# Euclidian logic

Dear all,
Imagine a rectangle U and two circles +/-A and +/-B inside or above (if above you can drag them inside U). I wonder if it is possible to write a program which can do the following. The well known rule is, that A and -A fill the rectangle totally, and so do B and -B, when they are dragged inside U.
3 Definitions:
Identity: =
Identity means being at the same time at the same place or in our case at the same part of euclidian 3d or on paper 2d say 5 square-inch space. So "two" things are identical or one if "they" are of the same size and occupy the same part of space at the same time ("at the same time" we could leave out, for simultaneity is a function of place).
whole: + or -
A whole "A" is a 3d (or on paper 2d) limited continuous magnitude. Every magnitude or quantity (in the sense of magnitude) finite or infinite big or small devides the universe into two parts, namely A and -A, where "" and "-" mean "the whole" and the "whole non-". No part of +A occupies any part of the space of -A.
part: (+) or (-)
A part
� is (always!) smaller than its whole
� is totally inside its whole
� occupies therefore the same part of space as the part of its whole or is identical with it.
� "(+)" means "part of +"
� "(-)" means "part of -"
There should be the rectangular U filled with one color.
Then there are the two quantities A and B above the universe. A and B are circles can be inscribed in U via drag and drop. The size of A and B can be changed with the mouse. The maximum diameter of A or B is the diameter of the universe (or the height if the universe is a rectangle), the minimum size can be an infinite small quantity but not a point without parts. You can switch between the two signs + and - of A and B. When you drag say +A totally into the universe the name of the universe "U" or "+U" disappears and it is devided into two parts, +A and -A in two colors, so that the sum of +A plus -A = U.
Now if you drag the second quantity say +B into the universe, the universe will be divided into two, three or into four parts in two, three or four colors. The program should be able to regognize and name these two, three or four parts.
Into two parts U is divided if +A and +B have the same size and are at the same place:
+A=+B, which means the whole A is identical with the whole B, one circle and
-A=-B, which means the whole non-A is identical with the whole non-B the rest of the universe.
The two equations appear besides the universe. Their letters have the same colours as the two sections the universe is devided in.
Into three parts if +A and +B are apart from each other
+ A=(-)B, which means the whole +A is identical with a part of non-B,
(-)A= + B, which means a part of non-A is identical with the whole B and
(-)A=(-)B, which means a part of non-A is identical with a part of non-B, the rest of the universe besides +A and +B.
The three equations appear besides the universe. Their letters have the same colours as the three sections. When moving +A or +B the equations should change in the proper way. For instance if you move the smaller +A into the bigger +B, so that +A becomes a part of +B:
whole A and part B:
+ A=(+)B,
(-)A= - B, everything outside B and
(-)A=(+)B, the rest between tho both above.
Or if you move the smaller +B into the bigger +A part A and whole B:
(+)A= + B,
- A=(-)B, the universe outside +A and
(+)A=(-)B, the part inside +A which does not belong to +B.
Finally the universe is divided into four parts if +A and +B cut each other,
(+)A=(+)B,
(+)A=(-)B,
(-)A=(+)B and
(-)A=(-)B.
The four equations appear besides the universe. Their letters have the same colours as the four sections. I wonder if it is possible that the intersection (+)A=(+)B gets a different color than the other three sections.
In all cases the sum of the two, three or four parts is the universe. But the universe itself never appears in any logical equation as well as the borders don't although there is no quantity without them.
And so the rest of the combinations, namely +A and -B, -A and +B and -A and -B.
Could it be that there is someone who has some interest in accompanying such a project with mathematical and computer know how? If so let me know. Then I make some graphical illustrations of the above and give some more informations.
Regards
Lothar Seidel, Frankfurt am Main, Germany
P.S.
A problem to be solved is: ">, <, =" and "whole, part, identity" have different meanings in both sciences, mathematics and logic. For instance being part of includes being smaller, but being smaller does not include to be part of.
If one understands the meaning of "A=B" used in here, she understands all the rest.
The 16 equations you can build are:
+ A= + B
- A= - B
+ A= - B
- A= + B
(+)A= - B
- A=(+)B
(+)A= + B
- A=(-)B
+ A=(+)B
(-)A= - B
+ A=(-)B
(-)A= + B
(+)A=(+)B
(+)A=(-)B
(-)A=(+)B
(-)A=(-)B

Could you rework your posting to make it a little more readable? It's obviously complicated but the rambling doesn't help. Try taking it one step at a time with clear definitions and no unnecessary words.

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