Publicaciones

Chrysippus on the Impossibility of Two Individuals in One Body por Javier Acevedo

Descargar Archivo PDF

CHRYSIPPUS ON THE IMPOSSIBILITY OF TWO INDIVIDUALS IN ONE BODY

Crisipo sobre la imposibilidad de dos individuos en un solo cuerpo

Abstract: In this paper I contend that the ancient Chrysippean puzzle of Dion and Theon which is understood as a puzzle of synchronic identity, can be understood differently from a common interpretation of it as an instance of the problem of the many. This interpretation first appeared in Sedley (1982), and continues to be the common one (see Carmichael 2020). In the puzzle, as reported by Philo, Chrysippus relies on a principle seeming to affirm that: no two individuals can occupy one body. The problem in the puzzle is rather that Chrysippus’ principle expresses a symmetric relation; as such it cannot itself account for the asymmetric result, which is that one individual displaces another individual from occupying the same body. This present paper does not account for the ordering of the displacement. But it makes an argument for why Chrysippus should have sought the conclusion he affirms; for it demonstrates that his materialism is sensitive to some changes being apparently qualitative rather than quantitative. In other words, the passage, when read carefully, is a sign of Chrysippus’s confidence in the sophistication of his own materialism, something that has been misdiagnosed by the literature on its interpretation as an instance of the problem of the many.

Keywords: Chrysippus, materialism, philosophy, identity.

Resumen: En este artículo sostengo que el antiguo problema de Crisipo de Dion y Theon, que se entiende como un problema de identidad sincrónica, puede entenderse de manera diferente a el problema de los muchos. Esta interpretación apareció por primera vez en Sedley (1982) y sigue siendo la común (ver Charmichael 2020). En el problema, según lo informado por Philo, Chrysippus se basa en un principio que parece afirmar que: dos individuos no pueden ocupar un cuerpo. El asunto del problema es más bien que el principio de Crisipo expresa una relación simétrica; como tal, no puede explicar por sí mismo el resultado asimétrico, que es que un individuo desplaza a otro individuo de ocupar el mismo cuerpo. Este trabajo no toma en cuenta el ordenamiento del desplazamiento, pero presenta un argumento de por qué Crisipo debió de haber buscado el resultado que afirma; pues demuestra que su materialismo es sensible a que algunos cambios sean aparentemente cualitativos más que cuantitativos. En otras palabras, el pasaje, cuando se lee con atención, es un signo de la confianza de Crisipo en la sofisticación de su propio materialismo, algo que ha sido mal diagnosticado por la literatura sobre su interpretación, por ejemplo, el problema de los muchos.

Palabras clave: Crisipo, materialismo, identidad, filosofía.

The Puzzle of Dion and Theon

I will discuss a passage where we find Chrysippus, the third head of the Stoic school who lived during II to III century BCE, endorsing a view to defend his materialism in the face of Academic skepticism. Philo of Alexandria’s (20 BCE — 50 CE) reports Chrysippus’ response to the Growing Argument. This is an argument claiming that if a part of an individual changes with respect to its subtraction or addition of material parts, then the whole individual is no longer the same that it was before the respective change. Diogenes Laertius reports the following argument from Epicharmus, a comic poet who lived during the period of the opening decade of the fifth century. In the story, a man that will be represented as a owes money to another man b. Finding himself without money to pay his debt to b, the debtor states the following riddle to his creditor:

a.    […] suppose some one chooses to add a single pebble to a [pile] containing either an odd or an even number, whichever you please, or to take away one of those already there; do you think the number of pebbles would remain the same?

b.    Not I.

a. Nor yet, if one chooses to add to a cubit-measure another length, or cut off some of what was there already, would the original measure still exist?

b. Of course not.

a. Now consider mankind in this way. One man grows, and another again shrinks; and they are all undergoing change the whole time. But a thing which naturally changes and never remains in the same state must ever be different from that which has thus changed. And even so you and I were one pair of men yesterday, are another to-day, and again will be another to-morrow, and will never remain ourselves, by this same argument (Diogenes Laertius, Life of Eminent Philosophers Plato, III 11). [i]

The amusement is important in this plea for irresponsibility. If character a owes money to character b, then a can get away from paying his debt with the Growing Argument. Namely, if human bodies are constituted by matter like piles of pebbles are also constituted, then as long as a is a human, and has undergone some change in his body, e.g., ate something, cut his hair, clipped his toenails or whatever material change has undergone since the last time b saw a, then having different properties from the ones a had at the time when he contracted his debt, a should not be same person who contracted the debt. Hence, he owes nothing to b.

The importance of this argument relies in that, for example, we can think that if a member of a set is added or subtracted from the same set, some properties of the set will vary, and it will no longer be the same set. The set could change from being odd in number of members to be even in number of members. By Leibniz’s law, this change would preclude the set from being the same set that it was before; we necessarily end up with a different set. But, humans, cats, clouds, and other familiar objects are not like sets in this respect, e.g., if a cloud loses certain droplets on its blurry limits, that cloud would still be the same cloud; if a cat loses some hair, that kitten would still be the same kitten; if a person suddenly grows a third arm, that person will remain the same person. No responsibility could be dismissed from the person by claiming that she is not the same because she grew a third arm. Same if we chop someone’s foot. If we cut a foot from Dion, we would still end up with Dion.

Chrysippus answers the challenge coming from the Growing Argument, a challenge to his materialist position claiming that the bodily substance is the most fundamental substance (see Bailey 2014). Hence, any change could be explained by the bodily substance. Chrysippus, in what is reported by Philo of Alexandria to be a response to the Growing Argument, presents the following answer:

(1) ’Chrysippus, the most distinguished member of their school […] creates a freak of the following kind. (2) Having first established that it is impossible for two peculiarly qualified individuals to occupy the same substance jointly, (3) he says: 'For the sake of argument, let one individual be thought of as whole-limbed, the other as minus one foot. Let the whole-limbed one be called Dion, the defective one Theon. Then let one of Dion's feet be amputated.’ (4) The question arises which one of them has perished, and his claim is that Theon is the stronger candidate. (5) These are the words of a paradox-monger rather than of a speaker of truth. For how can it be that Theon, who has had no part chopped off, has been snatched away, while Dion, whose foot has been amputated, has not perished? (6) ’Necessarily’, says Chrysippus 'For Dion, the one whose foot has been cut off, has collapsed into the defective substance of Theon. And two peculiarly qualified individuals cannot occupy the same substrate. Therefore it is necessary that Dion remains while Theon has perished” (Philo, On the Indestr… 48 (SVF 2, 397) = LS 28P. I indicated with italics where Von Armin believes to be a direct quotation from Chrysippus).

As we see from the beginning of the passage, Philo reports this argument in outrage. He thinks Chrysippus is presenting an unreasonable paradox. My argument is an exegetical one. In this work I aim to defend the Chrysippean response on the face of Philo’s skeptical reaction, as well as other similar contemporary reactions.

Various interpretations of this answer have arisen. For Van Inwagen (1981), Theon is just an arbitrary undetached part of Dion, and arbitrary undetached parts just don’t exist. Van Inwagen’s argument runs on the grounds of rejecting mereological essentialism, namely, the principle in sets presented above where if some part changes in an object, that object is destroyed because it is no longer the same object. Just as sets, by changing in number of members, cannot be the same that they were before, objects cannot be the same objects if some part in them is subtracted. Van Inwagen argues that the doctrine of arbitrary undetached parts entails this form of mereological essentialism in a peculiar way, namely, in the case of subtraction, and mereological essentialism is false exactly because there are things like humans, who can miss a part and still be the same individual. Parallel to the example of Dion and Theon, Dion and Theon cannot be identical when we detach Theon’s missing foot from Dion’s body. Hence, the doctrine of arbitrary unattached parts is false if Dion survives the chopping of his foot. According to Van Inwagen, this shows that Theon just doesn’t exist, because arbitrary undetached parts don’t exist. But, I rather claim that Theon dies, because one of them has to die.

At the start, I am more inclined to think like Olson (1997) does: there is nothing wrong in the set up of the experiment conceiving Dion and Theon as two individuals. [ii] I take it at the start, that (3) Dion and Theon are two human living beings, two peculiarly qualified individuals with different properties; Theon has never had, say, the right foot, while Dion enjoyed some time as a fully fledged biped. Hence, they have different histories and are different individual human beings, and will always be. We can think that Chrysippus endorses the view that having different properties amounts to a sharp distinction between different individuals.

For Chrysippus, it seems that two distinct individuals become one when we cut Dion’s part (his foot), and it happens to be exactly the one Theon was missing already. So, the way Chrysippus presents the problem implies that these distinct properties make Dion and Theon eternally distinct, where, if a property P is had at one time t, then P-at-t is had at all times. If X is distinct from X at some time in virtue of having P-at-t when Y lacks P-at-t, then X will eternally be P-at-t and Y will eternally be not-P-at-t. Dion and Theon will be eternally distinct and therefore, when we cut Dion’s foot that Theon is missing already, we cannot end up with two individuals in the same body: an impossibility that should arise within the materialist Stoic system.

It is worth putting forward an answer to a possible tension that might be thought to arise in this conception of material objects. I think here Chrysippus is endorsing the claim that if we have the same material parts at t and located at the exactly same place, then we have the same individual. But the answer to the Growing Argument comes when the same material parts at a certain exact time and place are enough to keep just one individual. The distinctness of Dion and Theon dependent in the body they occupy at time t shows that there can be distinct individuals, but not with exactly the same material parts. Hence the impossibility in no two determinate individuals that can occupy one and the same substance. This is evident after (3) a surgery in Dion’s foot that will make Dion occupy the same body as Theon’s body. We get a result: (6) the death of a human being, where for the reason that a man can lose a part and survive, then Theon is the better candidate for perishing. In other words, within the materialist framework Chrysippus is endorsing, the claim that Dion and Theon have the same material parts after the amputation implies that there should not be a problem if we face the Growing Argument. Not only subtraction or addition explains all changes in matter. [iii] We can have a major qualitative change like a man dying when we are not even touching him (as Philo wonders). The explanation is rather a dramatic explanation to show that a major qualitative change, like the dying of a person, and not a part named Theon that is not even a person (contra Burke, 1994), can be explained within the Stoic standards. Those are the standards I aim to clarify in turn.

Philo wonders why Theon, the one we did not touch, is the one who dies. But this is answered by considering that in (2) we find a symmetrical principle. The symmetry among individuals as bodies may be expressed thus: If X and Y are different individuals, and Z is some body, then if either of X or Y has the body Z, one at most can. If X has Z as body, then Y does not. If Y has Z as body, then X does not. All this tells us is that X and Y exclude one another. This is not entailing that they cannot share some parts. They can. It only entails that exclusion is a symmetrical relation. But the displacement of Theon is an asymmetric result. Whatever is displaced cannot displace what had already displaced it. It might be thought that this shows why it becomes easy to endorse Philo’s worries; why do we have from a symmetrical principle this asymmetric result, the displacement where Theon dies without contact? But this is so because of the impossibility of Dion and Theon as two human living beings ending in exactly one body. The prime substance where causes reside, for the Stoics, is still the bodily one. This notion of causes as bodily, is what sets the Stoic standards of explanation:

Zeno also differed from the same philosophers [Platonists and Peripatetics] in thinking that it as totally impossible that something incorporeal [...] should be the agent of anything, and that only body was capable of acting [...] (Cicero, Academica 1.38, LS 45A p. 272).

According to [the Stoics] the incorporeal is not of a nature [...] to act [...] (Sextus Empiricus, Against the Professors 8.263 LS 45B p.272). 

Chrysippus as head of Zeno’s school, I presume, endorses this part of the Stoic notion of causes. Only what is bodily can cause.

As we have seen, this problem has worried many contemporary philosophers (See, Van Inwagen (1981), Burke (1994), Carmichael (2020), to name but a few) in different ways. But, different from most worries on the matter, when I target (3) —the distinctness of Dion and Theon— I take it that this is a puzzle about survival. Although, this puzzle might led to a problem with regards to parts and wholes, namely, a problem about how material objects as parts can be material individuals within the same individual when read in coordination with the doctrine of arbitrary undetached parts, I think this puzzle is just the problem of the two individuals in one body. Its solution is that qualitative differences making distinct individuals are still dependent on bodies, they might be explained by rearrangement in bodies. But before showing this, I will provide the reasons for why this is not necessarily an instance of the problems falling under the umbrella of the many as it is still thought to be (see Carmichael 2020).

The Problem of Two Persons and One Body: Not the Problem of the Many

The puzzle involving Dion and Theon has long been understood to be about identity, both synchronic (how many men are involved in the set-up) and diachronic (who survives the material change specified in the set-up). With regards to synchronic identity, it has been thought in the first instance as a version of a problem characteristically named, the problem of the many (see Unger 1980). David Sedley (1982) has argued for this perspective on Dion and Theon’s puzzle:

The paradox concerns two individuals, Dion and Theon, who somehow manage to be so differentiated that when Dion's foot is amputated he becomes indistinguishable from Theon. This is seen as conflicting with the principle that two peculiarly qualified individuals cannot jointly occupy the same substance, and part of Chrysippus’ job seems to be to describe the result in a way which will leave the principle unscathed… The solution is clear once one recognises that the Stoic paradox is all but identical to a modern one… (p. 268).

And here Sedley points into the direction of Wiggins-Geach’s (1968) example of the problem of the many:

Take a cat called Tibbles; concentrate your thought on that portion of her which includes everything except her tail; and give the name Tib to that portion. Since Tibbles and Tib do not occupy all of the same space at the same time, they are non-identical. But what if we then amputate Tibbles’ tail? Tibbles and Tib now occupy exactly the same space as each other. If Tibbles is still a cat, it is hard to see by what criterion one could deny that Tib is a cat. Yet they are distinct individuals, because their histories are different. (For example, it may be true of Tibbles that she once had her tail run over, but it cannot be true of Tib: the tail was never part of her). Hence we have two cats occupying precisely the same space at the same time. The conclusion is clearly unacceptable, and the problem is to locate the false step (Sedley 1982, pp. 268 - 269).

A problem is raised by this thought experiment [IV]: We have a whole. That whole enjoys a certain property: it is an F, in this case, it is a cat. If that whole has proper parts and a complement of that proper part enjoying the very property that is the same had by the individual as a whole, namely, being a cat, then we have a problem: we numerically distinguish the two individuals enjoying that very property of being the same F in the complement of the proper part and the whole. Extend this reasoning into many other proper parts and we have an iteration of numerically distinguishable complements of proper parts that are the same F, namely, the same cat in this case. Certainly, there is a problem in this reasoning. We don’t have as many cats in a cat as at least there are as many hairs in the cat (see Geach, 1980).

It could be that there is simply no such thing as my body-minus-my-right-arm because that is not a human being (See Carmichael 2020). But if I cut my arm I am still a human being. It could be that synchronic complements of proper parts that are still attached to me are nothing over and above what identifies me, as a human being, at least, not even if I miss a part. Hence, moreover, it is still weird to claim that if I cut my right arm I cease to exist (See Van Inwagen 1981), as well as it is weird to claim that of course, my body-minus-my-right-arm is just me (see Wiggins 1968). This is the problem of the many.

The problem of the many also concerns objects with no clear boundaries, as most material objects have at some level of magnification. [v] According to Sedley, Chrysippus puzzle does the same thing: it falls under the umbrella of problems associated with the problem of the many. But, as I have noted in the beginning, I think Dion and Theon are living beings in the set up of the experiment. Theon could not be understood as the complement of a proper part of Dion. Neither could Theon avoid being an individual just as Dion. When the knife affects Dion’s body, then Theon loses his corporeality and dies. Abstractions like complement parts of proper parts are not subject to die. But Theon is not that. He perishes, he is destructed, or killed. The cause for getting the stump in the surface of Dion’s leg once Dion’s foot is cut, is not equivalent to getting rid of a complement of a proper part that is part of Dion (contra Carmichael 2020).

I don’t think we have a slippery slope into an overpopulation of individuals as parts in Dion and Theon’s puzzle. Bodies and parts are subject to fall into the problem of the Many. Not Dion and Theon, who are two individuals in the same body, eternally distinct. I think that rather Chrysippus’ puzzle of Dion and Theon shows that there is an impossibility among living beings. So, for Sedley, we are confronted with the same puzzle as the one presented by Wiggins-Geach (1968: 1980). But, in Chrysippus puzzle, I argue, we are not necessarily led into Geach’s problem (contra Sedley 1982).

Once the analogy is done between the problem of the many and Chrysippus’ puzzle involving Dion and Theon, as Sedley does, he concludes that: “Chrysippus himself should surely never have accepted at the outset that Dion and Theon are two distinct peculiarly qualified individuals [because] Theon is a part of Dion” (p. 269). But Theon is a man, and not a complement of a proper part of Dion (contra Carmichael 2020; Van Inwagen 1981), neither a part —although his body is occupying a part of Dion’s body. If we stick to what Chrysippus claims, namely, that Theon is another living human individual, maybe, with certain unclear boundaries in his body (which should not necessarily lead us into the problem of the many), then I still find reasons to think that there is something better to be said about the outset that Sedley rejects. Hence, I will aim the argument to what should happen if we are to dispel from the association of the Chrysippean puzzle from the problem of the many.

If we do not distinguish between the two individuals and the body they occupy, then Chrysippus’ puzzle naturally leads to ways to state the problem of the many as Sedley shows. But we clearly find that Dion and Theon are two individuals; the question of their survival could hardly be raised if they were not. In other words, there would be no point for Chrysippus in stating that Dion survives and Theon perishes in (6), as well as no point in Philo rejecting the argument in outrage because we did not touch Theon when killing him. So, as long as we are talking about two individuals already, about a bisection in a body, and two individuals that will not occupy that body (only we can end up with two bodies in this bisection, but not with two individuals living still), the problem is not that of the many. Theon is an individual human being just as Dion, only Theon starts as an imperfect human being in the experiment; and only because he is a one-footed human being, as he will always be. This is what I take Chrysippus to mean by claiming that Theon is “defective” in (3).

Likewise, we may agree with Sedley that it is clear how many, indeed whose, bodies are involved in (3). They occupy some ‘substrate'. [vi] But it cannot be exactly the same exact substrate. My interest in this paper is only focused on what is well understood by the Chrysippean puzzle: (3) how many men start the thought experiment, and what body belongs to each, which is where (6) the killing with no contact comes from (the upshot). So, after noticing that this is not necessarily leading us to the problem of the many, my argument can proceed from the main question that should be raised by this puzzle: why from a symmetrical rule — if there is a single body, and two individuals and no more than one of them can occupy that body — we end up with an asymmetric result: the survival of Dion alone? The displacement occurred without contact. This displacement is an asymmetric relation as the relation between causes and effects. Whatever displaces something is not displaced by whatever is displaced, as whatever causes something cannot be caused by what it causes. Our task now is to connect the chopping of Dion’s foot when the individual’s respective bodies are rearranged into one and dispensing with Theon. This is easily shown within the Stoic standards, namely, pithing Chrysippus’ materialism.

I will argue that this latter task will be done by arguing that every cause is bodily as the Stoics want it. My argument will be a compatibilist one. If I succeed, it will hopefully convince you that there is a compatibility between all causes being bodies, and still explaining why there are qualitative changes like the killing of a person without contact. I will argue that this could be like a bruise, parts making a qualitative difference, the changing of color, without losing or adding any part. Or more aligned to the analogy of the person; it could be like a domino game of chute, a major qualitative difference made, having a winner, by the rearrangement of the same number of pieces.

I will show that by focusing our attention in the rearrangement, the notion of the perishing without touch might become even more compelling. So, let’s focus our attention on the perishing of our poor Theon after we sliced Dion’s leg: there is some rearrangement now of the same quantitative matter that is killing an individual. Any qualitative change, even the most dramatic qualitative change that can happen to a human being, namely, dying, can be an asymmetric result from bodily causes.

Accounting for the Asymmetry Through the Rearrangement in a Body

Bodies can have their parts rearranged and still be the same individuals, just like a jigsaw puzzle is a single collection of matter whether it has been solved or not, and it would still be the same jigsaw puzzle. As long as bodies can persevere during a life, they can be considered as the same collection of matter and hence a living human individual. Take the following example. By analogy with an arbitrary body, take each part of a domino as a part of a body. There is a domino game named “chute”. It requires the presence of all the 27 dominoes for each game. Necessarily there are three players, where each one is playing with 9 dominos from the 27 that are available. Only these details are required for my analogy. They are rearranged in each play and there is only one winner for each game. The rearrangement of all the pieces in each game will deliver a new winner. But no pieces are left or added every time that a new winner emerges, and there are no draws.

Imagine now that there are three players, Mary, John and Phillip, and at successive stages each one is a winner; each one wins a round. If the winner first becomes Mary, then John, then Philip, these are three changes, hence three states calling for a cause to explain why there are these changes. No change calls for the addition or abstraction of matter in any relevant sense: no one wins by acquiring more dominoes, or losing them, or altering the quantity had by another player. Everyone always has 9, there are always exactly 27 dominoes in place — and yet there are these three changes, changes in who is the winner.

Chrysippus, an ardent materialist who can recognize only bodies as causes, might think something like this when the body with which we started becomes the sole property of Dion by his principle stated in (2), accounting for (6), namely, that Theon must die by losing his corporeality. Theon’s body has not been added to or subtracted from, like John’s dominoes when he loses to Philip. In both cases there is some qualitative change (whose body belongs to whom; who is the winner of chute). But there is no need to invoke anything non-materialist to account for this qualitative change. It entirely depends on the matter involved in the situation. Maybe there is a problem about whether the individuals are occupying certain roles, i.e., losers or winners. And yes, individuals are not their roles. But what we should mind about is that at least in one respect, it is a major qualitative change that arises because of the rearrangement of some matter. Being the winner is a role that is shifting but it emerges from the rearrangements of the dominos. In the same vein, a winner, as a role held by a person in a game of chute, can be shifting from individual to individual.

Contact within bodies is perplexingly present when we add or subtract something from a body. Chrysippus presumably thinks that a body can change — for it can become the sole body of Dion when once it was the sole body of Theon — without any material subtraction or addition. (Remember, we did not add or subtract anything from Theon’s body). Chrysippus therefore thinks there can be genuine material change that is not merely quantitative and appealing to contact. But is this so bizarre? I think not.

Take now a bruise as a part of a body. It is a body too. If I have a bruise in my arm, it will vanish at some point. In between, it will change color. It will change from red to purple and then from purple to the color of my skin. The qualitative change, the changing of color, does not depend on how many erythrocytes are added or subtracted in my blood, neither on how many skin cells are added or subtracted. There may be the same number of erythrocytes in the blood and the same number of skin cells at a certain moment, but merely the rearrangement of that very quantity might make the change of color: the change does not require more or less of anything.

Rearrangement can make a qualitative difference without calling for any incorporeal causes, without, that is, calling for exactly those causes Chrysippus denies the existence of. [vii] There is just a rearrangement of the cells. So, on one hand, with this example we can now distinguish between the quantitative aspect —the number of cells beneath the skin—the qualitative—the color in the bruise, and we can infer that a qualitative change can occur by bodily causes. On the one hand, we have the example of chute, accounting for different rearrangement on pieces making of a body occupied by the individual considered as winner, a major qualitative difference that depends entirely on the arrangement of domino pieces. One and only one individual player can be the winner.

Both examples account for changes that are materialist but do not involve addition or subtraction. For Chrysippus, this is how the even most dramatic qualitative change can occur without the resources of a different sort of cause than that involved in the bodily causes: Theon dies. Hence, the claim that all causes are material and efficient does not entail those qualitative changes, and any other kind of changes, cannot be explained.

Conclusion

The death of Theon needs to be understood involving no contact between bodies. The death of Theon involves an asymmetry as explained by rearrangement of bodily parts. That is why the example of the bruise shows that bodily causes can result in a qualitative difference in the individual, an asymmetric effect, but still caused within the Stoic standards. The example of the chute shows that the individuals can remain in the same body when the rearrangement of parts changes, only the qualitative aspect of who is the winner is changing: and we have an asymmetric result. So, I think the claim that there can be major qualitative changes —like that involving the killing of Theon without touching him— is consistent with the examples provided, and therefore is not in tension with the Stoic conception of causes as bodily. I also have argued that if my interpretation is correct, then this is not necessarily an instance of the problem of the many.

References

Bailey D (2014). “The Structure of Stoic Metaphysics” Oxford Studies in Ancient Philosophy 46, 254-309.

Burke M (1992). “Dion and Theon: An Essentialist Solution to an Ancient Puzzle” The Journal of Philosophy 91, p 129-139.

_______ (1997). “Dion and Theon and The Many Thinkers Problem” Analysis 64, 242-250.

Carmichael C (2020) “How to Solve the Puzzle of Dion and Theon Without Losing Your Head” Mind 129, 205-224.

Geach P (1980) Reference and Generality, Ithaca: Cornell University Press.

Grube G (2002) “Plato’s Phaedo” Plato, Complete Works, New York: Hackett Publishing.

Long A, Sedley D (1987) The Hellenistic Philosophers Vol 1: Translations of the Principal Sources With Commentary, Cambridge MA: Cambridge University Press. (LS)

Hicks R (1925) “Plato Book III” Diogenes Laertius: The Lives of Eminent Philosophers Vol 1, Cambridge MA: Loeb Classical Library Harvard University Press.

Lewis D (1993) "Many, but Almost One” Ontology, Causality and Mind: Essays in Honor of D M Armstrong, New York: Cambridge University Press.

Menn S (2009) “On Socrates’ First Objections to the Physicists (Phaedo 95 E 8-97 B 7)” Oxford Studies in Ancient Philosophy 38, 37-68.

Olson E  (1997) “Dion’s Foot” The Journal of Philosophy 94, 260-265.

Rea M (1997) “Introduction” Material Constitution Maryland: Rowman Littlefield Publishing.

Sedley D (1982) “The Stoic Criterion of Identity" Phronesis 27, 255-275.

Unger P (1980) “The Problem of the Many” Midwest Studies in Philosophy 5, 411–467.

Van Inwagen P (1981) “The Doctrine of Arbitrary Undetached Parts” Pacific Philosophical Quarterly 62, 123-137.

Wiggins D (1968) “On Being in the Same Place at the Same Time” Philosophical Review 77, 90-95.