The Brain in Train: Tracks, Maths and Truth

I feel odd when I consider this possibility: that all my thoughts are strictly determined, no more under my control than a straw in a gale or a stone in an avalanche. It seems paradoxical to have strictly determined thoughts about strictly determined thoughts. But is it? And is strict determinism fatal for finding the truth? I don’t think so. In fact, I think that strict determinism is essential for truth. But irrelevant associations get in the way of our understanding this. If our thoughts are determined, they seem like automatic trains running on rigid tracks. We might want to go to the station marked “Truth”, but if the switches are set wrong, the train will never get there. Or it will thunder through and never stop.

So we picture ourselves as helpless passengers on the brain-train, watching as we’re carried willy-nilly through a landscape of facts and ideas. But it wouldn’t really feel like that. Consider these questions: Is the sun shining at the moment? Is it cold or hot? You might think you know the right answers, but how can you be sure? You might be hallucinating or your sense organs might be lying or not working properly. But you assume otherwise. Certainly you hope otherwise. We want our sense organs to work in a deterministic way: to respond reliably and predictably to the stimuli of light, sound, heat, smell and so on. We want them to report what’s actually there in external reality. So why, once we have sense-data, do we want free will to organize and arrange them and draw conclusions from them? In short, why do we want free will in our thinking?

One answer might be: so we can correct errors in our thinking. But to correct errors of any kind we need to recognize them. However, we don’t want our mechanism-of-recognition to have free will. That’s already apparent in our attitude to our sense-organs. They are mechanisms-of-recognition too. They enable us to know whether things are so or not-so out there, in external reality. Is the sun shining? Is this fruit ripe? Is that a stone or a scorpion? And so on. But the same need for deterministic recognition applies in internal reality, in the world of logic and reasoning. Suppose you’re presented with this equation:

1 + 1 = 2

You recognize that as true and accept it (assuming you are sane and I am not hallucinating about what I have typed). But you have no choice about recognizing it as true and accepting it. Try as hard as you like: you cannot recognize “1 + 1 = 2” as false. Now try this:

2 + 2 = 3

You recognize that as false and reject it. But you have no choice about recognizing-and-rejecting. Try as hard as you like: you cannot recognize “2 + 2 = 3” as true. There are mechanisms in your brain that you don’t control. Nor do you understand them, even if you’re an expert neurologist. But they allow you to recognize errors and correct them, which is why some people think we need free will to reason. They’re wrong, because recognizing error does not involve free will. This applies to simple reasoning, like the above, or complicated reasoning, like that involved in proving Fermat’s last theorem:

A recent false alarm for a general proof was raised by Y. Miyaoka (Cipra 1988) whose proof, however, turned out to be flawed. … In 1993, a bombshell was dropped. In that year, the general theorem was partially proven by Andrew Wiles (Cipra 1993, Stewart 1993) by proving the semi-stable case of the Taniyama-Shimura conjecture. Unfortunately, several holes were discovered in the proof shortly thereafter when Wiles’ approach via the Taniyama-Shimura conjecture became hung up on properties of the Selmer group using a tool called an Euler system. However, the difficulty was circumvented by Wiles and R. Taylor in late 1994 (Cipra 1994, 1995) and published in Taylor and Wiles (1995) and Wiles (1995). (Fermat’s Last Theorem at MathWorld)

When the data are very complicated, human beings make mistakes in recognizing the truth. Andrew Wiles thought he had proved Fermat’s last theorem. He was wrong: he had only partly solved it. In the end, he completed the proof. In other words, he perfected a deterministic chain of reasoning that imposed the truth on any brain that could follow it. Mathematics chains minds: the point of proof is to remove free will. We have no choice about accepting valid mathematics. For example, it is incontrovertibly true that primes are infinite in number and all maps can be filled in using only four colours. That is why all knowledge aspires to the condition of mathematics. We want reality to determine our beliefs, not our beliefs to determine reality. Or some of us want that, anyway. But that’s another story.


Previously pre-posted (please peruse):

The Brain In Pain: Choice, Joyce and the Colour of Your Hair
At the Mountains of Mathness — general index

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