Blogtrek

Accidents are contradictions

Recently I observed contradictory positions come from two people at my workplace. This continued for a while until a third issue related to both of them caused them to be exposed to each other. Of course the people involved have to revise their positions and the experience can be described as . . . an accident. Which leads me to my sophism of the day: Accidents are contradictions.

A contradiction is a pair of statements that say opposite things; actually it is more than that. Two statements are said to be in contradiction if they both can't be true. For example, "The car was in the garage in Binghamton overnight." and "Mary drove the car to Philadelphia last night." are contradiction: a car can't be in Binghamton and on a highway to Philadelphia at the same time. Logically, a contradiction is any statement S(x, y, …) in logical variables x, y, . . . such that all combinations of truth values (true or false) for the x, y, . . . make S false. An example would be "x and not x." If x is true then not x is false, so that "x and not x" is false. If x is false, then "x and not x" is false. No matter what x is, this statement is false, so it is a contradiction. A collection of statements S, T, … contradict each other if S and T and … is a contradiction, yielding false on every truth-value substitution.

A well-known formula in logic is P -> (not P -> Q). This is logically true for all statements P and Q. It says that once a contradiction occurs (P and not P) then anything goes. Another variant is (P and not P) -> (Q and not Q). This says if you have one contradiction, you have them all. That is a major disaster in a logical theory. If everything is true, then the logical theory tells us nothing. Not even one contradiction can enter into a logical system, else it becomes worthless.

So how is an accident a contradiction? A well known property of physics says that if an object, such as an automobile, is at point (x, y, z) at time t, then no other automobile can be at point (x, y, z) at time t. If an automobile occupies such a point, or rather, it tries to occupy such a point, the result is crash! an accident. Viewed in this way, an automobile accident is simply the results of trying to maintain a contradiction in the positions of cars. It is a contradiction just like the contradiction in the workplace was. The results are not too good.