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.
This sounds like hedging to me. But consider the theory of relativity. To this day new tests of Einstein’s theory continue to be designed. To date, none have falsified relativity. As this record builds, the theory of general relativity gains acceptance of scientific truth.
Hmmm … “gains acceptance” sounds a little like truth by committee, don’t you think?
Does this mean we will every “know” that the theory of relativity is correct? Let me know if I’m wrong about this, but I think the answer is no. More likely, it will be found that relativity is true and useful under most conditions but breaks down under others (such as the micro-realm of quantum mechanics).
So how can scientists agree about the validity of quantum mechanics, evolution, and global warming? It’s a combination of testability, a lack of falsification, and common sense.
In the end we fall back on the ability of our brains to model the physical world. Our internal feeling of trugh is strong enough it can persist in the face of contradiction. Note that contradiction is different than falsification. If you both believe that god exists and that god doesn’t exist, you tolerate a contradiction. In reality, neither assertion is testable or falsifiable.
String theory lies in this purgatory of truth/untruth. String theory is a highly developed and sophisticated quantum mechanical theory which explains many facets of the universe. However, to date it makes no predictions which are falsifiable. As long is this is the case, it will remain difficult for many physicists to take it seriously.
It is my observation as a psychiatrists that we gain wisdom, flexibility, and breadth of knowledge as our ability to tolerate contradiction increases. “Is the world getting better or is it getting worse?” — Laurie Anderson. The answer depends on perspective. Is it wrong to kill someone? Yes, but the principal of self defense is a time-honored exception.
In psychotherapy opposites are often two sides of the same coin. Excessive anger is similar to the inability to become angry. They are both problems with modulating anger. The opposite of love is not hatred but indifference. Ask someone in marital counselling what originally attracted them to their mate. “He was so strong and confident.” It will often be the chief complaint. “He never listens and always thinks he is right.”
BREAKING NEWS: String theory may predict an experimental result.
Does the valus of paradox suggest the desirability of ambivalance? I suspect so, but this would be another blog.