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The Debtor's Paradox

Epicharmus of Syracuse (fl, 500-460 BCE) was one of the authors of early Greek comedies. He may have studied briefly with Pythagoras. In one of his plays he used the ideas of Heraclitus, that everything is in flux, all is change. If you can't step into the same river twice, maybe you are not the same person today that you were yesterday?

One of Epicharmus' comedies introduced a man who wants to break his contract with a lender on the grounds that he is not the same man that made the contract. The lender beats the debtor, who sues the lender for assault. When called before the courts, the lender uses the same argument, that he is now not the same as the person who committed the assault.

Modern metaphysicians also question the intrinsic connection between our "temporal parts." Are our bodies newly created at every instant? Can there be a principle of individuation that preserves our identity over time?

Plutarch says that some Sophists used the Heraclitean doctrine of change to prove that a man who borrowed money in the past does not owe it in the present. In his Theaetetus (152D-E, 160D), Plato cites Epicharmus as saying "nothing is, but everything becomes" and that he and Homer are the founders of the Heraclitean tradition.

The Stoics opposed the ancient "Growing Argument (Auxanomenos Logos), still being debated by the Academic Skeptics, that matter is the sole principle of individuation, so that a change of matter constitutes a change of identity.

The Stoics therefore anticipate the modern view of some (but not all) metaphysicians that material constitution is not identity.

The classicist David Sedley reconstructed the debtor's paradox as follows, and why it had to wait for the Stoic era and Chrysippus for full resolution of the Growing Argument:

The story starts with a scene from an early Greek comedy. Its author is the Syracusan comic playwright Epicharmus, and it probably dates from the opening decades of the fifth century B.C. The following reconstruction is based on one verbatim quotation of twelve lines, plus two indirect references to it in later authors.

Sedley here shows that the Sophist's metaphysical concept of "numerically distinct" or materially distinct individuals may not be the basis of a principle of individuation and able to explain the persistence of our identity over time
Character A is approached by Character B for payment of his subscription to the running expenses of a forthcoming banquet. Finding himself out of funds, he resorts to asking B the following riddle: 'Say you took an odd number of pebbles, or if you like an even number, and chose to add or subtract a pebble: do you think it would still be the same number?'

'No,' says B.

'Or again, say you took a measure of one cubit and chose to add, or cut off, some other length: that measure would no longer exist, would it?

'No.'

'Well now,' continues A, 'think of men in the same way. One man is growing, another is diminishing, and all are constantly in the process of change. But what by its nature changes and never stays put must already be different from what it has changed from. You and I are different today from who we were yesterday, and by the same argument we will be different again and never the same in the future.'

B agrees. A then concludes that he is not the same man who contracted the debt yesterday, nor indeed the man who will be attending the banquet. In that case he can hardly be held responsible for the debt. B, exasperated, strikes A a blow. A protests at this treatment. But this time it is B who neatly sidesteps the protest, by pointing out that by now he is somebody quite different from the man who struck the blow a minute ago.

To subsequent generations, the argument used in this scene read like a remarkable anticipation of a philosophical doctrine associated with the names of Heraclitus and Plato, that of the radical instability of the physical world; and Plato himself was pleased to acknowledge such evidence of the doctrine's antiquity. But although the puzzle is a serious challenge to ordinary assumptions about identity, never in the fourth century B.C., the era of Plato and Aristotle, does it meet with a proper philosophical analysis and repudiation. That is not to say that materials for answering it cannot be found in Aristotle's metaphysical writings.

There is very little sign that modern metaphysicians have understood Stoic thinking well enough to see that they contain the solutions of these ancient puzzles if one interprets their "peculiarly qualified individuals" as immaterial information, as mental properties, rather than matter.
My point is that it was not until the generation after Aristotle, with the emergence of the Stoic school, that the solution of such puzzles became an absolutely central route to philosophical discovery. This fact is becoming a familiar one with regard to Stoic logic, but very much less so when it comes to their metaphysics. In fact, the story which I shall be piecing together in this paper has as far as I know featured in none of the modem reconstructions of Stoic philosophy.

An especially important historical fact here is that when the Stoic school emerged in Athens at the opening of the third century B.C. there sprang up alongside it a dialectical gadfly, a new generation of radical sceptics, under the leadership of Arcesilaus, who had seized the reins of power in Plato's old school, the Academy. For the next two centuries every philosophical move by the Stoics was liable to be covered and challenged by these Academics, and Stoic theories were constantly designed and redesigned to circumvent the attacks. Many of the Academic countermoves exploited philosophical puzzles, some of which have remained classics.

Information philosophy resolves the Debtor's Paradox
Most of our metaphysical puzzles start with a single object, then separate it into its matter and its form, giving each of them names and declaring them to be two coinciding objects. Next we postulate a change in either the matter or the form, or both. It is of course impossible to make a change in one without the other changing, since we in fact have only one object.

But our puzzle maker asks us to focus on one change and insist that the change has affected the status of only that one, usually claiming that the change has caused that one to cease to exist. This follows an ancient view that any change in material constitutes a change in identity. Has the debtor's identity really changed with a change in his material?

The modern metaphysicist knows that all objects are always changing and that a change in identity may always preserve some information of an entity. The puzzle claims that an aspect of the object persists if the relative identity, or identity "in some respect" has not changed.

To create a paradox, we use two of our three axioms about identity,

Id1. Everything is identical to everything else in some respects.

Id2. Everything is different from everything else in some other respects.

We (in our minds) "pick out" one respect whose identity persists over time because of Id1 and a second respect which changes in time because of Id2.

We now have one object that both persists and does not persist (in different respects, of course), the very essence of a paradox. We call them different objects to create the puzzle.

In the Debtor's Paradox, Epicharmus emphasizes the change in the debtor's matter. But material constitution is not identity. The material parts of the debtor do not make contracts.

As the Stoics would have said, it is both material substance and immaterial qualities (the Skeptics suspect two things in one place?) taken together that constitute a person.

Just as Dion can survive the loss of a foot, just as human beings survive the almost complete replacement of their atoms and molecules - several times in a lifetime, so the person can survive the destruction and regeneration of material parts

In the Academic Skeptic version of the Growing Argument, any change of material produces a numerically distinct individual. But the Stoics say this is just destruction and generation, not true growing. Real growth and decline happens to the entity whose identity we can trace through time by its bundle of peculiar qualities. This includes the debtor's memory of making the contract, when he claims "I am not the same person who made that contract."

As Aristotle would have argued, it is the mindful thinking persons, of the debtor and the lender, who agreed on the contract. Their material bodies, and perhaps external materials such as paper and ink, merely embodied that contract.

References
Baker, L. R. (1997). "Why constitution is not identity." The Journal of Philosophy, 94(12), 599-621.
Johnston, M. (1992). "Constitution is not identity". Mind, 101(401), 89-105.
Noonan, H. W. (1993). "Constitution is identity." Mind, 102(405), 133-146.
Sedley, David. 1982. "The Stoic Criterion of Identity." Phronesis 27: 255-75.
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