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.

Species flourishing

As an Aristotelian who believes in individual forms, I’m puzzled about cases of species-level flourishing that don’t seem reducible to individual flourishing. On a biological level, consider how some species (e.g., social insects, slime molds) have individuals who do not reproduce. Nonetheless it is important to the flourishing of the species that the species include some individuals that do reproduce.

We might handle this kind of a case by attributing to other individuals their contribution to reproduction of the species. But I think this doesn’t solve the problem. Consider a non-biological case. There are things that are achievements of the human species, such as having reached the moon, having achieved a four minute mile, or having proved the Poincaré conjecture. It seems a stretch to try to individualize these goods by saying that we all contributed to them. (After all, many of us weren’t even alive in 1969.)

I think a good move for an Aristotelian who believes in individual forms is to say that “No man or bee is an island.” There is an external flourishing in virtue of the species at large: it is a part of my flourishing that humans landed on the moon. Think of how members of a social group are rightly proud of the achievements of some famous fellow-members: we Poles are proud of having produced Copernicus, Russians of having launched humans into space, and Americans of having landed on the moon.

However, there is still a puzzle. If it is a part of every human’s good that “I am a member of a species that landed on the moon”, does that mean the good is multiplied the more humans there are, because there are more instances of this external flourishing? I think not. External flourishing is tricky this way. The goods don’t always aggregate summatively between people in the case of external flourishing. If external flourishing were aggregated summatively, then it would have been better if Russia rather than Poland produced Copernicus, because there are more Russians than Poles, and so there would have been more people with the external good of “being a citizen of a country that produced Copernicus.” But that’s a mistake: it is a good that each Pole has, but the good doesn’t multiply with the number of Poles. Similarly, if Belgium is facing off Brazil for the World Cup, it is not the case that it would be way better if the Brazilians won, just because there are a lot more Brazilians who would have the external good of “being a fellow citizen with the winners of the World Cup.”

Infima species

There is a classic controversy in interpreting Aristotle: Is there one form per individual or one form per species?

One of the main arguments for individual forms is that the form of the human being is the soul, and it would be crazy to think that you and I have the same soul.

But what if—though this is surely not what Aristotle thought—the truth were this: There is one form per species, but humans, unlike other organisms, are each their own species (much as Aquinas thought the angels were).

This creates a discontinuity between non-human and human animals. This discontinuity is in itself a disadvantage of the view—it makes things more complicated.

However, at the same time the discontinuity would correspond nicely with some ethical intuitions. It wouldn’t be reasonable for a human to sacrifice her life for a Komodo dragon. But it could be reasonable for her to sacrifice her life for the Komodo dragon species. The view also fits with the widespread, though far from universal, intuition that it is permissible to kill non-human animals for food, but that the killing of a human being is a morally far weightier thing. Moreover, the idea that humans are infima species seems to capture important things about human individuality (I am grateful to Richard Gale for this observation), including the idea that while there is a teleological commonality between human beings, it is also the case that individual humans have individual vocations, telè that are their own only.

The main disadvantage of the view is theological. In Athanasian soteriology, it is crucial that Christ is metaphysically same species as we are. But one might hope that a Christology could be modified where being of the same genus would play the same role as being of the same species does for St Athanasius—or perhaps one where what plays the role is just the fact of a shared rational animality (which we also share with any non-human rational animals outside of the Solar System).

I don’t think the view is true, because the radical discontinuity the view posits between non-human and human animals just seems wrong. But I think there is more to be said for this view than is generally thought. And for those who think that they are not animals—for instance, people who think that they are constituted by an animal—the view seems even better.

Extinction, creationism and presentism

An intuition a lot of people have is:

1. The extinction of a species is a very bad thing.

On the other hand, extinction is central to the evolutionary process. Some species go extinct, making room for others, and thereby producing a greater diachronic biodiversity. Diachronic biodiversity is a very good thing, and the production of this diversity (wholly or at least to a significant degree) by natural evolutionary processes is a very good thing. This suggests:

2. If species at least typically arise by evolutionary processes, (1) is false.

What can we say given (2)? Well, we could argue:

3. Species at least typically arise by evolutionary processes. (Scientifically known fact)
4. Therefore, the extinction of a species is not a very bad thing. (By 2 and 3)

I am inclined to go for this. To soften the counterintuitive consequence, we might note that what is particularly bad is extinctions where no new species are likely to evolve to fill the niche, and the kind of environmental degradation that we want to oppose not only leads to the extinction of species but stands in the way of the evolution of new species that fill the niche. Though that's an empirical question, and I don't know if it's so.

Another move is to argue:

5. Both (1) and (2) are true.
6. Therefore, species do not arise by evolutionary processes, even typically. (By 5)
7. If species do not arise by evolutionary processes, creationism is true. (Since creationism is the best alternative to evolution.)
8. So, creationism is true. (By 6 and 7)

A yet different move is to deny (2). My thinking behind (2) was based on the value of diachronic biodiversity. But perhaps diachronic biodiversity is only as valuable as I think it is if presentism is false. It is only if the past organisms in extinct species really exist, even if pastly so, that they contribute in a valuable way to biodiversity. So one might replace (2) by:

9. If species at least typically arise by evolutionary processes and presentism is false, (1) is false.

And then one might argue:

10. Claims (1) and (3) are true.
11. Therefore, presentism is true. (By 9 and 10)

So I think we have three main options:

• Deny that extinction is a very bad thing.
• Deny evolution and affirm creationism.
• Affirm presentism.

I should note that in (1), I am thinking of on-balance badness rather than just intrinsic badness.

Abortion and destruction of animal life

Say that an entity has "very high value" provided that it is wrong to destroy that entity for the sake of any good less than that of the saving of a typical life of a human person. (This is rough and heuristic, because incommensurability is very problematic here.) Human persons, then, have very high value. If fetuses have very high value as well, then it follows that typical abortions are wrong, but it does not follow that abortions done to save the mother's life are wrong. (My view is that they are wrong, because fetuses not only have very high value but are deserving of the same moral respect as adults. But I shan't be defending that here.)

One might try to argue that fetuses lack very high value on the basis of the following argument:

1. Only things that exhibit P have very high value.
2. Fetuses lack P.
3. Therefore, fetuses lack very high value.

Here, P is some "personal feature", like personhood, self-awareness or valuing one's existence.

But with these ways of filling in P, the argument is unsound because (1) is false for such P. Here is one example (taking "things" widely to include mereological sums or other collectives): the genus Equus, which currently comprises horses, donkeys and zebras. No member of this genus has P, and the genus as a whole also lacks P. But it would be wrong to wipe out the genus for the sake of any good less than that of saving a typical human life. My evidence for this is that a lot of people will think that it would not be irrational to sacrifice one's life to save the genus from extiction, and that it would be problematic even to save one's life at the expense of the genus. Where something less than a human life is at stake, it seems that it would be wrong to destroy the genus.

If this example does not convince, let's up the numbers. Suppose there is a galaxy, containing a hundred thousand planets teeming with life. The intellectual level of the life in that galaxy does not individually exceed that of a horse, and there is no collective intelligence, either. Then that galaxy, with all its living contents, does not exhibit P. But, surely, it has very high value—it would be wrong to destroy it, with all its contents, for any good that is less than that of the saving of a typical human life. And it is not implausible that it would be wrong to engage in such vast destruction of animal life even to save a typical human life.

Two problems for conspecificity as primitive

Here is something growing out of last night's neo-Aristotelian metaphysics class with Rob Koons. Suppose we take the relation of conspecificity as a primitive, in order to be a nominalist about species. (The context here is Aristotelian, so "species" may include "Northern leopard frog", but it may also include "electron".) Then we will have a hard time making sense of claims like:

1. Possibly, none of the actual members of x's species exist (in the timeless sense), but there is some member of x's species.

Suppose for instance x is an electron. Then, surely, there is a possible world where there are electrons, but none of the actual world's electrons exist. But to make sense of (1) on an account that takes conspecificity to be primitive would require a conspecificity relation between an electron in the actual world and an electron in the possible world. But how can there be a relation one of whose relata does not exist? (Intentional relations are like that, but I don't think we want conspecificity to be like that.) The realist about species doesn't have this particular problem. She just explains (1) by saying that if s is the species of x, then possibly none of the actual members of s exist but s nonetheless has a member. Also, if one takes conspecificity as primitive but allows the existence of non-actual individuals, the problem disappears, since then we can unproblematically relate a non-actual individual with an actual one.

The problem here is that of interworld conspecificity. What makes an individual a₁ in a world w₁ conspecific to an individual a₂ in w₂? If there is an individual a₂ in w₁ conspecific to a₁ who also exists in w₂ and is conspecific to a₂, by transitivity of (Aristotelian) conspecificity this is not a problem. We can generalize this solution by saying that a₁ in w₁ is conspecific to a₂ in w₂ provided that there are chains of worlds W₁,...,W_n and entities A₁,...,A_n such that

• W₁=w₁, W_n=w₂, A₁=a₁, and A_n=a₂
• b_i is in both W_i and in W_i+1 for i=1,...,n−1
• b_i and b_i+1 are conspecifics in W_i+1 for i=1,...,n−1.

For this approach to give a good account of interworld conspecificity it has to be the case that conspecificity is transitive and that species membership is essential. (But the approach can also work if species membership is not essential, as long as we have individual forms, and the membership of an individual form in a species is essential. For then we can give the story not in terms of chains of particulars, but chains of individual forms.)

The above account does, however, entail the following metaphysical principle:

2. Whenever worlds w₁ and w₂ contain individuals a₁ and a₂ who are members of species s (understood nominalistically), then there is a finite chain of possible worlds, starting at w₁ and ending at w₂, such that every pair of successive members of the chain has a common member of s.

Is (2) true? Well, it seems hard to come up with counterexamples to it, at least. If we could imagine a species whose possible members could be divided into two classes, A and B, such that no member of A could exist in a world that contains a member of B, then we would have a violation of (2). But I am not sure we have much reason to think such species exist.

But now consider a different problem for the account. Two photons can collide and produce an electron-positron pair. Suppose we are in a world where there are lots of photons, but only one collision has occurred, producing electron e (and a positron that I don't care about). We now want to be able to say this:

3. A pair of photons p₁ and p₂ jointly have the power of producing an electron.

Presumably this should reduce to some claim about how they have the power of producing a conspecific to e. But that is an extrinsic characterization of the power of the photons. Yet it is an intrinsic feature of the joint power of p₁ and p₂ that it is a power to produce an electron (and a positron). Moreover, supposing that no collisions occurred, and hence there was no e in sight, we would still want to be able to say this:

4. A pair of photons p₁ and p₂ jointly have the power of producing a conspecific to something that photons p₃ and p₄ jointly have the power of producing.

Tricky, tricky. Here is a suggestion. We slice powers, considered as particulars ("x's power to do A") finely enough that we can talk of a particular power that p₁ and p₂ jointly have (or maybe one has the power to operate on the other in some Aristotelian way), the power of producing an electron (this power can only be exercised together with a power to produce a positron). Now, we can talk of the primitive conspecificity not just of particles, but of productive powers, and we can characterize the conspecificity of two entities disjunctively:

5. e₁ and e₂ are conspecific (non-primitively) if and only if either e₁ and e₂ are primitively conspecific or e₁ results from the exercise of a power primitively conspecific to a power the exercise of which results in e₂ or e₁ results from the exercise of a power which results from the exercise of a power primitively conspecific to a power the exercise of which results in a power the exercise of which results in e₂ or ....

Assuming that powers are characterized by what they produce, any disjunct further down in the disjunction entails all the disjuncts further up in the disjunction. Now we can make sense of (3) and (4) in an intrinsic way, in terms of the conspecificity of the powers of producing electrons. Moreover, we can make the chain-of-worlds move as needed for non-primitive conspecificity. This will yield a very complicated analogue of (2), but that analogue will, if anything, be even more plausible than (2).

This is all too messy, but maybe mess is unavoidable.

Species, biological and metaphysical

The concept of a species is quite important to an Aristotelian metaphysics. All the members of an Aristotelian species have qualitatively exactly the same nature. But it is difficult to figure out exactly which individuals are conspecific in this metaphysical sense.

It would be mistaken to think that metaphysical species are always co-extensive with biological ones. Biological species are defined in terms of populations that exhibit gene interchange. Thus, some biologists think there are six giraffe species. Suppose this hypothesis is right—if it's not right of giraffes, there will be some related case where it will be right. In nature, these different putative species of giraffes do not appear to interbreed, though in captivity they apparently do. If we thought metaphysical species to be coextensive with biological ones, we would have to answer tough questions about the offspring of different giraffe species. Suppose that the father is of metaphysical species A and the mother of metaphysical species B. Then any reason to think the offspring to be a metaphysical conspecific of the father is a reason to think it to be a conspecific of the mother, and these reasons seem to cancel out. So it seems better to suppose the offspring to be a member of a third metaphysical species. But if so, then with six species of giraffes, we could get up to 18 or maybe even 36 offspring metaphysical species. And when those bred, the metaphysical species would seem to keep on multiplying. This seems excessive, and so it seems better to suppose that, whatever the biologists say, the different giraffes are all members of one metaphysical species.

But all this reasoning strikes me as seriously ad hoc. If different biological giraffe species are metaphysically one species, why stop there? Why not suppose that all the members of the biological family Giraffidae, including giraffes and okapis, are one biological species?

It is not clear whether this is a metaphysical or an epistemological question. It might be that if we were clear enough on what metaphysical species are, we would make some progress here. On the other hand, people not sympathetic to Aristotelian metaphysics will take these difficulties as significant arguments against Aristotelianism.

I suspect that the answer here has a lot to do with teleology and the notion of normalcy. The Aristotelian nature encodes or defines how an organism ought to be, what its normal arrangement of parts is, what behavior is normal to it. Perhaps on the epistemological side, one can make a move here rather like that which David Lewis makes in regard to laws of nature. The metaphysical species provide a level of classification that offers the best balance between simplicity of normative description and richness of normative implications. If the metaphysical species included both giraffes and okapis, then the common nature would have to encode many conditional normative claims such as: if the individual has such-and-such features, then it should have a short neck, but if the individual has such-and-such features, then it should have a long neck. On the other hand, if giraffes and okapis are separate species, then we get a classification system with greater simplicity—the giraffe nature encodes having a long neck with no complicated conditionals, and the okapi nature encodes having a short neck again with no complicated conditionals.

How, then, do we know male and female giraffes to be members of one species? Because just about all the normative properties of males and females are the same, and we get a simpler classification system that just includes conditionals like if the individual has such-and-such features, then it should have ovaries, but doesn't reduplicate other normative claims.

But what about species, like Osedax worms, where male and female individuals seem to be very different? Maybe we Aristotelians just have to say that the balance of simplicity and richness account is only epistemic, and in this case is trumped by an analogical argument from other metaphysical species in which males and females are more easily seen as members of the same metaphysical species.

What's so bad about species extinction?

A couple of weeks ago, an article in BMC Biology argued that there may be six reproductively isolated species of giraffes: "By analyzing mitochondrial DNA sequences and nuclear microsatellite loci, we show that there are at least six genealogically distinct lineages of giraffe in Africa, with little evidence of interbreeding between them." Reproductive isolation is, of course, the primary feature of species as defined in a modern biological way. Let's grant, for the sake of the argument, that the geneticists did their job correct, and that there are six biological species of giraffes (if not, the following will be hypothetical, but the same conclusions will follow).

So far, then, so good. But the The BBC says:

Mr Brown [the first author of this study] also highlighted the conservation implications of this study: "Lumping all giraffes into one species obscures the reality that some kinds of giraffe are on the brink.
"Some of these populations number only a few hundred individuals and need immediate protection."

Here is one place where things get philosophically interesting. The idea is that once we find out that, e.g., the Nigerian giraffe, of whom the BBC says "[t]he last 160 individuals are found in West and Central Africa", is a species, we have strong reason to prevent the extinction of the Nigerian giraffe.

Let K be a kind, natural or not, of organism. For some kinds K, we do not think there is anything bad about the extinction of Ks. Granted, the deaths of the individual members of K may be bad, but whether a kind K goes extinct or not, each individual has exactly one death to die (the last point I got from a comment by Jeff Schloss at a workshop we both attended; he may not endorse the use I make of the remark). Suppose K is the kind Dalmatian with exactly one spot shaped like in the diagram on right. There really is nothing bad about K ceasing to have members, over and beyond the individual members' deaths (note that one way for K to go extinct would be for the descendants of Dalmatians that have exactly one such spot to have two such spots, and there never again be any Dalmatians with exactly one such spot). Or maybe for diversity reasons, we think that in the best of all possible worlds all non-bad kinds are realized, and so there is something bad about the Ks dying out over and beyond the individual deaths, but it is a very minor bad.

I suspect what is going on here is that there is an equivocation between two senses of species: an intuitive non-scientific one (at least in the post-Aristotelian sense of "scientific") that understands a species as a kind of organism distinguished in a significant way from other organisms (the normative term "significant" is what marks this as non-scientific in the modern sense), and the modern scientific one in terms of reproductive isolation. For while there is something bad about a species in the intuitive sense going extinct, it is not at all clear what is so bad about a species in the reproductive-isolation sense going extinct. In particular, it is not clear why one of the giraffe species going extinct would be worse than Dalmatians with exactly one spot of some precise shape going extinct.

All this suggests that there is a need for a notion of species going distinct from the biological one. I rather hope that the Aristotelian notion of species as defined by qualitative identity of essence will do the job here.

Let me end with a question: Suppose that some kind of subatomic particle were to cease to exist forever, with no way of bringing it back. Would there be any non-instrumental bad in that (there might be an instrumental bad, if there is some use for the particle, or if studying it empirically might help with the progress of science)? (I am inclined to say yes.)

Men and women are one species

I've always been puzzled by the following problem. The setting for it is the metaphysical Aristotelian concept of a "species", not the biological one (in the biological sense this is easy). How do we know that women and men are the same species? I.e., how do we know that the species that we belong to is human rather than there being two species, woman and man?

I think a partial answer can be given by taking into account the following observation (I've learned it from David Alexander here who attributes it Peter Geach, though neither may endorse my application): In general, from the fact that x is a good F and x is a G, one cannot infer that x is a good G.

Here, I intend "is a good F" to mean something like "flourishes at F-ness" or "is good at being an F". Moreover, I am thinking here in the context of Greek notions, so that to be a good human includes both having the virtues of the intellect and will, as well as the excellences of the body. This is at times a somewhat awkward use of "good", but I shall adopt it.

I shall be rough here. I know what I say is not exactly right. For full precision, one needs to work not with the coarse tools of entailment and necessity, but with more finegrained tools of explanation and truthmaking. But what I shall say seems approximately right.

Despite what I said above, sometimes inferences like the ones questioned above seem exactly right:
(1) If x is a good lieutenant in a military force, then x is a good officer in the same force.
(The "in the same force" condition is needed, because a spy might be an officer in more than one army, but is unlikely to be a good officer in more than one.) The converse I am less sure of, but it is also plausible:
(2) If x is a good officer in some military force and x is a lieutenant, then x is a good lieutenant in the same force.

Suppose, now, that F and G are kinds such that, necessarily, all Fs are Gs but not conversely, and necessarily x is a good F if and only if x is a G and x is a good G. I shall say that "F is normatively subordinated to G".

Conjecture 1: If F is a species and G is a higher genus, then F is not normatively subordinated to G.

Conjecture 1 embodies an Aristotelian notion of the primacy of species, in the normative realm. And I think the normative aspect of species-hood is central for Aristotelians (I would like read the characterization of the essence as to ti ên einai as normative, though it may be stretching the Greek: what [the thing] was [supposed] to be). The species encodes the normative properties for the individuals of that kind. If we can explain the normative properties of an x insofar as it is an F in terms of its aptness at fulling G-ness, then F-ness is not the normatively basic property here. F-ness specifies the x further, but does not add any nomrative force. For reasons of explanatory power, we should try to find as general a kind as we can without sacrificing any normativity when we are searching for. To be a good human is more than just being human and being a good mammal. One can be really good at mammality while being far from human flourishing. The converse, I think, is false, though: if we fully flourish at humanity, we also flourish at mammality.

Now one is a good woman if and only if one is a woman and a good human; similarly for a man. This is a controversial claim, but I think correct. Therefore woman and man are normatively subordinated to human. If woman and man were species, then human would be a higher genus, and hence Conjecture 1 would be violated. Hence, if Conjecture 1 holds, woman and man are not species.

An interesting question is whether one can come up with a full characterization of species in similar normative terms. Here is something that might come close.

Conjecture 2: A natural kind G is a species iff both (a) G is not normatively subordinated to any larger natural kind, and (b) if F is a proper natural subkind of G such that any good F is necessarily a good G, then F is normatively subordinated to G.

(The "F is normatively subordinated to G" condition in (b) can be replaced by "necessarily a good G who is an F is a good F", because more than half of the definition of normative subordination is implied by the antecedent of the conditional in (b).)

For instance, mammal is not a species. For human is a proper natural subkind of mammal such that to flourish at being a human entails flourishing at being a mammal, but human is not normatively subordinated to mammal. One can be really good at mammality while a miserable failure at all other dimensions of humanity. But one cannot be really good at humanity and a woman while being a failure at being a woman.

A different way to look at the above is to note that the flourishing of a man or a woman as such is basically no different--it is just a particular form of the flourishing of a human.