Plasmon:

So, they were lucky. It could have been that that-which-Pythagoras-calls-number was not that-which-Fibonacci-calls-numbers.

Why do you imagine that the introduction of an axiomatic system would address this problem?

Why do you imagine that the introduction of an axiomatic system would address this problem?

Because then the problem is not "Does this non-axiomatized stuff obey that theorem ?" but "Does that theorem follow from these axioms ?". One is a pure logic problem, and proofs may be checked by automated proof-checkers. The other directly or indirectly relies on the mathematician's intuition of the non-axiomatized subject in question, and can't be checked by automated proof-checkers.

3thomblake7yTo quote, just put a greater-than sign > at the beginning of the first line.
1Cyan7yLessWrong uses Markdown [http://en.wikipedia.org/wiki/Markdown] for comment formatting. Click the button labelled "Show help" under the right-hand side of the comment box.

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

by David_Gerard 1 min read14th Nov 201247 comments

11


"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.