Dion's foot

Here's an argument I've just rediscovered while trawling through some old files. It's a fun thing to think through and has generated some recent metaphysical reaction. I'll set it out here and then perhaps come back to it in later posts with any further thoughts.

Philo of Alexandria preserves a peculiar argument, which he says is taken directly from Chrysippus' work On the Growing Argument. This argument goes as follows.

Chrysippus, the most distinguished member of their school [the Stoics], in his work On the Growing Argument, creates a freakish thought (τερατεύεται) of the following kind. Having first established that it is impossible for two peculiarly qualified individuals to occupy the same space jointly, 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.’ The question arises which one of them has perished, and his claim is that Theon is the stronger candidate. These are the words of a paradox-monger rather than a speaker of the 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? ‘Necessarily’, says Chrysippus, ‘For Dion, the one whose foot has been cut off, has collapsed (ἀναδεδράμηκε)[1] 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 of Alexandria, De aeternitate mundi 48

[1] A pun? Dion can hardly do much running now...

The presentation of this is gruesome and somewhat absurd (Philo himself finds it 'freakish), so it might help for the moment to consider a less disturbing version. I shall return later to comment on the particular example chosen by Chrysippus. Imagine a swiss roll, which I will call A. Now let us imgine distinguishing two smaller sections of the swiss roll. Call these: B and C. Chrysippus wants us to imagine taking the whole of A and then cutting off (and, perhaps, eating) the section labelled C. Now the question is: What is left? Is the swiss roll left on the plate still A or is it B? Chrysippus replies: Easy. It is A. But the reason he has for saying this is unclear, at least in Philo’s presentation. Chrysippus merely argues that since in the absence of C we cannot be left with both A and B (since then there would be two 'peculiarly qualified individuals' occupying the same matter), we must choose between the two, and A – he says – is to be preferred. Philo understandably complains in favour of B. After all, nothing has been done to B. Nothing has been removed from it, whereas A has suffered a loss. (B has, at most, undergone a bit of 'Cambridge' change.)

This notion of 'removal', however, is probably what Chrysippus relies upon. Perhaps his thought is the following. If I say that B is left, then what have I just cut off and eaten? Surely I have cut off part of A. But if I have cut off part of A then there must be the rest of A left.

The gruesome amputation of Dion's foot, and the less gruesome cutting up of a swiss roll are about diminution rather that growth, but the principle remains the same whichever process we imagine. Chrysippus is keen to maintain that there is some persistent subject which undergoes change, diminution, or addition of its material constituents. Otherwise the danger is that all such material change threatens to become substantial change.

Imagine some miraculous medical procedure which can regenerate feet. Poor Theon has limped all his life with only one foot, so he is extremely keen to take part in this procedure. He undergoes the treatment, and a second foot appears. Now, is this new and happy biped still Theon, or has he disappeared only to be replaced by a new individual, Dion? If so, then Theon is indeed unfortunate. He has signed up for a new foot only to commit metaphysical suicide in the process. The Growing Argument, of course, threatens to make all such material change as dangerous – indeed fatal – as this foot-growth.

This much should be fairly straightforward. But it seems to me to be reasonable to ask why, if Chrysippus could have chosen an example like my swiss roll, he instead decided to conjure up the gruesome and bizzare picture of Dion, Theon-the-part-of-Dion, and Dion’s detachable foot. It is not sufficient, I think, to claim that the Stoics commonly use Dion and Theon in their examples as ‘peculiarly qualified individuals’ (much as Aristotle commonly uses Socrates or ‘the snub’ is his metaphysical expositions). True, the Academic argument which would make all material change into the coming into or passing out of existence of some individual may be most threatening if applied to people, but the threat to personal persistence could be countered by pointing to any metaphysically similar example. Is it just a memorable thought-experiment? (Perhaps, but the danger of this approach is the less usual the situation envisaged the less confident we can be in our intuitive reactions to it.)

It seems to me, therefore, that it is important to understand the particular example chosen in all its detail. Above all, it appears essential to the success of the argument that it is Dion’s foot which is detachable.