WR-INI may entail IM but does not so necessarily: it is conceivable that personal identity relations consist in something which is itself neither identical with nor reducible to a spiritual substance nor identical with nor reducible to aggregates or parts of psychologies and physiologies. In fact, Descartes' own view that personal identity is determined by "vital union" relations between pure Egos and bodies, with the persistence of the Ego being regarded as sufficient for the persistence of the person but the person not being wholly identifiable with the Ego, could be a weakly reductive view of persons. It is merely weakly reductive, however, because the identity of the phenomenon that specifies the necessary and sufficient conditions for personal identity does not itself follow from anything other than itself. While a weakly reductive criterion of personal identity relations is explicable in terms of the identities of phenomena other than persons, the identities of these phenomena themselves are not explicable in other terms: their identity may be, as we would suppose "soul identity" to be, "strict and philosophical", and not merely "loose and popular" (Butler 1736).
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