Thursday, May 14, 2009

Is time a continuum?

The following argument is valid:

  1. (Premise) If one compressed all the events of an infinitely long happy life into a minute, by living a year of events in the first half minute, then another year of events in the next quarter minute, and so on, then one would be exactly as well off as living the finite life as the infinite one.
  2. (Premise) If supertasks are possible, then the antecedent of (1) is possible for any infinitely long happy life.
  3. (Premise) If time is an actual continuum, supertasks are possible.
  4. (Premise) There is a possible an infinitely long happy life that would make for full human well-being.
  5. (Premise) A finitely long life could not make for full human well-being.
  6. (Premise) If a life makes for full human well-being, then so does any life that makes one exactly as well off.
  7. Therefore, if supertasks are possible, there is a finitely long life that would make for full human well-being (1, 2, 4, 6).
  8. Therefore, supertasks are impossible. (5, 7)
  9. Therefore, time is not an actual continuum. (3 and 8)

8 comments:

Matthew said...

Connecting happiness with a theory of time is weird.

Alexander R Pruss said...

These problems in metaphysics are hard, and one way to have hope of a solution is to connect them with other things.

Matthew said...

Well, a physicalist might simply argue that human happiness is just a chemical reaction that's just a little weird, but has no connection to the nature of time.

One might call this the "argument from weirdness": those premisses that try to connect seemingly distinc topics have conclusions too weird to accept, so that those premisses are irrational.

Alexander R Pruss said...

If happiness is not something objective that connects up with reality, then there is not much point to being a physicalist, because then there is not much point to anything, is there?

Beancan Tatterpants said...

Ah, and by tying time to happiness, you're not so much proving a point about time as you are making those who disagree with your concept marry themselves to some pills that are hard to swallow.

A pretty effective tactic, I'd say.

Plus, if time is a continuum, then it has a unique relationship to happiness. If it isn't a continuum, we may have to redefine happiness (and all experiences for that matter). Perhaps we should call in Kurt Vonnegut on this one. Or at least a Tramalfadorian.

Matthew said...

Both of you have a point.
Then let me say: Connecting happiness with a theory of time is interesting.

Alexander R Pruss said...

Actually, such connection is not that original, either. One of the standard argumentative moves in the A/B theory debate is to ask whether the B theory of time can account for various human phenomena like surprise or the asymmetry of the value of growth of virtue (it is better to live a life where one's vices are earlier and one's virtues later, rather than the other way around, even if the total vice and total virtue is the same).

Mark said...

So starting with premise one:

How could one compress an infinitely long life into one minute's time? Wouldn't it take an infinite amount of time to compress it, thus rendering it impossible to accomplish?

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