Isagoge: Chapter 11 — Of the Community and Difference of Species and Difference

You’d think, given the title of the chapter, that this would another compare and contrast. Not so. What we get instead is a disquisition on combinatorial math. (Feel free to skip to the bottom.)

We have shown then, wherein genus differs from the other four, but each of the other four happens also to differ from the rest, so that as there are five, and each one of the four differs from the rest, the five being four times (taken), all the differences would appear to be twenty. Nevertheless, such is not the case, but always those successive being enumerated, and two being deficient by one difference, from having been already assumed, and the three by two differences, the four by three, the five by four; all the differences are ten, namely, four, three, two, one. For in what genus differs from difference, species, property, and accident, we have shown, wherefore, there are four differences; also we explained in what respect difference differs from genus, when we declared in what genus differs from it. What remains then, viz. in what respect it differs from species, property, and accident, shall be told, and three (differences) arise. Again, we declared how species differs from difference, when we showed how difference differs from species; also we showed how species differs from genus, when we explained how genus differs from species; what remains then, viz. in what species differs from property and from accident, shall be told: these, then, are two differences. But in what respect property differs from accident, shall be discovered, for how it differs from species, difference, and genus, was explained before in the difference of those from these. Wherefore, as four differences of genus with respect to the rest, are assumed, but three of difference, two of species, and one of property with regard to accident, there will be ten (differences altogether), of which, four we have already demonstrated, viz. those of genus, with respect to the rest.

We have five things, genus, difference, species, property, and accident. We’re going to compare and contrast each pair of these; and once we’ve compared and contrasted A with B, we don’t need to compare and contrast B with A. So there are 10 pairs, rather than 20. Woohoo. In the next chapter, I imagine, we’ll get on with comparing and contrasting difference and species.

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