Monday, March 18, 2013

Presentism and abstracta: Two arguments

Here is an argument against presentism:

  1. If presentism is true, then to exist is to presently exist.
  2. Abstracta exist but do not presently exist.
  3. So, presentism is false.
And here is an argument for presentism:
  1. The number two existed yesterday and the day before yesterday.
  2. Anything that existed yesterday and the day before yesterday persisted.
  3. If growing block or eternalism is true, then persisting objects either have temporal parts or have locational properties.
  4. The number two does not have temporal parts.
  5. The number two does not have locational properties.
  6. If presentism is not true, growing block or eternalism is true.
  7. So, presentism is true.

My own take on the second argument is to distinguish between two senses of "x exists at t". The first sense is that x has tenseless existence-at-t. This we might call the narrow sense. But there is a broader sense of "x exists at t", which is that either x exists timelessly or x has existence-at-t. Ordinary language tends to use the second sense. If we take the broader sense in (4) and (5), I accept (4) (though with a divine conceptualist reduction) and deny (5). If we take the narrower sense, I deny (4) but accept (5).


Mike Almeida said...

But all of number 2's intrinsic properties are essential to it, so you do not need to relativize them to times or locations. The number 2 will be identical to each of its temporal 'parts' or stages over time. It's the degenerate case of a perduring object.

Alexander R Pruss said...

That sounds like endurantism. And endurantism seems to me to require locational properties: the object is at t1 and the object is at t2.

Mike Almeida said...

I think you're not taking seriously the idea that all of the number 2's properties are essential to it. Endurantism does not require relativization of essential properties, just contingent ones, since objects do not change wrt their essential properties over time. 4Dist who are perdurantists could urge that what endurantists call the endurance of a single object over time is what they call the perdurance of an object that is identical to its improper parts.

Michael Gonzalez said...

If I may address your first argument: Why is it the case that abstracta do not presently exist? Perhaps I'm unfamiliar with the terminology, but it seems to me that, on a presentist ontology, a necessary object (like an abstract object) cannot fail to presently exist. Or, to put it another way, at any given present moment, the necessary objects exist.

As to the second argument, why can't we just say that "at any given point, it is true that x exists timelessly". When dealing with an abstract, necessary object, it is always the case that it exists timelessly, but you can still give a tense to the statement about x. So, you end up with statements like "x had timeless existence yesterday, still has it today, and will have it tomorrow". Thus, your second argument does indeed seem to prove presentism is true, since the number 2 clearly did exist yesterday and the day before yesterday, and it clearly isn't sub-divided, but exists timelessly, therefore it persisted.