Wednesday, March 26, 2008

A Particular Universal Proposition

Jacques Louis-David's The Death of Socrates, 1787
Logic has long used the proposition, "all men are mortal," as a staple of syllogisms: as in "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." The proposition is a universal affirmative proposition to the extent that there is a necessary connection between "man" and "mortal." That is, a universal proposition ("all men are mortal") states that all members of a class (men) carry a further designation (mortality). (A particular proposition holds only that some members of a class have that particular designation).

Universality as a metaphysical notion further holds to the extent that the proposition is true for all times and places. "2+2=4" is a universal proposition in this sense. Its truth doesn't change if you're in medieval Calcutta, ancient Rome, or modern Dekalb.

But, although long considered universal both logically and metaphysically, the proposition "all men are mortal" may not really be true. For one thing, developments in genetics and cellular biology suggest new possibilities for extending life, even indefinitely. Other developments in artificial intelligence suggest a transformed notion of life and immortality in which one could upload human consciousness to virtual bodies.

It's curious to think of this proposition above all as a black swan. If "all men are mortal," that well-worn absolute certainty of Intro to Logic, is simply a false, formally universal proposition, what does this say about universal propositions or metaphysical universality? I also wonder what this does to the central proposition of most Asian religions - but specifically the religions of Tibet, Nepal, and India - that everything that lives, dies.

6 comments:

Steve Gimbel said...

Its a universal proposition in virtue of its form, in logic we don't really care whether it's true or false -- just what necessarily follows from it if it were true. The question in Aristotelean logic is one of validity -- given two categorical propositions, what other categorical propositions follow as a necessary result.

At the same time, immorality does raise all sorts of weird issues, just not ones that Aristotle is concerned about...because he's already dead.

helmut said...

Yes, and that's why I said a "false, formally universal proposition." But the thing that's curious to me is that for the purely formal relationship of validity re categorical props, there's no need to bother with any propositions having truth values at all (or perhaps as long as the premises are not true while the conclusion is false). The famous "mortal" proposition could be nearly anything as long as the formal relationship holds. E.g., all funky lemurs are vacuum cleaners - so, the syllogistic form could be All funky lemurs are vacuum cleaners. Socrates is a funky lemur. Therefore, Socrates is a vacuum cleaner. Certainly. Yet... we generally don't use such syllogisms in logic. We tend to use ones that have clearly ascribable truth values. Maybe that's just a pedagogical thing - makes it easier for 101 students to understand. Just a random thought for the day....

Aristotle's dead? I didn't even know he was sick!

Anonymous said...

I remember McDermott insisted he had no idea whether or not it was true that "all men are mortal." He didn't see how anyone could make that sort of claim. It was as if the whole enterprise of professional philosophy was illegitimate because of the universal use of this claim. This point took a small amount of colored chalk and some growling to make, as I recall.

Professor Pea

helmut said...

Whoa.... You just blew my mind. Did I just unsuspectingly dig up something out of the dark corners of my memory, cackling back there in a NY Irish accent? Or is it coincidence?

MT said...

Is this going to be like Y2K for the philosophical canon? The year molecular genetics gives us black swans and immortality? I hope Google Books has some kind of plan. What could this mean for foundations of Western thought?

MT said...

BTW that "Therefore, Socrates is mortal" always bugged the hell out of me. Socrates isn't: Socrates was, and mortality is a condition that afflicts only people who are. I doubt it's even a once universal proposition (as if a transient universal would illustrate universality anyway). Seems more like an utterance that was stillborn.