Consider an alternative version of Chrysippus’ story. Imagine Dion as before, but rather than imagining Theon to be that part of Dion which omits only Dion's foot, now assume Theon to be only Dion's foot. Again, Theon is a part of Dion. (True, Theon cannot – in this example – be easily thought of a potential persisting individual in his own right, but this is itself an interesting point to bear in mind for later.) Now, rather than considering what will happen if the foot is removed, we might ask what would remain if everything other than the foot is removed. That is to say, let us remove all that constitutes Dion but which is not also part of Theon. Is what is left Dion or Theon? (It cannot be both.) Now, if we have any intuitive response to this admittedly peculiar position, I think that the more likely answer is that the single disembodied foot before us is more likely to be considered to be Theon than Dion. Now this thought experiment was just like that provided by Chrysippus, but it produces quite the opposite result. In both cases the part discarded is the 'overlap', the portions of Dion which are not shared by Theon, and in both cases what is left was at one time both part of Dion and part of Theon. Indeed, in both cases what is left was once part of Dion and is the whole of Theon.
So if these two examples are relevantly similar, how can we explain the different reactions to them? Chrysippus' original example offers us a picture of two conceivable and viable individuals and focuses on one small part which one has and the other has not: a part which is, we would agree, inessential to the larger individual. (But: Polly Low once pointed out to me that for some people it may be the case that their feet are so essential to their persona (if not their identity as a persisting individual) that for them the removal of a foot may be a more telling loss. What if David Beckham’s right foot were removed?)
It may be suggested that Chrysippus' example is not unfair, indeed that it is perfectly suited to his purposes, since – remember – it appears in the context of a counter to the 'Growing argument'. This argument proceeds precisely by asking if small and apparently minor alterations in material constitution, namely the gradual process of growth or diminution, should in truth be thought to be cases of coming to be or passing away of whole individuals. Chrysippus counters this by generating the conclusion that Dion persists throughout the process of losing a foot, even though there is another candidate for what remains once the foot has been removed – namely Theon. On this account, there is no need for Chrysippus to consider such radical cases as that of my alternative formulation of the story of Dion and Theon. He is not concerned with such radical cases as this, and might well agree that is all that is left at the end of the process is a single foot, then it is in fact reasonable to conclude that Dion has passed away! All that remains is a foot, strangely designated by the name Theon.
But the Stoics assert that the part is neither other than (ἕτερον) the whole nor the same; for the hand is neither the same as the man (for it is not a man) nor other than the man for it is included in the conception of the man as man (σὺν αὐτῇ γὰρ ὁ ἄνθρωπος νοεῖται ἄνθρωπος).
SE M 9.336, trans. R.G. Bury
The first part of this is straightforward. A hand is not the same as a man (presumably the man whose hand it is) since one is a hand and the other is a man. But there is of course a link between hands and men, and this is what the Stoics try to characterise in the second half of this text. A hand is not 'different from' a man, since when you think of a man you think of a man with hands. Hands are not, in other words, merely optional accessories for humans.
But the Stoics do not make so clear exactly what this last claim amounts to. Does it, for example, make 'handed-ness' an essential property of a human, so that anything which does not have hands cannot be a human? I assume that the Stoics would have known of cases of people losing their hands in accidents or in battle, and if so then they would have to give an account which allows these too to count as humans. Perhaps 'having at some point had hands' is an essential characteristic of a human.
In any case, what does this mean for Dion and his foot? It might explain why it is a foot which is removed rather than a hand, since the footless Dion is not on anyone's account in danger of failing to be a human. And a foot on its own is on no-one’s account likely to be thought of as an individual. Having feet, after all, is not a peculiar characteristic of humans as having hands might perhaps be thought to be; lots of creatures have feet, but not many have hands.