[LINK] Steven Landsburg “Accounting for Numbers”—response to EY’s “Logical Pinpointing”

“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.