The principle of the identity of indiscernibles would seem, in the forms in which it is usually stated, to be at best contingently true. It does not appear that even Leibniz held it to be logically inconceivable that different things should have all their properties in common. That ‘no substances are completely similar, or differ solo numero’1 was established, in his view, by the principle of sufficient reason, but he conceded that ‘the supposition of two indiscernibles seems to be possible in abstract terms’.2 Indeed, it may plausibly be argued that even to ask whether things can be different without being discernible from one another is to admit that it is logically possible. For what sense could there be either in affirming or in denying that two things could have all their properties in common unless they were already distinguished? As Russell put it, ‘it is a sheer logical error to suppose that, if there were an ultimate distinction between subjects and predicates, subjects could be distinguished by differences of predicates.
KeywordsInfinite Series Sufficient Reason Relational Predicate Predicative Function Philosophical Essay
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