> wrote:
> :> :> : stephen@nomail.com wrote:
> :> :> : <snip>
> :> :> :> Let E be the set of even integers. Let I be set of integers. Define
> :> :> :> a mapping f: I -> E where f(n)=2n. This maps every integer to a unique even
> :> :> :> integer and ever even integer to a unique integer. We know this works
> :> :> :> because of the definitions of integer, multiplication and even.
> :> :>
> :> :> : But have you thereby said anything useful?
> :> :>
> :> :> What do you mean by useful?
> :>
> :> : I mean that, other than giving pleasure as a form of mental
> :> : masturbation for mathematicians, does it have any utility to
> :> : Science? There are no infinities in reality, only very large
> :> : numbers of things.
> :>
> :> Why the hostile tone?
>
> : Sorry, didn't mean to sound hostile. This conversation about
> : infinities, counting and cardinality just seemed to me to be
> : banging it's head against a brick wall of "My definitions are
> : better than your definitions."
>
> Definitions are fundamental. If you do not define things,
> than how is anyone supposed to know what you are talking about?
> If someone wants to propose some new definitions, there is no
> problem with that.

Indeed. And in that new definitions are so easy to invent, then
why not invent some new words to go with them, rather than having
one word with multiple contradictory definitions. Only a madman,
  or a mathematician, would do so, knowing the chaos it would
generate in conversations with non-mathematicians.

> But arguing with standard definitions is
> like claiming that "pineapple" should mean something else.

Yes. Mathematicians do that all the time. As is obvious in this
thread.

> Afterall, what does a "pineapple" have to do with an "apple"?

Or what does the word 'countable' have to do with 'infinity'?

> I am sure a simple web search will explain the etymology
> of the word, but that is not the point.

There is no etymology that can explain a mathematician's use of
words. Old well used words with well known common meanings are
appropriated helter-skelter and assigned new meanings that have
only random and coincidental relationships to the old meanings,
if that much, as anyone reading this thread will note.

<snip>
> : Counting in real life is different than in mathematics.
>
> How is it different?

In real life you actually *do it*. In mathematics you simply
define an algorithm for doing it, but never actually *do it*.

> In real life when you count you
> pair up the items you are counting with the numbers.
> If you did not have the language to express large numbers,
> which was true for a long stretch of human history, you
> would likely pair up the items you are counting with
> some other set of objects, such as sticks, stones or shells.
> Historically this is what people did. Counting is all
> about pairing up one set of objects with another set of objects.

Except that mathematician's never actually do that. See above.

> :> One real consequence of Cantor's ideas is that unsolvable
> :> problems exist.
>
> : OK. Good for Cantor. But a philosopher could have told him that
> : if he had just asked. But given that, what is the utility of
> : defining infinities, counting and cardinalities the way he told
> : you to?
>
> Another definition problem here. I have a very specific
> definition of "unsolveable problem" in mind, which is likely not
> what you have mind.

Which is why, I suppose, that you left your sentence above about
Cantor purposely ambiguous.

> These are problems that have a solution, there is
> just no way to actually calculate it.

Like counting infinities? That is never actually done. Instead
an algorithm is offered explaining how it could be done if anyone
had infinite time to do it.

> However that is a whole-nother
> crank magnet and this thread as become far to unwieldly.

As well it should. 

-- 
"Mercifully free of the ravages of intelligence"
	-- Time Bandits

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