Some weird dudes with a big blue van were mumbling around beeler as I left the house this morning. I think one of them knocked on the door but was mysteriously absent when I managed to get to it.
Wow, Raymond Smullyan can write really creepy stories. This was pointed to by Don Knuth's "Things a Computer Scientist Rarely Talks About," which was loaned to me by lincoln3, in the sense that I stole it out of his office. The Smullyan story (and, I seem to recall, a similar one in the Hofstadter-Dennett-edited "The Mind's I") has a lot of reasoning which lines up very neatly with the stereotypes I have in my mind of the sort of argumentation in favor of religions that I find so irritating. (That is, the sort of argumentation that I find irritating. I don't harbor any particular ire towards any particular popular belief-systems in that vein) However, in this particular story, it is a little harder to see why it fails.
This got me thinking about Yishan's post about analogical arguments. Perhaps this is covered in his footnote, but I do think that analogies can actually prove things sometimes, namely by serving as counterexamples. So let P(x) be some proposition parameterized by x. I'm arguing for P(a). In my mind, I actually believe ∀x.P(x), and I think I have a good argument for it, and tacitly I am using that argument to argue P(a). You say, "it's like... P(b). You agree that it can't possibly be that P(b), right?". I pause to consider, and realize that, no, I don't agree with P(b). So I look for the flaw in my mental argument that ∀x.P(x), and hunt for another good argument for P(a), if I still think there is one. So bringing up P(b) hasn't established not-P(a), certainly, but it has demolished my reason for thinking P(a), and I had better come up with a new one, and in the meantime remain P(a)-agnostic.
I like this paper that kaustuv dug up, more the more I read it. It looks nice and plasticky and algebraic and not quite as down-'n'-dirty as most of this other stuff. Or at least there is a clean side to it that can be separated off and hacked on and experimented with, I think.
Got the databases midterm back. I did fuck up exactly the bits I thought I would.
Need to read mumble mumble uniform proofs mumble mumble.
functor.org seems to have died again. Yarrrr. I need a can-o'-air or something.