On the off-chance any of my readers are unfamiliar with the ship-of-Theseus question (also sometimes simplified as the grandfather's ax paradox), it goes a little something like this:
Theseus has a ship, and he sails around the ancient Greek world having various adventures. As he goes, he replaces things - a plank is rotten, so he swaps it out, the sails have holes, so he buys new ones, etc. Eventually, every single piece of the ship is replaced with a new, equivalent piece.
Some demigod fanboy, however, is following Theseus around, collecting all these cast-off pieces. Once he has the full set, he reassembles the ship from its original constituent parts, and sails off to MythiCon. He then finds a collector at the con and says "hey, I've got the real deal, here - the ship of Theseus, 100% authenticity guaranteed!". The collector, of course, says "hey, what do you take me for? Theseus is still out sailing his ship, so this can't be it!"
Who's right? Which ship is the real one?
And, of course, if we revisit the idea from a few strips ago of all your cells swapping out every seven years... which you is the real you?