Learning formal logic, for example, isn't that much help in understanding what logic is.

It certainly doesn't hurt! Learning formal logic gives you data with which to test meta-logical theories. Moreover, learning formal logic helps in understanding everything; and logic is one of the things, so, there ya go. Instantiate at will.

Likewise, knowing how people make moral decisions is not at all the same as knowing what the moral thing to do would be.

Sure. But for practical purposes (and yes, there are practical philosophical purposes), you can't be successful in either goal without some measure of success in both.

I gather your point is that it's only certain concrete questions that have any real meaning.

Where does lukeprog say that? And by 'meaning' do you mean importance, or do you mean semantic content?

But the problem with logical positivism is that its claim about what's meaningful and what isn't fails to be a meaningful claim under its own criteria.

Lukeprog and Eliezer are not logical positivists in the relevant sense. And although logical positivism is silly, it's not silly for obvious reasons like 'it's self-refuting;' it isn't self-refuting. The methodology of logical positivism is asserted by positivists as an imperative, not as a truth-apt description of anything.

Dismissing those questions—failing to think through the assumptions on which your viewpoint rests—only guarantees that your answers to those questions will be pretty bad.

In some cases, yes. But why do you think lukeprog is dismissing those questions? He wrote, "I think many philosophical problems are important. But the field of philosophy doesn't seem to be very good at answering them. What can we do? Why, come up with better philosophical methods, of course!" Lukeprog's objection is to how people answer philosophical questions, more so than to the choice of questions themselves. (Though I'm sure there will be some disagreement on the latter point as well. Not all grammatical questions are well-formed.)

Likewise, knowing how people make moral decisions is not at all the same as knowing what the moral thing to do would be.

Quite. It is a perfectly coherent possibility that the moral instincts given to us by evolution are broken in some way, so that studying morlaity form the evolutionary perspective does't resolve the "what is the right thing to do" question at all. The interesting thing here is that a lot of material on LW is dedicated to an exactly parallel with argument about ratioanlity: our rationality is broken and needs to be fixed. How can EY be so open to the one possibility and so oblivious to the other?

Is this problem limited to philosophy?

Good work in virtually every discipline requires a semi-decent grounding in math (with the possible exception of menial work)

• History? math
• Linguistics? math
• Medicine? math
• Philosophy? math
• And why not: Art? math

Indeed, the universities teaching such subjects would do well to realize this and make math an integral part of the curriculum in most subjects, as opposed to the tackled-on (or non-existent) math courses they have now.

The things on your curriculum don't seem like philosophy at all in the contemporary sense of the word. They are certainly very valuable at figuring out the answers to concrete questions within their particular domains. But they are less useful for understanding broader questions about the domains themselves or the appropriateness of the questions. Learning formal logic, for example, isn't that much help in understanding what logic is. Likewise, knowing how people make moral decisions is not at all the same as knowing what the moral thing to do would be. I gather your point is that it's only certain concrete questions that have any real meaning.

This naive logical positivism is dismaying in a blog about rationality. I certainly agree that there is plenty of garbage philosophy, and that most of Aristotle's scientific claims were wrong. But the problem with logical positivism is that its claim about what's meaningful and what isn't fails to be a meaningful claim under its own criteria.

Your dismissal of certain types of philosophy inevitably rests on particular implicit answers to the kinds of philosophical questions you dismiss as worthless (like what makes a philosophical idea wrong?). Dismissing those questions—failing to think through the assumptions on which your viewpoint rests—only guarantees that your answers to those questions will be pretty bad. And that's something that you could learn from a careful reading of Plato.

See my reply to Chappell here and the enclosing thread: http://lesswrong.com/lw/f1u/causal_reference/7phu

From my perspective, when I've explained why a single AI alone in space would benefit instrumentally from checking proofs for syntactic legality, I've explained the point of proofs. Communication is an orthogonal issue, having nothing to do with the structure of mathematics.

From my perspective, when I've explained why a single AI alone in space would benefit instrumentally from checking proofs for syntactic legality, I've explained the point of proofs. Communication is an orthogonal issue, having nothing to do with the structure of mathematics.

The motivation for the extremely unsatisfying idea that proofs are social is that no language—not even the formal languages of math and logic—is self-interpreting. In order to understand a syllogism about kittens, I have to understand the language you use to express it. You could try to explain to me the rules of your language, but you would have to do that in some language, which I would also have to understand. Unless you assume some a priori linguistic agreement, explaining how to interpret your syllogism, requires explaining how to interpret the language of your explanation, and explaining how to interpret the language of that explanation, and so on ad infinitum. This is essentially the point Lewis Carroll was making when he said that "A" and "if A then B" were not enough to conclude B. You also need "if 'A' and 'if A then B' then B" and and so on and so on. You and I may understand that as implied already. But it is not logically necessary that we do so, if we don't already understand the English language the same way.

This is, I think, the central point that Ludwig Wittgenstein makes in The Philosophical Investigations and Remarks on the Foundation of Mathematics. It's not your awesome kitten pictures are problematic. You and I might well see the same physical world, but not agree on how your syllogism applies to it. Along the same lines, Saul Kripke argued that the statement 2+2=4 was problematic, not because of any disagreement about the physical world, but because we could disagree about the meaning of the statement 2+2=4 in ways that no discussion could ever necessarily clear up (and that it was therefore impossible to really say what the meaning of that simple statement is).

In math and logic, this is typically not much of a problem. We generally all read the statement 2+2=4 in a way that seems the same as the way everyone else reads it. But that is a fact about us as humans with our particular education and cognitive abilities, not an intrinsic feature of math or logic. Proof of your kitten syllogism is social in the sense that we agree socially on the meaning of the syllogism itself, but not because states of affairs you represent in your pictures are in any way socially determined.

And if this is normally much of an issue in mathematics, it is incredibly problematic in any kind of metamathematical or metalogical philosophy—in other words, once we start try to explain why math and logic must necessarily be true. The kep point is not that the world is socially constructed, but that any attempt to talk about the world is socially constructed, in a way that makes final, necessary judgments about its truth or falsity impossible.