John Edser wrote:
>>>>JE:-
>>>>There's a good tautology: " Set elements are set elements".
>>>>All the set elements within PURE MATHEMATICS are numbers.
>>>
> 
>>>BOH:-
>>>No they're not.  They are objects, and will be defined to have certain
>>>properties (e.g. colour, size).  Of course, numbers can be set elements,
>>>if the sets are so defined.
>>
> 
>>>JE:-
>>>You appear to be confusing propositions of mathematics
>>>such as sets of numbers with propositions that
>>>are not of mathematics e.g. “objects” that “will be defined
>>>to have certain  properties (e.g. colour, size)”.
>>>Mathematics only concerns itself with defined abstract
>>>concepts and not real world concepts.
>>
> 
>>BOH:-
>>Fine.  We can define "colour" in an abstract way.  The
point is that we
>>can define elements as having certain properties.
> 
> 
>>JE:-
>>Yes but in mathematics these are
>>JUST the properties of number.
> 
> 
> BOH:-
> NO! NO! NO!  They are properties of the element.  Or are you claiming
> that the number 4 is blue, or that "yellow" > "pink"?
> 
> JE:-
> All numbers are ONLY _sets_ of _identical_
> basic number elements: THE NUMBER ONE. All 1's are
> exactly the same as each other within _mathematics_.
> They can't have "certain properties" like "colour"
> or "size" within mathematics only OUTSIDE of mathematics.
> Mathematics just processes NUMBERS i.e. sets of
> identical, ONE'S.
> 
OK, but what about sets that are not sets of numbers?  How do you define 
colours as "properties of number"?

Bob

-- 
Bob O'Hara

Dept. of Mathematics and Statistics
P.O. Box 4 (Yliopistonkatu 5)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 23743
Mobile: +358 50 599 0540
Fax:  +358-9-191 22 779
WWW:  http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: http://www.jnr-eeb.org
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