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In 'Aristotle and the Finitude of Natural Kinds', 1 I argued against the view of James Franklin 2 that Aristotle's natural kinds form a continuous or dense series.I argued that this would involve an infinity of natural kinds and that Aristotle denies any actual infinity.I also argued that Aristotle would not tolerate an infinite series of natural kinds composed of both actual and potential kinds.Actual kinds have actual instances; potential kinds are merely possible kinds, which have no actual instances.I argued that natural kinds are actual or real for Aristotle and that their reality depends on their having actual instances.In 'Species in Aristotle', 3 Franklin seems to concede that natural kinds do not form an infinite series of actual kinds.He finds plausible, however, the suggestion that natural kinds form an infinite series of actual and potential kinds.He points out that Aristotle holds that quantities such as length are continuous and infinitely divisible, even if only potentially infinitely divisible, since they can never actually be so divided.There would be no actual infinity of lengths, but none the less they would form a dense series; it is just that some lengths are instantiated by actual objects and others are not.Why could not, suggests Franklin, an analogous situation hold for natural kinds?If Aristotle countenances the continuity of length, even though not every length can be actually instantiated, then he could countenance a continuity of natural kinds, dense and infinite, in which some kinds are instantiated and others are not.What relevant differences could there be between natural kinds and lengths that would bar this parallel?An important distinction holds.Each division in an object of length brings into existence more actual lengths.Since divisions of this sort can go on generating lengths indefinitely, and in principle to infinity, Aristotle holds that lengths are infinitely divisible, at least potentially, and thus form a continuum of lengths.(Perhaps he should say that they form only a 'potential continuum'.)What analogous situation could there be for the generation of a dense, or infinite, series of natural kinds?We cannot divide an instance of a natural kind indefinitely, and thereby generate more natural kinds.Aristotle does not accept the
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