Tuesday, August 8, 2017

"Finite"

In conversation last week, I said to my father that my laptop battery has a “finite number of charge cycles”.

Now, if someone said to me that a battery had fewer than a billion charge cycles, I’d take the speaker to be implicating that it has quite a lot of them, probably between half a billion and a billion. And even besides that implicature, if all my information were that the battery has fewer than a billion charge cycles, then it would seem natural to take a uniform distribution from 0 to 999,999,999 and think that it is extremely likely that it has at least a million charge cycles.

One might think something similar would be the case with saying that the battery has a finite number of charge cycles. After all, that statement is logically equivalent to the statement that it has fewer than ℵ0 charge cycles, which by analogy should implicate that it has quite a lot of them, or at least give rise to a uniform distribution between 0, inclusive, and ℵ0, exclusive. But no! To say that it has a finite number of charge cycles seems to implicate something quite different: it implicates that the number is sufficiently limited that running into the limit is a serious possibility.

Actually, this may go beyond implicature. Perhaps outside of specialized domains like mathematics and philosophy, “finite” typically means something like not practically infinite, where “practically infinite” means beyond all practical limitations (e.g., the amount of energy in the sun is practically infinite). Thus, the finite is what has practical limits. (But see also this aberrant usage.)

2 comments:

SMatthewStolte said...

If someone said to me that the battery had fewer than a billion charge cycles, I would might take her to be implying that a billion charge cycles is a practical limitation. (This would lead me to think I must not really understand what is meant by a ‘charge cycle’, so that would be my first question.) I would also, I agree, think that she meant it had somewhere between half a billion and a billion charge cycles, but given my new confusion about the meaning of ‘charge cycle’, I wouldn’t be sure if that was a lot or not.

Alexander R Pruss said...

That sounds right.