In this post I'll quickly go over the Quine-Putnam indispensability argument in math, and describe two ways that I can think of applying this argument to ethics.
Here's a version of the indispensability argument (and it's sorta sloppy with the ideas, but hopefully clear)
(1) We should believe that something exists if, when we describe the world with our best scientific theories we are forced to speak as if that something exists.
(2) When we describe the world with our best scientific theories we are forced to speak as if mathematical entities exist.
Therefore:
(3) We ought to believe that mathematical entities exist.
Now, how could we apply this argument to ethics? In short, we can change premise (1) above, or we can change premise (2). Here's how.
Version #1:
(1) We should believe that something exists if, when we describe the world with our best scientific theories we are forced to speak as if that something exists.
(2) When we describe the world with our best scientific theories we are forced to speak as if ethical entities exist.
Therefore:
(3) We ought to believe that ethical entities exist.
Would it shock you to learn that such arguments have been made? I'm still at a very low level of familiarity with this kind of argument, but it's my impression that Sturgeon makes an argument very similar to this one. He argues that we should believe that ethics is objective, because if we don't believe that ethical statements are literally true and objective we are at an explanatory loss! I need to read more about this, and I also need to read about the relationship between the indispensability argument and inference to the best explanation.
Here's the second, less audacious version of the argument applied to ethics:
Version #2
(1) We should believe that something exists if, when we do something that we are really committed to taking seriously we are forced to speak as if that something exists.
(2) When we do that something that we are really committed to taking seriously we are forced to speak as if ethical entities exist.
Therefore:
(3) We ought to believe that ethical entities exist.
In short, this version can get off the ground by asking why, in the original Quine-Putnam version of the argument, we let science decide what we're committed to existing? Then you say, "the reason we give science such a privileged position is because X". The next step is to argue that there is something else that is X, and that something else makes us committed to ethical entities.
Just to make something up that sounds the tiniest bit plausible: Why do we say that science has the ability to determine what we're committed to? Because science helps us live our lives in safety. If we weren't to take science seriously then our lives would be unsafe! But that means that anything else that is indispensable for living our lives in safety should have the same status as science, with respect to its ability to determine what we believe in. Perhaps we believe that ethics is necessary for living our lives in safety--otherwise chaos in society would break out!--so we need to take ethics as seriously as science. And then you argue that you can't talk about ethics without believing in ethical entities, so you're justified in believing in ethical entities. This argument isn't sustainable, but it's the form of the argument, the move that's made, that I want to draw out.
As it happens, David Enoch takes an approach that resembles this one. I need to read him more carefully, but he talks aobut non-explanatory indispensabilities.
So we're in good shape! We've recognized, abstractly, two ways that the argument could go, and we've found some names who make such arguments. Plus (and I didn't tell you this yet) I found a couple articles that review both of these strategies. One of them is by Brian Leiter. So we're making some progress here.
Thursday, September 24, 2009
"What if we're ALL in the matrix?"
So, one of the stereotypes of philosophy is that it's a field that trades in justifying counter-intuitive things that nobody actually would seriously believe. Like, nobody believes that we live in a matrix or that experience is some dream. Right, yeah, but can you, you know, prove it? Well no, and I don't really care to, is the response that comment probably deserves.
But the truth is that the defense of counter-intuitive claims constitutes a lot of philosophy. I mean, that's predictable in a way. If something's intuitive, there's a good chance that it'll be said pretty early on in the discussion and won't be so interesting. And after a while, if you study a field long enough, you begin to lose your intuitions. This is a feeling familiar to philosophers of language and to linguists--you spend hours trying to explain why an analysis of language is bad because it runs counter to our intuitions about language, and by the time you're done you can't remember which one was the intuitive analysis and which was the non-intuitive one.
My introductory textbook in philosophy of math starts by saying that mathematics stands out because its a priori--that is, you don't bring empirical evidence to support the claims of math. And that's standard, and that's intuitive. After all, has anyone here ever looked outside to see if their math problem was correct? That having been said, Quine makes the claim that math is empirical, and there is no such thing as a priori knowledge at all. So math is not a priori, and you do figure out what math is correct by looking at the world. (As a matter of fact, Quine uses this method to throw out large areas of math as being fictional).
One reason I like philosophy is because I like engaging in the practice of shifting my perspective. I think it's really cool to see a plausible version of something that I used to think was really crazy (like empiricism and mathematics, the claim that mathematics constitutes a posteriori knowledge). Moreover, it's important for figuring out where the stable resting points are in philosophy. If you restrict yourself to what seems intuitive, you'll be missing out on a lot of stable points in philosophy, a lot of viable positions.
So I don't mind when somebody says "Maybe we're all in the matrix" even though it's really counter-intuitive and there's very little chance that I'll believe it. OK, that's not true. I do mind. But not because I don't like dealing with possibilities that run counter to my intuitions. I do, and I think it's fruitful, but the matrix thing has just been overdone already. So, lesson: wild ridiculous claims=good. Talking about the matrix=bad.
But the truth is that the defense of counter-intuitive claims constitutes a lot of philosophy. I mean, that's predictable in a way. If something's intuitive, there's a good chance that it'll be said pretty early on in the discussion and won't be so interesting. And after a while, if you study a field long enough, you begin to lose your intuitions. This is a feeling familiar to philosophers of language and to linguists--you spend hours trying to explain why an analysis of language is bad because it runs counter to our intuitions about language, and by the time you're done you can't remember which one was the intuitive analysis and which was the non-intuitive one.
My introductory textbook in philosophy of math starts by saying that mathematics stands out because its a priori--that is, you don't bring empirical evidence to support the claims of math. And that's standard, and that's intuitive. After all, has anyone here ever looked outside to see if their math problem was correct? That having been said, Quine makes the claim that math is empirical, and there is no such thing as a priori knowledge at all. So math is not a priori, and you do figure out what math is correct by looking at the world. (As a matter of fact, Quine uses this method to throw out large areas of math as being fictional).
One reason I like philosophy is because I like engaging in the practice of shifting my perspective. I think it's really cool to see a plausible version of something that I used to think was really crazy (like empiricism and mathematics, the claim that mathematics constitutes a posteriori knowledge). Moreover, it's important for figuring out where the stable resting points are in philosophy. If you restrict yourself to what seems intuitive, you'll be missing out on a lot of stable points in philosophy, a lot of viable positions.
So I don't mind when somebody says "Maybe we're all in the matrix" even though it's really counter-intuitive and there's very little chance that I'll believe it. OK, that's not true. I do mind. But not because I don't like dealing with possibilities that run counter to my intuitions. I do, and I think it's fruitful, but the matrix thing has just been overdone already. So, lesson: wild ridiculous claims=good. Talking about the matrix=bad.
Tuesday, September 22, 2009
An indispensability argument for math
I just need to get this on the table, because it's basic to the topics that I'm currently learning more about. I'm going to quickly present the Quine-Putnam argument indispensability argument here, so that I can build off of it and delve deeper in future posts. Just to experiment with form a little bit here, I'm going to make it into a series of dialogues.
----
A: Zebras exist.
B: What makes you say that?
A: Well, I observed a bunch of zebras. I saw them. They're over there [points to zebras].
B: So what? That's inconclusive. You could be hallucinating.
A: That's hardly the best explanation of the fact that I observed those zebras. The best explanation is that I'm not hallucinating, and that there's a bunch of things over there, and those things are called zebras.
B: Fair point. You're always justified in believing things if belief in them is necessary for the best explanation you have of the evidence.
----
A: Electrons exist.
B: What makes you say that?
A: Well, I observed a bunch of stuff [note: I don't know physics], and the best explanation I have of it is that there is something that exists that we hadn't previously known of. I call it an electron.
B: Oh, fair point. After all, it's the best explanation that you have of the evidence, and that explanation requires you to believe that electrons exist.
----
A: Numbers don't exist.
B: Wait a second, that doesn't sound right.
A: Why not?
B: You believe in zebras and electrons because your best explanation of the world requires your belief in their existence, right?
A: Right.
B: And what does it mean for your explanation to "require you to believe in their existence"?
A: I can clarify that. In order to give my best explanation of the world, I have to speak as if zebras and electrons exist. So if I'm committed to my explanation, I can't really avoid being committing to talking as if zebras and electrons exist. I think that this justifies my belief that zebras and electrons exist.
B: Is the law of gravity an important part of your best explanation of the world?
A: Sure--as long as it's up to date with current research...
B: Now, here's the important question for my argument: when you talk about the law of gravitation in your best explanation, is there any way that you can avoid talking as if numbers exist.
A: Well, errrm, no. How else can I talk about distances?
B: That's my point, then. Your best explanation of the world requires you to talk as if numbers exist. But that's the exact same justification you gave for why you believe that zebras and electrons exist. So if you're justified in believing that zebras exist, then you're justified in believing that numbers exist too.
------
----
A: Zebras exist.
B: What makes you say that?
A: Well, I observed a bunch of zebras. I saw them. They're over there [points to zebras].
B: So what? That's inconclusive. You could be hallucinating.
A: That's hardly the best explanation of the fact that I observed those zebras. The best explanation is that I'm not hallucinating, and that there's a bunch of things over there, and those things are called zebras.
B: Fair point. You're always justified in believing things if belief in them is necessary for the best explanation you have of the evidence.
----
A: Electrons exist.
B: What makes you say that?
A: Well, I observed a bunch of stuff [note: I don't know physics], and the best explanation I have of it is that there is something that exists that we hadn't previously known of. I call it an electron.
B: Oh, fair point. After all, it's the best explanation that you have of the evidence, and that explanation requires you to believe that electrons exist.
----
A: Numbers don't exist.
B: Wait a second, that doesn't sound right.
A: Why not?
B: You believe in zebras and electrons because your best explanation of the world requires your belief in their existence, right?
A: Right.
B: And what does it mean for your explanation to "require you to believe in their existence"?
A: I can clarify that. In order to give my best explanation of the world, I have to speak as if zebras and electrons exist. So if I'm committed to my explanation, I can't really avoid being committing to talking as if zebras and electrons exist. I think that this justifies my belief that zebras and electrons exist.
B: Is the law of gravity an important part of your best explanation of the world?
A: Sure--as long as it's up to date with current research...
B: Now, here's the important question for my argument: when you talk about the law of gravitation in your best explanation, is there any way that you can avoid talking as if numbers exist.
A: Well, errrm, no. How else can I talk about distances?
B: That's my point, then. Your best explanation of the world requires you to talk as if numbers exist. But that's the exact same justification you gave for why you believe that zebras and electrons exist. So if you're justified in believing that zebras exist, then you're justified in believing that numbers exist too.
------
Monday, September 21, 2009
Philosophy is a mess
The point of this post is to show how a discussion that would seem to be restricted to the world of ethics quickly becomes entangled with very different parts of philosophy. (And I'll be paraphrasing Harman throughout). And I take the argument to show that a good philosopher can't study only (say) ethics or only (say) math. The nature of philosophy is such that you need to know your way away around a bunch of different areas.
Is ethics objective--is there a matter of fact that is independent of any one of us, with our biases, whether an action is wrong? Or maybe ethics is (at least) subjective? As I've argued before, this question matters largely because we want to know if we can disagree and agree with what other people think about ethics.
A plausible first attempt at answering this question could sound like this: ethics isn't objective, because the way we justify ethics isn't up to the standards of the rest of our objective knowledge. Take, for example, our knowledge that zebras exist. We know that zebras existing is an objective truth because we can observe zebras with our senses (our eyes see 'em at the zoo or in pictures). But ethics--feh! how do you observe an ethical truth? Now, it's true that some people form ethical beliefs after observing (seeing) something. For example, someone can decide that it's wrong to burn cats after observing a cat burning. But that's not a pure observation, like seeing a zebra. Nope. Rather, what you see and observe is a cat burning, but what you decide is that it's bad, after you observe a cat on fire. But you haven't SEEN bad. There was no "badness" that you saw at the cat burning. What would "badness" look like anyway?!
But, as Hanson points out, this idea runs into trouble. Because you're not just making a claim about ethics here; you're also making a claim about the way we observe zebras.
Is it true that when you see a zebra you've made something like a pure observation, that has nothing to do with how you think? Some people (most people, actually) argue that this is not the case. After all, you know what a zebra is before you look into the world and observe one. You have some kind of theory and understanding about the world in order for you to be able to conceptualize what a zebra is, and that has to come before having an observation of it. To realize this, imagine that I ask you whether bliggles exist. I say that they do, because I've observed them directly. You've never observed them directly, but that's because you have no idea what they are. Would it be right to say that you've observed bliggles when you have no idea what they are? (It turns out the bliggles are what I call the combination you get when you duct-tape a parrot to an elephant, a strange object indeed. I'm not just renaming some normal object.)
The point is: in order to make your ethical argument, you also have to make a completely different argument about the way we observe things in general, and how that counts as justification for our empirical beliefs.
And if things weren't complicated enough, we also have this weird thing called "math." Do we observe all mathematical truths the same way we observe empirical truths? Yes? Then with which of our senses? Our eyes? Sure, we can see that 2 stones and 2 more stones make 4 stones, but have you ever seen 2 million stones be added to 2 million stones, and counted to make sure that we have 4 million stones? No, you haven't. So should we doubt that 2 mil+ 2 mil=4 mil? Well, that makes no sense. So maybe we don't observe mathematical truths. Well, maybe we can be sure about things without observational evidence. But then what about ethics? Maybe ethics gets off the hook, and you can be objective without having observational evidence? Or maybe math gets on the hook, and it isn't objective, just like ethics isn't objective.
So now we have three problems entangled: how do we justify our belief in empirical truths, how do we justify our belief in ethical truths, and how do we justify our belief in mathematical truths? Dissolving this tangle isn't really possible; a good philosopher would need answer to all three of these questions.
So maybe philosophy needs to be done as a whole. This is more the way that philosophy was done in the past than the way that it is sometimes done now. And I think the philosophy that tends to get remembered now, the good stuff, doesn't restrict itself to just one domain. After all, if all of philosophy is really tangled up like this, a good idea in one domain is probably going to be a good important idea in the other domains too.
Is ethics objective--is there a matter of fact that is independent of any one of us, with our biases, whether an action is wrong? Or maybe ethics is (at least) subjective? As I've argued before, this question matters largely because we want to know if we can disagree and agree with what other people think about ethics.
A plausible first attempt at answering this question could sound like this: ethics isn't objective, because the way we justify ethics isn't up to the standards of the rest of our objective knowledge. Take, for example, our knowledge that zebras exist. We know that zebras existing is an objective truth because we can observe zebras with our senses (our eyes see 'em at the zoo or in pictures). But ethics--feh! how do you observe an ethical truth? Now, it's true that some people form ethical beliefs after observing (seeing) something. For example, someone can decide that it's wrong to burn cats after observing a cat burning. But that's not a pure observation, like seeing a zebra. Nope. Rather, what you see and observe is a cat burning, but what you decide is that it's bad, after you observe a cat on fire. But you haven't SEEN bad. There was no "badness" that you saw at the cat burning. What would "badness" look like anyway?!
But, as Hanson points out, this idea runs into trouble. Because you're not just making a claim about ethics here; you're also making a claim about the way we observe zebras.
Is it true that when you see a zebra you've made something like a pure observation, that has nothing to do with how you think? Some people (most people, actually) argue that this is not the case. After all, you know what a zebra is before you look into the world and observe one. You have some kind of theory and understanding about the world in order for you to be able to conceptualize what a zebra is, and that has to come before having an observation of it. To realize this, imagine that I ask you whether bliggles exist. I say that they do, because I've observed them directly. You've never observed them directly, but that's because you have no idea what they are. Would it be right to say that you've observed bliggles when you have no idea what they are? (It turns out the bliggles are what I call the combination you get when you duct-tape a parrot to an elephant, a strange object indeed. I'm not just renaming some normal object.)
The point is: in order to make your ethical argument, you also have to make a completely different argument about the way we observe things in general, and how that counts as justification for our empirical beliefs.
And if things weren't complicated enough, we also have this weird thing called "math." Do we observe all mathematical truths the same way we observe empirical truths? Yes? Then with which of our senses? Our eyes? Sure, we can see that 2 stones and 2 more stones make 4 stones, but have you ever seen 2 million stones be added to 2 million stones, and counted to make sure that we have 4 million stones? No, you haven't. So should we doubt that 2 mil+ 2 mil=4 mil? Well, that makes no sense. So maybe we don't observe mathematical truths. Well, maybe we can be sure about things without observational evidence. But then what about ethics? Maybe ethics gets off the hook, and you can be objective without having observational evidence? Or maybe math gets on the hook, and it isn't objective, just like ethics isn't objective.
So now we have three problems entangled: how do we justify our belief in empirical truths, how do we justify our belief in ethical truths, and how do we justify our belief in mathematical truths? Dissolving this tangle isn't really possible; a good philosopher would need answer to all three of these questions.
So maybe philosophy needs to be done as a whole. This is more the way that philosophy was done in the past than the way that it is sometimes done now. And I think the philosophy that tends to get remembered now, the good stuff, doesn't restrict itself to just one domain. After all, if all of philosophy is really tangled up like this, a good idea in one domain is probably going to be a good important idea in the other domains too.
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