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:

2. 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:

3. 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.

Two beauties

In a number of cases of beauty, beauty is doubled up: there is the beauty in an abstract state of affairs and there is the beauty in that state of affairs being real, or at least real to an approximation. For instance, the mathematics of Relativity Theory is beautiful in itself. But that it is true (or even approximately true) is also beautiful.

This shows an interesting aspect of superiority that painting and sculpture have over the writing of novels. The novelist discovers a beautiful (in a very broad sense of the word, far broader than the “pretty”) abstract state of affairs, and then conveys it to us. But the painter and sculptor additionally doubles the beauty by making something real an instantiation of it, and it is by making that instantiation real that they convey it to us. The playwright is somewhere in between: the beautiful state of affairs is made approximately real by a play.

The above sounds really Platonic. But we can also read it in an Aristotelian way, if we understand the abstract states of affairs as potentialities. The painter, sculptor and novelist all discover a beautiful potentiality. The painter and sculptor brings that potentiality to actuality. The novelist merely points it out to us.

"In the right way"

When I was in grad school, we were taught that one should abandon all hope of solving “in the right way” problems, such as the problem of how exactly an intention has to result in an action in order for the action to be done from that intention.

I think that with a robust metaphysics of causation, the problem is soluble.

Solution 1: Causal powers have a teleology: to produce a certain effect in a certain way. That teleology is metaphysically written into the causes. The “in the right way” condition may be infinitely complex, but it has a metaphysical home: it is found in the causal power. What makes it be the case that William James’ mountaineer who intended to kill his buddy by dropping the rope, and then dropped the rope because of the nervousness resulting from the intention did not intentionally drop the rope is because the outcome of events is a mismatch to the description in the teleology of the causal powers constituting the intention.

Solution 2: It is a Thomistic maxim that the effect is the actuality of the cause qua cause. This maxim I suspect needs a qualification: the proper effect—the one that happens in the right way—is the actuality of the cause qua cause. So now we have a neat and simple criterion for when a cause C has caused an effect E in the right way: this happens precisely when E is the actuality of C qua cause. (See here for more discussion.)

I think the reason we were taught to eschew the problem of “in the right way” conditions was because of an implicit reductionistic metaphysics. If we think that the cause is just an arrangement of particles, it is hopeless to have a distinction between proper and improper effects.

Moving from world to world

If the A-theory of time is true, then it is (metaphysically) possible that the year 2010 have the objective property P of presentness and it is also possible that the year 2019 have P. For it is true that 2019 has P, and what is true is possible. But by the same token in 2010 it was true that 2010 has P, and so it was possible that 2010 have P. And what is metaphysically possible does not change. So even now it is possible that 2010 have P.

But a proposition is possible if and only if it is true at some possible world. Thus, if the A-theory of time true, there are possible world where 2010 has P and possible worlds where 2019 has P, and in 2010 we lived in one of the worlds where 2010 has P, while now in 2019 we instead live in a world where 2019 has P.

Consequently, given the A-theory of time, what world we inhabit continually changes.

This seems counterintuive. For now it looks like caring about what will happen is caring about what happens in some merely possible world.

If open futurism is true, then there are possible worlds that can't ever be actual

Assume open futurism, so that, necessarily, undetermined future tensed “will” statements are either all false or all lack truth value. Then there are possible worlds containing me such that it is impossible for it to be true that I am ever in that world. What do I mean?

Consider possible worlds where I flip an indeterministic fair coin on infinitely many days, starting with day 1. Among these worlds, there is a possible world w_H where the coin always comes up heads. But it is impossible for it to be true that I am in that world. For that I ever am in that world entails that infinitely many future indeterministic fair coin tosses will be heads. But a proposition reporting future indeterministic events cannot be true given an open future. So, likewise, it cannot be true that I am ever in that world.

But isn’t it absurd that there be a possible world with me such that it is impossible that it be true that I am in it?

My presence is an unnecessary part of the above argument. The point can also be put this way. If open futurism is true, there are possible worlds (such as w_H) that can’t possibly ever be actual.

Four grades of normative actuality

Here are four qualitatively different grades of the normative actuality of a causal power:

0. Normative possession (zeroeth normative actuality): x has a nature according to which it should have causal power F. (An adult human who lacks sight still has normative possession of vision.)
1. First normative actuality: x has a normal (for x’s nature) causal power F. (The human with closed eyes has first actuality of vision.)
2. Second normative actuality: x exercises the normal causal power F. (The human who sees has second actuality of vision.)
3. Full (third) normative actuality: x exercises the normal causal power F and achieves the full telos of the causal power. (The human who gains knowledge through seeing has full actuality of vision.)

What I call normative possession is close to Aristotelian first potentiality, but is not exactly the same. The newborn has first potentiality for speaking Greek—namely, she is such that eventually she can come to have the power of speaking Greek—but she does not have normative possession of speaking Greek, since human nature does not specify that one should be able to speak Greek. However, the newborn does have normative possession of language in general.

I think each of the four grades of normative actuality is non-instrumentally valuable, and that the grades increase in non-instrumental value as one goes from zero to three.

Grade zero can carry great value, even in the absence of higher grades. For instance, normative possession of the causal powers constitutive of rational agency makes one be a person (or so I say, following Mike Gorman). And it is very valuable to be a person. This may, however, be a special case coming from the fact that persons have a dignity that other kinds of things do not; maybe the special case comes from the fact that persons need to have a fundamentally different kind of form from other things. For other causal powers, grade zero doesn’t seem to carry much value. Imagine that you found out that (a) normal Neanderthals have the ability to run five hundred kilometers and (b) you are in fact a Neanderthal. By finding out these things, you’d have found out that you have normative possession of the ability to run 500km—but of course, you have no actual possession of that ability. The normative possession is slightly cool, but so what? Unless one has a higher grade of actuality of this ability, simply being the kind of thing that should have that ability does not seem very valuable. And the same is true for abilities more valuable than the running one: imagine that Neanderthals turn out to have Einstein-level mathematical abilities, but you don’t. It would be a bit cool to be of the same kind as these mathematical geniuses (maybe this is a little similar to how it’s cool for a Greek to be of the same nation as Socrates), but in the end it really doesn’t count for much.

Grade one is also valuable even in the absence of higher grades. It makes for the difference between health and impairment, and health is valuable. But I can’t think of cases where first normative actuality carries much non-instrumental value. Imagine that I know for sure that I am going to spend all my life with my eyes tightly closed (e.g., maybe I am hooked up to machine that will kill me if I attempt to open them). It is objectively healthier that I have sight than that I do not. But it seems rational to sacrifice all of my sight for a slight increase in the acuity of touch or hearing, given that I can actually exercise touch and hearing (second or third actuality) while I can’t exercise sight. Even slight amounts of second or third normative actuality seem to trump first normative actuality.

Grade two seems quite valuable, even absent grade three. Here, examples can be multiplied. Sensory perception that does not lead to knowledge can still be well worth having. Sex is valuable even absent successful reproduction. Running on a treadmill can have a value even if does not achieve locomotion. While it seems to be generally true that a great amount of first actuality can be sacrificed for a small amount of second actuality, this is not as generally true with second and third actuality. One might reasonably prefer to run two kilometers on a treadmill—even for the non-instrumental goods of the exercise of leg muscles—instead of running two meters on the ground.

All of the lower grades of normative actuality derive their value in some way from the value of full normative actuality. But full normative actuality does not always trump grade two. It seems to generally trump grade one. Grade zero is special: most of the time it does not seem to carry much value, but it does in the case where it constitutes personhood. (Maybe, though, the dignity of personhood shouldn’t be thought of in terms of value.)

Hiddleston's review of Actuality, Possibility, and Worlds

NDPR has a review of my Actuality, Possibility, and Worlds by Eric Hiddleston.  I think it's quite a helpful review--the concerns about my account are powerful and interesting.

This post is a very rough bunch of responses to Hiddleston, and will not be comprehensible without reading his review.

I am inclined to endorse some version of the "externalist" way out that Hiddleston gives.  I think this will damage at least one of my arguments against Platonism, the one that says that opponents of Platonism are "horribly confused" if Platonism is true. But Hiddleston is right that that's a bad argument.

I think Hiddleston doesn't give enough credit to my dogs argument against Platonism.  There, I am imagining that the Platonist heaven is augmented with the necessity of there being no dogs, but all earthly stuff is unchanged.  I claim in the book that nonetheless dogs would remain possible.  My line of thought behind that was that dogs would remain possible, because they would remain actual, and the actual is possible, no matter what the Platonist heaven says.  I think Hiddleston's Little-P = Big-P position doesn't help here.

(It occurs to me, by the way, that the Platonist could have a theory that escapes my dogs argument as it stands in the book. Here's the theory. The primitive property is mere possibility. Possibility is then defined in terms of mere possibility: a proposition is possible provided that it is either true or merely possible. But I think this version still has a problem. The original Platonic version has the puzzle of why it is that actuality implies possibility. This version doesn't have that problem. Instead it has the problem of why it is that that mere possibility implies non-actuality.)

Hiddleston also worries a lot about Euthyphro-type questions, like:

• (E1) Why should God be incapable of bringing about really impossible propositions, such as contradictory ones?
• (E2) Why should God be capable of bringing about really possible propositions?

I think there is a neat counter to the "contradictory ones" part of E1 that favors my view over other views. The following seems true to me:

1. If, per impossibile, God or any other agent were capable of bringing about a contradictory proposition, that proposition would be possible.

This suggests to me that what agents can bring about is actually more fundamental than what is contradictory. Notice that the plausibility of (1) highlights a difference between my view and divine command theory. In the case of divine command theory, the following seems false:

2. If, per impossibile, God were to command a horrendous deed, that horrendous deed would be obligatory.

(But see this paper of mine for a more detailed discussion of whether (2) is a good objection to divine command theory.)

I do think Hiddleston's question about what explains why God can do contradictory things is a good and difficult question, but I don't think they're quite species of the Euthyphro problem. I think I can say that there just does not exist any being with the power to bring about contradictory propositions. This is in need of no more grounding than the fact that there are no unicorns--it's just a negative existential. Is it in need of an explanation? My official line on the PSR restricts it to contingent truths. But maybe there still is an explanation of it in terms of some deep facts about the divine nature (maybe its beauty, say). Maybe Hiddleston's best bet here would be to push me in a way that Josh Rasmussen has done: I can't explain why God can't create square circles, just as the Platonist can't explain why everything that's actual is also possible, and so I don't have an advantage over the Platonist here. I don't know exactly what to say here, but I think one difference is with regard to per impossibile counterfactuals.

3. If dogs existed but the Platonic heaven didn't say that they were possible, dogs would still be possible.
4. If God were capable of creating a square circle, square circles would be possible.

I think (4) favors my view and (3) disfavors Platonism. But I am not happy to hang too much on per impossibile counterfactuals.

As for (E2), I don't feel the force of that. First of all, the primary view doesn't mention God: it's quantified over all agents. So the modified question is:

• (E2b) Why should every really possible proposition be such that there is an agent who can bring it about (or, more precisely, bring about a chain of causes leading to it)?

I don't feel much intuitive force to this question. Maybe I've just been thinking along the lines of my view for too long. I am tempted to say that the question is exactly like: "Why should every sample of water contain hydrogen atoms?" That's what Hiddleston labels the externalist way out, so I guess I am with him on that, and I wish I was explicit about that in the book.