Saturday, November 7, 2009

Responding to some of a commenter's points

But is it necessary for numbers to exist for me to be able to use them in my explanations of the world? In physics, we talk about the world as if there were a big three-dimensional grid running through it, but it doesn't actually exist.

It's absolutely necessary for numbers to exist in order to use them in my explanations of the world...unless it's not. What I mean is that the burden of proof is on the "fictionalist" to show that belief in the existence of numbers isn't necessary for their use in science. This is because it kinda seems that mathematical truths make explanations better--our explanations of the world would be worse if we didn't have math and didn't think that numbers existed. But, hey, if you can give a convincing account of how science uses math in a way that doesn't commit you to their existence, power to you. Hell, you might even think of calling your book "Science Without Numbers."

I find your examples somewhat problematic, in that leaky pipes and protons are both objects in the physical world, which numbers clearly are not. I think part of the issue is figuring out what it means for mathematical or ethical things to exist, but I don't know if thinking about pipes will really help with that. You mentioned gravity in a previous post, and that's closer, but maybe something like color or the principles of musical harmony would work better? (Depends what parallels you want to draw.)

This argument doesn't follow through; it stops before finishing. Because it's obvious that there are differences between protons and numbers. Sure, protons are physical objects, and (according to most) numbers are not. But so what? Do only physical things exist? Can you argue that, or do we just assume that from the start?

Asking what it means for non-physical objects to exist is a fair point. Here's the way the indispensability argument for mathematical objects works: Whatever it means for something to exist, we do know that being an indispensable part of our best explanation is sufficient for us to say that something exists. And numbers pass that test. You still probably need some sort of account of what existence means (does it just mean that the facts are true independent of human thinkers? does it mean that we can disagree? does it mean that we can know facts about them? etc.), but that's not essential to the argument. Of course, you could come back and counter "Well then, I have a different principle for how to determine what things exist" and we'll have to see how that one fares.


The question is, would it matter if you actually observed a cat burning in the real world? If I made an animation of children burning a cat (even a really crude one), or just talked about burning a cat, you would have the ethical observation that burning cats is bad. It seems then more like a making aware of something that you already know, rather than something you learn from observation (it crucially doesn't matter whether or not anybody has ever burned a cat). In science, on the other hand, I can talk about flying pigs as much as I want, but you won't get any biological insight out of it. Ethics seems to only require thought experiments, which makes it much easier to claim that it is simply an analysis of human thought processes, rather than of the world "out there".


...unless that's not true. I think we should distinguish between intuitions and observations, both in science and in ethics. A physicist might perform a thought experiment and come to some conclusion about what is possible or not possible. A biologist could do that too. So could an ethicist, reasoning out what situations were bad. But what your claim depends on is that there is no role for observation in ethics--that's exactly what's at issue here. And I do recognize that observation doesn't play the role in ethics that it does in science. Like I've said, there are no ethics laboratories, and it doesn't make sense for a guy in a lab coat to run a few tests to figure out if something is ethical or not. At the same time, it does seem possible to me that through observing the world one would reach ethical conclusions that one wouldn't reach from the armchair.

For example, suppose that you've never seen a guy rip off a customer in business. You think about it, imagine it, and say "Hmm, that doesn't seem SO bad." And that's fine, until you witness some guy get ripped off. When you observe him getting cheated, you realize that there was cruelty where you didn't expect it, and you conclude that the action was unethical. Now, why doesn't this count as observation? "Well, if you had thought through everything carefully enough, you could've reached that conclusion from the armchair. You just needed to think a little bit more clearly, and then you would've realized that it's cruel." But that seems like an unfair standard to hold ethics to for a couple of reasons. First of all, maybe the cruelty was extremely non-obvious, and needed observation to show it to you. Maybe the cruelty comes from the knowledge the businessman has that through some complex transaction this will ruin his customer's financial life. Second, it seems that there are scientific observations where you COULD'VE figured it out from the armchair in a similar way. Maybe we should be told that if we thought carefully enough about our own way of learning language we should be able to figure out a perfectly good psychological or linguistic theory. But that seems unfair. But isn't that what we're asking of ethics--to rely only on intuitions and never on observational insight? But observation is helpful, just as helpful as it is in the sciences (well that's an exageration, but at least observation doesn't seem totally irrelevant).


My temptation as a non-philosopher is to view this as a psychological question--different people are satisfied with different levels of proof. I believe, for example, that Neil Armstrong walked on the moon in 1969. I also know people (otherwise normal and intelligent) who believe this is not the case. Clearly, we each believe ourselves to apply reasonable standards of proof in determining what is in fact the case. I don't know that this really transfers to math and ethics, but it might. (For example, in people's different reactions to the idea of triage in epidemics--some people can't get past the gut reaction, while others are willing to entertain the idea of trade-offs. There was a NYT article about triage today, which made me think of this.)


But there is a wholly separate question from the psychological one, which is the question of justification. We might be interested in human reasoning as something to understand and explain, but what about understanding what human claims and principles of reasoning are justified? That's the philosophical question. (I might as well copy and paste the opening paragraphs from Frege's "Foundations of Arithmetic," because I'm trying to make exactly the same point.)

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