The Ship of Theseus and “The Outer Limits of Reason”

In his book The Outer Limits of Reason, MIT computer scientist Noson S. Yanofsky explores a number of paradoxes that, he argues, are intrinsic to the process of cognition. According to his argument, the universe does not contain contradictions, but our thinking about it does and must. If this is true, any representation of the universe must be inaccurate, not simply in details, but also in substance. They can illuminate some things, to be sure, but only at the cost of obscuring others. Thus the mind-independent state of the world cannot be known, but only approximated. Moreover, only certain features of it can be approximated at any one time within any one system. Either pursuing all of the logically necessary consequences of one system, or invoking multiple incommensurable systems (to use Thomas Kuhn's vocabulary), will produce insoluble contradictions, and thus paradox.

One of the paradoxes that Yanofsky discusses in order to make this point is called the Ship of Theseus. According to a story related by Plutarch, Theseus was the king of Athens and a great sailor. In order to honor him, the Athenians decided to set up his ship in the harbor as a kind of public monument. But after a while the sail got tattered, so they replaced it. Then some of the wood started to rot, so they replace that too. Then the oars, the ropes, the fittings, and so on, until eventually every component of the ship had been replaced. So, was it still the ship of Theseus?

This question was discussed by the ancients, and they arrived at a number of different answers. Heraclitus held that it was not the same ship, since the concept of “The Ship of Theseus” bears an unstable relationship to the actual thing designated at any given time. If I point to the ship one day, and say, “Here is the ship of Theseus,” and you point to it on the next day and say the same thing, we are designating approximately the same thing, but not exactly so, since the ship has undergone at least some change in the interval. The longer the time duration, the more extensive the change is bound to be. After an interval of centuries, what is left except the concept itself? But the concept derives its apparent solidity only through reference to some actual thing. If that thing is insubstantial, the concept must be as well. Thus Heraclitus’s famous saying, “one cannot step into the same river twice” is equally applicable to all phenomena. It’s not the same river, it’s not the same ship, neither you nor I are the same as we were yesterday, etc. “All is flux”; it is only the fictitious stability of language that makes it seem otherwise.

According to Aristotle, it was the same ship, because it had only undergone insubstantial changes. We need to distinguish between essential and accidental features of objects. An essential feature is one, in virtue of which an object is what it is. A bookcase is for holding books, an axe is for chopping, and a ship is for sailing. It is in virtue of these properties that they are so-called. A bookcase that can’t hold books is no bookcase, an axe that can’t chop is no axe, and a ship that can’t sail is no ship. But as long as they can do these things, they are properly so-called, no matter what other changes they undergo. In the same way, the Ship of Theseus really is still the Ship of Theseus, because its essential properties remain the same. What does it matter if the accidental features, like the sails or oars, change? After all, they probably changed in Theseus's time as well. He may have changed them himself. Did he think it was no longer his ship? If he didn’t, why would we? Consider also where Heraclitus’s philosophy is likely to lead us. If language can’t latch on to reality, what’s the point of philosophy? What’s the point of thinking systematically at all? Heraclitus’s philosophy seems to negate, or to render trivial, the very concept of truth—surely an undesirable result for a philosopher!

A more recent explanation has been proposed by Ted Sider, who holds that identity is a matter of persistence over time. While there is considerable debate over just what time is, one position (held by Kant and Einstein) is that time is best understood as a dimension, just like the three dimensions of space. If that is true, then there is one and only one state for each object at any given moment of time, not only for the past and present but also for the future. Change is only apparent. Actually, everything that has or will or can happen is, in some extra-temporal sense, already there. Our perception of time is just that—a perception—and properly located in the mind rather than the universe itself. If we accept this view, then there is no paradox about the Ship of Theseus. What makes it the Ship of Theseus is neither an arbitrary naming convention nor an accumulation of essential properties, but the fact that the object bears a temporal and uninterrupted relation to its own past and future.

Or we can hold, with Yanofsky, that the question has no good answer: that it is a true paradox. This is how he explains his own position:

The ship of Theseus does not really exist—as the ship of Theseus. There is no exact definition of what is meant by the ship of Theseus. It exists as a collection of sensations but not as an object. Yes, if you kick it you will feel pain in your toes. When you look at it, you will see brown wood. If you lick it, you will taste stale wood and salt water. But these are all just sensations that one learns to associate with something we call “ship of Theseus.” Human beings combine these sensations and form the ship of Theseus. Of course, the ship exists as atoms. But it is made of atoms—as atoms. The atoms are not tagged as the ship’s atoms. Rather, it is we who make these atoms into a whole entity called a ship. It is we who further demarcate this ship as somehow belonging to the mythical general Theseus. … It’s all in our mind. (p. 37–8)

In other words, language, and thus thought, cannot latch on to reality as it is. In reality there is no mind-independent Ship of Theseus, only sensations so designated, and whatever it is in back of those sensations that produces them. We can conjecture about what it is that produces those sensations, and some of those conjectures may prove more useful than others, but since the “thing in itself” (to borrow Kant’s terminology) can neither be experienced apart from sensations, nor cognized apart from language, both of which are mind-dependent, their mind-independent nature cannot be known. We are up against a true limit of reason, and one that language does not provide a solution to, but in fact creates.

We are left to conclude that the Ship of Theseus both is and is not a real object. It is real in that it is a given object of perception: standing next to this ship one cannot doubt its tangible reality, or its distinctness as apart from other ships, and so on. If one wants to think about or communicate those sensations, one is forced to think and speak as if it had a real and distinct identity. But the moment one treats that “as if” as an “it is,” one invites all sorts of unanswerable questions about the “it is.”

The solution is the same here as it is in a Zen koan—to realize that there are limits to what reason can actually do for us. We can neither abandon the “as if,” nor define it such that it is isomorphic to the “it is.” By the same token, we know that there really is an “it is” and that our “as if” does tell us something about it. We cannot dispense with either of these concepts, nor reconcile the contradictions they produce. Reason requires that we recognize that reason has limits—and that is a paradox.

Daniel Halverson is a graduate student studying the History of Science and Technology of nineteenth-century Germany. He is also a regular contributor to the PEL Facebook page.

by