Re: Epistemology 201: The Science of Science
From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 03/20/05
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Date: Sun, 20 Mar 2005 20:24:06 GMT
On Sun, 20 Mar 2005 12:31:09 -0500, "robert j. kolker"
<nowhere@nowhere.net> in comp.ai.philosophy wrote:
>Lester Zick wrote:
>
>> On Sun, 20 Mar 2005 11:26:04 -0500, "robert j. kolker"
>> <nowhere@nowhere.net> in comp.ai.philosophy wrote:
>>
>>
>>>Lester Zick wrote:
>>>
>>>>There is a distinction between mathematics, Bob, and modern math.
>>>
>>>So you claim. Now show the difference. Be very explicit.
>>
>>
>> The difference between your first modern math definition for a circle
>> which actually defines a sphere and your second Euclidean definition
>
>You said there was a difference between mathematics and modern math.
>That is a very general statement. Substantiate it. Address yourself to
>the question I asked.
I just did. The difference between your first and second definitions
for a circle, Bob1 and Bob2, is what defines the difference between
modern math and mathematics respectively.
>> for a circle which allows you to pretend that circles are well defined
>> as the set of all points equidistant from any point without definition
>> for spatial dimensionality that allows you to pretend dimensionality
>
>Schmuck. What is the dimension of a plane, in the sense of maximal
>number of mutually orthagonal lines lying on a plane? Think! Put all 13
>of your neurons to work.
Very good, Bob. I'll have to borrow your 2 neurons. Why don't you
defne a plane for us so I can do the higher modern math needed to
define the number of mutually orthogonal lines lying on it for you so
you won't have to think for yourself.
>> is just so much vulcanized rubber.
>
>When I made the defnition complete (my appologies for the initial
>omission) I made it plain that it was a figure on a plane. Now what can
>be plainer than a plane.
The question is, I think, what could be plainer than your lack of
definition for a plane in terms of the points you use to define a
sphere instead of the circle you call it. In other words, you have to
define the plane, Bob, and not just ask rhetorically what could be
plainer than a plane. Obviously you don't know.
> Dimnsionality for vector spaces is not rubber,
But the dimensionality of space is?
>it is the cardinality of the maximal set of linearly independent vectors
>in the vector space.
Yada yada, whatever. If you say so, Bob. Of course what you're saying
isn't anything worth writing home about much less posting.
> One must show that all maximal linearly independent
>sets have ths same cardinality (easy for finite dimensional vector
>spaces, not so easy for infinite dimensional vector spaces).
Lots of things are easy for mathematikers, Bob, especially when they
feel comfortable drawing circles in the air to pretend they've defined
planes.
>Except for specifying that a circle is a figure on a plane the
>definition gives no refernce to dimensionality whatsovery.
Oh, well, Hello? Earth to Bob. Earth to Bob. What in the hell do you
suppose gives reference to dimensionality other than references to
dimensionality?
> In fact one
>can show a circle on a plane (a two dimensional surface) is a one
>dimension set since it can be parametrically generated by one variable,
>to with the angle an arbitrary radius makes with a reference radius.
Gee, Bob. So now a circle is a one dimension parametric which only
relies on two dimensions in space for its parametrization? You should
have quit while you were ahead. Oh, that's right, you were never
ahead. You just keep going backward and stumbling over your own feet.
>That conclusion is not immediately clear from the definition. A lot of
>theorems have to proven to show that.
None of your conclusions are immediately clear from your definitions,
Bob, because so far you haven't given any definitions for the spatial
dimensionality your definitions for a circle rely on and assume.
Regards - Lester
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