Anatoly_Vorobey comments on Gap in understanding of Logical Pinpointing - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (13)
Second-order logic does have a computable definition of provability, it's just that the logic is incomplete under that definition. It may be disconcerting to work with an incomplete logic, since you know there are universal truths you can't prove even before you get to a particular theory and its consequences.
In general, using SOL to pinpoint the truths of natural numbers doesn't seem like an appealing idea: