1. Concerning the Mohists and their competition:
The critic says that the Mohists agree with "normal
people" on the propositions
in Section II. All agree that the superset is more
relevant than the subset.
They disagree with normal people on the propositions
in Section III because they
want to affirm that the subset can be more relevant
than the superset. In the
propositions in Section IV, everybody else originally
maintains that in these
cases a subset is indeed a subset, i.e., that we have a
situation like this:
{cats (Fluffy)}
rather than like this
(pets {Rover) working dogs}
where we are really considering two
intersecting sets. But these other people
are not consistent. For when we talk
about life spans and fate, we find {total
life cycle (death)} being believed by
the Mohists, whereas "everybody else"
believe this picture:
{normal life
cycle ( ** } deaths).
Most deaths fit in the joint region ( ** } but some
are found outside the normal
life cycle, according to "the world."
2. On Logic in Early China:
I think that upon examination of this chapter it is very clear that the author(s) were well aware of the need for clarity in talking about sets and subsets, and were clearly aware that the Mohists and other thinkers could come to opposite conclusions and that they could not both be right. So it seems to me that there was a substantial basis for logic here some three hundred years B.C. If the Chinese language did not make it impossible to begin this enterprise, and if, indeed, the enterprise was taken forward a considerable distance, then it must be that there were other, non-linguistic forces that inhibited the development and use of logic in China.
3.
Regarding the "shi er ran" etc., characterizations:
(I replace S and H, B and H,
and A and F from the above formulations with A for
antecedent and C for
consequent in order to make the comparisons of these cases
easier.)
1.
shi` er/ ran/ A --> C, paradigmatic: A=1, C=1; counter: A=1, C=0
2. shi`
er/ bu` ran/ ~(A --> C), paradigmatic: A=1, C=0; counter: A=1, C=1
3. bu/
shi` er/ ran/ ~A --> ~C, paradigmatic, A=0, C=0; counter: A=0, C=1
The three cases indicate that shi` and bu/ shi` may refer to the truth status of the antecedent and consequent, while ran/ and bu` ran/ refer to whether the conditional is affirmed or denied.
If we try to state things in terms of sets and subsets, then:
1. shi` er/ ran/ both superset and subset characteristics apply; superset is essential, subset is accidental. If we lost members of the superset we would not care that we might incidentally lose that member as the member of a particular subset. But we affirm (ran/) applicability of the predicate involved in the proposition to all members of the superset. (Subset membership is accidental.)
2. shi` er/ bu` ran/ superset membership is irrelevant to what is being predicated of the subset member; superset is not relevant, subset is essential.. We deny (bu` ran/) applicability of the predicate involved in the proposition to all members of the superset.
3. bu/ shi` er/ ran/ When any member is removed from the superset we may in so doing be removing a member from a needed subset. Having no eggs to try to hatch is a serious problem for the poultry business. Denial (bu/ shi`) of superset membership analytically guarantees denial of subset membership. And we affirm (ran/) that this is the way things work. (But I think things break down here, because, following (1), I should be able to say that "subset membership is accidental," i.e., non-essential, while it clearly is not. In fact, the whole discussion pertains to how it would be impossible to find a subset member that was not also a superset member. The point of (1) was that we didn't care that something belonged to the subset. The character of these cases, however, is that the subset is defined as the "successful terminations," so we care about them very much.)
Thus, oddly, the formal characterization of these kinds of sentences by translating them into implications seems more appropriate to the "shi` er/ ran/" kind of terminology than is describing them in terms of sets -- even though the main body of the discussion appears to be about sets. It almost seems that the issue of implication is a subtext of the discussion that did not get carried over into the actual writing of this chapter.