Re: Misunderstanding Bateson

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

Date: Thu, 24 Mar 2005 13:13:50 -0600

Daryl McCullough wrote:
> 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.

Which is certainly why you, having only a limited vocabulary,
reject dictionary definitions.

> 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.

No. That is *not* a definition of 'even' but only a definition of
positive even integers.

> 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.

It is also inadequate for negative integers.

> 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.

False. That is *not* a definition of 'infinite'. That is only a
definition of an 'infinite set', assuming 'set' and 'infinite'
are previously defined. A proper definition of 'infinite' would
not include the words 'infinite', 'set', 'bijection' or 'proper
subset'.

> Albert is under the mistaken impression that there is some absolute
> notion of the adequacy of a definition. That's just incorrect.

Wrong, math-breath.

==============================================================
Definition: A precise /explanation/ of meaning, marking out the
boundaries and limits of a word or phrase.

Rules of Definition

1. The definition must be clearer than the thing defined.
Metaphorical expressions, therefore, need to be avoided.
In other words, don't define a "lion" as the "king of beasts."
Metaphors are fine for poetry but not for logical thinking.
Words which are more unusual than the idea to be explained
should be avoided. Don't define a "lie" as an
"intentional terminological inexactitude."

2. The definition must not contain the idea to be defined.
Don't make a "circular definition." This is where a first
idea is defined by a second, and then the second is defined
by the first. If we define a "dollar" as "one hundred cents"
and then define a "cent" as "one-hundredth of a dollar,"
we would be guilty of a circular definition.

3. The definition must be convertible with the idea defined.
The definition must not be wider or narrower in comprehension
than the comprehension of the idea defined. If an "animal"
is a sentient, living, bodily substance," then a "sentient,
living, bodily substance" must be an "animal." On the other hand,
we shouldn't define "biology" as the "science which studies
the world around us." This is too wide a definition since
other sciences also study the world around us. We shouldn't
define "biology" as the "science which studies animals,"
because it is too narrow. Biology also studies plants.

4. Finally, the definition must be positive, not negative,
whenever possible. A definition should explain what a thing
is; not what it is not. "Health" is not the absence of
sickness. I can't know what sickness is without prior
knowledge of what "health" means.
==============================================================

> 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.

True. Note that it also contains no references to 'infinite',
'set', 'bijection' or 'proper subset'. Now try again to define
'infinite' without reference to 'infinite', 'set', 'bijection' or
'proper subset'. 

-- 
"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

Relevant Pages

  • Re: infinity
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  • Re: Misunderstanding Bateson
    ... Daryl McCullough says... ... of a phrase is adequate depends on the knowledge of the person ... that set and a proper subset of that set. ... The first definition for "infinite" ...
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  • Re: Misunderstanding Bateson
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  • Re: abundance of irrationals!)
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