Discussion of the Several Sections of the Text
The sentences in Section II the author calls propositions that are affirmed and are actually the case. (Or, the antecedent and the consequent are both affirmed, and the implication is affirmed.) They are things like:
(horses {white entities) ...}
There is a subset of horses called white horses, but for many purposes even though we know an individual belong to the subset that fact is irrelevant to whatever we want to get done in the real world. (Or he may mean that both propositions are affirmed, and the implication involved is a true implication.)
The propositions in Section III the critic calls propositions that are affirmed but cases where things are not really that way. (Or he may mean that when both the antecedent and consequent are affirmed, the implication is to be denied.)
(human beings [my relatives])
There is a subset of human beings called "my relatives," and it makes sense for me to love them although I do not love all human beings. Alternately, if we accept that bondservants may be said to serve their family members without being said to serve people, then it would seem equally correct to say that the state may execute bandits without being said to execute human beings. Another way to say the same thing would be to affirm that the state does legally execute certain criminals, but it does not go around killing citizens at random.
Section IV starts out with a passage that is corrupt. It has been emended, but I think the authorities who emended it got it wrong. The original is:
且夫讀書，非好書也。
I think the first two lines
should
be:
且夫讀書，非好書也。好讀書，好書也。
且夫鬥雞，非好雞也。好鬥雞，好雞也。
Moreover, the line beginning the Mohist half of this section should be:
且夭，非夭也。壽，止夭也。
(My emendation is similar to that of Sun Yirang, but more thoroughgoing.) My translation would be:
Reading a book is not the same as liking a book. Liking a reading book is liking some book. (Liking to read books implies that I like books.)
Pitting cocks against one
another is not the same as liking cocks. Liking game
cocks is liking some
cocks.
.
...
Being about to die at an early age is not to die at an
early age. To live to a
ripe old age is to avoid dying at an early age.
The critic literally says of the things in this block of texts that they are cases where [the Mohists] deny things and that that corresponds to the way things actually are. I think this may mean that the Mohists have made some denials and that in so doing they have got things right, or the passage means that both the antecedent and the consequent are denials, and the implication itself is a true one.
The sets all have the general form:
( preconditions
{fulfillments})
( preparation {execution})
( fowl {gamecock})
(
total course of one's life {act of dying})
The argument is that you cannot have just the tail-end of an event. You have to have the necessary steps that lead up to it. You can't have baby chicks without fertilized eggs being brooded over by a mother hen. On the other hand, you can have eggs that get brooded over yet do not hatch.
Most people are not avid fanciers of roosters. Some people are avid fanciers of game cocks. But you can't have a game cock that is not a chicken.
You can't fall in the well if you never approach it, but lots of people approach wells without ever falling in.
You cannot die lest you have first lived your life to its end. So it stands to reason that if you have died you have lived all of your life. So, paradoxically, anyone who dies "before his time" has lived what is (for him) a full life.
Being given a mandate does not mean that you will necessarily accept that task. So unless you have accepted the mandate you really don't have one.
OR:
Bestowal of a mandate for a certain life-span does not mean that you'll live that long. It you don't maintain the bestowed life-span properly, then you will in effect abrogate it. (I think this is a special case of the former interpretation.)
So the material in this section boils down to a discussion of the conditions under which "if X then Y" sentences are true, but it's done in terms of sets.
X --> Y, in Venn diagram form is
{Y [X] }.
If we restate the material in this section in terms of implications, then we might get hypotheses such as the following:
Approaching the well --> Falling in the well
A F A --> F
Positive Positive
hypothesis is supported
instances instances
Positive Negative
hypothesis is destroyed
instances instances
Negative Positive
hypothesis not tested
instances instances
Negative Negative
hypothesis not tested
instances instances
In fact we see lots of cases where people approach the well without falling into the well, so we reject the hypothesis. Let's try something else:
Fall into the well -->
previously Approached well (or, equivalently:)
Fall into the well <--
previously Approached well
(You can fall into the well only if you
previously approached the well.)
F A F --> A Positive Positive hypothesis is supported instances instances
Positive NULL
hypothesis would be destroyed if we found
instance Negative
instances of Approach along with
the positive instances of
Falling in.
Negative Positive hypothesis not tested
instances
instances
Negative Negative hypothesis not tested
instances
instances
In fact we see no small number of cases wherein people approach wells and then fall in, but we find no cases wherein people are magically transported into the mouth of the well without crossing the intervening distance, so this hypothesis is accepted.
Since the Mohists rejected the first hypothesis above, we can conclude that they knew how to evaluate an X --> Y schema in cases where X is positive and Y is negative. Since they accepted the second hypothesis, it is clear they knew how to evaluate an X --> Y schema in cases where X is negative and Y is positive. To get straight on these logical judgments is no simple matter.
Beginning logic students frequently have trouble accepting validity of the truth table for "if-then" statements. Why, they ask, does the logic text author accept examples such as: "If Churchill turns out to be a communist then the Allies will win WWII," as true implications? For some reason, logic text writers like to pick examples that strain students' credulity. Students don't have trouble with X and Y both being obviously true, e.g., "If Margaret Thatcher is a conservative then she will distrust Jerry Rubin." Nor do they have trouble with X and Y both being obviously false, e.g., "If the moon is made of blue cheese, then people can get there by sucking moonbeams through straws." But even when we pick appropriate examples, it is difficult to get people to create correct truth tables for implications, or to accept valid truth tables prepared by others. In fact, American students have been known to argue that since success does not follow with certainty upon completing a college education it is therefore pointless to continue with college. One must argue forcefully that it is unheard of for someone to be an illiterate sweeper of bar room floors one day and a world-famous brain surgeon the next day before they begin to see the error of their previous reasoning.
Since the Mohists did not have trouble with the tough cases, we can be reasonably assured that they did not have trouble with the trivial cases when both anteccedent and consequent are either both true or else both false, even though those cases are not directly treated. So I think it is safe to say that they had an adequate understanding of implication.
Finally, in Section VI, there are the composite sets where we would accept one of a pair of propositions and reject the other -- even though they are superficially alike:
Residing in vs. owning a residence in a
country, which is citizenship?
Name of the subset is taken as name of the
set? or name of the subset is not
taken as name of set?
Attitude taken
toward the subset is or is not attitude taken toward the
superset.
The part
doing something is or is not referred to as the whole doing that thing.
The
part being some way is or is not referred to as the whole being that
way.
Mention of set inclusion does not give an indication of whether the set has a single member or multiple members. Some characteristics pertain to individual members of the set, and some characteristics pertain to the set itself (e.g., whether the set is large or small). Indeterminacy pertains to which individuals you may encounter next, not to the individuals themselves. Individuals have enduring characteristics. If you encounter Silver you will always encounter a white horse. Whether you encounter a white horse (which has always been a white horse) or a black horse, or some other color of horse, will depend on many contingencies. So the "indeterminacy" rests with which individuals you encounter (with set members en masse), not with the individuals themselves.