  While Parfit's arguments against nonreductionism and in favor of  reductionism are striking and important, for our purposes what  matters is how he articulates and develops reductionism and how he  argues for the surprising conclusion that the identity relation is in fact not what matters in survival. To begin, he suggests at times  that the most plausible reductionist criterion of personal identity  is the Psychological Criterion. As we saw earlier, this criterion  maintains that in order for X to be identical to Y, X must be uniquely psychologically continuous with Y. Psychological continuity is potentially a branching, one-many relation, i.e., it could conceivably hold between me-now and more than one person in the future. But identity is an equivalence relation – it is reflexive, symmetrical, and transitive – so it holds only one-one. Thus only by including a “no branching” clause can this criterion of identity avoid a crippling contradiction.