The current situation in Afghanistan is unsolvable
Definitions:
^ : this is a “friendship” relationship. One can express the relationship “A loves B” by A ^ B
!^ : this is the “animosity” relationship. One can express the relationship “A does not love B” by A !^ B
India: I
United States: U
Afghanistan: A
Pakistan: P
Taliban: T
Transitivity Rules:
a) Transitivity rule of “friends of my friends are my friends too”: if X ^ Y and Y ^ Z then X ^ Z
b) Transitivity rule of “friends of my enemies are my enemies too”: if X !^ Y and Y ^ Z then X !^ Z
c) Transitivity rule of “enemies of my friends are my enemies too”: if X ^ Y and Y !^ Z then X !^ Z
Axioms:
1. I ^ U (India has always been a great ally of US, just look at all the historical facts)
2. U ^ A (otherwise they wouldn’t be there forever trying to help them to rebuild)
3. U !^ T (otherwise they wouldn’t be trying to kill them all)
4. P !^ I (from the many incidents in the past few years)
5. P ^ T (otherwise they wouldn’t be housing them)
6. T ^ A (otherwise they wouldn’t stay there)
7. T !^ U (from the 9/11 attacks)
Theorem A: Everybody else loves Afghanistan.
Proof:
- From (2): U ^ A
- From (6): T ^ A
- From (1) and (2): I ^ U ^ A, using transitivity rule (a): I ^ A
- From (5) and (6): P ^ T ^ A, using transitivity rule (a): P ^ A
Theorem B: Everybody else does not love Afghanistan.
Proof:
- From (3) and (6): U !^ T ^ A, using transitivity rule (b): U !^ A
- From (7) and (2): T !^ U ^ A, using transitivity rule (b): T !^ A
- From (1) and (3): I ^ U !^ T, using transitivity rule (c): I !^ T. With this result, and from (6): I !^ T ^ A, using transitivity rule (b): I !^ A
- From (5) and the result that T !^ A: P ^ T !^ A, using transitivity rule (C): P !^ A
Theorem C: The situation in Afghanistan is impossible to resolve as long as the Taliban, Pakistan, United States and India are involved.
Proof:
For the situation in Afghanistan to be resolved, we cannot have all parties involved loving and hating Afghanistan at the same time. But we have just proved that all parties involved love and hate Afghanistan at the same time (Theorems A and B). Therefore, we conclude that the situation is unsolvable as long as all the parties are involved.
^ : this is a “friendship” relationship. One can express the relationship “A loves B” by A ^ B
!^ : this is the “animosity” relationship. One can express the relationship “A does not love B” by A !^ B
India: I
United States: U
Afghanistan: A
Pakistan: P
Taliban: T
Transitivity Rules:
a) Transitivity rule of “friends of my friends are my friends too”: if X ^ Y and Y ^ Z then X ^ Z
b) Transitivity rule of “friends of my enemies are my enemies too”: if X !^ Y and Y ^ Z then X !^ Z
c) Transitivity rule of “enemies of my friends are my enemies too”: if X ^ Y and Y !^ Z then X !^ Z
Axioms:
1. I ^ U (India has always been a great ally of US, just look at all the historical facts)
2. U ^ A (otherwise they wouldn’t be there forever trying to help them to rebuild)
3. U !^ T (otherwise they wouldn’t be trying to kill them all)
4. P !^ I (from the many incidents in the past few years)
5. P ^ T (otherwise they wouldn’t be housing them)
6. T ^ A (otherwise they wouldn’t stay there)
7. T !^ U (from the 9/11 attacks)
Theorem A: Everybody else loves Afghanistan.
Proof:
- From (2): U ^ A
- From (6): T ^ A
- From (1) and (2): I ^ U ^ A, using transitivity rule (a): I ^ A
- From (5) and (6): P ^ T ^ A, using transitivity rule (a): P ^ A
Theorem B: Everybody else does not love Afghanistan.
Proof:
- From (3) and (6): U !^ T ^ A, using transitivity rule (b): U !^ A
- From (7) and (2): T !^ U ^ A, using transitivity rule (b): T !^ A
- From (1) and (3): I ^ U !^ T, using transitivity rule (c): I !^ T. With this result, and from (6): I !^ T ^ A, using transitivity rule (b): I !^ A
- From (5) and the result that T !^ A: P ^ T !^ A, using transitivity rule (C): P !^ A
Theorem C: The situation in Afghanistan is impossible to resolve as long as the Taliban, Pakistan, United States and India are involved.
Proof:
For the situation in Afghanistan to be resolved, we cannot have all parties involved loving and hating Afghanistan at the same time. But we have just proved that all parties involved love and hate Afghanistan at the same time (Theorems A and B). Therefore, we conclude that the situation is unsolvable as long as all the parties are involved.
posted by Marcelo De Barros at 11:27 AM
