Ben Thomas in Scientific American:
“Let’s say you have an axe. Just a cheap one, from Home Depot,” opens the horror-comedy novel John Dies at the End. “On one bitter winter day, you use said axe to behead a man.” This blow splinters the axe’s handle – so the story goes – so you get the hardware store stick a new handle on the blade.
The repaired axe sits in your garage until one day the next spring, when you damage the blade while fending off “a foot-long slug with a bulging egg sac on its tail,” which requires another trip to the store to replace the axe-head. Unfortunately, when you arrive home, you’re greeted by the enraged reanimated corpse of the man you beheaded last year. He takes a long look at the weapon you’re holding, and he screams, “That’s the same axe that beheaded me!”
The question is, Is he right?
It’s a riddle with a long and distinguished pedigree, dating at least as far back as ancient Greece, where the historian Plutarch posed essentially the same question by telling a story involving an aging ship, an adventurous crew, and a notable absence of vengeful zombies. Philosophers through the ages have regarded the riddle as a sort of dead end, because any given person’s answer hinges not on any actual attribute of the axe or ship in question, but on how the answerer chooses to define the word “same.” In one sense, if we swap the ancient Greek ship for a zombie-slaying axe, we’re not even posing the “same” riddle.
More here.