Thursday, September 18, 2008

Einstein and Benacceraf

The improved benacceraf epistemological argument went something like this:
1) humans exist entirely in space-time
2) if abstracta exist, they exist entirely outside of space-time
3) ((1)&(2))->(4)
4) it's likely that humans cannot have knowledge to abstracta
5) if platonism is true then ~(4)
6) platonism is not true

Consider the following argument that the previous argument is unsound:
1') humans exist entirely in the present
2') future events exist entirely outside the present
3') ((1')&(2'))->(4')
4') it's likely that humans cannot have knowledge of the future
5') ~(4')
6') (4')&~(4')
7') ~(1')v~(2')v~(3')
8') (7')->(9')
9') ~(1)v~(2)v~(3)

The claim is that (1')-(3') lead to absurdidty, and if this is right there must be something wrong with (1)-(3). Wes argued that (3') is false, since there's a way of knowing about the future. We simply reflect on the upstream causation that we've become aquainted with, and project that downstream. However, (3) can still be true, since there's no straitforward way of predicting what abstracta are like. I countered by saying that since causation makes sense only when looking at multiple times, (1') prevents us from knowing about causation as well (a similar argument could be formulated against knowledge of causation, instead of knowledge of the future). Appeal to memories doesn't seem to work, because if that's allowed then appeals to beliefs should be as well, and that would put pressure on (3). It was then considered that humans might be 4 dimensional time-worms, and thus (1') could be false. I countered that the argument could be run, not about humans, but about time-slices of humans. Hence the new absurdity would be that there's no human timeslice that knows anything about causation or the future (we don't know about the future or causation at any time). Curtis noted that I'm relying heavily on the notion of the present (in the first case) and on the notion of a timeslice (in the second case). Special relativity holds that there's no absolute present to appeal to, and similarly a timeslice in one inertial reference frame might be a 4-d time worm in another inertial reference frame. Thus appealing to timeslices is no good either. I believe I can counter this (blow the whistle on me if I'm doing any of this wrong Curtis).
Spacetime even A can cause spacetime event B iff B is in the future light-cone of A. Again, correct me if I'm wrong, but I believe if this relation holds between B and A, then B and A are said to be timewise seperated from each other. If neither B nor A is in the others future light-cone, then they are said to be spacewise seperated from each other. If they're right on the border, they're said to be lightlike seperated from each other. Ok so far?
So consider the huge 4-d mass of points that a human occupies. We can collect something that will act like a time-slice (for our purposes) by choosing a set of them that intuitively correspond to a complete body, such that no two of them are timelike seperated. By hypothesis, no two of these points are in a position to be causally related. Furthermore, that's an absolute, there's no reference frame in which they could be causally related.
I only need the claim that such a set of points exists that corresponds to a complete body. Then I can run the same argument about this entity to the effect that it cannot know anything about causation. Since it corresponds to an entire human body (and supposedly brain) then it will do for a timeslice that should know about causation, but does not not bennaceraff sorts of reasons.
I can think of a response or two to this, but I think I'll stop here.


Wes McPherson said...

Sorry, I'm just curious about the notion of time. It seems ambiguous between the notion of time as presence, the kind of time Heidegger likes, or a more spatialized notion of spacetime that has coordinates, that someone like Einstein seems to have in mind.

I wonder if we face a problem if we cross the two different notions at all.

Wes McPherson said...

I'm asking this in relation to:

1') humans exist entirely in the present

which I think I have a problem with.

Should have said that before. I think that humans exist entirely within time but not the present.

Dan said...

what's the notion of time as presence?

Wes McPherson said...

I'm thinking of a sort of notion of solipsism where we are only in the present. But there is not a series of 'nows' but just one 'now' that we are always in. The past and future are far away, but we are always in the presence of things in the present.

So in some psychological sense maybe we are only in the present. We are always in the presence of things, with the past and future being distant from us, and the now and just now, about to be now, etc. being close to us.

Wes McPherson said...

Sorry, should have added: this account of time, that we live in the moment, as it were, seems to be a different notion of time than standard time that clocks follow, or the scientists notion of time as a measure.

Wes McPherson said...

I probably should have thought through my previous posts instead of posting again and again...

Can we equate being in time with being only in the present? It seems that on some theories of time we exist in the present only, like a Heideggerean view of presence. But if we think in terms of spacetime worms, we exist through time as events.