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

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

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (188)

You are viewing a single comment's thread. Show more comments above.

Comment author: dankane 09 January 2013 07:29:01PM 2 points [-]

Even though there are more complicated universes that perfectly generate our observations to date than there are simple universes that do so, given proper subsets of our universe, assuming a structurally simple universe tends to yield more accurate predictions than does assuming a structurally complex universe.

But when we are talking about which model of set theory to use to model our experiences, all of the non-standard models give exactly the same predictions to date (and will continue to do so until we reach non-standard times). And not all of these models are horribly complicated. There's the model of constructable set theory, where you only have the sets absolutely guaranteed you by the axioms. This gives you a countable model of set theory (and hence not the standard one), but it is still easily describable.