Comment author: Viliam_Bur 24 February 2014 08:31:23AM 1 point [-]

"whose only factors" -- that's where you are hiding the negation

("only" = "there is no other")

Comment author: Vej_Kse 24 February 2014 02:23:35PM *  0 points [-]

Not necessarily: see mathnerd314's comment below (or above). In fact, in “there is no other”, there is a double negation (the second being in “other”, which hides “not equal to”), which can be eliminated.

Comment author: Vej_Kse 15 December 2013 01:57:01PM *  1 point [-]

Coincidentally, a paper based on Yudkowsky and Herreshoff's paper has appeared a few days ago on the arXiv. It's Paradoxes of rational agency and formal systems that verify their own soundness by Nik Weaver. Here's the abstract:

We consider extensions of Peano arithmetic which include an assertibility predicate. Any such system which is arithmetically sound effectively verifies its own soundness. This leads to the resolution of a range of paradoxes involving rational agents who are licensed to act under precisely defined conditions.

In response to comment by [deleted] on Academic Cliques
Comment author: ChrisHallquist 08 November 2013 08:15:44PM 3 points [-]

I've wondered about that. Someone should try writing an iPad app that a toddler can play with to have their brain bombarded by math, and see if that leads to math coming as naturally to them as language. I doubt it would work but it might be worth trying.

Comment author: Vej_Kse 09 November 2013 03:23:45PM *  3 points [-]

It seems that simply bombarding the brain isn't sufficient, even for language, and that social interaction is required (see this study), so that playing math games with the child would be a better idea.