This is beginning to sound like burden of proof tennis, I claim that most causes can not be currently quantified to any useful degree, therefore restricting yourself to the quantifiable ones is a mistake. This isn't a problem that can be brute forced - what will be the effect of say open borders? Or human genetic engineering? Or charter cities? Or a new Standard Model of Physics? Or Basic Income guarantees? No one has a damned clue, although many would like to pretend. This list goes on and on.

But even for the somewhat quantifiable causes, the long term effects cannot be quantified. What is the effect of significant charitable giving on a person's other spending patterns? Does giving to charity reduce the number of children that effective altruists have, and is this a dysgenic effect? If so, is the dysgenic effect compensated for by the effects of the charity? Are effects such as this a problem? How does charitable giving affect the giver's work patterns, ambitions and life's trajectory? And of course, what is the long term effect of charitable giving on the target country's development and institutions? That last effect is probably where most of the positive consequences of giving show up, not silly short term metrics like DALYs. GiveWell's research into long term effects is noticeably much less than their research into short term effects - even though the long term effects dominate in the long run.

Why the time factor? I don't find it particularly matches my intuitions directly, and as pointed out it makes having children arbitrarily bad (which also doesn't match my intuitions). Say we give each person's death a particular negative utility - histories in which they die get that single penalty regardless of time (though other independent time factors might apply, such as the sadness of their loved ones). Does that fit any better or worse with your conception of death morality?

(Incidentally, I was thinking about this just a few hours ago. Interesting how reading the same comment can trigger similar lines of thought.)

Suppose sleeping beauty secretly brings a coin into the experiment and flips when she wakes up. There are now six possible combinations of heads and tails, each with their own possibilities:

HH: 1/4

HT: 1/4

THH: 1/8

THT: 1/8

TTH: 1/8

TTT: 1/8

When she wakes up and flips the coin, she notices it lands on heads. This eliminates two of the possibilites. Now renormalizing their values:

HH: 2/5

HT: 0

THH: 1/5

THT: 1/5

TTH: 1/5

TTT: 0

She can conclude that the coin landed on tails with 60% probability, rather than the normal 50% probability. She could flip the coins more times. Doing so, she will asymptotically approach 2/3 probability that it landed on tails.

Perhaps she gets caught with the coin, and has it taken away. This isn't a problem. She can just look at dust specks, or any other thing she can't predict and won't be consistent. For all intents and purposes, she's using SSA. There's a difference if she's woken so many times that it's likely she'll make exactly the same observations more than once, but that takes her being woken order of 10^million times.

Looks interesting - I've signed up. Definitely interested in a study group too, both as an external motivator and hopefully to get more value from the course.

Otherwise you will most likely struggle against the abstractness with few chances to understand what's truly going on.

Yes, it's not as if the textbooks will give you any examples.

It seems like you and Hul-Gil are using different formulae for evaluating utility (or, rather, disutility); and, therefore, you are talking past each other.

While Hul-Gil is looking solely at the immediate purchasing power of each individual, you are considering ripple effects affecting the economy as a whole. Thus, while stealing a single penny from a single individual may have negligible disutility, removing 1e9 such pennies from 1e9 individuals will have a strong negative effect on the economy, thus reducing the effective purchasing power of everyone, your victims included.

This is a valid point, but it doesn't really lend any support to either side in your argument with Hul-Gil, since you're comparing apples and oranges.

That's not how RoI works.

Why not? The investment here being the death of the donor.

Er, yes? I mean it's not like we're born knowing that cars behave like integers and outlet electricity doesn't, since neither of those things existed ancestrally.

No, not quite. The distinction is subtle, but I'll try to lay it out.

there are statements that are true (semantically valid) but unprovable, and hence they provide a counterexample to "If X |=Y then X |- Y"

This is not the case. The problem is with the 'and hence': 'X ⊨ Y' should not be read as 'Y is true in X' but rather 'Y is true in every model of X'. There are statements which are true in the standard model of Peano arithmetic which are not entailed by it - that is, 'Y is true in the standard model of Peano arithmetic' is not the same as 'PA ⊨ Y'. So this is not a counterexample.

Rather, the notion of 'complete' in the incompleteness theorem is that a model is complete if for every statement, either the statement or its negation is entailed by the model (and hence provable by semantic completeness). Gödel's incompleteness theorem shows that no theory T containing PA is complete in this sense; that is, there statements S which are true in T but not entailed by it (and so not provable). This is because there are models of T in which S is not true: that is, systems in which every statement in T holds, but S does not. (These systems have some additional structure beyond that required by T.)

Wikipedia may do a better job of explaining this than I can at the moment.

Meditation:

It has been claimed that logic and mathematics is the study of which conclusions follow from which premises. But when we say that 2 + 2 = 4, are we really just assuming that? It seems like 2 + 2 = 4 was true well before anyone was around to assume it, that two apples equalled two apples before there was anyone to count them, and that we couldn't make it 5 just by assuming differently.