Re: Epistemology 201: The Science of Science

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

Date: Thu, 24 Mar 2005 16:07:26 -0600

stephen@nomail.com wrote:
> In sci.math Albert Wagner <albertwagner@cox.net> wrote:
> : Wolf Kirchmeir wrote:
> :> Albert Wagner wrote:
> :>
> :>> Daryl McCullough wrote:
> :>>
> :>>> In article <4242d729.100336841@netnews.att.net>, Lester Zick says...
> :>>>
> :>>>> stevendaryl3016@yahoo.com (Daryl McCullough) in comp.ai.philosophy
> :>>>> wrote:
> :>>>
> :>>>
> :>>>
> :>>>
> :>>>>> No. x is a variable. What is being defined is the *predicate*
> :>>>>> x is even, or x is a perfect square, etc.
> :>>>>
> :>>>>
> :>>>>
> :>>>> Saying x is a variable doesn't mean you aren't defining it.
> :>>>
> :>>>
> :>>>
> :>>>
> :>>> Yes, it does.
> :>>>
> :>>>
> :>>>> What you're defining is x eveness, x perfect squareness, etc.
> :>>>
> :>>>
> :>>>
> :>>>
> :>>> No, that's not what is being defined. The point of a (free) variable in
> :>>> a definition is that you can substitute any constant term (of the right
> :>>> type) for the variable to get a true statement. So in
> :>>>
> :>>> x is even <-> x is a multiple of 2
> :>>>
> :>>> you can substitute any constant term of type natural
> :>>> for x and get a true statement:
> :>>>
> :>>> 0 is even <-> 0 is a multiple of 2
> :>>> 1 is even <-> 1 is a multiple of 2
> :>>> 2 is even <-> 2 is a multiple of 2
> :>>
> :>>
> :>>
> :>> A template for true statements is not a definition.
> :>>
> :>> (BTW. Is -4 even?)
> :>
> :> Yes.
>
> : I thought so. Then Daryl's definition above is incomplete.
>
>
> No, his definition made no mention of natural numbers.
> x is even <-> x is a multiple of 2
>
> There is no mention of natural numbers there. It
> applies to all possible values for x. It clearly
> applies to -4. -4 is a multiple of 2, therefore
> -4 is even.

Apparently, mathematicians define multiple in absolute terms. In
common usage there is no way that -4 is a multiple of 2. 

-- 
"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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