Eugine_Nier comments on Second-Order Logic: The Controversy - Less Wrong

24 Post author: Eliezer_Yudkowsky 04 January 2013 07:51PM

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Comment author: RobbBB 09 January 2013 01:30:55AM 0 points [-]

Simplicity is an important consideration. There are many more ways for complex universes to have violated our expectations already, while still making sapience possible, than for simple universes to have done so. That is, the space of simple universes is much more constrained by anthropic principles than is the space of complicated ones; so it is surprising that we seem to have found ourselves in a universe largely describable with very simple and uniform logic and mathematics, since there are many more ways to be complicated than to be simple. And this surprising fact may suggest that exotic logical, mathematical, or metaphysical structures do not exist, or are in some other respect not candidates for our anthropic reasoning. In other words, we can draw a tentative inductive conclusion regarding whether spacetime is nonstandard overall by considering all the ways in which our theories to date have been surprisingly successful and general while appealing almost exclusively to the simplest (which often corresponds to 'most standard,' with a few important caveats) conceivable systems. This won't be conclusive, but it's at least suggestive.

Comment author: Eugine_Nier 09 January 2013 11:13:50PM 1 point [-]

There are many more ways for complex universes to have violated our expectations already, while still making sapience possible, than for simple universes to have done so.

How do we know they haven't?

Comment author: MugaSofer 10 January 2013 11:35:52AM -1 points [-]

Interesting choice of example.

Not objecting to it, just interesting.