Sorting Through Sophistries:
The Fleet of Theseus
By Gabriel Blanchard
These are all simpler than they look. Just don't go putting them between a pair of mirrors that are facing each other.
Setup
This week, we turn to another family of closely-allied fallacies. They are exemplified in the following series of non-riddles:
A man sat before a heap of sand, trying to find which grain made it a heap. He examined them all, and none of them was meaningfully different from the others, yet when he had finished, the heap was gone.
One of the prized relics of Athens was the ship in which Theseus sailed home from defeating the Minotaur. As its planks and ropes and sails wore out, they were replaced, until one day none of the original material remained.
A man was set by his superior to govern Crete in his absence. Warning him that he must be shrewd, the superior told him, “A Cretan poet once said ‘All Cretans are liars’; he was certainly right about that.”
The reason these are not riddles is, riddles have answers.
This is, maybe, the only circumstance in which Alfred North Whitehead‘s rather bewildering metaphysics would start to seem appealing, as an easier way to understand things! But let’s tackle each of these one by one.
Punchline #1: The Heap Paradox1
To review: A man sat before a heap of sand, trying to find which grain made it a heap. He examined them all, and none of them was meaningfully different from the others, yet when he had finished, the heap was gone.
This is related to some of the first fallacies we covered back in January. Other sophistical ideas are effectively the same, like the continuum fallacy: a vase is a different thing from a cup, but where do you draw the line between a tall, oddly-shaped cup and a squat, rounded vase? The notion here is that distinctions which can’t be defined—or can’t be defined to the level of precision somebody is demanding—don’t exist; this too is a fallacy, one we shall have cause to return to in a post of its own. But that aside, insofar as ideas are tools,2 whether a tool does its job is only determined by how precise it is if its job is precision. That simply isn’t the job of every idea or of every word. Heaps do not need exact definition for us to know what they are; they’re one of those. There doesn’t need to be a specific grain of sand that makes something a heap or not a heap. Heaps aren’t that important! (In fact, they’re so trivial, it is even possible to spare the obvious joke about mountains and moleheaps.)
Punchline #2: The Ship of Theseus
The question of whether this still is the ship of Theseus is a rather famous (or infamous) one, first posed not later than Plutarch: One of the prized relics of Athens was the ship in which Theseus sailed home from defeating the Minotaur. As its planks and ropes and sails wore out, they were replaced, until one day none of the original material remained. So is it still Theseus’ ship?
The idea of the building, its design, are the essence of the building. The intention of the original builders is what survives. The wood of which the design is constructed decays and is replaced when necessary. To be overly concerned with the original materials is to fail to see the living building itself.
While it can be entertaining to pretend we don’t know the answer, we do: Yes, of course it is. The reasons we know this are legion; for example, if it weren’t, the fact that our cells are all physically replaced on a regular basis3 would be a major legal problem. One could also point to the fact, that, when making Theseus’ ship in the first place, as long as a piece of wood is the right shape for the bit we’re working on, it doesn’t matter whether it came from a tree eighteen yards north-northeast of the boulder that looks like a big mushroom, or a tree four yards west of that one: it’s all the same, as far as the ship is concerned. But the simplest way of putting it comes from C. S. Lewis.
“The days when I was a star had ceased long before any of you knew this world …”
“In our world,” said Eustace, “a star is a huge ball of flaming gas.”
“Even in your world, my son, that is not what a star is but only what it is made of.”4
Punchline #3: Recursion Into Recursion Into …
This particular recursion problem takes its name from a real Cretan poet, quoted in the first chapter of Titus, and is therefore known as the Epimenides paradox: A man was set by his superior to govern Crete in his absence. Warning him that he must be shrewd, the superior told him, “A Cretan poet once said ‘All Cretans are liars’; he was certainly right about that.”
This is an example of a self-referential paradox—a statement that, in some way, renders itself problematic; it is not merely self-defeating, but self-defeating “both ways,” so to speak. Another example, in which the “both ways” problem is more clearly illustrated, is the old chestnut
The following sentence is false. The previous sentence is true.
In the early and mid-twentieth century, many celebrated Austrian and British mathematicians (such as Kurt Gödel, Bertrand Russell, Alfred North Whitehead, and Ludwig Wittgenstein) worked in a discipline called set theory, a branch of mathematics aimed at disentangling paradoxes like this one. For practical purposes, of course, refutation is hardly needed! Nobody really does think that every single individual person from Crete tells nothing but lies; that would be ridiculous. The “paradox” is, in reality, only a joking exaggeration being interpreted too literally.
That being said. There is a remote kinship between this theoretical brain teaser and another of our fallacies—one that, by its name alone, might shock even Aristotle …
Tune in next week for more.
1In more formal contexts, this is occasionally called the sorites paradox, from the Greek sōreitēs [σωρείτης]—which simply means “heap.”
2This may feel like a counter-intuitive way of thinking about ideas and words. However, a good way to understand this approach to language can be found in the sciences: the job of a scientific theory is to help us understand how things work and make accurate predictions. If our best way of imagining a theory isn’t really accurate, that doesn’t necessarily matter, as long as the theory still does its job. (E.g., when atoms are shown in grade-school discussions of physics and chemistry, they’re usually drawn like little solar systems; atoms don’t really look much like that, but it’s an easier way of understanding them in the beginning, and the more complex stuff can be left for those students who pursue physics at a higher level.
3Talking in averages, all our cells are replaced every seven to fifteen years.
4The Voyage of the Dawn Treader, ch. XIV: The Beginning of the End of the World (p. 117).
Gabriel Blanchard™, whose cells are all original, is CLT’s editor at large; he lives in Baltimore, MD.
If you’d like read more about sophistries and thought-traps at the Journal, you can find our introduction to the topic here, or sample posts on common fallacies and mistakes like the Dunning-Kruger effect, cherry-picking or suppressing evidence, resorting to straw men, or the recently-named etiquette breach, sea-lioning. If you’d rather learn more about the ideas people tend to use fallacies on, you might enjoy our posts on beauty, truth, goodness (and evil), unity (and many-ness), or those on less abstract questions like medicine, technology, and war. Thank you for reading the CLT Journal.
Published on 8th August, 2024. Page image of replicas of the Olympias, a modern reconstruction of an ancient Athenian trireme. Triremes are known to have been in use in Greece by the sixth century BC, though the place and time of their invention is not known with certainty—if there was any historical Theseus, he probably lived in the ninth or eighth centuries, so that whether his ship was or could have been a trireme is an open question.