Heh - I'm amazed at how many things in this post I alternately strongly agree or strongly disagree with.

It’s important to distinguish between the numeral “2″, which is a formal symbol designed to be manipulated according to formal rules, and the noun “two”, which appears to name something

OK... I honestly can't comprehend how someone could simultaneously believe that "2" is just a symbol and that "two" is a blob of pure meaning. It suggests the inferential distances are actually pretty great here despite a lot of surface similariti... (read more)

This is defining numbers in terms of sets

But we don't need to use the full strength of set theory (or anything like it), so it might still be an improvement. Though I think there are still other problems.

[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.