Arguments In Philosophy Are Mysterious Like Arguments In Math

But one reveals obvious expertise

I remember when I was in first grade, I expected more advanced math to be addition and subtraction—and perhaps also multiplication and division—with increasingly large numbers. I followed the very reliable method of linear extrapolation—as the difference between the math I’d be doing in kindergarten and first grade had been simply that the first-grade addition involved bigger numbers, so too did I expect the math in, say, college to be addition with truly unwieldy numbers.

As math gets more advanced, it doesn’t just get trickier: it gets more mysterious. I don’t even know how one would begin trying to prove Fermat’s last theorem. Advanced math is its own strange, alien land with all sorts of grotesque subfields like topology that I could not invent if I had a billion years.

For someone like me who hasn’t studied advanced math, high-level mathematics is a black box. Not only am I unable to do advanced math, I don’t even have a faint sense of what the arguments in advanced math look like. While I can imagine what sorts of things convince historians of some conclusion about history, I haven’t the faintest grasp of what sorts of arguments convince mathematicians.

I think something is very similar when it comes to philosophy. Good philosophical arguments are similarly opaque. But there’s a crucial and tragic difference that leads to society venerating mathematical genius while ignoring philosophical genius: it’s obvious that high-level mathematics is intellectually serious, while it’s not obvious to outsiders that philosophy is.

David Lewis is one of the most brilliant philosophers of the last century, and I say that as a person who thinks that Lewis was, on almost every topic, wrong. Lewis might be the single philosopher other than Timothy Hsiao who I disagree with the most, but nonetheless, he was clearly brilliant.¹ One of his most famous works is a book in which he argues for modal realism—that every possible world, every possible way reality could be, really exists. There’s a genuinely existing world, as real as our own, filled only with balloons, for instance.

If you explain to ordinary people Lewis’s arguments, they’ll be baffled, and perhaps become a bit more sympathetic to the idea that philosophy will be defunded. It’s not just that they haven’t heard his arguments—when they hear them, they find them crazy. And yet philosophers don’t find them crazy even if they’re mistaken—philosophers can at least see, in a broad sense, the brilliance behind Lewis’s arguments. Even Lewis’s philosophical enemies have a grudging respect for him.

My friend

Dustin Crummett

has grown increasingly annoyed over the years at people butchering his extremely clever argument for God from psychophysical harmony. But it’s no surprise that people are unable to think about the argument in a serious way: doing so requires understanding something about philosophy of mind, which eludes the grasp of most people.

I’ve discussed the zombie argument against physicalism with tons of philosophically ignorant lay people. Almost none of them buy it (interestingly, they are more moved by Mary’s room). I don’t think this is because it’s a bad argument or is not intuitive—it’s because it requires a certain kind of philosophical sophistication that is rare among non-philosophers. Note, I’m not saying that these non-philosophers are dumb or that everyone who understands philosophy will automatically buy the zombie argument, just that it’s hard to get absent pretty detailed philosophical understanding.

People are often very skeptical of the idea that moral progress is possible. Many people are anti-realists about morality in large part because they think that morality is beyond the reach of reason—that there’s no way to argue convincingly about morality the way there is about math. While in math we can prove things and in history and biology we can persuasively argue for things, morality, they believe, just involves people stating their differing views. But this is totally wrong; people constantly convince others of moral conclusions. Philosophy is filled with people arguing for controversial moral conclusions, and people are often convinced by them. This explains why philosophers are far more likely to oppose meat-eating than the general public.

When people disagree about ethics they aren’t just at an impasse. There are a few dozen good arguments against deontology—the main alternative to utilitarianism. The millions of pages philosophers have written about ethics has all been about trying to convince each other of their ethical conclusions.

It’s no surprise that people think this way. Imagine that mathematics was not a well-developed discipline but instead, we argued about math the way we argue about philosophy. There would be no rigorous framework or assumption that some people are experts—instead, people would just try to beat each other over the head with arguments.

One who was not well-versed in mathematics would be skeptical of the existence of successful mathematical arguments. Mathematicians couldn’t convince lay people of controversial mathematical conclusions if they had to argue for them step-by-step—the only reason they can do so is that mathematicians are treated as experts worth deferring to.

But for some reason, no one treats philosophers this way. No one gives to charity because philosophers say they should—in fact, the only people who’d consider doing this are other philosophers. No one takes seriously non-physicalism about consciousness simply because a lot of philosophers do. If one reads the comments on videos where Philip Goff talks about consciousness, they’re largely smug and dismissive, while also demonstrating total confusion.

I’m sounding pretty smug and dismissive of these on-philosophers, but let me be clear: I did this too. I thought Huemer, for instance, was just basically confused when, in high school, I first spoke with him. I didn’t take philosophers at all seriously before I was pretty deeply embroiled in philosophy.

In fact, I still probably don’t take philosophers seriously enough. While I try to avoid being too confident in my views, I do find it hard psychologically to believe that there’s any possibility that, say, the self-sampling assumption is true, even though lots of philosophy super-geniuses believe it. It just seems too obviously false.

Philosophical issues have a unique ability to make people blind to the possibility that they’re wrong. There’s little else, other than politics, that does this as much as philosophy. And this is a shame.

Just as it would be foolish to ignore the conclusions of historians about history or the conclusions of physicists about physics, it is foolish to ignore the conclusions of philosophers about philosophy. Philosophers have opaque arguments not easily understandable by normal people, the same way mathematicians do. As a result, if you disagree with a philosopher, you should think there are decent odds that you’re just missing something big.

Speaking of arguments in philosophy, my paper arguing for the self-indication assumption just got published by Synthese.

1. He somehow managed to get wrong modal realism, moral anti-realism, physicalism, halfing in sleeping beauty, and almost every other subject he touched. At least he was right about mathematical platonism!