SYNOPSIS

The author of the "Xiao Qu" chapter of the Mo Zi seems to me to make three main points about the correct use of language and its connection to logic. These three points are covered in succeeding sections of the chapter:

Section II On the Irrelevance of Accidental Qualities

S H S → H
1 1 1
1 0
0
0 1 1
0 0 1

是而然 
being a Slave → being a Human
S → H
Paradigmatic case: S = 1 H = 1
Contrary case:        S = 1 H = 0

"是而然 "under real-world conditions wherein the antecedent and consequent are both true statements, the postulated implication is shown to be true.

Section III On the Irrelevance of Differentiae*

B H (B → H) ¬(B → H)
1 1 1 0
1 0 0 1
0 1 1 0
0 0 1 0

是而不然
¬(being a Bandit → being Human) 
¬(B → H)
paradigmatic case: B = 1, H = 0
contrary case: B = 1, H = 1

"是而不然" under real-world conditions wherein the antecedent and consequent are both true statements, the postulated implication is found to be false.

SECTION IV On Anti-fatalism

A F ¬A ¬F ¬A→¬F
1 1 0 0 1
1 0 0 1 1
0 1 1 0 0
0 0 1 1 1

不是而然
¬Approaching well → ¬Falling into well. 
¬A→¬F
paradigmatic: A = 0, F = 0
countercase: A = 0, F = 1  

"不是而然" under real-world conditions wherein neither the antecedent nor the consequent are true statements, the postulated implication is shown to be true.. 

This conclusion is rather remarkable, it seems to me. In Western symbolic logic the same conclusion is accepted, and one has to explain what it can mean to say that some statement such as, "If Abraham Lincoln was the thirty-second president of the United States then whales lay their eggs on the seashore." The Chinese example is more acceptable to our ordinary sense of causation. "If you do not approach the well, then you will not fall into the well." This logical consequence is, in spirit at least, like the maxim taught to kids given their first jack knife: "Always cut away from yourself." It's a good rule, but there are other ways to injure yourself with a knife. What about the cases where both terms of the if-then clause are false? Suppose that we negate both terms of: "If you do not cut toward yourself then you will not get cut," making a proposition such as, "If you do cut toward yourself then you will get cut." It happens that one can cut toward oneself and still escape getting cut. If you were born on a platform immediately over a well and the platform collapsed, then you could fall into a well without having moved toward it. So why do we accept the truth of (A = 0) → (F = 0) in formal logic? 

The principle in formal logic if rather like the observation in the natural sciences that theories cannot be proven true but can only be proven false. It is impossible to prove that, e.g., "All cetaceans cannot do calculus," because the next cetacean examined may be a whiz at calculus. A statement such as, "If Malia Obama is elected President of the United States, then the first human mission to Mars will be funded once more," is "true" because there is no possibility that it has been falsified. Malia Obama may at some future time become President of the United States, and a future mission to Mars may be funded, de-funded, and given funding once more. The only way to show the implication false would be to have Malia Obama elected to the White House, and to have the Mars mission be abandoned for lack of funding.

An easier way to get an understanding of the situation wherein both terms are false, perhaps, is to consider promises and lies.  Supposing that somebody says, "If I give you an puppy, then I'll give you a doghouse to house it in," is that person a liar if he or she gives you neither a puppy nor a doghouse? The person never promised to make a gift of a puppy. He or she only said that any such gift would come with something needed for the dog's care.

There is no indication that the early Chinese authors had thought things out to this point. Their reasoning seems to have been restricted to situations in which doing one thing is physically dependent on one and only one possible precursor activity, so if you can only fall down a well if you first move yourself or are moved by others across the intervening distance to the well, and you do not so move, then it is impossible that you could fall down the well. If that interpretation is correct, then 不是而然  means that if you do not provide the necessary conditions for something to happen, it will not happen.


* A more down-to-earth example of type III:
¬(thriving on Mushrooms → thriving on Toadstools)
M T ¬(M→T)
1 1 0
1 0 1
0 1 0
0 0 0

We do not have evidence to support the contention that if an organism thrives on mushrooms it will also thrive on toadstools (or, fungi in general). We know of a organisms that thrives on a subset of fungi, mushrooms, but not on all fungi. So we assert that it is not the case that if an organism thrives on mushrooms it will (necessarily) thrive on toadstools (or, fungi in general). (I don't know a word that includes just mushrooms and toadstools.)