John Edser wrote:

>>>JE:-
>>>________________________________________________
>>>If set intersection is just a _property_,
>>>exactly what _process_ is it just a property
>>>of?
>>>________________________________________________
> 
> 
>>AW:
>>I want to thank JE for the question, as it provided me with some points
>>to ponder that I found interesting. In any event, I thought that this
>>assertion (intersection a property rather than an operation) might come
>>back to bite me. Though my argument may end in being hoist by its own
>>petard, I'll try to explicate my thinking on the matter.
>>I made the observation in response to JE's statement, in several posts,
>>that sets of parental fitnesses are allowed to 100% intersect, from
>>which I inferred that it would be possible to 50% (or some other
>>percentage) intersect sets. This is clearly not possible, hence my
>>statement that once sets are defined, their intersection is also
>>defined - one cannot choose to 50 or 75 or 100% intersect them. In the
>>quote above, JE says that any two sets can be intersected; my point is
>>that once two sets are defined, so is the intersection - it is not a
>>question of intersecting them, the intersection already exists.
> 
> 
>>JE:-
>>propositions _outside_ of mathematics control the level of set
>>intersection. Mathematically, only the following intersections are
>>possible between a set A = 3 and set B = 5. Two equal, partly
>>overlapping circles should be drawn out on a sheet of paper
>>providing three separates areas. These areas from left
>>to right are:
>>Area 1 represents  all the set elements in circle A.
>>Area 2 represents all the set elements in the intersection
>>of both circles (in the overlap).
>>Area 3 represents all the set elements within circle B.
>>An empty intersection is represented by the numbers 3,0,5.
>>Here, 3 is in area 1, zero in area 2 (the overlap)
>>and 5 in area 3, respectively. All the possible intersections
>>between sets A and B are represented by 3,0,5 or 1,2,3,
>>or 2,1,4, or 0,3,2. Four possible self exclusive levels of set
>>intersection  exist ranging from nothing in the intersection to
>>a maximum of 3.
>>Maximum intersection is 0,3,2. Here all of set A is in set B,
>>i.e. A is just a subset of B. The level of intersection between
>>set A and set B can only be determined by the problem mathematics
>>is being applied to and NOT just the mathematics.
> 
> 
> BOH:-
> This is the nub of the problem - you seem to be the only person who 
> thinks this is true.
> 
> JE:-
> Yes it 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?

No.  Can you tell me of any other person who can?  Name names!

> Mathematics ALONE cannot choose which level of set
> intersection it should make. What else is required?
> A proposition _outside_ of mathematics. Godel 
> insisted that mathematics must also rely on propositions
> that are not of mathematics. This is an example.
> 
> BOH:-
> 
>  From http://whatis.techtarget.com/definition/0,,sid9_gci838379,00.html>:
> "Given two sets A and B, the intersection of A and B, written A INT B, 
> is the set C of all elements that are in both A and B."
> i.e. the mathematics tells you which elements are in the intersection 
> (and hence you can count them).
> 
> 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.
> 
Huh?  But which one of the intersections actually does exist is 
determined by which of the elements IS a member of both sets.  Whether 
an element is a member of both sets is purely determined by whether is 
has the properties associated with both sets.  If it doesm, then the 
maths says that it is in the intersection.

Note that with your A's and B's, you have not defined what the elements 
are.  You have to do that (the maths can't), but once you've done that, 
then we can see how many of the elements are in the intersection.



Bob

-- 
Bob O'Hara

Rolf Nevanlinna Institute
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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