Derek Parfit's “reductionist” account of personal identity (including the rejection of anything like a soul) is coupled with the rejection of a commonsensical intuition of essential self-unity, as in his defense of the counter-intuitive claim that “identity does not matter.” His argument for this claim is based on reflection on the possibility of personal fission. To the contrary, Simon Blackburn claims that the “unity reaction” to fission has an absolute grip on practical reasoning. Now David Lewis denied Parfit's claim that reductionism contravenes common sense, so I revisit the debate between Parfit and Lewis, showing why Parfit wins it. Is reductionism about persons then inherently at odds with the unity reaction? Not necessarily; David Velleman presents a reductionist theory according to which fission does not conflict with the unity reaction. Nonetheless, relying on the distinction between person level descriptions of first-person states and the first-person perspective itself, I argue that Velleman's theory does not eliminate fission-based conflict with the unity reaction.