Dion and TheonThe puzzle of Dion and Theon was invented by the Stoic philosopher Chrysippus (c. 280 - 206 BCE). Some philosophers say that we have no clear idea of Chrysippus' purpose, but we can guess from Stoic views on existence and subsistence that Chrysippus was probably contrasting his Stoic view with the Academic Skeptic view of what constitutes "growing." There are actually two Growing Arguments. The Skeptics said entities cannot survive material change. Stoics say that the immaterial, peculiarly qualified individual (ἰδίος ποιὸν) does survive material change of the individual's body or substrate (ὑποκείμενον). The only description of Chrysippus' Dion and Theon comes from an opponent, a later Academic Skeptic, Philo of Alexandria (c. 30 BCE.- 45 CE), who is here criticizing the Stoics as claiming two things can be in the same place at the same time (coinciding objects).
(1) Chrysippus, the most distinguished member of their school, in his work On the Growing [Argument], 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 [Chrysippus'] claim is that Theon is the stronger candidate. (5) These are the words of a paradox-monger rather than 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'
What Chrysippus May Have Been DoingIn his article Chrysippus' Puzzle About Identity, John Bowin (2003) agreed with David Sedley (1982) that Chrysippus' argument was a reductio ad absurdum of the Skeptical version of the Growing Argument. We can agree and present the reductio in seven simple steps:
S*: No two things of the same kind (that is, no two things which satisfy the same sortal or substance concept) can occupy exactly the same volume at exactly the same time. This, I think, is a sort of necessary truth... A final test for the soundness of S* or, if you wish, for Leibniz' Law, is provided by a puzzle contrived by Geach out of a discussion in William of Sherwood.Wiggins sees that "one cannot define into existence a cat" or a cat-part at the same place and time as part of another cat. But the Tibbles version has left out what Chrysippus wanted to achieve with his explanation of growing, that an individual can survive material loss. This was his whole point in cutting off a foot, generally not appreciated by modern accounts. In their great 1987 compilation of Hellenistic thought, A. A. Long and D. N. Sedley described Tibbles as an example of "two peculiarly qualified individuals coming to occupy one substance," something the Stoics explicitly denied. Long and Sedley clearly are following Wiggins's Tibbles, but they suggest that Chrysippus has given us an example of Dion surviving a diminution in his material without losing his identity, as opposed to what the Academic Skeptics claimed. A cat called Tibbles loses his tail at time t2. But before t2 somebody had picked out, identified, and distinguished from Tibbles a different and rather peculiar animate entity - namely, Tibbles minus Tibbles' tail. Let us suppose that he decided to call this entity "Tib." Suppose Tibbles was on the mat at time t1. Then both Tib and Tibbles were on the mat at t1. This does not violate S*. But consider the position from t3 onward when, something the worse for wear, the cat is sitting on the mat without a tail. Is there one cat or are there two cats there? Tib is certainly sitting there. In a way nothing happened to him at all. But so is Tibbles. For Tibbles lost his tail, survived this experience, and then at t3 was sitting on the mat. And we agreed that Tib ≠ Tibbles. We can uphold the transitivity of identity, it seems, only if we stick by that decision at t3 and allow that at t3 there are two cats on the mat in exactly the same place at exactly the same time. But my adherence to S* obliges me to reject this. So I am obliged to find something independently wrong with the way in which the puzzle was set up. It was set up in such a way that before t2 Tibbles had a tail as a part and Tib allegedly did not have a tail as a part. If one dislikes this feature (as I do), then one has to ask, "Can one identify and name a part of a cat, insist one is naming just that, and insist that what one is naming is a cat"? This is my argument against the supposition that one can: Does Tib have a tail or not? I mean the question in the ordinary sense of "have," not in any peculiar sense "have as a part." For in a way it is precisely the propriety of some other concept of having as a part which is in question. Surely Tib adjoins and is connected to a tail in the standard way in which cats who have tails are connected with their tails. There is no peculiarity in this case. Otherwise Tibbles himself might not have a tail. Surely any animal which has a tail loses a member or part of itself if its tail is cut off. But then there was no such cat as the cat who at t1 has no tail as a part of himself. Certainly there was a cat-part which anybody could call "Tib" if they wished. But one cannot define into existence a cat called Tib who had no tail as part of himself at t, if there was no such cat at t1. If someone thought he could, then one might ask him (before the cutting at t2), "Is this Tib of yours the same cat as Tibbles or is he a different cat?"
The key is to recognize this as the ancestor of a puzzle which has featured in recent discussions of place and identity. Take a cat, Tibbies, and assign the name Tib to that portion of her which excludes her tail. Tibbies is a cat with a tail, Tib is a cat without a tail. Then amputate the tail. The result is that Tibbies, now tailless, occupies precisely the same space as Tib. Yet they are two distinct cats, because their histories are different. The conclusion is unacceptable, and the philosophical interest lies in pin-pointing the false step. That Chrysippus' puzzle works along similar lines is made clear by Philo's later comments, in which he takes Theon to be related to Dion as part to whole. Dion corresponds to Tibbies, Theon to Tib, and Dion's foot to Tibbies' tail. The differences are twofold. First, the problem is about occupying the same substance, not the same place. Second, Chrysippus assumes both the validity of the opening steps of the argument and the truth of the principle that two peculiarly qualified individuals cannot occupy the same substance at the same Time. He therefore concludes that one of the two must have perished, and his problem is to see why it should be one rather than the other. Philo's elliptical summary leaves unclear his reason for selecting Theon for this honour (P 6), but it is probably that if we are asked whose foot has been amputated we can only answer 'Dion's'. Theon cannot have lost a foot which he never had. The title of Chrysippus' work shows that this puzzle was developed in connexion with the Growing Argument. But to what purpose? The following is a guess. According to the Growing Argument, matter is the sole principle of individuation, so that a change of matter constitutes a change of identity. Hence Socrates is a different person from the same individual with one extra particle of matter added. Now these two individuals are related as part to whole — just as Theon and Dion in the amputation paradox are related. Thus the paradox's presupposition that Dion and Theon start out as distinct individuals is not one that Chrysippus need endorse; it is a premise attributed for dialectical purposes to the Academic opponents, who cannot deny it without giving up the Growing Argument. But once they have accepted it, the Growing Argument is doomed anyhow. For whereas the Growing Argument holds that any material diminution constitutes a loss of identity. Chrysippus has presented them with a case, based on their own premises, where material diminution is the necessary condition of enduring identity: it is the diminished Dion who survives, the ^undiminished Theon who perishes.
An Information Philosophy AnalysisThe problems of Dion and Theon and Tibbles, the Cat both begin with denying that two objects can coincide and then immediatley assuming that two objects are in the same place at the same time. This is not a puzzle or a paradox. It is a contradiction that Chrysippus set up for dialectical purposes. What were his purposes?
ReferencesBowin, J. (2003). "Chrysippus' Puzzle About Identity." Oxford Studies in Ancient Philosophy 24: 239-251
Burke, M. B. (1994a). "Preserving the principle of one object to a place: A novel account of the relations among objects, sorts, sortals, and persistence conditions." Philosophy and Phenomenological Research, 54(3), 591-624.
Burke, M. B. (1994b). "Dion and Theon: An essentialist solution to an ancient puzzle." The Journal of Philosophy, 91(3), 129-139.
Burke, M. B. (1996). Tibbles the cat: A Modern "Sophisma". Philosophical Studies, 84(1), 63-74.
Burke, M. B. (1997). Coinciding objects: reply to Lowe and Denkel. Analysis, 57(1), 11-18.
Burke, M. B. (2004). Dion, Theon, and the many-thinkers problem. Analysis, 64(3), 242-250.
Chisholm, R. M. (1973). Parts as essential to their wholes. The Review of Metaphysics, 581-603.
Long, A. and D. Sedley, The Hellenistic Philosophers
Lowe, E. J. (1995). Coinciding objects: in defence of the 'standard account'. Analysis, 55(3), 171-178.
Rea, M. C. (1997). Material Constitution: A Reader. Lanham, MD: Rowman & Littlefield.
Sedley, David. 1982. "The Stoic Criterion of Identity." Phronesis 27: 255-75.
Van Inwagen, P. (1981). "The Doctrine of Arbitrary Undetached Parts," Pacific Philosophical Quarterly, 62, 123-137.
Varzi, Achille, Mereology,Stanford Encyclopedia of Philosophy
Wiggins, D. (1968). On being in the same place at the same time. The Philosophical Review, 90-95.
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