Today:
(a) More discussion of the divisions within "self-directed herding." It is easy to understand why John Cooper wrote the last paragraph of the dialogue introduction the way he did, exhorting the reader to work through the "visitor's use of lengthy 'divisions.'"
(b) Plenty here to help us try to answer Colfert's question from yesterday. What's pretty obvious is that part of the recommendation is not to split a class into class X and not-X, expecting an a priori guarantee that the not-X part will be a _class_. What's less obvious is (i) why this matters so much in context, (ii) what 'middle' means in this context, and (iii) what on earth a class is. Some brief, unresearched, and probably fairly obvious comments... re: (i), presumably the idea is that inquiry goes better if the things you're thinking about pick out (something like) natural kinds. Re: (ii), my sense is that 'middle' means nothing more being a location that allows for equal splitting, in a very deflated sense of "equal"--that is, the fact that a class splits into two classes under distinction X is sufficient to guarantee that distinction X counts as a 'middle.' Re: (iii), who knows! My instinct in (i) is to think roughly in terms of natural kinds.
(c) It's been a while since I groaned out loud at a math pun (see 266a-b). A brief note is that in the phrase "the power of the diagonal of our power," the phrase "the diagonal of our power" is not saying what the dunamis is the dunamis _for_, the way that the diagonal of the unit triangle is the dunamis of or for the two-foot square; rather, it is saying which dunamis the "animals' dunamis" is to be identified with; the diagonal of (what) our dunamis (is a dunamis for) is _itself_ a dunamis, and it is this dunamis that is the dunamis of the four-foot square.
That might not have made sense: the point is just that, unless I'm wrong, "diagonal" is coordinated (is that the right word?) with the first "power," not a statement of what the power is a power "for."
Happy reading!
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