= 27d567bc2d48d9f40e9ccc20ea370b15)
Eliezer_Yudkowsky comments on Second-Order Logic: The Controversy - LessWrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (188)
Second order logic may be able to express all expressible statements in 3rd order logic, 4th order, up to any finite Nth order, but perhaps there exist ∞th order statements that 2nd order logic cannot express. Albeit, such statements could never be fully decidable and would thus be, at best, semidecidable or co-semidecidable. This may not be complete, but science works the same way.
I don't think that infinitary logic is the same as ω-order logic.
Wouldn't ω-order logic be a subset of infinitary logic? Or do I have it backwards?
I don't think they have anything to do with each other. Infinitary logic is first-order logic with infinite proof lengths. Second-order logic is finite proof lengths with quantification over predicates. I don't know if there's any particular known relation between what these two theories can express.