LessWrong 2.0 Reader

Yeah, I got that, but it's a very counterintuitive way to describe probability, especially the negative thing.

I have spent a long time looking in vain for any reason to think ZFC is consistent, other than that it holds in the One True Universe of Sets (OTUS, henceforth). So far I haven't found anything compelling, and I am quite doubtful at this point that any such justification exists.

Just believing in the OTUS seems to provide a perfectly satisfactory account of independence and nonstandard models, though: They are just epiphenomenal shadows of the OTUS, which we have deduced from our axioms about the OTUS. They may be interesting and useful (I rather like nonstandard analysis), but they don't have any foundational significance except as a counterexample showing the limitations of what formal systems can express. I take it that this is more or less what you have in mind when you say

a view that maintains objective mathematical truth while explaining why we need to work with multiple models pragmatically.

It's disappointing that we apparently can't answer some natural questions about the OTUS, like the continuum hypothesis, but Gödel showed that our knowledge of the OTUS was always bound to be incomplete 🤷‍♂️.

Having said that, I still don't find the Platonist view entirely satisfactory. How do humans come to have knowledge that the OTUS exists and satisfies the ZFC axioms? Supposing that we do have such knowledge, what is it that distinguishes mathematical propositions whose truth we can directly perceive (which we call axioms) from other mathematical propositions (which we call conjectures, theorems, etc.)?

An objection more specific to set theory, as opposed to Platonism more generally, would be, given a supposed "universe" $V$ of "all" sets, the proper classes of $V$ are set-like objects, so why can't we extend the cumulative hierarchy another level higher to include them, and continue that process transfinitely? Or, if we can do that, then we can't claim to ever really be quantifying over all sets. But if that's so, then why should we believe that the power set axiom holds, i.e. that any of these partial universes of sets that we can quantify over is ever large enough to contain all subsets of $N$?

But every alternative to Platonism seems to entail skepticism about the consistency of ZFC (or even much weaker foundational theories), which is pragmatically inconvenient, and philosophically unsatisfactory, inasmuch as the ZFC axioms do seem intuitively pretty compelling. So I'm just left with an uneasy agnosticism about the nature of mathematical knowledge.

Getting back to the question of the multiverse view, my take on it is that it all seems to presuppose the consistency of ZFC, and realism about the OTUS is the only good reason to make that presupposition. In his writings on the multiverse (e.g. here), Joel Hamkins seems to be expressing skepticism that there is even a unique (up to isomorphism) standard model of $N$ that embeds into all the nonstandard ones. I would say that if he thinks that, he should first of all be skeptical that the Peano axioms are consistent, to say nothing of ZFC, because the induction principle rests on the assumption that "well-founded" means what we think it means and is a property possessed by $N$. I have never seen an answer to this objection from Hamkins or another multiverse advocate, but if anyone claims to have one I'd be interested to see it.

Do you have sources for those bulletpoints?

Should be fixed now. Thanks!

. . . This is going to mess up comparisons to previous years, I can already tell.

Wait. No. That market is for a release before 2025, not by the end of 2025. 

. . . I was pretty sure there was a market for end of 2025 and now I can't find it. Hrm.

By what year do you think the Singularity will occur? Answer such that you think, conditional on the Singularity occurring, there is an even chance of the Singularity falling before or after this year. If you think a singularity is so unlikely you don't even want to condition on it, leave this question blank

You won't be able to distinguish people who think singularity is super unlikely from people who just didn't want to answer this question for whatever reason (maybe they forgot or thought it's boring or whatever).

Some of the probability questions (many worlds, simulation) are like... ontologically weird enough that I'm not entirely certain it makes sense to assign probabilities to them? It doesn't really feel like they pay rent in anticipated experience?

I'm not sure "speaking the truth even when it's uncomfortable" is the kind of skill it makes sense to describe yourself as "comfortable" with.

fyi the spreadsheet is private atm

I would strongly bet against majority using AI tools ~daily (off the top of my head: <40% with 80% confidence?): adoption of any new tool is just much slower than people would predict, plus the LW team is liable to vastly overpredict this since you're from California.

That said, there are some difficulties with how to operationalize this question, e.g. I know some particularly prolific LW posters (like Zvi) use AI.

My rough first attempt at explaining the apparent paradox of poverty continuing to exist despite a ~100x increase in productivity:

Humanity as a whole may have gotten 100x more productive, but most people aren't able to individually contribute 100x more value to the economy (at least not in a way that they are monetarily compensated for).  It seems like the increase in productivity largely takes the form of finding more efficient ways to coordinate the efforts of many people (e.g. factories) rather than individuals being able to produce more value on their own, and that the few people doing the coordinating are reaping the benefits of this much more than the many people being coordinated.  Even in areas where the potential for individual productivity has greatly increased (e.g. digitally producing games, videos, music, etc.), attention remains scarce, people largely pay attention to things that already have attention, and again only a small number of people are able to produce such content and have a large number of people consume and pay for it.

If humanity's 100x productivity increase took the form of 100% of people becoming 100x more productive, and poverty persisted, that would indeed be pretty strong evidence for some sort of Poverty Restoring Force, but my sense is that it's a closer approximation of what actually happened to say that 1% of people became 10,000x more productive, in which case observing that many of the other 99% who were previously in poverty continue to be in poverty is not surprising - it's not an observation that requires one to postulate Poverty Restoring Forces in order to explain.  For this reason, I continue to lean towards optimism about UBI being an effective means of reducing poverty.