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Topic: Is Analytic Geometry really Geometry?
Replies: 91   Last Post: Jun 26, 2006 2:52 PM

 Messages: [ Previous | Next ]
 Toni Lassila Posts: 536 Registered: 12/13/04
Re: Is Analytic Geometry really Geometry?
Posted: Jun 22, 2006 5:37 PM

On Thu, 22 Jun 2006 09:01:15 -0400, Hatto von Aquitanien

>Toni Lassila wrote:
>

>> On Thu, 22 Jun 2006 05:43:00 -0400, Hatto von Aquitanien
>>

>>>Toni Lassila wrote:
>>>

>>>> On Wed, 21 Jun 2006 23:01:39 -0400, Hatto von Aquitanien
>>>>

>>>>>Lee Rudolph wrote:
>>>>>

>>>>>> Hatto von Aquitanien <abbot@AugiaDives.hre> writes:
>>>>>>

>>>>>>>How can one discuss points and lines without an a priori sense of a
>>>>>>>geometric continuum?

>>>>>>
>>>>>> Very simply. Gene may yet show you how.

>>>>>
>>>>>I don't believe it is possible to ever show such a thing. The continuum
>>>>>is a priori, and can, therefore, not be excluded from reasoning.

>>>>
>>>> http://planetmath.org/encyclopedia/FinitePlane.html

>>>
>>>Explain that to me without relying on the ordering of symbols on the
>>>page/screen, and without any reference to concepts of time such as the
>>>word "repeatedly".

>>
>> Why?

>
>To demonstrate that you can "discuss points and lines without an a priori
>sense of a geometric continuum?".

Finite geometries like many other special geometries do not fulfill
Dedekind's Axiom, so there is no appeal to "geometric continuum"
there.

>I'm quite capable of applying concepts from one area of thought to another.
>
>My contention is that our concept of
>continuity is a priori. I believe intuitively that the idea of real number
>continuity is neither in need of proof, nor does it admit of proof.

The idea that real numbers are "intuitive" has popped up here
recently, but I think it's blatantly false. Natural numbers, integers,
and to a certain extent rationals could certainly be said to be
intuitive. Real numbers are the result of a rather unintuitive
completion process that produces a lot of misunderstandings and
crankiness.

>Furthermore, I believe we innately understand certain other geometric
>principles without any need of instruction.

Maybe so, but that does not affect the nature of purely axiomatic
mathematical geometries.

Date Subject Author
6/20/06 Hatto von Aquitanien
6/20/06 Gene Ward Smith
6/21/06 Hatto von Aquitanien
6/21/06 Lee Rudolph
6/21/06 Hatto von Aquitanien
6/22/06 Toni Lassila
6/22/06 Hatto von Aquitanien
6/22/06 Toni Lassila
6/22/06 Hatto von Aquitanien
6/22/06 Gene Ward Smith
6/22/06 Hatto von Aquitanien
6/22/06 Lee Rudolph
6/23/06 Hatto von Aquitanien
6/23/06 Virgil
6/23/06 Hatto von Aquitanien
6/23/06 Virgil
6/23/06 Hatto von Aquitanien
6/23/06 Virgil
6/24/06 David C. Ullrich
6/24/06 Hatto von Aquitanien
6/24/06 William Hale
6/24/06 Hatto von Aquitanien
6/24/06 Virgil
6/24/06 Hatto von Aquitanien
6/24/06 Virgil
6/24/06 Hatto von Aquitanien
6/24/06 Virgil
6/24/06 David C. Ullrich
6/24/06 Hatto von Aquitanien
6/24/06 Gene Ward Smith
6/25/06 David C. Ullrich
6/24/06 Virgil
6/24/06 Gene Ward Smith
6/24/06 Hatto von Aquitanien
6/24/06 Gene Ward Smith
6/25/06 Hatto von Aquitanien
6/25/06 Virgil
6/26/06 Hatto von Aquitanien
6/26/06 Virgil
6/26/06 David C. Ullrich
6/24/06 Gene Ward Smith
6/24/06 Hatto von Aquitanien
6/24/06 Mike Kelly
6/25/06 Hatto von Aquitanien
6/24/06 Virgil
6/25/06 David C. Ullrich
6/24/06 Gene Ward Smith
6/25/06 Hatto von Aquitanien
6/25/06 Virgil
6/25/06 Gene Ward Smith
6/25/06 David C. Ullrich
6/26/06 Hatto von Aquitanien
6/26/06 Virgil
6/26/06 David C. Ullrich
6/26/06 Gene Ward Smith
6/24/06 Gene Ward Smith
6/22/06 Gene Ward Smith
6/25/06 Keith Ramsay
6/25/06 Gene Ward Smith
6/25/06 Gene Ward Smith
6/22/06 Toni Lassila
6/22/06 Hatto von Aquitanien
6/22/06 Virgil
6/22/06 Hatto von Aquitanien
6/22/06 Gene Ward Smith
6/22/06 Hatto von Aquitanien
6/22/06 Ryan Reich
6/23/06 Hatto von Aquitanien
6/23/06 Ryan Reich
6/23/06 Lee Rudolph
6/24/06 Shmuel (Seymour J.) Metz
6/22/06 William Hale
6/22/06 ZZBunker
6/23/06 Hatto von Aquitanien
6/23/06 Gene Ward Smith
6/23/06 Hatto von Aquitanien
6/23/06 Gene Ward Smith
6/23/06 Hatto von Aquitanien
6/23/06 Gene Ward Smith
6/23/06 Gene Ward Smith
6/24/06 Hatto von Aquitanien
6/23/06 Virgil
6/24/06 Hatto von Aquitanien
6/24/06 Virgil
6/23/06 ZZBunker
6/23/06 Hatto von Aquitanien
6/23/06 ZZBunker
6/24/06 ZZBunker
6/23/06 Virgil
6/23/06 Hatto von Aquitanien
6/23/06 Virgil
6/23/06 Hatto von Aquitanien