From Landsburg's "Accounting for Numbers," point 9:

numbers are indeed just “out there” and that they are directly accessible to our intuitions.

[Emphasis mine.]

I'm conflicted on whether to think the world is actually physical in a special way, or simply mathematical in such a way that all mathematical structures exist and are equally real. My greatest sticking point to accepting the latter position is the emphasized part of the quote.

Okay, if I grant that numbers are "out there," we do seem to interact with them via a cognitive algor... (read more)

What kind of cognitive algorithms generate the feeling that numbers are "out there"?

Perhaps the same sorts that generate feelings like 'lines and edges are out there' or that 'we say distinct words' (rather than continuously slurred together sounds) or which leads to http://en.wikipedia.org/wiki/Subitizing

[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.