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By Nicholas Jolley

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2 Any entity which lacks genuine unity is not a substance (by a stipulative definition of ‘substance’ as ‘that which has true unity’). 3 Therefore, any entity whose essence is extension is not a substance. Leibniz’s reply to Arnauld’s criticism is highly instructive. Leibniz firmly denies that he is simply defining ‘substance’ as ‘that which has true unity’. Nonetheless, he does recognize an equivalence between being a genuine unity and being an ultimate subject of predication; as Leibniz tells Arnauld: To cut the point short, I hold as an axiom the following proposition which is a statement of identity which varies only in the placing of the emphasis: nothing is truly one being if it is not truly one being.

We may wonder, then, why an army fails the test of being an ultimate subject of predication. An army of course is as much a subject of predication as honesty; we can say, for example, that the Fifth Army fought bravely. Leibniz’s explanation of why an army is 40 Leibniz not an ultimate subject of predication is found in a letter to Arnauld: ‘it would seem . . that what constitutes the essence of a being by aggregation is only the way of being of the things that make it up; for example, what makes the essence of an army is just the way of being of the men who make it up’ (WF 124).

Or I do not know what truth is’ (WF 111–12). Let us call this ‘the conceptcontainment theory of truth’. Leibniz’s concept-containment theory of truth is perhaps best understood as a bold generalization of a theory which seems natural in the case of universal truths. Consider the proposition: ‘Gold is a metal’.

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