Last night I listened to the podcast of last week’s show with Matt and Don. I am looking forward to being back in the “other” studio again, but not next weekend as scheduled, since I have plans to fly to Pennsylvania.
One of the responses to the callers caught my attention. Matt and Don, beginning at around 42:30 in the audio, were speaking to Gregory in Eugene, Oregon. Gregory first wanted to propose his own uninteresting (IMHO) redefinition of God. Then, later, he claimed that he “considered himself just as much an atheist as I do a theist.”
Matt asserted that this was ridiculous — which it is. To be a theist means that you believe in a god, while to be an atheist means that you do not believe in a god. Obviously these positions are mutually contradictory, and so it makes no sense to hold both of them.
But then Matt went one step further, claiming that Eugene could not hold both of these positions simultaneously, effectively accusing him of either lying or being deluded about his own beliefs. It is this point that I wish to respond to, because — as an enthusiast of formal logic — I think one can’t make such a blanket statement about other people’s beliefs.
Of course, it’s perfectly reasonable to assert that people should not hold contradictory beliefs, and to point it out vigorously when they try to slip that sort of thing past. However, it does not follow that one cannot hold contradictory beliefs, and in fact, I think that they do all the time.
Seen in abstract terms, you could say that a person’s state of mind is a set of propositions that they assert to be true. “The sky is blue” and “the sky is not green” are two such propositions; “There is a God” is another. Not all propositions need to be definite; they could be probabilistic, as in “There is probably no God” or “There may be intelligent life elsewhere in the universe.”
Now, given a particular proposition P, P can be either true or not true; and according to propositional logic it must be one or the other but not both. However, just because a proposition is false in reality does not mean that it is not a part of someone’s belief system. Indeed, we know that some people have false beliefs — just consider that many people are theists and many others are atheists. Either there is a God or there isn’t, and therefore one of these groups clearly holds a false proposition to be true, and most likely a host of related propositions as well.
Still, believing a false proposition P does not make your belief system inconsistent; you can easily believe something that is false but does not contradict any other proposition in your universe of beliefs. However, my point is that there is no reason in principle why somebody cannot comfortably believe the assertion P1: “X is true” and P2: “X is false”, at the same time.
As a computer geek, I happen to believe (though not entirely backed by affirmative evidence) that the human mind can be represented as a formal system, not entirely unlike a computer could behave in principle if it was outfitted with the right software. I am a believer in the possibility of artificial intelligence, though I definitely do not believe it has been achieved yet, and it may not be achieved within my lifetime, or even the entire span of the human race.
There is a famous theorem formulated by Austrian mathematician Kurt Gödel, which states that all formal systems are either incomplete or inconsistent. In other words, either there is some proposition P for which the system holds P to be both true and not true (inconsistent); or else there is some proposition P which really is true, but the system cannot prove it (incomplete, as P is true but missing).
Some opponents of AI see this as a fundamental limitation of computers, a proof that humans are somehow better than computers because they have intuition which is capable of somehow “jumping outside the system” and directly perceiving truths that cannot be proven formally. I see that as a fallacy. Sure, humans are capable of making logical leaps of intuition, but that doesn’t mean the leaps lead exclusively to true beliefs. We know for a fact that brains are often misled into believing things which are not true, and may even be contradictory, which we sometimes call “hypocrisy.”
Imagine a person who is completely insane, in the sense that he believes everything that is false and nothing that is true. Such a person must necessarily be inconsistent as well. Why? Well, consider the following untrue statements. P1: 2+2=3. P2: 2+2=5. These statements are contradictory — they cannot both be true at once. Yet the insane person must believe both, because they are both false.
But you don’t have to go so far as complete insanity in order to hold contradictory beliefs. In fact, I would speculate that everyone in the world probably has some beliefs that contradict one another. I do. Matt does. I’m not saying that this is desirable, or that you can’t minimize the number of contradictions you believe, but the mind is full of shortcuts and logical leaps and rules of thumb that let us analyze reality without becoming immediately paralyzed by an in-depth comparison of new information against every other single proposition you already believe.
In fact, I once read a beautiful proof by logician Raymond Smullyan that every person must necessarily be either inconsistent or conceited. It goes like this:
The human brain is finite, therefore there are only finitely many propositions which you believe. Let us label these propositions p1, p2, …, pn, where n is the number of propositions you believe. So you believe each of the propositions p1, p2, …, pn. Yet, unless you are conceited, you know that you sometimes make mistakes, hence not everything you believe is true. Therefore, if you are not conceited, you know that at least one of the propositions, p1, p2, …, pn is false. Yet you believe each of the propositions p1, p2, …, pn. So you believe at least one of these statements to be both true and false; hence you must be inconsistent.
Believing a contradiction does not make you crazy or a liar. Continuing to believe both “there is a god” and “there is no god,” even after the contradiction is explicitly pointed out to you, might make you a bit thick. But there’s no impossibility there. We know thick people exist, and most of us encounter them on a daily basis.