Friday, August 01, 2008

Logic I, Lesson 4: The Five Predicables, Pt. 2: Difference and the Porphyrian Tree


From Aristotle's Categories, 3:

If genera are different and co-ordinate [i.e., at the same level, and not subordinate to one another], their differentiae are themselves different in kind. Take as an instance the genus 'animal' and the genus 'knowledge'. 'With feet', 'two-footed', 'winged', 'aquatic', are differentiae of 'animal'; the species of knowledge are not distinguished by the same differentiae. One species of knowledge does not differ from another in being 'two-footed'.

But where one genus is subordinate to another, there is nothing to prevent their having the same differentiae: for the greater class is predicated of the lesser, so that all the differentiae of the predicate will be differentiae also of the subject.

From Porphyry's Isagoge to Aristotle's Categories, 3:

[Difference.] [O]ne is most properly said to differ from another, when it varies by specific difference, as man differs from horse by specific difference, i. e. by the quality "rational." Hence, those [differences] which render [a member of a genus] another thing [from the other species within the genus] are called specific differences, [...] for the difference "rational" being added to "animal," makes it [another a species of the genus "animal"] [...] so that [it] renders it another thing [...]. According then, to the differences which produce another thing do the divisions of genera into species arise, and the definitions arising from genus and such differences are assigned. [...]

They also define it thus, "difference is what is naturally adapted to separate things which are under the same genus," as "rational" and "irrational" separate "man" and "horse," which are under the same genus, "animal." Again, they give it in this way: "difference is that by which each singular thing differs," for "man" and "horse" do not differ as to genus, for both we and horses are animals, but the addition of "rational" separates us from them; again, both we and the gods are "rational," but the addition of "mortal" separates us from them. [...] Wherefore specific differences will be such as produce another species, and which are assumed in explaining the very nature of a thing: and concerning difference this is sufficient.
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