Tuesday, January 12, 2021

Change without a plurality of times

Assume presentism. Then Aristotle’s definition of change as the actuality of a potentiality seems to have a serious logical problem. For consider a precise statement of that definition:

  1. There is change just in case there is a potentiality P and an actuality A and A is the actuality of P.

Given presentism, quantification has to be over present items. Thus, the potentiality P and the actuality A are both present items (presumably, accidents of some substance). But if the actuality and potentiality can be simultaneous, then Aristotle’s definition of change does not logically require multiple times: one can have a moment t at which there is an actuality A of a potentiality P, and t could be the only time at which the underlying substance exists. But it seems obvious that if something changes, it exists at more than one time.

One way out of this problem is to deny presentism. I would like that, but Aristotle was probably a presentist.

A second way out is to be careful with tensing:

  1. There is change just in case there was a potentiality P and there is an actuality A and A is the actuality of P.

This makes being the actuality of a cross-time relation. Cross-time relations are awkward for a presentist, but probably unavoidable anyway, so this isn’t so terrible. However, there are other problems with (2). First, it seems that tense depends on time, and for Aristotle, time depends on change, so (2) becomes circular. Second, if we can help ourselves to tense, we can just define change as being in a state in which one previously was not.

I want to suggest a more radical way out of the problem for (1). This more radical way starts by embracing the idea that a substance can change even if it exists only at one time. One way to motivate that is to think of Newtonian physics. Suppose that the universe consists of a number of particles that come into existence at time t0. We may further suppose the state of the Newtonian universe at times after t0 is deterministically caused by the state at t0 (barring things like Norton’s dome). But this is only true if the state of the universe at t0 includes the momenta of the particles, some of which we can assume to be initially non-zero. In other words, the fact about what the momenta are has to be a fact about what the universe is like at t0, in the sense that even if God annihilated the universe right after t0, it would still be true that the particles had the momenta at t0 that they do. Thus, having a non-zero momentum at a time does not require existing at other times. But if one has non-zero momentum, then one is in motion. Hence, being in motion does not require existing at more than one time.

This sounds quite paradoxical, but I think it makes sense if we think of motion as that which explains the succession of states rather than as that which arises from the succession of states.

Next, let’s slightly tweak the English translation of Aristotle’s definition of change:

  1. Change is the actualizing of potentiality.

One can be actualizing a potentiality without ever being in a state of having actualized it. Imagine a substance that is falling, and thus on Aristotle’s account in the process of actualizing the potentiality for being in the center of the universe, and yet which never reaches the center of the universe. At every moment of its existence, that substance is striving to be in the center. That striving, that actualizing of its potential, is what makes it be in motion. It would be in motion even if it only existed for an instant.

One cannot, I take it, have actualized a potentiality while still having the potentiality. But one can be actualizing it while still having it. One is actualing it until one has actualized it, and once one has actualized it, one is no longer actualizing it.

Granted, on this view, change does not entail a plurality of times. It is possible to have a changing universe that exists only for an instant. This complicates the Aristotelian projects of grounding time in change: change is not sufficient for time. Nor does Aristotle say it is. He says that time is a kind of number for change. But a single change may not be enough for number (Aristotle thought that one is not a number: number, for him, requires plurality). Thus, the single-moment universe may have change, but not enough change to have time on Aristotle’s view.


Michael Gonzalez said...

A couple of things, since I am (most days) both a presentist and an Aristotelian:

1) On a non-presentist view (any view in which past states of affairs are actual), in what sense is anything a "potentiality"? Is it not just an actuality "over there"?

2) I applaud and heartily agree with your tensing of the definition as "was a potentiality", and would add that that is manifestly what must be meant! After all, it surely can't be that Aristotle or his successors think there must continue to be a potentiality (which is the only other option).

3) It intuitively seems to me that Aristotle would think the following about non-presentism: The whole 4D world exists changelessly and therefore timelessly. That it is unchangingly different "over there" than "over here" (along whichever coordinates of extension you like) has nothing to do with change, becoming, or time.

Michael Gonzalez said...

Not to beat a dead horse, but this has really got me thinking about the prospects for a proper conception of "change" or "time" on non-presentist, Aristotelian views. Surely we have to say that every moment of time is actual (otherwise, we are presentists), and therefore there are no potentialities and change doesn't exist (and, if we're Aristotelians about it, neither does time).

Am I missing something?

Alexander R Pruss said...

Potentiality as such is not in my ontology. My ontology is an ontology of powers. Some powers are actuated and some powers are not actuated.

Mauricio said...

How does your understanding of powers differ, Isnt a power an active potency?

Alexander R Pruss said...

God has powers (indeed one power, identical with himself) but God has no potencies of any kind.

But if you want to *call* a power an "active potency", that's fine with me.

Mauricio said...

Act is limited by potency but pure act is perfection or subsistent, God is as you said devoided of potentiality but in finite beings this isn’t the case. Your ontology does not include potentiality but powers, are finite being composed because they have multiple powers? I guess I just don’t see why an “ontology of powers” Perhaps it is just a problem of words but I don’t understand why do you prefer the word “power” and “actuation” instead of an ontology of act limited by potency.

Michael Gonzalez said...

So, if an object -- say, a huge Arrakis sandworm -- extends from San Antonio to Houston, and it has the power to vibrate at any point along its body, but only does so in the parts that are in Houston, are we supposed to think that the potentialities (the unactualized powers) in San Antonio are being actualized in Houston? Is this a case of the potentiality co-existing with its actualization? I wouldn't think so. It seems to me that the potentialities of the segments in Houston were actualized in Houston and so are no longer potential, but actual. The potentiality in San Antonio (and in the area between there and Houston) remains unactualized.

Am I incorrect (or using the terms in an inappropriate way)? Even if so, do you at least see what I'm getting at? It doesn't seem right to think that powers of San Antonio segments are what are getting exercised or actualized in the Houston segments....