errata/updates to post on “modal logic, flow analysis, and concurrency”
March 24th, 2004 | Tags: philosophy | 2 Comments
John Halleck helpfully points out a couple of caveats about my recent post on modal logic and PL applications. First, I assert that “all or most” of the classical connectives are truth-functional, “depending on whom you’re willing to believe.” John reminds me that it’s never safe to make generalizations about logic; my assertion, of course, is untrue for formalists. John also points out that my example using time as possible worlds, in which I state that it is necessarily false that I watched SportsCenter last week, is not true in every modal system; it fails in the temporal logics of (the aptly-named) Arthur N. Prior. John recommends Prior’s Papers on Time and Tense and Past, Present, and Future.)
Finally, John reminds me of J. Jay Zeman’s fine modal logic text online. I’ve referred to this one a few times while writing on logic, so I really should have linked to it sooner. It uses prefix notation, which is perhaps off-putting if you didn’t have a similar programming culture to the one in which I was indoctrinated as a computer science undergrad.
I’m currently listening to Vorspiel/Prélude from the album “Wagner – Die Meistersinger von Nürnberg (Karajan, Dresdener Staatskapelle)” by Herbert von Karajan & Staatskapelle Dresden
March 27th, 2004 at 09:16:34 PM (#)
Minor nit:
It fails in SOME of the logics that Prior covers.
Minor expanson:
Prior’s books use also use Polish notation, in the same manner that J Zeman’s book does.
I suspect that all three would be more read nowadays if they used traditional notation.
Expansion:
It may not be obvious in what sense that Will’s sports watching statement could be anything other than necassarily false. (Since even most temporal logics follow Aristotle’s lead and take the past as fixed.)
The crux is whethter or not it is the case that it has always been the case that whatever has always been true is true. [Like most modal logic expressions, they read bizarrely in English.]
If you (like modern Science Fiction) assume that the past can be changed, then things that are in the past lose the “necessity” of being the why they were. If you don’t have that assumption, then (obviously) what was can’t be changed.
March 28th, 2004 at 03:40:34 PM (#)
John is right; the time-based modal system that I informally described implied that the past is fixed and that some things can be permanently true. (It was, in that sense, a not particularly compelling example of modal logic.) The most straightforward examples of “permanent truth” that I can identify involve irrevocable changes to essence.
In dealing with modal logics in general, the concept of what it means for a sentence to be necessarily true is a tricky one, in my opinion. (That is, if we’re talking about sentences that aren’t vacuously necessarily true, like tautologies.) I think some pretty good treatments of this idea come from Plantinga and Kripke.