Re: Misunderstanding Bateson

From: Daryl McCullough (stevendaryl3016_at_yahoo.com)
Date: 03/24/05 

Date: 24 Mar 2005 08:30:44 -0800

Daryl McCullough says...

>In practice, whether something is a suitable explanation or not
>depends on the knowledge of the person asking for an explanation,
>and on what gap in that knowledge the person is trying to fill.

To continue, the same is true of definitions: whether a definition
of a phrase is adequate depends on the knowledge of the person
asking for the definition. If you already understand what it means
for one integer to be a multiple of another integer, then a perfectly
adequate definition of "even" is this:

    An integer is defined to be even if it is a multiple of 2.

If you *don't* know what "multiple" means, or you don't know what "2"
means, then of course this isn't an adequate definition.

In the case of "infinite", if you already know what "bijection" means,
and you know what "proper subset" means, then a perfectly adequate
definition of "infinite" is this:

    A set is defined to be infinite if there exists a bijection between
    that set and a proper subset of that set.

Albert is under the mistaken impression that there is some absolute
notion of the adequacy of a definition. That's just incorrect. Take
just about any dictionary definition: The first definition for "infinite"
on dictionary.com is this:

    Having no boundaries or limits.

That definition is certainly useless if one doesn't already know
what "boundary" and "limit" means. 

--
Daryl McCullough
Ithaca, NY

Relevant Pages

  • Re: Misunderstanding Bateson
    ... > Daryl McCullough says... ... whether something is a suitable explanation or not ... > that set and a proper subset of that set. ... That is *not* a definition of 'infinite'. ...
    (sci.math)
  • Re: infinity
    ... > Daryl McCullough said: ... >>>What IS at issue here is whether there are a finite or infinite number of ... >> Okay. ... > but not a proper subset. ...
    (sci.math)
  • Re: Misunderstanding Bateson
    ... >> only if there exists a bijection between that set and a proper subset, ... >Except what 'infinite' means. ... Daryl McCullough ...
    (sci.math)
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