An interesting problem in
NonMonotonicLogic, and one which demonstrates why simple, deterministic
PredicateLogic is often a poor model for the
RealWorld.
Consider US president Richard Nixon. Two well known facts about Nixon are:
- He was a Republican
- He was a Quaker (a small Protestant denomination. How devout a Quaker Nixon was is an interesting question...)
The Quaker faith is quite pacificist, so in a logic system we could write:
Quaker(x) -> Pacifist(x)
The Republican Party has (at least since WWII) been the more bellicose of the major US political parties, and has generally been willing to flex US military muscle.
Republican(x) -> !Pacifist(x)
Now: From those facts and rules, is Nixon a pacifist or not? If we are to consider the above system of axioms, we discover a contradiction. This is the
NixonDiamond.
In real life, of course, we realize that the two rules given above, are both approximations and not absolute. In Nixon's case, he was demonstrably not a pacifist, despite his Quaker faith - he oversaw a major escalation of the Vietnam War. OTOH, the bit about Republicans not being pacifists is also not absolute; a former Republican senator from Oregon - Mark Hatfield - was a strict pacifist, and one of the few (if only) senators to vote against the first Gulf War. He has since retired from office.