Is income before or after taxes?

Took it!

Did any one else have trouble copy-pasting the links?

I normally score insanely high on Openness to experience (says she of the massive amounts of really weird hobbies), but for this test, I scored really low on Openness. Must be feeling particularly close-minded today. Weird.

Done

the NYC LW/OB community had two babies and is expecting a third

This sounded a bit cultish. Babies aren't the property of LessWrong.

members of the NYC LW/OC have had two babies, and another is expecting a third

Sounds better.

This is a really good post.

If I can bother your mathematical logician for just a moment...

Hey, are you conscious in the sense of being aware of your own awareness?

Also, now that Eliezer can't ethically deinstantiate you, I've got a few more questions =)

You've given a not-isomorphic-to-numbers model for all the prefixes of the axioms. That said, I'm still not clear on why we need the second-to-last axiom ("Zero is the only number which is not the successor of any number.") -- once you've got the final axiom (recursion), I can't seem to visualize any not-isomorphic-to-numbers models.

Also, how does one go about proving that a particular set of axioms has all its models isomorphic? The fact that I can't think of any alternatives is (obviously, given the above) not quite sufficient.

Oh, and I remember this story somebody on LW told, there were these numbers people talked about called...um, I'm just gonna call them mimsy numbers, and one day this mathematician comes to a seminar on mimsy numbers and presents a proof that all mimsy numbers have the Jaberwock property, and all the mathematicians nod and declare it a very fine finding, and then the next week, he comes back, and presents a proof that no mimsy numbers have the Jaberwock property, and then everyone suddenly loses interest in mimsy numbers...

Point being, nothing here definitely justifies thinking that there are numbers, because someone could come along tomorrow and prove ~(2+2=4) and we'd be done talking about "numbers". But I feel really really confident that that won't ever happen and I'm not quite sure how to say whence this confidence. I think this might be similar to your last question, but it seems to dodge RichardKennaway's objection.

Mainstream status:

The presentation of the natural numbers is meant to be standard, including the (well-known and proven) idea that it requires second-order logic to pin them down. There's some further controversy about second-order logic which will be discussed in a later post.

I've seen some (old) arguments about the meaning of axiomatizing which did not resolve in the answer, "Because otherwise you can't talk about numbers as opposed to something else," so AFAIK it's theoretically possible that I'm the first to spell out that idea in exactly that way, but it's an obvious-enough idea and there's been enough debate by philosophically inclined mathematicians that I would be genuinely surprised to find this was the case.

On the other hand, I've surely never seen a general account of meaningfulness which puts logical pinpointing alongside causal link-tracing to delineate two different kinds of correspondence within correspondence theories of truth. To whatever extent any of this is a standard position, it's not nearly widely-known enough or explicitly taught in those terms to general mathematicians outside model theory and mathematical logic, just like the standard position on "proof". Nor does any of it appear in the S. E. P. entry on meaning.

Agreed, however, Eliezer's phrasing of #9 made it sound like he was referring to individual incentive.

I'm dubious about your point #9 due to Fisher's principal.

I am confused by these posts. On one hand, Eliezer argues for an account of causality in terms of probability, which as we know are subjective degrees of belief. So we should be able to read off whether X thinks A causes B from looking at conditional probabilities in X's map.

But on the other hand, he suggests (not completely sure this is his view from the article) that the universe is actually made of cause and effect. I would think that the former argument instead suggests causality is "subjectively objective". Just as with probability, causality is fundamentally an epistemic relation between me and the universe, despite the fact that there can be widespread agreement on whether A causes B. Of course, I can't avoid cancer by deciding "smoking doesn't cause cancer", just as I can't win the lottery by deciding that my probability of winning it is .9.

For instance, how would an omniscient agent decide if A causes B according Eliezer's account of Pearl? I don't think they would be able to, except maybe in cases where they could count frequencies as a substitute for using probabilities.