Gracious Living


A Couple Nuances
December 6, 2010, 03:01
Filed under: Logic, Math | Tags: , , ,

Started reading through Peter Smith’s “Gödel Without (Too Many) Tears” lecture notes yesterday, and I realized I hadn’t been as clear as I should have been in my treatment of Peano arithmetic.  So I started typing some errata, and I ended up typing a super-long exposition about All the Logic I Know.  This isn’t very much, because really I find mathematical logic a fascinatingly dull subject: it’s the sort of thing that looked cool when I was a kid because I could actually understand it, but now everything I read about it seems like this confusing haze of definitions and pseudophilosophical “theorems” about things actual math has left behind years ago.  So yeah.  What this means is: if you’re a logician, correct me if I get something wrong and please please try to convince me that your subject is cool and point me to a place where I can see that again.  I feel bad casting scorn on an entire branch of math just because it feels too weird and abstract.

Anyway, read on if you’re curious.  If you’re not, don’t.  I’ll cite this post whenever I prove Gödel’s Theorems but probably at no other time, so you won’t really miss much.  I do define quantifiers, which are these useful math symbols I might reuse: \forall x means “for all x” and \exists x means “there exists an x such that.”  Okay?  Okay.

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