Section II On the Irrelevance of Accidental Qualities
|S||H||S → H|
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)|
¬(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
¬Approaching well → ¬Falling into well.
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.
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.)