Aug. 01 2010

The Permutation Game

Kant had already said that this proof was baloney, because “exis­tence” wasn’t a pred­i­cate like good­ness or knowl­edge. But Rus­sell and ana­lytic phi­los­o­phy took it one step fur­ther. In math and for­mal logic, exis­tence isn’t a pred­i­cate — it’s a quan­ti­fier. Like in the sen­tence, “For every nat­ural num­ber, there is a larger nat­ural num­ber.” We’re not mak­ing deep exis­tence claims here, just sin­gling out an ele­ment in a system.

So if we can come up with a model that’s foun­da­tion­ally and struc­turally sound, and works, let’s use it. What looked like an impos­si­ble prob­lem wasn’t a prob­lem after all; we’d just got­ten twisted up in the way we talked about it.

So phi­los­o­phy of math­e­mat­ics => math­e­mat­i­cal phi­los­o­phy. Change of gram­mar => change of perspective.

shaking off logical ambiguity.