Well, the topic is "logical pinpointing", and the attempt to logically pinpoint logic itself sounds rather circular...

However, if we really want to, we can describe a computer program which systematically checks any given input string to decide whether it constitutes a valid string of deductions in FOL. Then "first order logic" is anything to which the program gives the answer "Valid". That's possible for FOL, but not for SOL. If you want to further pinpoint what a "program" is, the best way to do that is to find a computer and run the d**n thing!

[LINK] Steven Landsburg "Accounting for Numbers" - response to EY's "Logical Pinpointing"

by David_Gerard 1 min read14th Nov 201247 comments


"I started to post a comment, but it got long enough that I’ve turned my comment into a blog post."

So the study of second-order consequences is not logic at all; to tease out all the second-order consequences of your second-order axioms, you need to confront not just the forms of sentences but their meanings. In other words, you have to understand meanings before you can carry out the operation of inference. But Yudkowsky is trying to derive meaning from the operation of inference, which won’t work because in second-order logic, meaning comes first.

... it’s important to recognize that Yudkowsky has “solved” the problem of accounting for numbers only by reducing it to the problem of accounting for sets — except that he hasn’t even done that, because his reduction relies on pretending that second order logic is logic.