Identity and Parmenides

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.

Heraclitus and the Doctrine of Opposites and Universal Flux

Plato and Aristotle both attribute to Heraclitus the doctrines that
1) Everything is always changing
2) There is an identity of opposites, such as hot and cold.

Plato and Aristotle argue that these two doctrines are self contradictory because they entail that everything both is and is not at the same time.

Heraclitus, however, probably did not hold to a strong universal flux theory (textually evidenced), nor did he hold to a strict identity of opposites theory (also textually evidenced). Rather, it seems that Heraclitus held to a more moderate flux theory (while the water ever flows, the river itself stays the same and is in fact defined by the flowing water); and he held to a unity of opposites theory, as opposed to an identity of opposites theory. In other words, it is not the case that hot is equal to cold, but that hot and cold are united in their exchange. X can go from hot to cold and back again. It does not go from hot to apricot and back again. Hot and cold are in fact a unity.

What Heraclitus gives us then is not a contradiction, but, rather, a more interesting question regarding persistence through change, i.e., identity. What are the conditions for x to persist through change.