This thesis examines Derek Parfit's theory of personal identity. Parfit argues that what matters in the continued existence of persons through time is psychological connectedness and continuity (relation R), and that the identity relation does not matter. He makes this claim through a series of arguments which, he says, inevitably lead to the conclusions that relation R is the only relation that matters, in all cases. I argue that Parfit does not convincingly demonstrate that relation R is in fact all that matters. In examining each of Parfit's arguments, I show that it is possible to draw conclusions that are inconsistent with those drawn by him. I argue that this shows Parfit's position to be an arbitrary one. If Parfit's arguments do not necessarily lead to the conclusion that relation R is all that matters in questions of survival, then his theory is not an adequate solution to the problem of personal identity.

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