User:Thepigdog/Morality Axioms

THe purpose of this page is to explore intuitionalist reasoning, which is the encoded as axioms. If intuitionalist set theory is self contradictory because of Russels Paradox, would the attempt to axiomatise other intuitions suffer the same fate.

The moral laws of killing
It is not legal to kill someone unless they will or have killed someone illegally.

To encode this in logic let us ignore when the event hapenned or will happen. Let us represent,
 * A intends to or has killed B ..... do(kill, A, B)

The legality (lawfullness) of A killing B is represented by
 * A killing B is legal(lawfull) ... Legal(kill, A, B)

Then the law for murder might be encoded as,


 * do(kill, A, B) and not legal(kill, A, B) = legal(kill, C, A)

Scenario
A hates B so thinks,


 * If legal to kill B, kill B ..... legal(kill, A, B) = do(kill, A, B)

B hates A so thinks,


 * If legal to kill A, kill A ..... legal(kill, B, A) = do(kill, B, A)

Implications
If A and B intend to or have killed each other,

do(kill, A, B) and do(kill, B, A) then,


 * do(kill, A, B) and not legal(kill, A, B) = legal(kill, B, A)
 * do(kill, B, A) and not legal(kill, B, A) = legal(kill, A, B)

reduces to,


 * not legal(kill, A, B) = legal(kill, B, A)
 * not legal(kill, B, A) = legal(kill, A, B)

gives not legal(kill, A, B) = not legal(kill, B, A)

which tells us nothing. So in this situation we dont know if there actions were legal or illegal.