Why I Am (Not) A Dialetheist

The Utility of Aporia and The Problem with Stopping

In my last post I argued for Dialetheism, that there may be statements about the world that are both True and False. In this post I’m going to argue that Dialetheism itself is one of such statements. Like a true dialetheist, I’m going to argue that dialetheism is right, and also wrong. It’s both! Just… don’t think about it too hard. Or maybe you should; maybe that’s the problem.

This post is going to be somewhat different than the previous three. I’m going to use a notion of truth that is different than I have been, in a way that makes it significantly weaker.[1] Rather than thinking of truth as a theory that explains the data, I’m going to talk about truth as that which, when believed, leads us to correct understanding. In other words, what is useful to believe. This is weaker, dependent on human psychology, and in some sense subjective. This blog post is less an argument then, and more an exploration of some consequences of dialetheism. This really is Why I am, and am not, a Dialetheist.

So to begin with I’m going to illustrate how dialetheism can be useful for your thinking. How believing in dialetheism can lead you to a better understanding of things. I’m going to start with a dive into the philosophy, or anti-philosophy, of Socrates, who was definitely not a dialetheist, but would have made a good one.

Socrates is famous for making people look stupid. He does this often in the Socratic dialogues by leading his interlocutor to argue for both sides of an argument, and therefore conclude a contradiction, showing that they are simply confused. This is often where the conversation ends, in a state of Aporia, or philosophical confusion, and socrates says “Well, I guess you’re not as much of an expert as you thought. We’ll just have to keep searching for an expert.”

In his dialogue with Laches, the two of them discuss Courage. I will summarize in broad strokes their discussion, but I recommend reading it yourself to get a fuller picture. The relevant part starts halfway through: “Tell me, if you can, what is courage?”

Laches attempts to define courage as a sort of “endurance of the soul”. Socrates convinces him of two things. First, that courage is always a positive, or “noble” thing, and second that enduring in some circumstances is not noble, but foolish. So then they conclude that courage is *wise* endurance. But then he notices that when we are likely to succeed, when endurance is the wisest course of action, it isn’t not courageous to do so. The opposite is true; it is courageous to endure when we are likely to fail. But that is exactly when it is most foolish. So at the same time courage and foolishness are correlated, and anti-correlated. On the one hand, the more foolish the situation, the more courageous we would say someone is being, on the other hand courage is a positive thing and foolishness a negative.

At this point another character Nicias takes a turn trying to define courage. That conversation proceeds similarly, and I’ll leave it to you to read through. Spoiler alert: Socrates convinces them that his definition is contradictory as well. He says, near the end “Then, Nicias, we have not discovered what courage is.”

While Socrates’ dialogues are an amusing “fail” compilation of the wise and authoritative, it feels like they’re missing something substantive.[2] I think what it’s missing is that by the end of the discussion, we aren’t at the same place as when we started. When Socrates ends by declaring epistemological bankruptcy, and deciding we don’t know what we’re talking about, he returns us to where we were at the beginning of the conversation, knowing nothing.

But maybe it’s better to say “both of these incompatible things are true.” After all, we have just explored justifications for both. When I finish reading The Laches, I am left with the idea that courage is tricky to pin down, and that there is tension between courage and foolishness. I am left wondering about the relationship between courage and wisdom, and whether courage is about enduring in the best of situations, or the worst. I am not left thinking that either of those possibilities are entirely bunk.

Truth claims, in many contexts, are shorthands for the arguments which justify them. If you are committed to a single truth value for a statement, you can only encode one argument. You lose the context, the nuance.

I was thinking about this post while I read I and Thou a little while ago, and I saw the perfect exposition of this idea in Walter Kaughman’s introduction.

What is manifold is often frightening because it is not neat and simple. Men prefer to forget how many possibilities are open to them.

They like to be told that there are two worlds and two ways. This is comforting because it is so tidy. Almost always one way turns out to be common and the other one is celebrated as superior.

…Not all simplicity is wise. But a wealth of possibilities breeds dread. Hence those who speak of many possibilities speak to the few and are of help to even fewer. The wise offer only two ways, of which one is good, and thus help many.

What Kaughman is pointing to here is a tendency among people to prefer simple, black-and-white ideological statements, to the full complexity of an issue. Without dialetheism, people tend to slide into absolutism. Dialetheism offers us a way to appease that tendency towards simplicity, and at the same time build an escape hatch to let the complexity back in. Allows us to be human, and also to retain flexible thinking.

So why am I also not a dialetheist? How can it lead to worse understanding? I started on the subject of dialetheism on this blog, because I found myself arguing for both sides of the same debate, for and against platonism. But there’s a problem with my argument in Why I’m Not A Platonist.

My argument was that platonism entails classical logic, and yet we see that intuitionism is an effective foundation for mathematics.[3] I said at the end “platonism is on probation, with a lot of explaining to do”, and that’s true. But the explaining can be done! The assumption that I made, that people often make, is that platonism entails classical logic, and intuitionism entails non-platonism. Ironically, intuitionism is so non-intuitive that people can’t reconcile it with an idea of Real Mathematical Objects.

But something being weird doesn’t make it not True. People consider quantum mechanics weird. And yet, it is true about the real world. Why can’t intuitionism be weird, and still be true of platonically real mathematical objects? The idea that if an object is Real, it must have defined properties is just a hazy intuition people have. Why can’t it simply be True that some mathematical objects have indefinite properties? Why can’t I be a platonic intuitionist; an intuitionistic platonist?

But I was able to paper over this problem in my own mind because once I cried dialetheism, I could stop looking for ways to reconcile seemingly contradictory philosophies.

Another example, that came up in Why I’m A Dialetheist, is a unified theory of physics. Even though I think we should seek to understand the way we use quantum mechanics and general relativity together in a paraconsistent way, it would be all too easy and foolish to then stop looking for a unified theory of everything. It is still better to have a non-contradictory theory. In many ways non-contradiction is easier to work with. Dialetheism lets you stop looking for that, and I think that’s a problem.

So which is it? Is dialetheism useful or detrimental to our thinking? As usual, I’ll say: both. We should use it when it enables us to expand our thinking, and eschew it when it prompts us to be lazy with our thinking. Seek consistent theories, but try to understand rigorously the inconsistencies in the ones we have.

I have a few more ideas related to Dialetheism, but for now I’m going to turn to other topics.

[1] I think it’s a defensible notion of truth, but defending it is outside the scope of this article, just go along with me on this one.

[2] Well, a few things. but lets ignore the fact that expertise is not determined by your ability to define words in an air-tight way.

[3] Go read it. I’m not going to repeat the whole argument here.