Intersubjectivity is Key

by Luke Breuer

How can you know if you are thinking clearly? In Orthodoxy (free ebook), GK Chesterton writes:

Thoroughly worldly people never understand even the world; they rely altogether on a few cynical maxims which are not true. Once I remember walking with a prosperous publisher, who made a remark which I had often heard before; it is, indeed, almost a motto of the modern world. Yet I had heard it once too often, and I saw suddenly that there was nothing in it. The publisher said of somebody, “That man will get on; he believes in himself.” And I remember that as I lifted my head to listen, my eye caught an omnibus on which was written “Hanwell.” I said to him, “Shall I tell you where the men are who believe most in themselves? For I can tell you. I know of men who believe in themselves more colossally than Napoleon or Caesar. I know where flames the fixed star of certainty and success. I can guide you to the thrones of the Super-men. The men who really believe in themselves are all in lunatic asylums.”

In other words: insane people have no need for anyone else to see things their way. They may want others to believe their view of things (probably delusions, but not necessarily), but this desire is not strong enough for them to prioritize

  1. getting other people to see things their way, over
  2. believing that things truly are as they think they are.

I claim there are two different ways to err:

  1. holding to contradictory thoughts about reality
  2. thinking that you understand all of reality that could be

The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (X) and an equant (larger black dot).

(stolen from WP)


Some of you may see the allusion to Gödel’s second incompleteness theorem; I will talk about that at a later time, or in the comments if someone asks. The type-I error is easy to understand, but the type-II error could some some explication. Time for a history lesson!

Due to the ancient Greeks’ love of spheres, they thought that all planetary motions must be circular. When the ancients carefully watched the sky, they realized that they weren’t always observing circular motion. To ‘fix’ this, Ptolemy formalized the epicycle (Apollonius of Perga discovered them). Look at the diagram at the right: it’s made entirely of circles! Ptolemy found out that if you have planets moving in circles, within circles, you can better approximate their observed motion. And so the ancients had their cake and ate it too: the planets only ever moved in circles, their observations matched theory, and no barbarian impurity was permitted.

You might think that it took until Johannes Kepler to figure out that planets actually move in ellipses. This isn’t quite right; as is often the case, the Muslims had figured it out first. Ibn Bajjah discovered a model of planetary motion which did not require epicycles in Spain during the twelfth century. Too bad we didn’t pay attention to him, or we might know more, today.

It turns out that epicycles are actually the first step in a fully valid mathematical approximation of ellipses, or actually any other step. Nevertheless, they had a weakness: it was hard to do math with them. The circular mathematical world was too small: a type-II error had been committed. The circular mathematical world may not have been incomplete theoretically, but it prevented minds from making progress.

How do I know if I have made a type-II error? Occasionally, I might be able to introspect and see that I have. That being said, I believe it is far better to try to convince other people to see things my way. Suppose my idea is not subject to a type-I error. The more people to whom I successfully describe my idea, the more likely they will either i) verify that my way is the most economical [known] way; or ii) show me a better way.

Now, other people can equally well show me that I have made type-I errors in my thinking. But this is well-known and kind of boring. Type-II errors seem to be less-well understood, and yet extraordinarily important! Any given [human] mind is only able to hold so many symbols in memory at once: if the number of symbols required to represent an idea can be reduced somehow, it is almost always a win. Furthermore, Gödel hinted that there will always be truths which cannot be proven with our current beliefs; if this is true, we must always be willing to admit that our world needs enlarging.

Ok, let’s suppose I have decided against insanity, by ensuring I can get other people to see things my way (with them hopefully making me see things differently at times!). Call this ‘intersubjectivity’. Am I all set? Is there nothing better? No.

The next step is to expose your thinking to people vastly different than you. This is a really hard task. Groupthink is easy. Groupthink lets you avoid asking certain questions—whether they are uncomfortable, obnoxious, or otherwise. There are even psychological reasons to delay questioning certain assumptions: we cannot question everything at once, and if we do too much criticism before we’ve built ideas up enough, they may come crashing down even though something valid was being constructed. More on that in another post.

Any scientist will verify that we only “see through a glass dimly”. In other words, we are prone to drawing invalid conclusions from the observations we make. But scientists have discovered that when enough people are able to see the same thing through the glass, things are less dim. This is called intersubjective agreement (WP). The more different people I can get to agree with me on how I see things, the more confident I am that I have a pretty good idea about things. There is no guarantee that it is the best way, but it is a guarantee that if someone knows a better way, he/she isn’t part of the group, or he/she is staying silent.

What it means to think clearly is arguably a relative term: if I am the clearest thinking caveman in a group of cavemen, I may still have an awful lot of wrong ideas. But that’s ok, because it just seems to be a property of ‘mind’ that when they congregate, they can help each other think more clearly. Then again, they can choose the less energy-intensive echo chamber option. I vote for expending more energy so we can go more interesting places.