SECTION III

Introductory Remarks -- What this section appears to me to be about:

On the Irrelevance of Differentiae to Mohists

The question examined is this sections is how to correctly evaluate an implication,  X → Y, in the real world—even if ordinary people have preconceptions that suggest another conclusion.

¬(being a Bandit → being Human)  (This statement in formal language means: "It is not the case that: 'If one is a Bandit, then one is a human being.'" This negation expresses the view of the non-Mohist majority.

是而不然  (I think this means something like "the antecedent and consequent are both true, but the compound proposition (involving logical connectives) does not express the way things really are. Remember Abraham Lincolns riddle: "If you count a tail as a leg, how many legs does a cow have?" Lincoln's answer was, "Four, because calling something a leg doesnt make it a leg." I infer that many people in the society of Mo Zi's time wanted a moral justification for executing people. They claimed that it was acceptable to execute bandits because they were not really people. They argued, in effect, "It is not the case that if one is a bandit one is a human being.")

¬(B → H)  ("B" stands for "One is a bandit," and "H" stands for "One is a human being.")

The proposition under study here claims that it is not true that being a bandit implies being a human being. Common opinion has it wrong. The truth is that to kill a human being necessarily implies killing a bandit. So here is a case of confusing  X → Y with Y → X.  

paradigmatic case: B = 1, H = 0
contrary case:        B = 1, H = 1

When someone is a bandit and not a human being, we see that this logical expression would evaluate as true.  That belief is what the general public seems to have accepted as true.
(B = 1 and H = 0, so ¬(1 → 0), and then ¬(0), so 1)

Truth table for the negation of an implication:

"是而不然 " indicates that were the antecedents and consequents both instanced then the implication would be shown false.  Formal logic shows that the Mohists are right, and that the common opinion is wrong. Supposing that John is a bandit, then it is still true that John is a human being. So executing John would be killing a human being.

Examples:     It is not the case that if Ma Barker loves her son she therefore may be known to love human beings in general. (This "bù rán" or denial of validity is correct because the part about her loving all human beings is false. So saying that since she loves her son she loves all people is wrong, so it is "rán" or correct to say that the implication is invalid.)  
                      It is not the case that if a parrot can safely eat crackers then it can safely consume all grain products. (Grain products include things like 200 proof grain alcohol.)

獲之親，人也，獲事其親，非事人也。                    [This implication is invalid.]
The parents of a bondservant are people. For a bondservant to serve his parents is not for him to serve people.
    • Commentary: Here the issue for the majority group of early Chinese thinkers may have been that the idea of  "serving" in "serving parents" is not of the same meaning as the "serving" in "serving people." It is a different relationship. If "to serve" does have the same meaning in both cases, then it is necessary to observe that the statement should be qualified to speak of not serving other people, or to speak of not serving all people.  The Mohists will object that the parents who are served did not cease to be human beings when they became parents. They just joined a different subset of human beings. Saying that bondservants serve human beings does not mean that they serve all human beings, nor does it necessarily mean that they treat all people whom they serve in the same way.

其弟，美人也，愛弟，非愛美人也。                        [This implication is invalid.]
A person's younger brother is a beautiful person. For that person to love his/her younger brother is not for him/her to love a beautiful person. 

車，木也，乘車，非乘木也。                                    [This implication is invalid.]
A wagon is [a] wood[en artifact]. To ride a wagon is not to ride wood.
    • Commentary: It would be fair to say that someone's riding a wooden artifact does not amount to saying that he or she rides all wooden things, but all that is involved here is restricting the range of wooden things that the rider is said to employ.

船，木也，<人>[入]船，非<人>[入]木也。              [This implication is invalid.]
A boat is [a] wood[en artifact]. To enter a boat is not to enter wood. 

盜人，人也，多盜，非多人也。無盜，非無人也。[This implication is invalid.]
A bandit is a human being. An excess number of bandits is not an excess number of human beings. To not have any bandits is not to be without people. 
    Commentary: All this set of statements really establishes is that for some purposes bandits are being counted separately from other kinds of people and given a quota.

奚以明之？                                                   
How are we to get clear on this? 

惡多盜，非惡多人也。                               
To loathe there being lots of bandits is not to loathe there being lots of human beings.

欲無盜，欲無人也。               
To desire that there not be any bandits is not to desire that there not be any human beings.

世相與共是之。                                   
Everybody in the world would affirm these propositions.

[However,]

若若是，則雖盜人人也，愛盜人非愛人也，
If those propositions are the case, then although [we know that] a bandit is a human being, loving a bandit is not loving a human being, 

不愛盜人非不愛人也，                                
Not loving a bandit is not to fail to love a human being, 

殺盜人非殺人也，                                       
and killing a bandit would not be killing a human being. 

    [However, we have already seen above that loving a bondservant is to love a human being, and loving a slave is to love a human being. So what is going on?] 

無難矣。                        
There is no difficulty in this matter:

此與彼同類，世有彼而不自非也，             
The former set of propositions (i.e., the propositions in the previous section) and the latter set of propositions are of the same general form. The people of the world accept the lattrr cases and do not condemn themselves or hold themselves to be in self-contradiction. 

墨者有此而非之，                                       
The Mohists hold the latter propositions, and are opposed.

無<也>  [他]  故焉，                                       
There is no other reason for it:

所謂內膠外閉與?                                            
Is not this just a case of [the others being] what is called "being stuck solid on the inside and being locked closed on the outside,"

心毋空乎內，膠而不解也。                        
"There is no space left in their hearts; they are stuck and cannot get loose."

此乃是而不然也。 
These are all [propositions] that are affirmed but which are [actually] not the way things really are.  

    • Commentary: When both the constituent statements about the real world are found to be true, combining the statements according to the logical operators gives a statement that is in fact not true. In a situation wherein "X is a bandit" is true, and the statement "X is a human being" is also true,  then it will be true to say, "If X is a bandit, then X is a human being." But the people who support the accepted "wisdom of the world" have said: "It is not the case that if X is a bandit then X is a human being." They want to affirm that being a bandit excludes one from the set of all human beings.

Relationships that the author discusses include: 

(1) Bondservants love their parents.

human beings ∋   parents of bondservants

parents of bondservants ∈ human beings

So it is correct to say that bondservants love a subset of human being, that subset being their parents.

bondservants love parents, a subset of human beings 

Schematic: Bondservants  ⇒ ({parents} human beings) 

(2) An elder sibling loves his or her younger brother. Λ That younger brother is a beautiful human being.

the aforesaid younger brother ∈ beautiful people

beautiful people ∋ the aforesaid younger brother

If this discussion were generalized, then it would become somewhat more complicated because the set of younger brothers and overlaps the set of beautiful human beings. Not all beautiful human beings are younger brohers, and not all younger brothers are beautiful human beings. 

So it is correct to say that an elder sibling loves a subset of beautiful people, that subset containing the younger brother of the elder sibling.
Schematic:  elder sibling  ⇒ (younger brother {beautiful human beings) } 

(3) Human beings ride wagons.

wagons ∈ wooden artefacts ∈ wood

wood ∋ wooden artefacts ∋ wagons

So it is correct to say that human beings ride a subset of wooden artefacts called wagons, and that wagons are a subset of things called wood.

The situation is more complicated than the Mohist philosophers have bothered to note because a wagon is also a subset of things that have some kind of provision for seating or standing securely while in motion. Wagons are wooden artefacts that provide a place on which to ride.

Schematic: humans ⇒ ({[wagons] wooden artefacts}wood)

(4)  Human beings enter into wooden boats.

wooden boats ∈ wooden artefacts ∈ wood

wood ∋ wooden artefacts ∋ wooden boats

So it is correct to say that human beings get into a subset of wooden artefacts called boats and that wooden artefacts are a subset of things called wood.

The situation is more complicated than the Mohist philosophers have bothered to note because a boat is also a subset of things that have some kind of an inside. Boats are wooden artefacts that enclose a volume of space.

Human beings enter a subset of wooden artefacts called boats, that subset of artefacts itself being an element of a larger set of things called "wood."

Schematic: humans ⇒ ({[boats] wooden artefacts}wood)

(5) Bandits are human beings. An excess number of bandits is not an excess number of human beings: To not have any bandits is not to be without people. 

(I am going to treat this second sentence immediately above as meaning that for people to regard the number of bandits as being excessive is not for people to regard the number of people as being excessive. I will regard the third sentence as meaning that people desire to eliminate bandits, and so forth. I will summarize this behavior by saying that normal people detest bandits.)

bandits ∈ human beings
human beings ∋ bandits 

(bandits == null set) != (humans == null set) (Saying that there are no bandits is not the same thing as saying that there are no human beings.)

Normal people detest bandits.
Normal people ⇒ {(bandits) human beings}

The above schematics show the reality involved in the cases that the Mo Zi talks about. 

It is also possible to discuss a situation in which there are bandits that happen not to be human beings. Perhaps they are extraterrestrial beings, or perhaps they are raccoons or baboons.
Normal people ⇒ {(bandits) non-human beings}

Here are the truth tables for a couple of logical expressions that investigate the circumstances under which logical connections of two simple expressions are true. (For instance, let the compound logical expression be: "Miss Y is the President of the United States, and Mr. X is the Vice-President of the United States." Supposing that the circumstances, the real-world state of affairs, demonstrate that Miss Y is the President and Mr. X is the Vice-President, then the compound statement turns out to be true. Supposing that Miss X turns out to be President and some third person turns out to be V.P., then the original compound statement was an incorrect. If a contestant in a quiz show is required to identify both the President and the Vice-President, but only gets the identify of one person right, then the contestant does not win.

By examining the truth table above we can see that both verbal formulations amount to the same thing. It is impossible to make a true statement that asserts, one way or another, that bandits are not humans. 

Examining the Venn diagram for this problem we see the same thing given visual form:

The set "bandit" must consist of elements all of which bear the special characteristics of bandits, and they must also bear all of the characteristics of human beings. An analogous set diagram would have "mushrooms" where "bandits" is written, and "toadstools" where "humans" is written. Since it is easier to be dispassionate about fungi, let it be noted at this point that for all mushrooms, to eat a mushroom is to eat a toadstool, but that only some toadstools are the non-poisonous ones we call mushrooms. So while we ordinarily say that humans eat mushrooms, it is nevertheless true that in eating a mushroom one is also eating a kind of toadstool. Similarly, although one may do certain things only to bandits, whatever one does to any bandit is also done to a human being because bandits are also elements of that larger set. When a person becomes a bandit, he or she does not lose the status of human being. 

Now let us examine the statements that the "Xiao Qu" chapter of the Mo Zi makes in regard to slaves and other humans:

1. 盜人，人也。 "To be a bandit is to be a human being."
2. 愛盜人非愛人也。 "To love a bandit is not to love a human being."
3. 不愛盜人非不愛人也。"To fail to love a bandit is not to fail to love a human being."
4. 殺盜人非殺人也。"To kill a bandit is not to kill a human being."

Just as (some) human beings eat mushroom but avoid eating other kinds of toadstools, (some) human beings may kill bandits but avoid killing other kinds of human beings. However, that statement is not the equivalent of what the Mo Zi actually says. The last three statements that are recorded are wrong, and the Mo Zi intends to demonstrate that they are wrong.

The only way that statements 2, 3, and 4 could be correct would be if there were some set of individuals called "bandits" that were not human beings. Perhaps these "bandits" would be raccoons, baboons, or some extraterrestrial creature. But statement 1 says that bandits are human beings.

Statements of this form are called "是而不然."  It migbt be paraphrased to say: "A set of statements that, individually, are objectively true can be used to assert a conclusion that is not true.

"是而不然" indicates that were the antecedents and consequents both true in this world, then the implication would be shown false. Since it is the case that :
"All members of some set, B, are bandits," and "all members of some enclosing set, H, are humans," it is proven that those who dehumanize bandits are in the wrong. They are the people who would assert sentences 2, 3, and 4 above.

The "Xiao Qu" chapter is generally regarded not to have been written by Mo Zi himself, but to have been written by members of a younger generation who worked in or associated themselves with his school. Mo Zi taught jian aior "universal love," and maintained that it is not good for individual members of any society to discriminate in any way against other members. He would not say, "To love a bandit is not to love a human being." Instead, he would say, "To fail to love a bandit is to fail to love a human being."