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Will_Newsome comments on The conscious tape - Less Wrong
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Comments (113)
I think you're right that what we disagree about is
The dichotomy you've provided seems to me to be an excellent definition of the difference between mathematical epistemological proof and empirical epistemological proof...it happens all the time that we may not be able to rigorously show N, but we nevertheless have extremely good reason to believe N with near-certainty, and even stronger reason to act as if we believed N.
If I hear you correctly, you think that we could plug in "the Universe is merely a mathematical object" for N.
I disagree. For me, the difference between epistemology and ontology is that there is a difference between what we can know and what exists. There might be things that exist about which we know nothing. There could even be things that exist about which we cannot know anything. One could reasonably call for scientists to ignore all such hypothetical objects, but, philosophically speaking, it doesn't stop the objects from existing.
It boggles my mind to hear the claim that a mathematical object, as you have just defined it in your last comment, "exists* in this second, ontological sense. The mandelbrot set expresses a relationship among points. If several small spheres exist and it turns out that the points approximate the relationship defined by the Mandlebrot set, then we might say that a Mandlebrot-ish shape of spheres exists. But the set itself doesn't have any independent existence. This result doesn't seem to me to depend on whether we use spheres or rays or standing waves -- you still have to be vibrating something if you want to talk about things that actually exist. I'm not the sort of nut that believes in good old-fashioned aether, but mathematical relationships alone won't get you a flesh-and-blood universe where things actually exist...they'll just get you a blueprint for one. Even if, epistemologically, we can know everything about the blueprint and model all of its parameters, it still won't exist unless it's made of something.
That, at any rate, is my modestly informed opinion. If you can see any flaws in my analysis, I would be grateful to you for pointing them out.
I think your intuition is relying a little too much on the absurdity heuristic (e.g., "It boggles my mind...") and flat out assertion (e.g., "But the set itself doesn't have any independent existence."). Metaphysical intuition is really misleading. I think most people underestimate that, especially because the absurdity heuristic is strong and therefore it's easy to reach a reductio ad absurdum that is nonetheless true. I'll give an example.
Once upon a time I didn't think copies 'counted' in a multiverse, either morally or for purposes of anthropic reasoning. 200 Jacks had the same weight as 1 Mary. The opposite was absurd, you see: You're claiming that 3 copies of the exact same computation are worth more than 2 computations of 2 different people, leading separate and diverse lives? Absurd! My moral and metaphysical intuition balks at such an idea! I came up with, like, 3 reductio ad absurdums to prove my point. Eliezer, Wei Dai, Steven Kaas, Nick Bostrom, what did they know? And there was some pride, too, because they way I was thinking about it meant I could easily deal with indexical uncertainty, and the others seemed clueless. ... Well, turns out those reductios weren't absurd: I just hadn't learned to think like reality. I had to update, because that's where the decision theory led, and it's hard to argue with mathematics. And it came to my attention that thinking doubled computations had the same measure had a lot of problems as well. Since then, I've been a lot more careful about asserting my intuition when it disagrees with people who seem to have thought about it a lot more than I have.
In the case of the Mathematical Universe Hypothesis or permutations thereof (Eliezer seems to think the mysterious 'reality fluid' or 'measure' has a lot to do with directed acyclic graphs, for instance), there's a lot of mental firepower aimed against you. Why do you believe what you believe? If it turns out the reason is metaphysical intuition, be on guard. Acknowledge your intuition, but don't believe everything you think.