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hen comments on Self-Congratulatory Rationalism - Less Wrong
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Hold on now, you're pattern matching me. I said:
To which you replied that this is a fact about me, not the universe. But I explicitly say that its not a fact about the universe! My evidence for this is the only evidence that could be relevant: my experience with literature, science fiction, talking to people, etc.
Nor is it relevant that science is full of people that say that something has to be true because they can't imagine the world otherwise. Again, I'm not making a claim about the world, I'm making a claim about the way we have imagined, or now imagine the world to be. I would be very happy to be pointed toward a hypothetical universe that isn't subject to mathematical analysis and which contains thinking animals.
So before we go on, please tell me what you think I'm claiming? I don't wish to defend any opinions but my own.
Hen, I told you how I imagine such a universe, and you told me I couldn't be imagining it! Maybe you could undertake not to gainsay further hypotheses.
I found your suggestion to be implausible for two reasons: first, I don't think the idea of epistemically significant qualia is defensible, and second, even on the condition that it is, I don't think the idea of a universe of nothing but a single quale (one having epistemic significance) is defensible. Both of these points would take some time to work out, and it struck me in our last exchange that you had neither the patience nor the good will to do so, at least not with me. But I'd be happy to discuss the matter if you're interested in hearing what I have to say.
You said:
I'm not sure what you mean by "necessary", but the most obvious interpretation is that you think it's necessarily impossible for the world to not be run by math or at least for humans to understand a world that doesn't.
This is my claim, and here's the thought: thinking things are natural, physical objects and they necessarily have some internal complexity. Further, thoughts have some basic complexity: I can't engage in an inference with a single term.
Any universe which would not in principle be subject to mathematical analysis is a universe in which there is no quantity of anything. So it can't, for example, involve any space or time, no energy or mass, no plurality of bodies, no forces, nothing like that. It admits of no analysis in terms of propositional logic, so Bayes is right out, as is any understanding of causality. This, it seems to me, would preclude the possibility of thought altogether. It may be that the world we live in is actually like that, and all its multiplicity is merely the contribution of our minds, so I won't venture a claim about the world as such. So far as I know, the fact that worlds admit of mathematical analysis is a fact about thinking things, not worlds.
What do you mean by "complexity"? I realize you have an intuitive idea, but it could very well be that your idea doesn't make sense when applied to whatever the real universe is.
Um, that seems like a stretch. Just because some aspects of the universe are subject to mathematical analysis doesn't necessarily mean the whole universe is.
For my purposes, complexity is: involving (in the broadest sense of that word) more than one (in the broadest sense of that word) thing (in the broadest sense of that word). And remember, I'm not talking about the real universe, but about the universe as it appears to creatures capable of thinking.
I think it does, if you're granting me that such a world could be distinguished into parts. It doesn't mean we could have the rich mathematical understanding of laws we do now, but that's a higher bar than I'm talking about.
You can always "use" analysis the issue is whether it gives you correct answers. It only gives you the correct answer if the universe obeys certain axioms.
Well, this gets us back to the topic that spawned this whole discussion: I'm not sure we can separate the question 'can we use it' from 'does it give us true results' with something like math. If I'm right that people always have mostly true beliefs, then when we're talking about the more basic ways of thinking (not Aristotelian dynamics, but counting, arithmetic, etc.) the fact that we can use them is very good evidence that they mostly return true results. So if you're right that you can always use, say, arithmetic, then I think we should conclude that a universe is always subject to analysis by arithmetic.
You may be totally wrong that you can always use these things, of course. But I think you're probably right and I can't make sense of any suggestion to the contrary that I've heard yet.
One could mathematically describe things not analysable by arithmetic, though...
Fair point, arithmetic's not a good example of a minimum for mathematical description.