Aristotelian abstraction

On the Aristotelian account of abstraction, we abstract the forms of things via perception. But here is a problem. First of all, we sometimes have better knowledge of things not perceived than of things perceived. Let’s say you read a detailed scientific book about pangolins, though you’ve never encountered one, while I once saw a koala in a zoo, but don’t much know anything more about them than that they are cute marsupials. It seems quite problematic to say I have the form of the koala in my mind, but you do not have the form of the pangolin. For that would make the mental possession of the form of the thing an unimportant flourish to what really epistemically matters, since clearly you are better off epistemically for reading the book about pangolins than I am for seeing the koala.

Of course, presumably, the author of the pangolin book presumably saw the pangolin. But that doesn’t seem to matter much, either. There are many dinosaur species where the paleontologist knows more about the species than I know about koalas, and yet no human ever perceptually interacted with a dinosaur, but typically only with minerals that have displaced their carcasses.

What should someone committed to the Aristotelian story about abstraction say? Two options come to mind, a modest and an expansive one.

Modest option: It really doesn’t really matter much epistemically whether one has the form of a pangolin or a koala in one’s mind. What matters is the propositional knowledge. However, it is essential to our possession of the propositional knowledge that our thoughts have intentionality, that they refer to the world. And it is crucial to securing intentionality that we have Aristotelian abstraction at the interface between the world and the mind. The triceratops expert’s intentionality with respect to triceratopses is derivative from the causal chain from triceratopses to their corpses to their fossils to the light reflecting from the fossils into the expert’s eyes to (eventually somehow) the expert’s thoughts. Where the causal chain crosses from the world to the mind, we need a transmission of form to ensure intentionality for the whole chain. Maybe the transmission happens when the minerals that have replaced the bones transmit their mineral forms to the expert’s mind, in some mysterious way mediated by the light.

Expansive option: Everything in the world carries the forms of everything nondivine that is causally upstream from itself. The triceratops corpse somehow has the form of the triceratops in it, and so do the bones of the triceratops, and so do the minerals that replace the bones, and so does the light modulated by reflection from the minerals, and so do the electrical impulses in the nerves from the retinal receptors to the brain. It is easier to extract the form when it comes from seeing a live koala than when it comes from seeing fossils, so that a layman can do the former while the scientist is needed to do the latter. Similarly, when you read a book about pangolins, the ink on the page, being causally modulated by the author’s knowledge, carries the form of the pangolin (in addition to any forms naturally contained in the ink, say those of the particles constituting the ink).

Medievals already said something like this about the modulated light, so it’s just a matter of extending the story. And while the problem I am concerned about is one that does not require any science or technology beyond what the medievals had—the medievals knew about the gaining of expertise from books (if anything, they might have overestimated it!)—in a modern setting we it feels like an Aristotelian has to do this. After all, it is hard to deny that one can gain the same kind of knowledge of koalas by looking at them through high-end augmented reality goggles as from directly seeing them with our eyes. Thus, on a form-transmission story, the electrical potentials of the capacitors in the computer memory in the goggles have to somehow carry the form of the koala. But given the many ways that computer memory can be realized (think of magnetized rings versus capacitors versus markings on a CD), it seems plausible that any effect will have to have to be admitted to carry the form of its cause. It is tempting to say the form is only found in substances where there is sufficient data to reconstruct significant information about the causally-upstream object the form is of, but I think is not tenable. Presumably each bacterium is a substance, and we could have a type of biological memory in augmented reality glasses where each bit of information is stored in a different bacterium.

This story coheres very nicely with the essentiality of origins. It is a kind of a reversal of the principle of proportionality of causation on which the reality of the effect is actually or eminently found in the cause: the formal reality of a cause is found in the effect. I think it’s a defensible story. But I also find it hard to believe.

Virtues in heaven

Here are two Aristotelian theses:

1. Complete human flourishing requires the exercise of all the human virtues.

2. Courage is a human virtue.

Add a highly plausible thesis that likely everyone will accept:

3. The exercise of courage requires apparent or real danger.

Now add some theses that a Christian will surely accept:

4. In heaven, there are no apparent danger.

5. In heaven, there is no real danger.

6. In heaven, there is complete human flourishing.

Contradiction!

I find it nearly impossible to deny 3-6. That leaves 1 and 2.

One move available to the Christian Aristotelian is to weaken 1. Perhaps complete human flourishing only requires the exercise of fundamental virtues, and courage is a non-central virtue. But traditionally fortitude also counts as a cardinal virtue, cardinal seems to imply fundamental, but fortitude is a virtue of dealing with evil—whether in the form of real or apparent danger, or of suffering, or of hardship, while there is no evil in heaven. So the problem comes back for fortitude. One solution is to deny the traditional cardinal virtues as being fundamental, and insist that the only fundamental virtue is love. Fortitude is just a central situational way for love to manifest.

Another move is simply to deny 1 altogether, of course, denying the whole link between virtues and flourishing. This is probably too radical.

And of course one might just deny 2. The most plausible move would be to say that only love is a virtue.

Aristotle on sexual reproduction

Infamously, Aristotle thought that in animal reproduction (including the human case) the male contributed form and the female the matter.

I think it would have made for a neater metaphysics if he thought it was the other way around. For his story involves the complication that there are three ways that a form of an animal exists:

1. as informing a piece of matter and making it an animal of the relevant type

2. as being transmitted by semen, without turning the semen into an animal of the relevant type

3. as being found abstracted in an intellect thinking about the animal.

But if he supposed instead that the form was contributed by the female, he could have said that the semen contributes a small packet of initial matter for the organism and the female’s form works upon that packet in utero. At no point in this process is there a form that is separated out from an organism with that form (such a case will still have to happen when an intellect abstracts that form from matter), and so case (b) disappears, along with all the consequent metaphysical complications to the system.

It’s not clear to me how exactly Aristotle handled this. In Generation of Animals, he talks of the “power of the male residing in the semen”. This sounds like a kind of virtual presence of the form of the animal, a presence of the form as implicit in a causal power. It would be nice to be able to skip this complication. (Granted, Aristotle would still have a similar problem with regard to his view of delayed ensoulment, on which the offspring of a human is first a kind of plant, then gains an animal form, and then gains a rational form, for then the plant has a power to make an animal and the animal a human.)

I guess one might try to find Aristotle a way of reducing (b) to (a) while making the male still be the contributor of form as follows. One might think the semen is a living part of the male’s body, metaphysically like other parts, but separated spatially from the rest of the body (given what we know about how we are made of molecules, it is clear that spatial separation cannot be a bar to bodily unity). Thus, the semen would still be informed by the father’s form, in exactly the same way that the father’s ear or heart is. But this would have a downside. Suppose the father apparently died while the semen continued living, as does happen. Then it seems that the father would not have actually died—instead, his body would be reduced to a packet of semen, and he will have literally gone to seed. This seems absurd.

Why did Aristotle not go for the female as source of form solution, which is so neat metaphysically? Maybe for two reasons. First, the semen obviously could only contribute very little matter. (But then why not suppose that the initial organism is very small?) Second, sexism.

Aristotle on flourishing

Aristotle thinks that the flourishing of a kind of organism is primarily defined by the excellent exercise of the distinctive functions of the kind. This works great for us: our flourishing is primarily given by the excellent exercise of rationality.

But it doesn’t, I think, work well for other organisms. Think of cats and bears. It seems plausible that their primary flourishing is found in functions that they have in common, such as growth, reproduction, sensation, hunting, feeding, etc. They do have significant distinctive features, but these distinctive features are not central constituents of their flourishing.

One might take the above observations to be evidence for the three-species view of organisms, that there are three metaphysical species: plants, brute animals, and rational animals. But I think this runs into a problem with plants. For the flourishing of a plant is presumably constituted by growth and reproduction, which plants have in common with brute and rational animals.

I think we should reject the emphasis on distinctiveness in flourishing. Instead, we should probably say that the nature of an organism also specifies a prioritization in the functions of the organisms.

Discrete time and Aristotle's argument for an infinite past

Aristotle had a famous argument that time had no beginning or end. In the case of beginnings, this argument caused immense philosophical suffering in the middle ages, since combined with the idea that time requires change it implies that the universe was eternal, contrary to the Jewish, Muslim and Christian that God created the universe a finite amount of time ago.

The argument is a reductio ad absurdum and can be put for instance like this:

1. Suppose t₀ is the beginning of time.

2. Before t₀ there is no time.

3. It is a contradiction to talk of what happened before the the beginning of time.

4. But if (1) is true, then (2) talks of what is before the beginning of time.

5. Contradiction!

It’s pretty easy to see what’s wrong with the argument. Claim (2) should be charitably read as:

• Not (before t₀ there is time).

Seen that way, (2) doesn’t talk about what happened before t₀, but is just a denial that there was any such thing as time-before-t₀.

It just struck me that a similar argument could be used to establish something that Aristotle himself rejects. Aristotle famously believed that time was discrete. But now argue:

6. Suppose t₀ and t₁ are two successive instants of time.

7. After t₀ and before t₁ there is no time.

8. It is a contradiction of what happened when there is no time.

9. But if (7) is true, then (7) talks of what is when there is no time.

10. Contradiction!

Again, the problem is the same. We should take (7) to deny that there is any such thing as time-after-t₀-and-before-t₁.

So Aristotle needed to choose between his preference for the discreteness of time and his argument for an infinite past.

What if there is no tomorrow?

There are two parts of Aristotle’s theory that are hard to fit together.

First, we have Aristotle’s view of future contingents, on which

1. It is neither true nor false that tomorrow there will be a sea battle

but, of course:

2. It is true that tomorrow there will be a sea battle or no sea battle.

Of course, nothing rides on “tomorrow” in (1) and (2): any future metric interval of times will do. Thus:

3. It is true that in 86,400,000 milliseconds there will be a sea battle or not.

(Here I adopt the convention that “in x units” denotes the interval of time corresponding to the displayed number of significant digits in x. Thus, “in 86,400,000 ms” means “at a time between 86,399,999.5 (inclusive) and 86,400,000.5 (exclusive) ms from now.”)

Second, we have Aristotle’s view of time, on which time is infinitely divisible but not infinitely divided. Times correspond to what one might call happenings, the beginnings and ends of processes of change. Now which happenings there will be, and when they will fall with respect to metric time (say, 3.74 seconds after some other happening), is presumably something that is, or can be, contingent.

In particular, in a world full of contingency and with slow-moving processes of change, it is contingent whether there will be a time in 86,400,000 ms. But (3) entails that there will be such a time, since if there is no such time, then it is not true that anything will be the case in 86,400,000 ms, since there will be no such time.

Thus, Aristotle cannot uphold (3) in a world full of contingency and slow processes. Hence, (3) cannot be a matter of temporal logic, and thus neither can (2) be, since logic doesn’t care about the difference between days and milliseconds.

If we want to make the point in our world, we would need units smaller than milliseconds. Maybe Planck times will work.

Objection: Suppose that no moment of time will occur in exactly x₁ seconds, because x₁ falls between all the endpoints of processes of change. But perhaps we can still say what is happening in x₁ seconds. Thus, if there are x₀ < x₁ < x₂ such that x₀ seconds from now and x₂ seconds from now (imagine all this paragraph being said in one moment!) are both real moments of time, we can say things about what will happen in x₁ seconds. If I will be sitting in both x₀ and x₂ seconds, maybe I can say that I will be sitting in x₁ seconds. Similarly, if Themistocles is leading a sea battle in 86,399,999 ms and is leading a sea battle in 86,400,001 ms, then we can say that he is leading a sea battle in 86,400,000 ms, even though there is no moment of time then. And if he won’t lead a sea battle in either 86,399,999 ms or in 86,400,000 ms, neither will he lead one in 86,400,000 ms.

Response: Yes, but (3) is supposed to be true as a matter of logic. And it’s logically possible that Themistocles leads a sea battle in 86,399,999 ms but not in 86,400,001 ms, in which case if there will be no moment in 86,400,000 ms, we cannot meaningfully say if he will be leading a sea battle then or not. So we cannot save (3) as a matter of logic.

A possible solution: Perhaps Aristotle should just replace (2) with:

4. It is true that will be: no tomorrow or tomorrow a sea battle or tomorrow no sea battle.

I am a bit worried about the "will" attached to a “no tomorrow”. Maybe more on that later.

Aristotle and Aquinas' Third Way

Aristotle seems to have thought that the earth and the species inhabiting it are eternal. This seems extremely implausible for reasons that should have been available to Aristotle.

It is difficult to wipe out a species, but surely not possible: all it takes is to kill each of the finitely many individuals. Given a species s that cannot have more than n members, and given a long enough time, we would expect there to be a very high probability that all the members of s would have died out during some hour due to random events. Given any finite number of species each with a bound on how many members it can have, and given a long enough time, we would expect with very high probability that all the members would die off.

Now there is a finite limit on how many species there are on earth (as Aristotle knew, the earth is finite), and a finite limit on how many members the species can have (again, the earth is finite). So we should have expected all the species that existed some long amount of time ago to have died out.

The above provides an argument that if the world is eternal, new species can arise. For if new species can’t arise and the world is eternal, then by now there should have been no species left.

How could Aristotle have gotten out of this worry without rejecting his thesis about the eternity of the earth?

One way be to suppose a powerful protector of our ecosystem that would make sure that the species-destroying random events never happen. This protector would either itself have to be sufficiently powerful that it would not be subject to the vicissitudes of chance, or there would have to be an infinite (probably uncountably infinite!) number of such protectors.

Another option would be for Aristotle to reject his thesis that there is only one earth (which was based on theory of gravitation as attraction to the center of the universe: if there were more than one earth they would have both collapsed into the center of the universe by now).

If there were infinitely many earths, then it’s perhaps not so crazy to think that some earth would have lucked out and not had its species die out. Of course, this would not only require Aristotle to reject his thesis that there is only one earth, but also the finitist thesis that there cannot be an infinite number of co-actual things. (Interestingly, given the plausibility that any given species has probability one of dying out given infinite time, and given the countable additivity of probabilities, this way out would require not merely infinitely many earths, but an uncountable infinity of earths. Assuming an Archimedean spacetime for our universe, it would require a multiverse.)

In any case, Aristotle’s commitment to new species not coming into existence (or at least new species of interesting critters; he may be OK with worms coming into existence) is in tension with what he says about the earth’s eternity.

Change and matter

Aristotle’s positing matter is driven by trying to respond to the Parmenidean idea that things can’t come from nothing, and hence we must posit something that persists in change, and that is matter.

But there two senses of “x comes from nothing”:

1. x is uncaused

2. x is not made out of pre-existing materials.

If “x comes from nothing” in the argument means (1), the argument for matter fails. All we need is a pre-existing efficient cause, which need not be the matter of x.

Thus, for the argument to work, “x comes from nothing” must mean (2). But now here is a curious thing. From the middle ages to our time, many Aristotelians are theists, and yet still seem to be pulled by Aristotle’s argument for matter. But if “x comes from nothing” means (2), then theism implies that it is quite possible for something to come from nothing: God can create it ex nihilo.

There are at least two possible responses from a theistic Aristotelian who likes the argument for matter. The first response is that only God can make things come from nothing in sense (2), and hence things caused to exist by finite causes (even if with God’s cooperation) cannot come from nothing in sense (2). But there plainly are such things all around us. So there is matter.

Now, at least one theistic Aristotelian, Aquinas, does explicitly argue that only God can create ex nihilo. But the argument is pretty controversial and depends on heavy-duty metaphysics, about finite and infinite causes. It is not just the assertion of a seemingly obvious Parmenidean “nothing comes from nothing” principle. Thus at least on this response, the argument for matter becomes a lot more controversial. (And, to be honest, I am not convinced by it.)

The second and simpler response is to say that it’s just an empirical fact that there are things in the world that don’t come from nothing in sense (2): oak trees, for example. Thus there in fact is matter. This response is pretty plausible, but can be questioned: one might say that we have continuity of causal powers rather than any matter that survives the generation.

Finally, it’s worth noting that I suspect Aristotle misunderstands the Parmenidean argument, which is actually a very simple reductio ad absurdum:

3. x came into existence.
4. If x came into existence, then x did not exist.
5. So, x did not exist.
6. But non-existence is absurd.

The crucial step here is (6): the Parmenidean thinks the very concept of something not existing is absurd (presumably because of the Parmenidean’s acceptance of a strong truthmaker principle). The argument is very simple: becoming presupposes the truth of some past-tensed non-existence statements, while non-existence statements are always false. Aristotle’s positing matter does nothing to refute this Parmenidean argument. Even if we grant that x’s matter pre-existed, it’s still true that x did not exist, and that’s all Parmenides needs. Likewise, Aristotle’s famous actuality/potentiality distinction doesn’t solve the problem. Even if x was pre-existed by a potentiality for existence, it’s still true that x wasn’t pre-existed by x—that would be a contradiction.

To solve Parmenides’ problem, however, we do not need to posit matter or potentiality or anything like that. We just need to reject the idea that negative existential statements are nonsensical. And Aristotle expressly does reject this idea: he says that a statement is true provided it says of what is that it is or of what is not that it is not. Having done that, Aristotle should take himself as done with Parmenides’ problem of change.

Two implications of Aristotle's theory of time and locality

Aristotle thinks that time is infinitely subdivisible but only finitely subdivided. Thus, there will be moments t₁ < t₂ such that there is actually no moment between t₁ and t₂, but there could have been. What would make there have been a moment between t₁ and t₂? Presumably, this would be if something happened strictly between those times. Time is the measure of change, so if, say, some object started or finished changing at a time between t₁ and t₂, then there would have been a time between them, say t_1.5.

But here is a curious consequence. Suppose that in the actual world, w₀, I am living from t₁ to t₂, which are so close together in time that there are no time between them. But in another world, t₁, where everything in our galaxy was the same, in some other galaxy indeterministically an event happened between t₁ and t₂, namely at t_1.5. Then:

• In w₀, it is not true that I exist at t_1.5 (because there is no t_1.5).

• In w₁, it is true that I exist at t_1.5.

And what is responsible for that difference is that indeterministic event in another galaxy. So it seems that something in another galaxy is responsible, in a faster-than-light way, for whether I exist at t_1.5. In other words, the Aristotelian theory seems to imply highly non-local influences.

There is perhaps a way out. Perhaps fundamentally time sequences are internal to substances. Thus, I have a time sequence internal to me, you have one internal to you, and things in that other galaxy have time sequences internal to them. There are, additionally, connections (probably causal ones) between objects that allow one to form a global time sequence. That global time sequence will include moments that don’t correspond to any moments internal to me. For instance, it will include moments earlier than my conception, but more interestingly, it could be that for me t₂ immediately succeeds t₁, but something else has a time that fits between t₁ and t₂, and so global time could have times corresponding to t₁ and t₂, but also some intermediate time between them.

The difference between w₀ and w₁, then, would not be a difference in my internal time sequence. What happened in that other galaxy wouldn’t affect my internal time except perhaps once the light from that galaxy could reach me.

On this account, while it is true that I exist at t_1.5, my existing at t_1.5 is not an intrinsic feature of me. The difference between my existing at t_1.5 in w₁ and my not existing at t_1.5 in w₀ is a merely Cambridge difference.

I think it is hard to make this story fit with presentism. When t_1.5 is present, then it had better be intrinsic to me that I exist presently, i.e., at t_1.5. A similar point applies to growing block.

Maybe, though, there is a way of making this story fit with a moving spotlight A-theory. We could suppose that at global time t_1.5, what is “lit up” by the spotlight is the time t_1.5 for the thing in the other galaxy that has something happening to it then, but for me what is lit up is the entire interval between t₁ and t₂.

If I am right, then

1. Locality, and

2. Aristotle’s theory of time

seem to imply:

3. Internal time is primary

4. Eternalism is true.

Instrumental and non-instrumental goods

Aristotle writes at times as if the fact that something is non-instrumentally good for one makes it a greater good than merely instrumental goods. That’s surely false. Among the non-instrumental goods are many quite trivial goods: knowing how many blades of grass there are on one’s front lawn, enjoying a quick game of Space Invaders, etc.

Risability

Aristotle says that a necessary accident of the human being is risability—the capability for laughter. As far as I can tell, necessary accidents are supposed to derive from the essence of a thing. So, how do we derive risability from the essence of the human being?

Here’s an idea. The essence is to be a rational animal. A rational being reflects on itself. But to have an animal that is simultaneously rational—that’s objectively funny. Thus, a rational being that is an animal is always in a position to discover something objectively funny, namely itself. And it just wouldn’t be rational not to laugh at that funny thing!

Saints and faith

There are many ways of life that people claim to be virtuous. A central thesis of Aristotelian ethics is:

1. The virtuous person knows what is the virtuous human form of life, at least insofar as this is relevant to her own circumstances.

She knows this by living virtuously, which enables a from-the-inside appreciation of the virtue of the virtuous life she lives. This is a mysterious thing, but it means that the virtuous person does not need to worry sceptically about the fact that other people disagree with her about this way of life being virtuous (maybe they say to her: “You should have a stronger preference for people of your country over foreigners”, and she just knows that her preference should not be stronger). These other people are not virtuous, and hence lack that from-the-inside view on what it is to live a virtuous life, and hence they are not her epistemic peers with respect to virtue.

Suppose we accept (1). Now imagine that Therese leads a kind of life L that is deeply intertwined with a particular religion R, in such a way that clearly L would be unlikely to be virtuous if R were false, but is very likely to be virtuous if R is true.

It is easy to imagine cases like this. Perhaps most religious and non-religious views other than R would object to significant aspects of L—perhaps, L includes forms of activism that R praises but most other religious and non-religious views look down on, or lacks forms of activity that most religious and non-religious views other than R think are required for a fulfilling human life. The life of a good contemplative Catholic nun is like that: most non-Catholic views will see it as a waste.

Suppose, further, that Therese is in fact virtuous. Then she knows that L is virtuous, and this gives her significant evidence that R is true because of how much L is bound up with R.

One may have a Christian worry about what I just said. What about humility? Would Therese know that she is living a virtuous life? But she might: true self-insight is compatible with humility. However, my argument does not assume that Therese knows that she is living a virtuous life. All that (1) says is that Therese knows that L is a virtuous life—but she need not know that she is in fact living out L. She knows the model of the virtuous life by living it, but she may not know that she is living it. (Aristotle wouldn’t like that.)

Now, suppose that Therese’s virtue in fact comes from God’s grace. Then Therese has a deep reason to know R on the basis of grace: the grace leads to virtue, and the virtue leads to knowledge of what is virtuous.

So, we have a model for how saints of the true religion can know the truths of their faith, because their radical forms of life are so tightly bound up with their religion that their knowledge that this way of life is virtuous (a knowledge compatible with certain ways of agonizing about whether they are in fact living that way) yields knowledge of their religion.

Can this help those of us who are not saints? I think so. It is possible to see the virtue of another’s form of life even when one does not have much virtue. And then the tight intertwining between the saint’s life of virtue and the saint’s religion provides one with evidence of the truth of their religion.

(Note the similarities to the line of thought in van Inwagen's deeply moving "Quam Dilecta".)

Is this immune to sceptical worries in the way that the virtuous person’s knowledge of the virtue of the form of life she follows is? I don’t know. I think there is room for some proper-functionalism here: we may have a faculty of recognition of a virtuous form of life.

Note, finally, that there are multiple virtuous forms of life, some less radical than others. The more radical ones are likely to be more tightly bound up with their religion, and hence provide more evidence—even if they are not necessarily more virtuous. Perhaps the difference is in how specific a religion is testified to by the virtue of the way of life. Thus, the contemplative cloistered saint’s life may give strong evidence of Catholicism, or at least of the disjunction of Catholicism and Eastern Orthodoxy, while the life of a married saint as seen from the outside may “only” give strong evidence of Christianity.

Reid's critique of Aristotelian accounts of perception

Reid thinks that the Aristotelians make the same mistake as the Lockeans and Berkeleians: they all think that the phenomenal qualities or “ideas” (in the Lockean sense) in our minds are similar to the properties of physical objects. Thus, the sensation of hardness when I press my hand on the table is supposed to be similar to the physical hardness of the table. But Reid thinks that a bit of reflection shows that the mental entity is quite different from the physical entity.

Presumably, the reason the Aristotelian is accused of this mistake is that the Aristotelian is supposed by Reid to think that a single objectual quality, such as hardness, is found in the table and in the mind (presumably in different ways).

However, I think the criticism of the Aristotelian fails. Let’s take the Aristotelian theory to be as Reid seems to think of it. We still have a choice as to what item in the Aristotelian view we identify with the phenomenal qualities. There is

1. the hardness itself

and

2. the sort-of-but-not-quite-inherence relation between the mind and the hardness.

Which one of these is the phenomenal quality or “idea”? The difficulty here is that Reid seems to accept two claims about Lockean “ideas”:

3. we always have immediate awareness of “ideas”

and

4. “ideas” are the states of awareness.

On the Aristotelian view in question, (1) satisfies (3) and (2) satisfies (4). But (1) does not satisfy (4), and I don’t think the Aristotelian should allow that (2) satisfies (3).

The Aristotelian can now give this story in response to Reid. If we identify (1) as the phenomenal quality, the “what I feel”, then there is nothing absurd about saying that what I feel—namely, hardness—is what is in the extramental table. If we identify (2) as the phenomenal quality, on the other hand, then the Aristotelian will agree with Reid that the phenomenal quality is not found in the extramental object, because the inherencish relation is only found in the mind.

In fact, the Aristotelian’s refusal to accept that there is a single sense of “ideas” that satisfies (3) and (4) is a very good thing. For if we accept both (3) and (4), then for anything we are aware of, our state of awareness will itself be something we are aware of, and any awareness will immediately imply infinitely many levels of higher-order awareness, which is empirically false.

I am not a Reid scholar, however. I might be badly misreading Reid.

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.

Change and potentiality

Aristotle defines motion or, more generally, change as the actuality of potentiality.

Imagine a helicopter hovering in one location, x. Its being at the same location x at time t₂ as it was at time t₁ is an actualization of its potentiality at t₁: namely, its potentiality to keep itself hovering in the same place by counteracting the force of gravity. Thus, by Aristotle’s definition it seems that the helicopter’s motionless hovering is motion.

Perhaps, though, we need to distinguish between potentiality and power. The helicopter, unlike a rock, has a power to stay in one place in mid-air. But neither the helicopter nor the rock has a potentiality to stay in one place, because a potentiality is necessarily for a state that does not yet obtain.

This suggests a view of potentiality like the following:

1. An object a has a potentiality for a state F just in case the object a has a possibility of being in state F and a is not in state F.

Here, “possibility” is used in the modern sense as not excluding actuality.

The helicopter has a possibility of being at location x in the future, but since it is already at location x, that possibility is not a potentiality.

Now, let’s go back to Aristotle’s definition. When are the actuality and potentiality predicated? Given that, as we saw, a necessary condition for a potentiality is lack of the corresponding actuality, it seems they cannot be predicated at the same time. This suggests that the Aristotelian account is:

2. An object changes provided it has a potentiality at one time and some other time actualizes that potentiality.

But now consider the simple at-at theory of change.

3. An object changes provided that it has a state at one time and lacks it at another.

We might call (2) “Aristotelian change” and (3) “at-at change”.

The following is trivially true:

4. Aristotelian change entails at-at change.

But what is curious is that the converse also seems to be true:

5. At-at change entails Aristotelian change.

For suppose that an object a is in state F at one time and not in state F at another. Swapping F and non-F if needed, we may assume for simplicity it is earlier in state non-F. Let t₁ be the earlier time. Since the object will later in be in state F, at t₁ it has a possibility for being in state F. That possibility is a potentiality by (1). And at t₂ that possibility is realized and hence is actual. Thus, at one time a has a potentiality for F and at another that potentiality is actualized. Hence, we have Aristotelian change.

So:

6. Necessarily, at-at change occurs if and only if Aristotelian change occurs.

So what does the Aristotelian account add?

Perhaps, though, we might say that (1) is too simplistic an account of potentiality. Perhaps not every unrealized possibility is a potentiality, but only an unrealized internally-grounded possibility. For instance, I have an internally-grounded possibility of standing up. But I do not have an internally-grounded possibility of instantly doubling in mass: rather, this possibility is grounded in the power of God.

On this view, however, the Aristotelian account of change appears to be false. For suppose that I have a possibility for a non-actual state F, but that possibility is not internally-grounded. Then if that possibility comes to be realized, clearly I have changed. Thus, if God miraculously doubles my mass, I have grown more massive, that’s a change. But that change isn’t a realization of an internally-grounded possibility.

One can escape this objection by insisting that every possibility for an object has to be internally-grounded. If so, then the Aristotelian account of change applies precisely to the same cases as the at-at account does, once again, but it adds a richer claim that change is always related to an internally-grounded possibility.

Aristotle's optimism and pessimism

Aristotle seems to accept these three claims:

1. For the most part, things behave in a natural way.

2. Most people are bad.

3. To behave well is to behave in accordance with your nature.

I always thought there was a contradiction between (1) and (2) given (3). But actually whether there is a contradiction depends on the reference class of the “For the most part” operator in (1). Suppose the reference class is all behaviors of all things. Then it is quite likely that most of these behaviors are natural, bad human behaviors being far outnumbered by the natural behaviors of insects and elementary particles.

Back when I thought there was a contradiction, I assumed the reference class was the behaviors of a particular kind of thing, a sheep or a human, say. That may be correct exegetically, but even so it does not yield a contradiction. For morally significant activity is only a small fraction of the activity of a human being. Leibniz thought that about three quarters of the time we behaved as mere animals. That’s likely an underestimate. So even if all our morally significant activity is bad, it may be far outnumbered by non-moral activity, and hence it may well be that most activity of humans is good. But when we say that a human is good or bad, we only refer to their moral activity.

The only hope for a contradiction is to take the reference class of (1) to be all the activities of every subsystem type. Even so, I do not know that there is a contradiction. For to say that a person is bad is not to say that the majority of their morally significant actions are bad. Suppose that Monday in the morning Bob kicked a neighbor’s puppy. At noon, she sent a harsh and false email to a struggling student saying that he had never seen worse work than theirs. At three, he googled for articles in obscure Romanian journals that I could translate and plagiarize. And in the evening he cheated while playing chess with his daughter in order that she might never win. It would be fair to say that Bob am very bad person indeed, but that’s only on the strength of four morally significant actions. There were many other morally significant actions Bob engaged in. Each time he was asked a question, he had the possibility of lying. When driving, he had the possibility of murder. He did many things that were morally neutral and no doubt a number of things that were good. But the four bad things he did were enough to show that he was a bad person.

Our standards for moral okayness are much higher than the standards for a hard calculus exam where you just need to get more than half the questions right.

See also the quote from George MacDonald here.

Change, time and contradiction

According to Aristote:

1. Time is the measure of change.

2. The law of non-contradiction says that a thing cannot have and lack the same property in the same respect at the same time.

The law of non-contradiction seems to be the fundamental basis of logic. Yet it presupposes the concept of time, which in turn presupposes that of change. Thus, it seems, for Aristotle, the concept of change is more fundamental than logic itself. That doesn’t seem very plausible to me.

But perhaps there is a different way to understand the “at the same time” qualifier in (2). Sometimes, we give a rule with something we call an exception, but it’s not really an exception. For instance, we could say: “It is an offense to lie to an officer of the law, except unintentionally.” Of course, there is no such thing as an unintentional lie, but it is useful to emphasize that unintentional falsehoods are not forbidden by the rule.

Now, Aristotle is, as far as I know, a presentist. On presentism, the only properties a thing has are its present properties, and it lacks precisely those properties it doesn’t presently have. So it’s not really possible for an object to have and lack the same property, since the having and lacking would have to be both present, and hence at the same time. But it is useful to emphasize that having the same property at one time and lacking it another is not forbidden by the law of non-contradiction, and hence the logically unnecessary qualifier “at the same time”. Strictly speaking, I think “in the same respect” isn’t needed, either.

Time is not the measure of change or animals are not essentially temporal

Imagine that beings like us come into existence at the very first moment of time and they are the only contingent beings. To aid imagination, suppose we are these beings, and it is now the very first moment of time. Then, barring divine promises or other such divine moral considerations, it is possible that both (a) we won’t exist at any point of the future, and (b) it’s not the case that anything else will come into existence. Thus:

1. It is possible that the only contingent beings there are are human-like beings and that contingent beings exist at one and only one moment.

But:

2. Change requires at least two moments of time.

Putting all of the above together, we get:

3. Either (a) human-like beings can exist without time or (b) time does not require change or (c) time cannot have a beginning or (d) time cannot have an end.

I think theists are likely to deny both 3c and 3d: God can create and terminate a timeline. That leaves the theist 3a and 3b. I think both 3a and 3b are plausible moves.

Aristotle famously held that time depends on change, but he thought that time couldn’t have a beginning or an end, and thus he accepted both 3c and 3d. The argument he actually gave for 3c and 3d doesn’t work (basically, it fails to distinguish “not was” from “was not” and “not will” from “will not”), but we can now see that there actually is a plausible Aristotelian reason to accept that time can’t have a beginning or an end if we think time is the measure of change.

Why am I talking of human-like beings rather than human beings? Well, maybe, “human being” is a biological kind, and biological kinds depend on evolutionary history, so maybe it is not possible for human beings to come into existence at the first moment of time, as they wouldn’t have an evolutionary history. But beings just like humans could.

Natural hope

One of the striking things to me about Aristotle is the pessimism. For instance, in Book IX of the Nicomachean Ethics, we’re told that vicious persons shouldn’t even love themselves, and that when one friend sufficiently outstrips another in moral excellence—whether through the one improving or the other declining—the friendship must be dropped. I do not see the virtue of hope in Aristotle, say, hope that the vicious may improve, too. For the wicked, there is just despair. (Aristotle’s odious doctrine of “natural slavery” has some similarities.)

Christianity, on the hand, professes hope to be a virtue. But the hope that Christianity talks of is a supernatural infused virtue, a virtue that comes only as a gift of God’s grace. And Aristotle, of course, is interested in the natural virtues.

But grace builds on nature. So one would expect there to be a natural counterpart to the supernatural virtue of hope. Compare how there are natural loves that are a counterpart to the supernatural virtue of charity. There should be a natural virtue of hope, too.

But given the dark empirical facts about humanity, a habit of hope apart from grace would seem to be an irrational optimism rather than a virtue.

Perhaps, though, there is something in between irrational optimism and supernatural hope: perhaps there is room for a hope grounded in natural theology. Natural theology teaches that there is a perfectly good God. Yet there is so much that is awful in the world. But given theism there is good reason to think that the future will bring something better, and hence there is a natural justification for hope.

I am not sure I want to say that natural hope requires actual belief in God. But for that hope to be a virtue and (hence) a part of a rational state of mind, it may well require that the hoping individual be in an epistemic position to rationally believe. Thus, for natural hope to be a virtue seems to require that hopers be in a position to believe that there is a God.

Aristotle, of course, did believe in a God, or gods. But these gods were uninvolved with human affairs, and hence not a good ground for hope.

Reflecting on the above, it seems to me that to overcome the pessimism of Aristotle, one needs more than just a remote hope, but a seriously robust hope.

Aristotelianism, classical theism and presentism

A fundamental commitment of Aristotelianism seems to be that all reality supervenes on substances and accidents. If according to worlds w₁ and w₂ there are the same substances and accidents, then w₁ = w₂.

But this seems incompatible with presentism. For given indeterminism, there is a world just like the actual one but which tomorrow will diverge from ours. The fact that tomorrow the other world will diverge from ours, however, does not make any difference as to what substances and accidents presently exist, and hence, given presentism, to what substances and accidents exist simpliciter.

It is usual for presentists to posit tensed properties like being such that yesterday you mowed the lawn or being such that tomorrow you will mow the lawn. But the future-tensed property, at least, is not a good candidate for being an Aristotelian accident. Aristotelian accidents are real qualities of things. So that won’t help the Aristotelian presentist.

Here’s another way to put the problem. According to Aristotelianism, facts cannot change without a change in the substance and accidents. But this is not compatible with presentism. Now imagine that there is only one substance, a radioactive atom that will decay in a week. Suppose this substance undergoes no other changes besides that decay. Then today it is a fact that the atom will decay in seven days. Tomorrow this will no longer be a fact—instead, it will be a fact that the atom will decay in six days. Thus, the facts will change between today and tomorrow. But no substances or accidents will come in or out of existence between today and tomorrow, as we supposed that the decay—which is a week away—is the only change that will happen.

There is a simple solution for the Aristotelian, and it is one that Aristotle himself opted for: accept open futurism, i.e., a temporal logic on which there are no facts of the matter about undetermined future events. Assuming this is the only option, the above arguments show that:

1. (Presentism + Aristotelianism) implies open future.

However, given the doctrinal understanding of omniscience in classical theism:

2. Classical theism implies the denial of open future.

We can get a variety of implications from 1 and 2. The one that I like the antecedent of is:

3. (Classical theism + Aristotelianism) implies the denial of presentism.