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Thread: Ship of Theseus paradox

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    creator kari's Avatar
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    Ship of Theseus paradox

    Theseus owns and sails a ship. Every month, when he sails to port, he has one old plank of his ship replaced with a brand new plank. By the time 10 years has passed, not a single original plank of wood remains in Theseusí ship. Unbeknownst to Theseus, however, the ship repairman has saved all of the old planks that he removes from Theseusí ship.

    Slowly, he constructs a new ship. By the time 10 years has passed, he has acquired every single original plank from Theseusí ship and arranged them exactly as they were in Theseusí original ship.

    Which of the two existing ships is numerically one and the same ship as Theseusí original ship? Is it the ship with all new parts, or the re-constructed ship with all of the original parts?
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    Now we know... Asteroids Champion ACow's Avatar
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    Which of the two existing ships is numerically one and the same ship as Theseus’ original ship? Is it the ship with all new parts, or the re-constructed ship with all of the original parts?
    Ah, but what do you mean by numerically one and the same?

    The programming language lisp is interesting in this case because it has several different notions of "equality", whereas many people/other languages are only familiar with thinking in terms of one, even though using it might be ambiguous or multifaceted. We can extrapolate some of these concepts to cases of real life, or indeed, philosophical problems :P

    We might say things are 'eq' when they literally refer to the same object. To the same identity. For example: I am not comparing this banana with another banana. I am comparing this banana with itself. A banana is 'eq' to itself.

    We might say things are 'eql' when they are numbers of the same value and representation, or characters that are the same. So '3' is eql to '3'. But does the '3' on the left literally share the same identity as the '3' on the right? That is to say, are they 'eq'? It does not follow that 3 eq 3, if we can distinguish between the two "3"'s, it seems reasonable to state they are not eq. We might say they are two different "instances" of "three". Of course, if you're a Platonist...maybe you think they really do refer to the same ideal '3'. Even here there are ambiguities. Bloody math. '3' is not 'eql' to '3.0' which is not 'eql' to the complex number represented by #C(3 0).

    We might say things are '=' when they are "numerically" the same. 3 = 3. Does 3 = 3.0? They are not literally the same identities, so they aren't eq. They are the same number, but not the same representation. So they aren't 'eql'. But numerically, they refer to the same number, so we say they are '='. 3 = 3.0 = #C(3 0).

    Then we can go up a bit more. I have a volkswagen car. Its green. You have the same model volkswagen car. It too, is green. My car is 'equal' to your car. They are not literally "the same object", so they aren't 'eq'. And they aren't numbers....are they?....so they don't appear to be '=' or 'eql' either. We might, in the general sense, say that things are 'equal' when they are both instances of 'isomorphic' objects.

    And we can even go up from there. What about testing equality between two humans? If they are identical twins, then we might say that they are 'equal'. But can we come up with an equality predicate that isn't 'eq', 'eql', '=' or 'equal', but which represents common membership or derivation from some class or set? Lets maybe call that 'equalp', and say that one human is equalp to another human. They aren't intuitively as "similar" as our two particular volkswagens, but maybe they're the same in the sense that two volkswagens that are two different models are still volkswagens. Oh god...how far can we go?

    /rather than try to answer the question directly with our friend theseus, I'll reflect that there's some interesting eastern philosophy parallels. There is of course the analogy of never being able to step into the same river twice, because the water that is in the river now is not the water that was in the river then. There's even a groovier buddhist story that I can't for the life of me remember the name of, where a man comes between two fighting demons, one which wants to kill him and the other which tries to keep him alive. The first demon tears the man's arm off, the second demon finds another arm and sticks it back onto his body. The first demon pulls his eye out, the second demon puts another eye back in. The man lives to tell the tale...or does he? He wonders who he is, and about the nature of self, and whether he is the same man as he was before, even though all parts of him have now been replaced.

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    Dr.Awkward Robcore's Avatar
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    Neither ship has all new parts if the plank exchanges happened over 10 years. Neither is the original ship. Both are aged versions of it...expressions of two different potentials of the original ship.

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    <3 gator's Avatar
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    Both ships and iterations in between are Theseus' ship. The ship isn't the physical materials. It is the design, ownership and continual use of those materials. What makes them all Theseus' ship is their common history of being used as Theseus' ship.

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    凸(ಠ_ರೃ )凸 stuck's Avatar
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    I had an existential crisis about this once, and discovered the word "perdurantism".

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    Meae Musae Servus Hephaestus's Avatar
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    Which one does Theseus own? That's his ship.
    --Mention of these things is so taboo, they aren't even allowed a name for the prohibition. It is just not done.

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    I wonder if future people will undergo a similar process to the ship. Replace all the aging bits (brain, bones, eyes, etc) until it's a whole new you, then repeat.

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    This is like the body. Except for a few extremely slow growing, persistent tissues, all the cells of the rest of the body get replaced--I don't know what the turnover rate is but I do know that it's different for different cells. So, given that your cells are different from the original cells you started with, are you the same person you were ten years ago? Obviously, you get older, you learn new things, you gain/lose strength, agility, etc. But, based on your body, what about your identity? This is a biological version of the paradox.

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    凸(ಠ_ರೃ )凸 stuck's Avatar
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    ^
    That's the existential crisis I was talking about.

  10. #10
    Quote Originally Posted by Hephaestus View Post
    Which one does Theseus own? That's his ship.
    Yep. If I'm looking out of it and in control of it then it's mine.

    As far as whether two things are the same, there are different types of equivalence and those parameters have to be defined. I don't see how two ships could ever be 'numerically' equivalent though, since ships aren't numbers.

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