Infallible, part 2: Consistency is Insufficient

Kurt GödelMichael, on his way to establish the infallibility of the Catholic Church, makes the claim that consistency is the defining characteristic of truth:

The hallmark of truth is consistency. Error can always be shown, at the core of the argument, to
be logically inconsistent and ultimately self­refuting. Ergo, consistency is contingent to any claim
of truth.

This is of course an error of monumental proportions.

Consistency is necessary but not sufficient. Sagan's dragon in the garage is perfectly consistent, but still untrue. Alchemy was, as far as I can tell, logically consistent, and turned out to be false nonetheless. Galilean relativity is consistent, but it’s Einstein’s Relativity that coincides with observation.

In physics, consistency is not even achieved as a whole, but only within theories (quantum field theory is incompatible with general relativity for example, although each is self-consistent), which should tell you something about the usefulness of the concept. Second, nothing is ever accepted in physics based only on consistency. You need confrontation to reality. That is the real test. Superstrings are consistent, and even plausible and compelling, but as long as we haven't obtained solid evidence for them, they are not going to be accepted. The graveyard of physics is full of failed hypotheses that were consistent but did not pass the test of reality.

Even in mathematics, consistency is not proof. As Gödel has shown, no non-trivial formal mathematical system can prove its own consistency.

I'll also point out that mathematical truth is essentially different from physical reality, and that it is always circumscribed by the axiomatic system in which they are expressed. For example, the proposition “only one line parallel to a given line passes through a given point” can be true or false depending on whether we are expressing it for Euclidean or non-Euclidean geometries. The geometry of our universe is not determined by consistency.

Michael makes a stupendous but too common error when he says that “error can always be shown, at the core of the argument, to be logically inconsistent and ultimately self-refuting”. This is the illusion apologists are under when they attempt to prove the existence of God through “logic”. If I claim that if I use a flashlight from a train, the speed of the photons is going to be the sum of the speed of light and of the speed of the train, I am making no logical error, and there is nothing self-refuting here. Still, I am in error, because my claim can be demonstrated to be wrong by experimentation.

Consistency is wholly unimpressive, and saying so is not at all the same thing as saying math or physics are unimpressive. Those disciplines have a lot more behind them than just consistency. Catholic dogma? Not so much. I remain unimpressed, except by the unwillingness of apologists to understand the difference between necessity and sufficiency.

Next time, we’ll examine the claim that the Bible’s cosmogonic myths are unique in describing creation ex-nihilo.

Tags: Religion, Science, Naive philosophy

Wednesday, May 29, 2013 6:17:00 AM

No Comments

Add a Comment