Limits of Reason
In class we studied how formal reasoning works. It turns out that any formal reasoning system starts out with basic assumptions (called axioms) and works up from there. No useful logical system can be built without these assumptions, but these assumptions have to be taken on faith - they are outside of the system. So many arguments are pointless because the participants are starting with radically different assumptions. Given how enormously important our assumptions are, it is shocking how unaware we typically are of them. When I talk about our mental machinery this is a major component.
Traditionally, rationalists start with the assumption that only their rational mind can be trusted as a source of truth. Everything else is fallible. Descartes “Meditations” is a great example of this mindset. The legend is that the philosopher Descartes had a bad cold, and was cooped up in a rustic cabin. His thoughts started to turn a little weird and he came up with this little essay titled “Meditations”. Descartes points out in this essay that when you think carefully about it, you start to realize that there really is no way to know that anything is actually as it seems. You don’t even know what you are seeing is real because just like in the Matrix movie it might turn out that everything is getting fed to you by some malevolent power.
The problem, though, as Descartes himself points out is that given this mindset you start to doubt that anything up to and possibly including even yourself is real. Descartes concludes that the only thing he can know for sure is that he is thinking – hence the famous “I think therefore I am” quote. Note that this is a very different mindset from “I have a body therefore I am”. Doubting that anything at all in the world except your own mind is real is a pretty weird view on life, and I don’t particularly recommend it. But many followers of pure reason find themselves sliding here. Without realizing it they get caught in a trap; at their core they only have faith in their rationality to guide them and so everything else including their own senses comes into suspicion.
In the Computability and Cognition seminar at Evergreen we also looked at what computers could tell us about reasoning. Could computers be as smart as humans? Could they even pass for human? At the time (mid ‘80’s), a surprisingly large number of people thought so. The thinking was that human intelligence can be completely captured by mathematical symbols. The actual physical substrate is almost irrelevant - it is the pure reason behind it that is all that matters. Since the 1950’s computer scientists have been arrogantly predicting the imminent dawn of Artificial Intelligence, and they’ve always been embarrassingly wrong. The only examples that we have of consciousness (ourselves and animals) are very biological, why would we immediately assume that the body has absolutely nothing to do with consciousness? What proof do we have of this? The answer is so far absolutely none.
We stand profoundly ignorant of our own minds. In our arrogance we assume that the same methods that teased out the secrets of the stars would work just as well to tease out the secrets of the soul. It hasn’t happened that way. We don’t understand how and why we have consciousness. We certainly can’t artificially create consciousness, nor have we come close to doing so. We don’t, in short, have a mathematics of the mind. Until we do develop such a system we need to stand humbly and admit how much we still do not know. Really, this is the only possible rational response - don’t assume we know something when we in fact do not.
The seminar culminated with Goedel’s theorem. It turns out that there are mathematical truths that cannot be proven correct. Let me say that again because it is very important. Something can be a true statement in a formal reasoning system, but you can not use that formal reasoning system to prove it so. In other words, any system of rational thought can not answer all questions, even some rational questions.
Why do I think this is so important? If you remember earlier I talked about how philosophers try to closely mimic math proofs. But here was a mathematical proof that showed that it is impossible to reach out to all truths by using just one system. Reasoning systems are inherently incomplete – they have to be supplemented by other methods. Again this might sound painfully obvious, but it really isn’t. How do I know if something is true? Some of us are truth seekers – we are determined to get to the deeper truth of things no matter where that might take us. And reasoning, despite its difficulty, is very attractive to us because it lets us “feel” the inherent truth of things. But now I was learning, if you restrict yourself to just using rationality, you are never going to reach important truths – and this can be proven mathematically!
When I realized that reason in fact has limits to what it can tell me, I became curious to explore what else was out there. For a time, I became a very serious Zen Buddhist, and meditated diligently. It was a revelation that I could calm my chattering mind and enter into another, larger mental space. Zen meditation requires an almost athletic ability to focus the mind and body to absolute stillness. At the peak of my ability, I spent a week at a Zen monastery just north of San Francisco, and every morning we would start the day by meditating for two early hours in the austere but beautiful temple. One morning at breakfast a woman who had been noisily struggling with the severe discipline of Zen meditation asked if everyone had heard the ocean this morning. One of the monks smiled and simply said the ocean had always been there she just had gotten quiet enough to hear it. And it was true, you had to get very, very quiet and still your body to complete motionlessness to hear the ocean waves hitting the beach in the distance, but once you did they were always present.
And that was my answer. It turns out that when I quiet my rational mind there are other sources of knowledge available to me. My mind had been so loudly talking to me that I could not hear the ocean. My rational mind might have an answer for just about everything, but that doesn’t guarantee that what it has to say is terribly useful. In mathematics it is possible to arrange mathematical symbols so that they fit the syntactic rules, but what they represent are meaningless. In the same way it is possible to ask a number of questions that seem to make sense, but are meaningless, really, if you try to answer them rationally. Questions like “Should I commit suicide?” or “What is the meaning of life?” only have truly satisfying answers if you quiet your mind down enough to hear the actual answers. But I did not yet have access to those other answers. That took some work. It was a good start, though. I at least now was open to hearing other answers, and I started to pay closer attention to the states my mind went to.
He thought up the Matrix first
Renegade mathematician