Monday, May 23, 2016

Accretion of particles

There is good Aristotelian reason to think that when a particle accretes to a substance--say, when I eat it--the particle ceases to exist. For prior to being accreted, it seems the particle is an independent substance. But a substance can't have substances as parts. And it seems absurd to think that the particle would change from being a substance to a non-substance.

But the view that post-accretion the object that is now a part of the substance is distinct from the object that was accreted is counterintuitive. Here I want to run a partners in crime response to this by showing how a very different and yet fairly mainstream set of assumptions leads to the same counterintuitive conclusion. This should help make that conclusion a little less counterintuitive.

To that end, assume reality is four-dimensional, that objects have lots of temporal parts and that parthood is transitive. This is a fairly commonly accepted set of assumptions. Now suppose I ate a particle x. I will argue that the particle perished in the process. For suppose that x is still a part of me. Let u be a temporal part of x prior to the accretion. Then x is a part of me. But u is a part of x. So by transitivity of parthood, u is a part of me. But that's absurd. So we must deny that x is a part of me on this set of assumptions, too. Hence, this set of assumptions leads to the same conclusion that it is impossible for an object to exist as not a part of something and then continue to exist as a part of that object.

9 comments:

entirelyuseless said...

This is a weak argument. If something becomes a part of something else, and objects have temporal parts, then it is only a temporal part which becomes a part, not the whole.

Alexander R Pruss said...

Right: And hence the particle itself does not persist as part of the substance, just as on the Aristotelian story.

There is a difference between the two stories, too. On the 4D-temporal-parts story, the particle continues to survive, but not as a part of the substance it is accreted to, while on the Aristotelian story it perishes. I don't know which is more or less counterintuitive.

Christopher Michael said...

You are equivocating on “part” again! :-) Integral parthood isn't transitive with temporal parthood. So x is an integral part of you, and u is a temporal part of x, but nothing follows from this.

Alexander R Pruss said...

On a four-dimensionalist picture, there is no significant difference: both are just four-dimensional chunks (typically--though a really thin slice might be three-dimensional) of a four dimensional object.

Christopher Michael said...

If you go that route and deny the distinction, then I would be inclined, as I think most would, to deny that x is part of you, since there are 4D chunks of x that aren't part of you. So you either equivocate to get the transitivity going, or else the intuitive support for x being a part of you dissolves. The intuitive support for x being a part you came from treating x as a 3D object totally present now. If you give that up to amalgamate integral and temporal parts, the intuitive support for your premise goes with it, no?

Alexander R Pruss said...

Christopher:

But then our 4Der ends up agreeing with the Aristotelian that it never happens that a particle exists first as not a part of a substance and then as part of that substance.

William said...

I'm confused about the use of time-unspecified statements in the 4D case.

If I am the 4Der, and I say "there is rain outside," can this be considered true from the 4D perspective if it rained outside last week, even if it has not rained today?






Alexander R Pruss said...

Well, in ordinary contexts statements are relativized to some interval of times containing the statement. Thus, "There is rain outside" can be read as: "Let T be a relevantly small interval of times containing this sentence. The manifold contains rain outside within T."

But in more philosophical contexts, such relativization is gone.

= MJA said...

Truth accretes everything, absolutely and equally. =