Re: Epistemology 201: The Science of Science
From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 02/03/05
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Date: Thu, 03 Feb 2005 19:29:06 GMT
On Thu, 3 Feb 2005 16:55:22 +0000, Richard Herring <junk@[127.0.0.1]>
in comp.ai.philosophy wrote:
>In message <4202459e.85589322@netnews.att.net>, Lester Zick
><lesterDELzick@worldnet.att.net> writes
>>On Thu, 3 Feb 2005 10:00:40 +0000, Richard Herring <junk@[127.0.0.1]>
>>in comp.ai.philosophy wrote:
>>
>>>In message <42012aac.71626885@netnews.att.net>, Lester Zick
>>><lesterDELzick@worldnet.att.net> writes
>>
>>[. . .]
>>
>>>>>What fact? The fact that both the rationals and some irrationals can be
>>>>>"pointed out using right angles" tells us nothing about what
>>>>>"irrational" means.
>>>>
>>>>Sure it does. It tells us what the mechanics of irrationals is. Other
>>>>kinds of mechanics define other kinds or classes of numeric concepts
>>>>like transcendentals. When you say some irrationals can be and others
>>>>can't be pointed out the same way, I have to ask why you confuse the
>>>>two with the same name?
>>>
>>>*I'm* not the one who is confused here. But to answer your question
>>>literally, because neither kind of irrational can be "pointed out"
>>>*without* "using right angles".
>>
>>And if you're not the one who is confused here, how exactly does one
>>point anything out without using right angles?
>
>Personally I use my finger.
Hahahahaha. Scientifically and mathematically rather than personally?
You have to use right angles even to use your finger.
>>>> Because cardinal approximations run off to
>>>>infinity in convergent series? Cardinal approximations don't define
>>>>anything exactly except cardinal approximations.
>>>
>>>I haven't mentioned "cardinal approximations".
>>
>>You haven't mentioned anything except you consider me wrong ex
>>transcendental definition.
>>
>>>> The mechanics
>>>>underlying rationals, irrationals, and transcendentals does that and
>>>>are different between irrationals and transcendentals.
>>>
>>>ITYM "between algebraic numbers and transcendentals".
>>
>>You still don't make the case by inventing another name.
>
>I didn't invent it. It's been around ever since mathematicians decided
>they needed a name for those numbers which aren't transcendental.
Oookay. Are there other things you didn't invent?
The difficulty is algebra defines a variety of relationships some of
which are not transcendental and some of which are. I don't see the
problem using the term transcendental for transcendental concepts and
what? linear? for rational and irrational concepts. No point to
defining transcendental as irrational.
>http://mathworld.wolfram.com/AlgebraicNumber.html
>http://mathworld.wolfram.com/TranscendentalNumber.html
>
>>>>So I'll be
>>>>happy to qualify this observation as rational/irrational so it can be
>>>>examined for probity and qualify your observations as transcendental
>>>>so they can't.
>>>>
>>>>>> and not the wishful thinking of those who
>>>>>>merely see cardinal approximations for irrational and transcendental
>>>>>>numbers running off to infinity in covergent series.
>>>
>>>You're very entertaining, in small doses, but I think I'd go elsewhere
>>>for tuition in number theory.
>>
>>Not in your number theory. See, the problem I'm having lies in trying
>>to form certain tautologies of which mathematicians are so fond. I can
>>readily form irrational from rational but then I run into a problem
>>forming anything at all from not irrational.
>
>Then perhaps you shouldn't be starting from there.
Starting from there? I start where mathematics started with rational
and can't get anywhere definite tautologically. Same problem with the
term algebraic. We might just recast the terminology to reflect the
mechanics involved in the concepts rather than historical mistakes.
>> Perhaps you could do as
>>mathematikers are wont and simply provide a list of all things which
>>are not irrational
>
>That would be the things that are rational.
Including linear irrationals? Not according to my dictionary. Don't
think you can get there from here without specific directions as to
what is rational which kinda defeats the purpose of the tautologies.
Tautologically you can get from rational to irrational. The problem is
getting back tautologically without detours through not transcendental
land.
>http://mathworld.wolfram.com/RationalNumber.html
>http://mathworld.wolfram.com/IrrationalNumber.html
>
>>so we won't have to think the concept through,
>>which seems to be a problem in your number theory.
>
>Some people have trouble with thinking regardless of the theory.
Fortunately I'm not one of them.
Regards - Lester
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