Strong substrate independence: a thing that goes wrong in my mind when exposed to philosophy

Two mantras that work for me (YMMV):

• "Stop worrying about existence vs non-existence, and start worrying about accessible vs inaccessible".

• "Regardless of how many branches reality has, the one I live in is the one containing the consequences of my actions."

I think it's safe to say that the measure problem is still pretty wide open — not just at the compelling-but-speculative level IV, but even at lower levels that are pretty well-established as actually existing, as in the Born probabilities in MWI — so until that's solved comprehensively enough that level IV multiverse itself either adds up to normality or adds up to confusion that can be dissolved, I don't recommend deriving any apparently normality-defying conclusions from it, particularly sanity-impacting and morality-impacting ones. For now it's just a fascinating problem to solve, and the kind of thinking that keeps leading people to invent the level IV multiverse appears to be a step in the right direction, but it's by no means a complete solution — existence is still decidedly a confusing problem, and the nature and implications of a level IV multiverse are not yet clear enough that there really is any bullet to bite.

For what it is worth, if one does accept level 4 Tegmark it isn't clear what measure is the correct one. It isn't clear that it adds up to normality much less sanity.

I think you are forgetting Egan's Law.

If the universe is correctly described by Tegmark's mathematical universe hypothesis, it's still the universe.

Edit to add: Considering a philosophy should worry you only if you suspect that your motivation for caring about your visible universe is based on some principle or idea that is likely to be invalidated by that philosophy, if it proves correct. I don't think such motivations have a large amount of crossover with multiverse-type theories.

how do I accept that... and still care about things getting created and destroyed within my visible universe?

OK, I'll give it a shot... :-)

There will be mental entities in other universes also thinking about this, some using a similar decision process to you. Many of them will also have realized that there are others. Welcome to this club.

Those using the same decision theory will tend to make the same decision. So if you can commit to caring about your universe and trying to make it a better place, and go through with it, it's more likely that other members of the club will too.

Save a googolplex universes here, a googolplex there, and eventually you're talking real utility.

With some thought over the past few days, I think I'm saying I am increasingly treating people as more or less predictable systems based on past behaviour and stimulus/response, and ignoring the noises that come out of their mouths. I used to treat the noises as having anything much to do with what the people do, but the evidence is scant.

So it's conversational cynicism-signaling, but with a slightly useful point ;-)

I've read them both, which sort of answers that.

Edit: Not to be dismissive! I enjoyed them both, as fiction and as well-reasoned explorations of the subject. In fact, it's possible the first time I started thinking about this was when reading the short story Permutation City is based on.

The statement "1+1+1+1=4" exists in your mind. Your mind generated this expression as a result of contemplating your observations (from the story). This statement is a abstraction of your observations, specified in the terms of arithmetic. Your observations were formed based on your sensory input combined with your prior experience. Your sensory input depended on your relative context, your body's physical capabilities, and the physical laws of the universe.

The statement is only related to the physical reality of the nuts through a chain of inference. The statement does not represent anything about the nuts directly; it only represents something about the state of your mind.

Even the identification that nuts are individual items that can be counted is an abstraction that you hold in your mind. If you consider the nuts from the perspective of a single photon, the nut abstraction vanishes. With a single photon's perspective we can't tell a nut from a bear, much less count the number of nuts.

But asking whether 2+2=4 is "only true in your mind" (or whether it was "true before people existed") is like asking whether an octopus is true or false.

Absolutely -- but what is missing is a discussion of context. It isn't enough to just say that 2+2=4 is true, or that a particular octopus is false; we need to know what the context of evaluation is.

Why does arithmetic have to "exist" "in" places and times?

We need context for the same reason that Bayes' theorem needs priors. Without context we don't have meaning. In many cases we assume context in a way that is transparent to us; but whether explicit or implicit, a context is still in use.