Re: Epistemology 201: The Science of Science

From: Richard Herring (junk_at_[127.0.0.1)
Date: 02/04/05 

Date: Fri, 4 Feb 2005 10:17:57 +0000

In message <420274e7.89630635@netnews.att.net>, Lester Zick
<lesterDELzick@worldnet.att.net> writes
>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?

Algebraic, as people keep telling you.

> for rational and irrational concepts. No point to
>defining transcendental as irrational.

It's not *defined* as irrational, it follows from the definition of
"transcendental" that such numbers also meet the requirements of
"irrational".

Did you bother to look at the following references?
>
>>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?

Including *what*? Never heard of them. But if their name means anything,
they can't be rational. See that "ir-" prefix?

> 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.
> 

-- 
Richard Herring

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... >You have to use right angles even to use your finger. ... It's been around ever since mathematicians decided ... >Including linear irrationals? ... >what is rational which kinda defeats the purpose of the tautologies. ...
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  • Re: Epistemology 201: The Science of Science
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  • Re: Epistemology 201: The Science of Science
    ... You have to use right angles even to use your finger. ... >>to form certain tautologies of which mathematicians are so fond. ... Including linear irrationals? ... what is rational which kinda defeats the purpose of the tautologies. ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... You have to use right angles even to use your finger. ... >>to form certain tautologies of which mathematicians are so fond. ... Including linear irrationals? ... what is rational which kinda defeats the purpose of the tautologies. ...
    (sci.physics)
  • Re: Epistemology 201: The Science of Science
    ... You have to use right angles even to use your finger. ... >>to form certain tautologies of which mathematicians are so fond. ... Including linear irrationals? ... what is rational which kinda defeats the purpose of the tautologies. ...
    (sci.math)