John Edser wrote:
>>>>>JE:-
>>>>>________________________________________________
>>>>>If set intersection is just a _property_,
>>>>>exactly what _process_ is it just a property
>>>>>of?
>>>>>________________________________________________
>>>>
> 
>>>JE:-
>>>...is "the nub of the problem" but NO "I am
>>>not "the only person who thinks this is true". Do you 
>>>disbelieve the evidence set before you? Can you not see 
>>>that the intersection between set A = 3 and set B = 5
>>>has 4 possible self _exclusive_ levels of set intersection?
>>
> 
>>BOH:-
>>No.  Can you tell me of any other person who can?  Name names!
> 
> 
>>JE:-
>>Godel determined that mathematics
>>is not self consistent. 
> 
> 
> 
> 
> BOH:-
> Now can you answer the question.
> 
> JE:-
> I did. Which intersection out of the 4 possible
> ones IS NOT A PROPOSITION OF PURE MATHEMATICS
> verifying Godel.
> 
Huh?  Where did G”del show this?  The only theorem of his that I'm aware 
of is his demonstration of incompleteness - i.e. that there are 
statements in mathematics that cannot be shown to be true.  I'm not 
aware of him ever showing that one cannot determine how many elements 
there are in an intersection.  And, under the standard definition of an 
intersection, one can tell.

> 
>>>JE:-
>>>You simply did not understand the definition you supplied.
>>>Mathematics is applied logic. An application of logic within 
>>>mathematics produces a set property. Mathematics is therefore,
>>>limited by the logic being applied to it. Mathematics cannot 
>>>determine which of many possible logical processes are being applied 
>>>within mathematics at any moment. Yes, the intersection has
>>>"all elements that are in both A and B" but as we have seen 
>>>when set A = 3 and set B = 5 four different self exclusive set 
>>>intersections can exist and not just one, where in every case it remains
>>>true that the intersection contains "all elements that are
in both A 
>>>and B" depending entirely on how you define a minimum of two points 
>>>of commonality.
>>
> 
>>BOH:-
>>Huh?  But which one of the intersections actually does exist is 
>>determined by which of the elements IS a member of both sets. 
> 
>  
> 
>>JE:-
>>Yes, but this has 4 possible outcomes and not just
>>one outcome given A=3 and B=5. _Each_ of the 4
>>outcomes _satisfies_ the definition DEPENDING
>>on "a minimum of two points of commonality".
> 
> 
> BOH:-
> 
>>snip<
> 
> I assume you mean that A has 5 elements and B has 3.
> 
> JE:-
> Of course.
> 
> BOH:-
> But that is not 
> enough to define the sets A and B.
> 
> JE:-
> It is if the set elements are just sets
> of numbers.
> 
Not if you don't define which numbers.

>  
> 
>>>snip<
>>
> 
>>BOH
>>Note that with your A's and B's, you have not defined what the elements 
>>are. 
> 
> 
>>JE:-
>>Mathematics only defines set elements as _numbers_. 
> 
> 
> BOH
> Rubbish.  Set elements are set elements.
> JE:-
> There's a good tautology: " Set elements are set elements".
> All the set elements within PURE MATHEMATICS are numbers.
> 
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.

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/
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