There is this incredibly toxic view of predicate logic that I first encountered in Good Old-Fashioned AI.

I'd be curious to know what that "toxic view" was. My GOFAI academic advisor back in grad school swore by predicate logic. The only argument against that I ever heard was that proving or disproving something is undecidable (in theory) and frequently intractible (in practice).

And then this entirely different, highly useful and precise view of the uses and bounds of logic that I encountered when I started studying mathematical logic and learned about things like model theory.

Model theory as opposed to proof theory? What is it you think is great about model theory?

Now considering that philosophers of the sort I inveighed against in "against modal logic" seem to talk and think like the GOFAI people and not like the model-theoretic people, I'm guessing that the GOFAI people made the terrible, horrible, no good, very bad mistake of getting their views of logic from the descendants of Bertrand Russell who still called themselves "philosophers" instead of those descendants who considered themselves part of the thriving edifice of mathematics.

I have no idea what you are saying here. That "Against Modal Logic" posting, and some of your commentary following it strike me as one of your most bizarre and incomprehensible pieces of writing at OB. Looking at the karma and comments suggests that I am not alone in this assessment.

Somehow, you have picked up a very strange notion of what modal logic is all about. The whole field of hardware and software verification is based on modal logics. Modal logics largely solve the undecidability and intractability problems the bedeviled GOFAI approaches to these problems using predicate logic. Temporal logics are modal. Epistemic and game-theoretic logics are modal.

Or maybe it is just the philosophical approaches to modal logic that offended you. The classical modal logic of necessity and possibility. The puzzles over the Barcan formulas when you try to combine modality and quantification. Or maybe something bizarre involving zombies or Goedel/Anselm ontological proofs.

Whatever it was that poisoned your mind against modal logic, I hope it isn't contagious. Modal logic is something that everyone should be exposed to, if they are exposed to logic at all. A classic introductory text: Robert Goldblatt: Logics of Time and Computation (pdf) is now available free online. I just got the current standard text from the library. It - Blackburn et al.: Modal Logic (textbook) - is also very good. And the standard reference work - Blackburn et al.: Handbook of Modal Logic - is outstanding (and available for less than $150 as Borders continues to go out of business :)