The ship of Theseus is a good example of the problem of identity. Plutarch wrote about Theseus' ship which would be repaired plank by plank while out at sea. Philosophers have thought about this problem in relation to the ship: at what point is the ship no longer the same ship? The Mereologicaly Theory of Identity (MTI) states that the identity of the ship is located in the identity of its parts, such that X = Y if and only if all the part of X are also the same parts in Y. The advantage of MTI is in that it is very easy to draw the line of identity. The problem, however, is that we no longer can call identical many things that we believe persist through chance, including ourselves. If we deny MTI, however, then we must determine where the line is during change that transforms one thing into another.
Parmenides was concerned about such problems. His criticism of Heraclitus, and the paradoxes that Heraclitus seemed to introduce, was that if we take our observations about the world seriously, then we cannot help getting into logical trouble. Parmenides, therefore, determined to solve the problem of the one and the many (being and becoming) by ignoring the sensible world and arguing purely from reason, a priori. His became a deductive argument that all things are one and that change is an illusion.
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