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:

I think the first two lines should be: 且夫讀書,非好書也。好讀書,好書也。

Moreover, the line beginning the Mohist half of this section should be:


(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 may mean 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.


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 real-world sequences actually occur. A causal sequence, or, in other words, the assertion that the ending of an event follows the beginning of the same event, may be symbolized by writing: 

Beginning ⇒ Ending

B ⇒ E 

If we restate the material in this section in terms of these "practical implications" or "causal sequences," then we might get hypotheses such as the following:

Approaching the well ⇒ Falling in the well

Evaluating these sequential assertions depends on what happens in the real world. 

✔  means that something is observed in the real world for some time and place. ✖ means that something is not observed in the real world for the same time and place. Because of experimental error, good practice would mean making many observations and only then marking some 

B E B ⇒ E
Early termination of attempt
Not confirmed "Uncaused" event
Not confirmed "Fiction" or conjecture

Then "Approaching the well ⇒ Falling into the well" would be:

A F A ⇒ F
Careful people can stay safe.
Not confirmed How did that happen? Interesting! 
Not confirmed "Fiction" or conjecture at this point in history.

In fact we see many cases in which people approach the well without falling into the well. Should the hypothesis B ⇒ E be accepted then? Obviously it should not be accepted. However, it may be worth working with situations in which there is only one way for an event to procede. "Helium will be produced only if Two hydrogen nucleii are merged." That formulation amounts to saying that "If it is not the case that Two hydrogen nuclei are merged then Helium will not be produced." 

¬( h + h) ⇒ ¬ He  or  ¬(h + h) ⇥ He

By the above schema I mean to indicate that failing to have two hydrogen nuclei get merged, the process toward the generation of one Helium atom will be blocked.

Hypothesis: Whenever it is not the case that two hydrogen nuclei get merged, then the production of helium is blocked.
What could happen in the laboratory?

h h ¬ (h + h) He ¬ (h + h) ⇥ He Paraphrase
No test, so not confirmed. Helium was acquired by the expected means.
No test, so not confirmed. Two hydrogen nuclei merged but no helium! Strange!
Test was failed. Some unknown process must be producing helium!
Test was passed. Just as we thought. Nothing ever comes from nothing or even from not enough.

The hypothesis that is being tested is whether helium can be obtained without two hydrogen nuclei being merged, but in the first case two hydroged nuclei were merged, so the more stringent requirement was not tested. If two hydrogen nuclei were merged but something strange happened and helium was not produced, then the result was very strange, but the result says nothing about alternate ways of getting helium. If we are doing some other experiment, e.g., directing a beam of laser light through a block of blue cheese, and while the cheese remains as before, no light appears, the cheese does not heat up, but copious amounts of helium are evolved, then there is, contrary to all we have been taught, a novel way to produce helium. In that case, ¬(h + h) ⇒ H, and the hypothesis that there is only one way to produce helium must be abandoned. If very many experiments are done in which hydrogen nuclei are not merged and helium is not produced, it would be incorrect to say that the hypothesis has been scientifically proven, but it would be acceptable to say that the hypothesis has been well confirmed experimentally. 

The idea from the Mo Zi seems reasonable. How will it work out under closer examination? It said, "Being About to fall into a well is not Falling into a well." Earlier the idea was entertained that perhaps someone was able to fall into a well without having first moved up to it. Perhaps the person was born on a platform immediately above the well, and then the platform collapsed. The idea smacks of sophism since one could argue that even if the person is immediately over the well, he or she would still move some amount before actually being in the well, and, on top of that, who is to say that the person was not "about to fall" since he or she was born. Suppose that someone wanted to argue that there is no alternative way to fall into a well?  "The person will Fall into a well only if he or she is first About to fall into a well," or, "If it is not the case that the person is About to fall into a well, then the person will ⇥ (be blocked from) Falling into a well."

A ¬A F ¬A ⇥ F Paraphrase
Not confirmed
The person approached the well and fell in, as expected.
Not confirmed
The person approached the well but did not fall in. Lucky guy!
He was in bed and the next moment he was in the well! How?!
Confirmed Tried all my life. Never fell into well without first approaching it.

This process works out just as did the one above. We would not be surprised to learn that in the entire history of the world nobody has been moved by transporter beam or magic from a safe place into a well with no intervening steps. It still might happen someday, but for practical purposes it is appropriate to ignore the possibility.  If things did happen that way, everyone would be highly disturbed.

Since the Mohists rejected the first hypothesis above (B ⇒ E), 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 (A ⇒ F), 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 constitutes citizenship?
The name of the subset is taken as the name of the set? or the name of the subset is not taken as the name of the set?
The attitude taken toward the subset is or is not the attitude taken toward the superset.
The part of some entity doing something is or is not referred to as the whole entity doing that thing.
The part of some entity being some way is or is not referred to as the whole entity 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.

A further note on logic and computer control of processes in the real world. In many cases humans want to specify things to do under certain circumstances. For instance, "If the Temperature in the reactor reaches 200° C, then Sound the alarm."

In a computer circuit, truth is indicated by supplying current to an input or an output to a circuit. Suppose there is a computer chip with six legs. Two of the legs are used to power the chip, and are irrelevant to the logical decisions that the chip will deliver. Let leg 3 represent the "if" part of the logical construct, let leg 4 represent the "then" part of the logical construct. Let leg 5 represent the truth or falsity of the compound (if...then...) statement. This logic chip is to be used to monitor the functioning of the computer. It needs to assure the nuclear facility that when the temperature goes above specified limits the alarm actually sounds. But the "if-then" truth table does not give the right way for this logic chip to work:

T S T → S ¬(T → S) Interpretation of the output. Report this  output  initiates
1 1 1 O Temperature is high and alarm sounds.  No action needed. 
1 0 0 1 Temperature is high and alarm does not sound. Repairs are needed!
0 1 1 0 Temperature is normal and alarm sounds. ✖✖✖✖✖✖✖✖
0 0 1 0 Temperature is normal and alarm does not sound. No action needed.

It should not be possible for the alarm to go off when the temperature is normal. So an ordinary "if... then..." decision on correctness is insufficient to the needs of the nuclear facility because if the temperature is not out of range and yet the alarm sounds, no warning will be sent to the managers of the nuclear facility.  Ordinary language does not suggest the correct solution to this practical problem, which is a chip that evaluates a statement of the form, "It is not the case that: The Signal sounds if and only if the Temperature reaches 200° C."

S T ¬ (S ↔ T)
1 1 0 Functioning normally
1 0 1 Malfunctiong, send warning!
0 1 1 Malfunctioning, send warning!
0 0 0 Functioning normally

The statements about falling into the well that appear in the Mo Zi are not of this kind either. However, it is worth looking at the possibility that someone might maintain the following: "You will fall into the well if and only if you approach the well."  That sentence expresses the kind of fatalism that some people, but not the Mohists, would believe. The same kind of thinking is sometimes found in modern times, for instance in the cases where somebody maintains a scare scenario such as, "One drink and you're an alcoholic."