It’s hard to give examples of the importance of the rules of plausible reasoning without subjecting yourself to empty criticism, or even ridicule.
If I use examples that I personally care about, then that example is going to be steeped in years of economics training. So what do I do then? Back up and teach three semesters of economic theory in order to get other people caught up on the problem? And then start to discuss the rules of plausible reasoning, once we’re all agreed that the examples I’m using relate to genuinely important economic problems that we as a society face?
What if my training has led me to conclude something that is counter-intuitive? Contrary to what most non-economists would think? Are we going to be able to discuss plausible reasoning at all, or will the discussion get mired in the dispute over controversial points in economic theory, rather than the broader topic of logic and probability and statistics? Shouldn’t we discuss the logic of statistical belief first, and only after we’ve got a handle on that start discussing important issues of policy?
I don’t know how to thread that needle. I don’t know how to talk about what’s important to me, without also knowing that it’s important to you. So here, I’m just going to stay very general, very lacking in detail, and go back to the basic idea: There are problems in this universe where it is crucially important to get the right answer.
Is that true for you? Are there problems in society — or even in your own life — that are legitimately so important that it’s actually worth investigating how to think more carefully about solving these problems? If that’s not true for you, then… okay. That’s fine. That’s cool. I guess I don’t know why you’re reading this? I don’t really see the reason for you to study probability or stats if it’s not for any specific purpose. But still, glad to have you here! Thanks for reading. But this discussion is more geared toward those people who agree with me that there are genuinely problems in our world about which we are not entirely certain of the outcomes, but which nevertheless we desperately want to get the answer right instead of wrong. This is for you! Let’s learn how to handle the big masses of data that the modern world throws at us, let’s learn some probability, some statistics, and let’s be part of the bigger conversation that’s going on in the world.
All of this means, fundamentally, taking the rules of plausibility seriously. But again, I don’t know what is important to you. I can’t use examples that are most relevant to your life and your concerns, because I don’t know them, or even if I did, what was important to you wouldn’t necessarily be important to the other non-you people who might possibly read this. So my solution? I’m going to use silly examples.
I’m going to use strong, evocative, silly Gun to the Head examples. Sometimes literally. For instance, we can go back to the conversation I discussed in my opening post, the person who talked about the lack of interest in applying probabilistic reasoning to problems to which he was personally indifferent. This is a direct quote from that discussion.
For example, why couldn’t it be that there were three uncertain propositions A, B, and C of which I had no reason to find A more or less plausible than its negation ~A, nor than B, nor than C, though A, B, and C are exclusive and mutually exhaustive? Why couldn’t I have total ignorance about a situation?
This is an easy thing to say when there is nothing at stake. But let’s get silly, in order to get serious.
There is a revolver with three chambers. Proposition A is that a bullet is in one chamber, Proposition B is that a bullet is in the second chamber, and Proposition C is that a bullet is in the third chamber. The propositions are mutually exclusive: there is only one bullet. The propositions are exhaustive: there definitely is one bullet in one of the chambers.
We can already see that we are not in a state of “total ignorance”, despite what was so hastily claimed. There are three chambers. That’s information. The bullet is definitely in one of the chambers. That’s information. The bullet can’t be in two chambers at the same time. That’s information. All of this was given as part of the setup to this problem, after which the state of knowledge was then inexplicably described as “total ignorance”. No. No no no no no. Total ignorance would mean not knowing there is a gun, not knowing there is a bullet, not knowing we were in danger. Total ignorance means no fear. You can’t be scared of what you don’t know exists. That’s not this situation. Not even close. We have very relevant information here.
If we had “no reason to find A more or less plausible than its negation ~A”, then we would be indifferent between the choice of facing a single pull of the trigger right now with the barrel pointing against our forehead, or of advancing the cylinder exactly one chamber and then firing twice. That is literally what it means to have no reason to find A more or less plausible than ~A. Proposition ~A is that the bullet is not in the first chamber, which necessarily means it is either the second or the third chamber.
What’s particularly frustrating for me about these kinds of discussions is how OBVIOUS this is.
The person who wrote the above does not actually agree with the words he wrote. He does not think those words are true, would not apply this sort of reasoning to any genuine problem which he found gun-to-the-head important. He had just never thought carefully about this kind of problem before. The strange lapse in reasoning happened only because nothing was at stake. But how do I communicate that effectively? I don’t actually know what real-world problems other people find important. I do know, however, that if I turned into an Evil Probability Maestro and showed up in the dark of night at his house with a six-chambered revolver (I’m evil but not evil enough to stick with only three chambers), there is no chance in hell that he would claim that he had “no reason to find A more or less plausible than its negation ~A”, when proposition A is that the bullet is in the current chamber. Proposition A means facing only one pull of the trigger. Proposition ~A means facing five pulls of the trigger. The decision makes itself, when you know what the stakes are.
I don’t know what’s important to you.
But I do know that you could personally have the same difficulties with kiddie stuff like the problem above if you don’t raise the stakes, inside your own mind, in order to consider shit that actually matters. Engage problems that get their claws into your fleshy scalp. If you can’t manage that, then you’re going to be stuck saying, and worse maybe even believing, dumb stuff like that quote above. Be rigorous now. Study this now. Get good at plausible reasoning before the stakes are high. Practice now, not later. There are important problems to solve, remember? We all agree with that, right? Then let’s build the tools together to help work on, and even better to have a conversation about this. We want to communicate and discuss these problems effectively and well, so that we can work on them together.
I’m writing this precisely because I want to get better myself. Reviewing it sharpens it for me, too. You can never practice this too much if you want to get good at it.
So let’s keep practicing together.