Wednesday, October 18, 2023

Losing track of time

Suppose that the full saturated truthbearers are tensed propositions (which I think is essentially what the A-theory of time comes to). Now consider an atom with a half-life of a week. I observe the atom exactly at noon on Monday, and it hasn’t decayed yet. I thereby acquire the belief that the atom has not decayed yet. Now suppose that for the next week I stop changing in any relevant respect, and maintain belief in the same truthbearers, and the atom doesn’t decay. In particular I continue to have the tensed belief that the atom hasn’t decayed yet.

But an odd thing happens. While my belief is reliable enough for knowledge initially—it has a probability 0.9999 of remaining true for the first minute after observation—eventually the reliability goes down. After a day, the probability of truth is down to 0.91, after two days it’s 0.82, and after a week, of course, it’s 0.5. So gradually I lose reliability, and (assuming I had it) knowledge, even though nothing relevant has changed in the world in me or around me.

Well, that’s not quite true. For something seems to have changed: my observation has “gotten older”. But it’s still kind of odd—the time slice of the world is relevantly the same right after the observation as a week after.

1 comment:

Christopher Michael said...

Doesn't this come as no surprise to people like you and me who already understand that both human and Divine knowledge is extrinsic? :-)