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.
> 
> 
> BOH:-
> OK, but what about sets that are not sets of numbers?
> 
> JE:-
> These are not objective sets, eg the
> set of Yin and the set of Yang, things.

What about the sets of spies and ex-spies? An Ex-spy is not a number.

> 
> BOH:-
> How do you define
> colours as "properties of number"?
> 
> JE:-
> Apply the numbers to sets of things,
> e.g. the set of 3 red apples. Here
> each counted apple = "one" where each "one"
> has EXACTLY the same properties "apple" and "red".

If you have a set of apples, some read and some green, then what?

Bob

-- 
Bob O'Hara
Department 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: www.jnr-eeb.org
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