Buddhism and Mathematics

One of the many topics that was raised during the talk on the Thai translation of Matthieu Ricard’s and Trinh Xuan Thuan’s book concerned the relation between Buddhist thought and mathematics. There have of course been quite a lot of talks about how Buddhism and science are related, but not much at all on Buddhism and mathematics. So that was a welcome change. Unfortunately we did not spend much time on this fascinating topic.

It was credit to Ricard and Thuan that they spend one entire chapter on this topic. The idea is how mathematics is related to reality and what the Buddhists think of that. The eleventh chapter of the book is entitled “The Grammar of the Universe” or something like that. What is interesting is how mathematics is an accurate description of reality at all. Which comes first, mathematics or the world?

On the one hand, this is a very simple point. We all know that two plus two equals four. So you have two things, add another two, and count the result, which is of course four. But the premise of mathematics is that you cannot get mathematics (or logic for that matter) out of empirical observation. You just cannot form a general statement “2 + 2 = 4” from just observing two things and another two things. The reason is that you have somehow to know before hand that two plus two equals four in order for you to be able to get the conclusion that these two things and these other two make four! This is Kant’s main argumentative strategy in his entire critical philosophy. And for Kant mathematics is a prime example of what he calls “synthetic a priori” judgments, e.g., judgments that are true by virtue of their correspondence with some outside measuring point but which is known entirely through thinking alone.

We are not actually discussing Kant here; the point is that if the truth of mathematics does not come from observation, then it must come from inside. Ricard and Thuan discussed that perhaps this situation implies that there is some universal and all powerful mind whose thinking made all mathematical statements true (all the true ones, of course). It is this big mind that guarantees that two plus two equals four, that the sum of the squares on the side of the two legs of a right angle triangle is equal to that on the hypotenuse, that the law of modus ponens (‘p’ and ‘if p then q’ always implies ‘q’), and so on.

So this big mind might refer to God. So here the discussion went on to see what the Buddhists think about this. I don’t quite remember what Ricard, the Buddhist representative in the book, made of this, so I am going to present my own thought. I also did this during the talk last Saturday, but time was so limited then.

I think the main difference between the theistic religions like Christianity and Islam and non-theistic one like Buddhism might not appear as large as one might think. Buddhism would have no problem recognizing the Big Mind alluded to above, so long as that refers, not to some external being, but in fact to our own minds. It is us who create mathematics and it is ultimately speaking our own minds, working together collectively, that create the world such that it is true of mathematics. In other words, we could also say that we human beings are gods unto ourselves. There is a Big Mind that creates reality corresponding to math, yes, but that Mind is not apart from us.

Whether this is shocking or not depends on your view on theism. If you believe that humans are apart from God, then you’d find this shocking. However, this is entirely correspondent with the Buddhist attitude that salvation is ultimately the person’s own responsibility and lies entirely within the person’s power to achieve. The Buddha is only a teacher. You don’t need to follow his teaching. The Buddha has no power to drag you to Liberation. No being does. You have to do it yourself.

Coming down from theological discussion and back down to earth, we see that the idea that it is human mind itself that creates mathematics to which reality belongs makes quite a lot of sense. We form mathematics and we perceive the world according to the same conceptual structure that formed the math in the first place, so no wonder the world corresponds to it. However, even thought mathematics looks very certain, it does not describe what reality is like ultimately speaking. This is because all mathematics depends on concepts and language (so is logic), and once you have concepts, you have to divide reality into separate chunks. So at best mathematics is a model or a map, and no map can become identical to the reality it is the map of. This refers to the doctrine of Emptiness or sunyata. We can say that math can always approach that, but never reach it, because if it does, then it would cease to be the math that it is.