## Tuesday, September 13, 2011

### A problem for my view of change

I think that claims like "x is green at t" should receive a relational analysis, like: GreenlyOccupies(x, t).  I also think this can be independently motivated: we need the relation of greenly occupying for other reasons and cannot reduce it to a monadic greenness, so the Ockhamly thing to do is to reduce greenness to greenly occupying.

But here is a hitch.  If x is green at t and non-green at t*, then how has x changed?  It seems that both at t and at t*, x greenly occupies t and fails to greenly occupy t*.  Granted, we might say that x is green at t and non-green at t*.  But on the view in question, being green or being non-green are not real properties.  So there seems to be no real change.  If there is a real property in view, it's being green at t and being non-green at t*. But it is always the case that x has both of these properties.  For every time t**, x is green at t at t**, and x is non-green at t* at t**.

Should this bother me?  Perhaps not.  I have a reductive analysis of accidental change.  Accidental change between two times is just standing in a relation to one time and not standing in that relation to another time.

But that doesn't seem right.  For instance, let's say that I am interested in the year 1716 (why? because I'd like to figure out what was going on in Leibniz's mind in that year given his correspondence with Des Bosses and Masson).  Then I stand in a relation of being deeply interested in to 1716, but I do not stand in the relation of being deeply interested in to 1715.  So on the view just offered, I have accidentally changed between 1715 and 1716.  But I didn't exist then, so I didn't change then.

Maybe I can rule out this case as follows.  The relation of being deeply interested in is a Cambridge relation in respect of its second relatum--1716 is no different for my being interested in it.  So perhaps accidental change between two times requires standing in a relation to one time and not to another, where the relation is non-Cambridge in respect of either relatum (it's easy to see that it also shouldn't be a Cambridge relation in respect of the changer).

But that may not be right either.  Suppose that times are constituted by the events that happen at them.  (A kind of Aristotelian view.)  Suppose in 2004, and only in 2004, there is an intense flurry of excitement about Leibniz's correspondence with Masson.  Then Leibniz stands in the relation of having caused an intense flurry of excitement in to the year 2004, but not to the year 2005.  Causing is a non-Cambridge relation in respect of either relatum, and since years are constituted of the events that stand in the causing relation, it seems that this relation is non-Cambridge in respect of the year, too.  But while Leibniz may have changed between 2004 and 2005 (e.g., in heaven, he may have come to a greater love of God), his being the cause of an intense flurry of excitement in 2004 but not in 2005 is not sufficient for change.

At this point, the unsatisfying state of affairs is that some relations imply change and some don't.  Greenly occupying 2004 but not 2005 does imply change.  Causing an intense flurry of excitement in 2004 but not 2005 does not imply change.

Interestingly, the relation of having caused an intense flurry of excitement in is actually a ternary relation.  Thus, we might say that in 1716, Leibniz caused an intense flurry of excitement to happen in 2004 (viz., by writing the letter to Masson): it is a relation between a substance (Leibniz) and two times (1716 and 2004).  And a difference between times in respect of the first temporal relatum (the one filled by 1716) does imply change, while a difference between times in respect of the second temporal relatum (the one filled by 2004) does not: if in 1715 Leibniz did not cause an intense flurry of excitement to happen in 2004, but in 1716 he did, then he changed between 1715 and 1716.  This means that we can't simply distinguish between relations and say some give rise to change and some don't.  For there are relations R such that R(x,t,u)&~R(x,t*,u) implies change in x but R(x,t,u)&~R(x,t,u*) does not.  What we need is some way of saying in respect of which pair of relata the relation gives rise to change.

The presentist has a nice story here.  She can say that the property of presently causing an intense flurry of excitement in 2004 is a non-Cambridge property, albeit a non-intrinsic one, and that Leibniz has this property at one time and doesn't have it at another.  But the kind of B-theorist that I am interested in does not say that: she just has a ternary relation of ___ in ___ causing an intense flurry of excitement in ___.

Now, it is true that the presentist's story does make use of the notion of a non-Cambridge property, a difficult notion to explicate that probably has to be made primitive.  Vaguely speaking, a non-Cambridge property is one that a thing has in part because of how it presently is.  Maybe the B-theorist can also primitively talk about a relation that an entity stands in in part because of how the entity is at one of the temporal relata of that relation.

Maybe, though, instead of talking about what it is to change, we should just talk about what it is to change in respect of some relation.  And that the B-theorist may be able to do.

Heath White said...

At this point, the unsatisfying state of affairs is that some relations imply change and some don't.

OccupyingGreen(x,t) is AFAICT equivalent to Green(x,t). Then the problem is that

Green(x,t) but ~Green(x,t*) implies change, while
InterestedIn(x,t) but ~InterestedIn(x,t*) does not.

Here the problem is that times are not functioning the same way; InterestedIn() really needs to be

InterestedIn(x,t1,t2)

That is, x is interested in t1 at t2. And then change in the t2 value implies change in x.

Alexander R Pruss said...

Right. So in your neat way of putting it, the puzzle is: Why is it that variation in respect of t1 in InterestedIn(x,t1,t2) implies change in x, but variation in respect of t2 does not.

Heath White said...

Ah. Harder! But might it be analytic?

Suppose we define “schmange” as variation along some other dimension of the space-time continuum, e.g. height above sea level. (This is not exactly a dimension of the STC but work with me here.) It turns out I am wider at the waist than at my head. So we might say

Widthof2Ft(heath,h1) but ~Widthof2Ft(heath,h2)

Where h1 and h2 are the heights above sea level of my waist and head respectively. By definition of schmange we have here a case of schmange.

Now suppose we asked the philosophical question, Why is variation on that dimension a case of schmange, rather than a case of change? And the answer, I think, has to appeal to the definition of schmange. By parallel reasoning one might say that change is variation along the time axis (and no other) by definition.

But here is a worry. Suppose we ask, rather, What makes one axis of space-time rather than another a time axis. I am inclined to appeal to our conscious experience here, and also to wonder if we don’t need to say more about time than simply that it is variation along a particular axis of space-time.

Heath White said...

A better way to put this concern: it is obviously unhelpful to define change and time in terms of each other:
(1) Change =df variation along the axis of time
(2) Time =df the axis along which change takes place
One or the other of these concepts needs a different analysis.

Alexander R Pruss said...

I am not particularly worried here about how to define the time axis: I think it's the axis, if there is one, along which causal relations tend to run. I was taking a time axis for granted.

But your spatial analogy is very helpful to me, because it shows that the issue isn't one about change per se, but about variation.

Consider this predicate that we might apply to a single file of people:
InterestedIn(x,d1,d2) iff the person at distance d1 from the front of the file x is interested in an object at distance d2 from the front of the file x.

Then, variation in respect of d1 for a fixed d2 shows that x is spatially non-uniform. But x's variation in respect of d2 for a fixed d1 doesn't show that x is spatially non-uniform (the objects need not be parts of the file, for instance).

So the problem I was giving is a general problem about defining non-uniformity, whether spatial or temporal.

Which means that B-theorists like me can just say: Everybody needs a story about spatial non-uniformity. Whatever story works for that will also work for temporal non-uniformity--we just rotate the spatial non-uniformity story to be along the time axis.

Thanks, Heath: this is really good news.

Alexander R Pruss said...

Let me add: The part theorist (spatial or temporal) can given an explicit account of both temporal and spatial variation. An object varies along an axis provided that equal thickness slices perpendicular to the axis are exactly alike. But I like neither temporal nor spatial slices, so I don't want to take that solution.

Heath White said...

A speculative suggestion: putting your views about change and time together, we have that change is variation along the axis along which causal relations tend to run. You are a fan of the PSR, as I recall, which I’ll gloss here as the idea that all changes have causes. There might be some way to tie change, time, and cause more closely together. E.g. if we can understand causation perhaps we can in some sense dispense with time.

Alexander R Pruss said...

Yes, it would be nice if something like that worked.

Alexander R Pruss said...

Another option worth thinking about is the notion of spatiotemporally located accidents.