Definition of Paradox: A seemingly contradictory statement that may nonetheless be true.
A paradox is supposed to define what is false.
The statement below is false.
The statement above is true.
You can go around and around on this one. But most of us try to work it out a couple of times, say, “Oh, it’s a paradox.” and go about our business. Unlike a computer, which could cycle over this classic paradox until eternity, or Windows crashes, which ever comes first.
What is it about our brains that allow us to tolerate paradox as well as we do? In general, it is considered incompatible with good math or physics. Godel’s theorem, discussed in a previous post, suggests that all mathematical systems, however rigorous, will turn up paradoxes, or fail to prove things that are true or both. How does Godel establish truth or falsity? By reference to common sense attributes of the real number system which we know to be true or false.
This is all related to the time-honored philosophical battle between ontology versus epistemology, or what is true versus what can be known. As they delve into relms of physics further removed from everyday experience, physicists have settled on the principal of falsifiability. A theory or hypothesis in physics may be considered true if it predicts the outcomse of experimental tests. Such tests accumulate and continue to be consistent with the hypothesis, the hypothesis is more likely to be true. If any such experiment fails, the hypothesis may be considered false.