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mannykannot

1. What if, for example, it is functions all the way down?

2. I think reasonableness is still in the eye of the beholder, or has Deutsch convinced everyone who counts?

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> What if, for example, it is functions all the way down?

What, an infinite hierarchy of functions? Since that's not very parsimonious, it's a very unlikely option.

> I think reasonableness is still in the eye of the beholder, or has Deutsch convinced everyone who counts?

Sure, there are other possibilities, but the point that there is plenty of evidence that makes many worlds a reasonable conclusion, so the original claim isn't accurate.

That looks to me rather like axiarchism, with parsimony as the specific form of goodness.

I don't see the connection. Parsimony is important for induction by defining a universal prior. Solomonoff induction formalized this notion by ordering all programs that could generate a particular set of observations by increasing Kolmogorov complexity.

Are you not conflating 'things that make problems tractable' with 'things that must be'?

I don't see how. Firstly, Kolmogorov complexity is incomputable, so it's not technically tractable, it's merely an idealised induction process.

Secondly, assigning a higher probability to an outcome isn't saying that how things are.

Correspondingly, no claim about the likelihood of an infinite hierarchy of functions is saying how things are.

Which I didn't say, I simply said it was unlikely. In fact, vanishingly unlikely because it relies on infinity.

You might not have written it in exactly those words, but the corollary of your observation still holds.

Saying that an infinite hierarchy of functions is unlikely is saying that we probably don't live in a world governed by an infinite hierarchy of functions. But that's all it says, and as I pointed out, we have good a priori reasons for believing this conclusion, without having to ontologically commit ourselves to accepting it as necessarily true.

So I disagree, it's still not conflating "things that are likely" with "things that are".

1. What if there was a function like the Y-Combinator that returns a fixed point?

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