By far the largest criticism here is the requirements of set theory:

Yudkowsky is relying on a theorem when he says that second-order Peano arithmetic has a unique model. That theorem requires a substantial dose of set theory. So in order to avoid taking numbers as primitive objects, he’s effectively resorted to taking sets as primitive objects. But why is it any more satisfying to take set theory as “given” than to take numbers as “given”? Indeed, the formal study of numbers precedes the formal study of sets by millennia, which suggests that numbers are

... (read more)

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

by David_Gerard 1 min read14th Nov 201247 comments

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"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.