Theseus' Clothes-Pin
Chandler (Hugh S.)
Source: Analysis, Vol. 44, No. 2 (Mar., 1984), pp. 55-58
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  1. Plutarch reports: “The ship wherein Theseus2 and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, in so much that this ship became a standing example among philosophers, for the logical question as to things that grow; one side holding that the ship remained the same, and the other contending that it was not the same. (Plutarch's Lives, 'Theseus')”
  2. This is the puzzle about Theseus3' ship in its original (pre-Hobbesian) form. The same puzzle can arise in regard to a tree, a frog, or a person. It is a mystery to me why some philosophers say the puzzle4 only arises in regard to artefacts (see, for example, "Wiggins (David) - Sameness and Substance", 1980, pp. 86-995). Consider Theseus6' tree. A golden-delicious apple tree suffers progressive rot. Bit by bit sections of its trunk, limbs, and even its roots, are removed and replaced by grafts from a Macintosh. Eventually there is so little golden-delicious left philosophers begin to argue about whether or not it's the same tree at all.
  3. I'm going to concentrate on just one of the many issues Theseus7' ship brings to light; but, for simplicity's sake, I turn the ship into a clothes-pin named 'Alice'. Alice is composed of two wooden legs, a and b, and a metal spring, c. In addition, there are two spare legs, d and e (the spring is not likely to wear out). I assume that our 'intuitions' about whether or not a clothes-pin can survive successive destruction and replacement of both legs (as opposed to the destruction and replacement of just one) are in conflict. Simplifying again, we have two possible sequences: (diagram omitted)
    • Along track 1 Alice suffers no loss of legs.
    • But look at the sequence of events along track 2. First leg a is destroyed and Alice gets d as a replacement. Then leg b goes the way of leg a and is replaced by e. This means either that Alice no longer exists, or that Alice has two new legs.
  4. The case helps us see problems about the denotation of the name 'Alice', and problems about its intension, or, if you prefer, the range of Alice's 'counterparts'. I think Alice shows that ordinary proper names for things like ships, frogs and so forth, cannot be regarded as rigidly designating8 just one individual, or a cluster of individuals.
  5. We are going to need two kind terms9 linked to the two obvious disambiguations of the identity conditions for clothes-pins. So let's say that a 'clothes-pin two' can survive successive destruction and replacement of both legs, while a 'clothes-pin one' cannot (that is to say, successive destruction of both legs destroys a clothes-pin one). And let's suppose that, in point of fact, Alice endures10 without any replacement of parts until after 2. Then Alice is caught in a fire and reduced to ashes and a molten blob. Thus the world takes track 1.
  6. The problem about the intension of the name 'Alice' is this: are both the clothes-pin one and the clothes-pin two on track 2 possible Alices (Alice counterparts), or is just one of these Alice? The problem about the denotation of the name is this: does 'Alice' (partially) denote two individuals, namely the clothes-pin one and the clothes-pin two on track 1, or does it denote just one individual there? (For an exposition of 'partial denotation' see "Field (Hartry) - Quine and Correspondence Theory", 1974.)
  7. It would be absurd to hold that only the clothes-pin one or only the clothes-pin two on track 2 is Alice and also hold that 'Alice' partially denotes the clothes-pin one, and partially denotes the clothes-pin two, on track 1. Eliminating this absurdity, we have three candidate theories:
    1. Only the clothes-pin one or the clothes-pin two is the possible Alice on track 2; and 'Alice' denotes just the clothes-pin one, or the clothes-pin two, on track 1; but not both.
    2. Both the clothes-pin one and the clothes-pin two on track 2 are (partially) possible Alices; and 'Alice' denotes just one individual on track 1.
    3. Both the clothes-pin one and the clothes-pin two on track 2 are (partially) possible Alices; and 'Alice' (partially) denotes the clothes-pin one and (partially) denotes the clothes-pin two, on track 1.
  8. It's fairly clear that theory A is unacceptable. What are we to suppose determines whether Alice is a clothes-pin one or a clothes- pin two? It cannot be actual future clothes-pin talk, for we may never bother to 'clarify' this matter (why on earth should we?). Are we to pretend that diligent research would – at some ideal limit – reveal that clothes-pins can, or cannot, survive replacement of both legs?
  9. One might imagine that theory A is only implausible in regard to artefacts. But surely it fares no better as applied to trees or frogs? Future researchers may find it useful to stipulate that an individual frog can, or cannot, be said to exist after such and such replacement of parts. But then alternative stipulations would be equally 'correct'. Which of these possible future stipulations fixes the present denotation of a frog's proper name?
  10. Consider theory B (I intend theory B to be one David Lewis could accept; see especially his Postscripts to "Lewis (David) - Counterpart Theory and Quantified Modal Logic", pp. 39-43). 'Alice' denotes just one individual with somewhat indeterminate potentialities. If 'Alice' denotes one individual, then, I take it, that individual must be both a clothes-pin one and a clothes-pin two. Suppose we name this clothes-pin one 'Alice one' and this clothes-pin two 'Alice two'. Presumably both of the new names, and 'Alice', all denote the same thing. Here we approach an inconsistent triad (see "Kripke (Saul) - Naming and Necessity", e.g. p. 3; see also Keith Donnellan, 'Kripke and Putnam on Natural Kind11 Terms', "Ginet (Carl) & Shoemaker (Sydney) - Knowledge and Mind").
    1. 'Alice one' and 'Alice two' rigidly designate their extensions.
    2. At t2 on track 2 Alice one is not the same thing as Alice two.
    3. Alice one is (in fact, i.e. on track 1) the same thing as Alice two.
  11. Claim (ii) looks all right. Alice one no longer exists on track 2 at t2. (Destruction of leg d, and, later, of leg e, destroy Alice one.) But Alice two still exists. Hence Alice one and Alice two cannot there and then be the same thing. Thus we must reject (i) or (iii). Theory B, I take it, commits us to (iii), and therefore to the rejection of (i).
  12. The same point can be made in the language of counterpart theory. Theory B commits us to holding that 'Alice', 'Alice one', and 'Alice two', all denote the same thing. But Alice one and Alice two do not have the same counterparts on track 2. Hence theory B forces us to hold that one individual, qua Alice two, has a counterpart it lacks qua Alice one.
  13. If 'Alice one', or 'Alice two', does not designate its extension rigidly, how can 'Alice' do so? Theory B yields that 'Alice' in fact denotes Alice one and Alice two. But it is not the case that wherever 'Alice' partially designates something it partially designates Alice one (remember track 2 at t2). Hence, on this theory, 'Alice' does not rigidly designate its extension.
  14. Let's shift to theory C. Here we suppose that 'Alice' partially denotes the clothes-pin one on track 1 and partially denotes the clothes-pin two there. The clothes-pin two survives (or has a counterpart) at t2 on track 2; but the clothes-pin one does not. Proponents of this theory can hold that 'Alice one' and 'Alice two' are proper names rigidly designating their extensions.
  15. What about 'Alice'? A name designates each of the things it partially designates. Thus 'Alice' designates both Alice one and Alice two on track 1. At t0 and t1 on track 2 'Alice' still designates Alice one and designates Alice two. What happens at t2? 'Alice no longer exists' is there and then true in so far as 'Alice' is interpreted as 'Alice one', and false in so far as 'Alice' is interpreted as 'Alice two'. Hence (by the move Hartry Field recommends in such cases) 'Alice no longer exists' is neither true nor false there and then.
  16. Does this theory allow 'Alice' to designate its extension rigidly? The theory says that 'Alice' does not designate just one individual, hence it certainly can't designate just one individual rigidly. But can the name rigidly designate both Alice one and Alice two? No; look again at t2 on track 2. Thus 'Alice' does not rigidly designate each of the individuals it partially denotes.
  17. In counterpart terms: Alice one and Alice two have different counterparts. Are we to think that Alice has a counterpart only where both Alice one and Alice two do? Clearly not, for, on that view, Alice does not have a counterpart at t2 on track 2 (whereas, in fact, it is indeterminate whether or not Alice has a counterpart there then). Should we hold that Alice has a counterpart wherever either Alice one or Alice two has one? That won't do either since it would yield that Alice could survive successive destruction and replacement of both legs and this is indeterminate. The counterparts of Alice one and Alice two are Alice's partial counterparts.
  18. In its generalized form, theory C will strike some readers as extravagant. C theorists presumably hold that an ordinary proper name partially denotes a distinct individual for each of its partial intensions. For many names, one guesses, the number of such intensions is non-denumerable12. The idea that ordinary names denote so many individuals may make theory C look less attractive than B. We naturally suppose that a frog, or a clothes-pin, is just one individual.
  19. Summing up; theory A was declared unacceptable. Theory B may be all right; but it will not permit us to regard 'Alice' as rigidly designating its extension. Those who are fond of rigid designators must turn to C. 'Alice one' and 'Alice two' are rigid by hypothesis. But ordinary names like 'Alice' remain a disappointment.


Claims (contra Wiggins) that the "Ship of Theseus13" paradox doesn't just apply to artifacts.

In-Page Footnotes

Footnote 1: Less a diagram and one statement of symbolic logic.

Footnote 4: Footnote 5: Ie. "Wiggins (David) - Sortal Concepts: and the Characteristic Activity or Function or Purpose of their Compliants (S&S)".

Footnote 8: This is a radical claim.

Footnote 9: Footnote 10: Is verb this carefully chosen to distinguish “endurance” from “perdurance”?

Footnote 12:

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  1. Blue: Text by me; © Theo Todman, 2019
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