I got this puzzle from The Futility Closet, which I have decided to add to my links:
Suppose we have a complete wooden ship, and one day we replace one of its wooden planks with an aluminum one. Most people would agree that the ship survives this operation; that is to say, its identity remains unchanged. But suppose that we then replace a second plank, and then a third, until our wooden ship is made entirely of aluminum. Is this the same ship that we started with? If not, when did it change?
Thomas Hobbes adds a wrinkle: Suppose that, as we did all this refurbishing, someone had gathered up all the discarded wooden planks and used them to assemble a second ship. What are we to make of this? “This, without doubt, had also been the same numerical ship with that which was at the beginning; and so there would have been two ships numerically the same, which is absurd.”
And philosopher Roderick Chisholm adds another: “Let us suppose that the captain of the original ship had solemnly taken the vow that, if his ship were ever to go down, he would go down with it. What, now, if the two ships collide at sea and he sees them start to sink together? Where does his duty lie — with the aluminum ship or with the reassembled wooden ship?”