Surgeons replace one of your neurons with a microchip that duplicates its input-output functions. You feel and behave exactly as before. Then they replace a second one, and a third one, and so on, until more and more of your brain becomes silicon. Since each microchip does exactly what the neuron did, your behavior and memory never change. Do you even notice the difference? Does it feel like dying? Is some other conscious entity moving in with you?
-Steven Pinker on the Ship of Theseus Paradox