科技回声

This is great for understanding why simpler logics (Boolean) are computable but too expressive ones (FO) are not. As soon as the logic is able to make statements about itself, things get 'weird'. A not formal(!) but imho still intuitive example:"This sentence has five words."This is a true statement. And we know that the conjunction of two true statements should also be true."This sentence has five words and this sentence has five words."With eleven words each part of this statement is obviously false and here we can't rely on the "and", which we are used to from the simpler logics, anymore.

An excellent paper, especially reviewing the connections of Peano, Tarski, and Godel.I'm surprised that he did not mention Jim Propp's self=referential aptitude test. It starts with:> 1. The first question whose answer is B is question > (A) 1 > (B) 2 > (C) 3 > (D) 4 > (E) 5And, of course, Bolander's paper ends with an utterly delightful final sentence!

Footnote 17 mentions a proposed approach of "extending logic to include contexts", but doesn't name any names. Anyone have a reference I can follow?

If this sentence is true, then Santa Claus exists. Therefore, Santa Claus exists.

Runtime Error: Stack Overflow in recursive function.

Footnote 17 mentions a proposed approach of "extending logic to include contexts", but doesn't name any names. Anyone have a reference I can follow?

If this sentence is true, then Santa Claus exists. Therefore, Santa Claus exists.

Runtime Error: Stack Overflow in recursive function.

Self-reference and Logic (2005) [pdf]

5 条评论

Self-reference and Logic (2005) [pdf]

5 条评论