Implications, inverses and wholly illogical interpretations

Implications, inverses and wholly illogical interpretations

One cannot estimate the amount of despair and anger that one, versed with logic, has to absorb in a world where logic is thrown to the wind

Aristotle, long back, recognized that persuasion may be achieved via appealing to credibility, to emotions or to logic. Among them, the most convincing and the most satisfying is, unarguably, an appeal to logic.
Emotional arguments cannot be counted equal to logical arguments. In the words of Douglas Adams, “All opinions are not equal. Some are a very great deal more robust, sophisticated and well supported in logic and argument than others.”
Language is used for persuasion, emphasis, communication besides making one’s point, exercising one’s power and entertaining others. The fact remains that language is used in a plethora of ways, but it is misused in no less manners. More often than not, language is blown out of proportion.
Among the most misused or ill-used connectives of language is that of an implication. Implications are also called conditional sentences. Before we embark upon the journey of getting wind of how and where implications are misused, let us try to gauge what constitutes an implication.
An implication is a statement of the type “If p, then q”. For example, the statement “If the Sun is a star, then the Moon is a satellite” is an implication. The p-part of an implication is termed as its hypothesis or antecedent. The q-part is termed as the conclusion or its consequent. In our example, “The Sun is a star” is the hypothesis, and “The Moon is a satellite” is the conclusion.
One of the most important things about implications is understanding their truth values. In other words, one ought to know which implications are true and which are false. It may come to many as a surprise, but the fact is that an implication is always true except the case when the hypothesis is true and the conclusion is false. This means that implications with false hypotheses are true irrespective of what their conclusions be.
After one has grasped this, one should be able to understand that implications such as “If the Sun is a chocolate, then the Moon is a hockey stick” is true irrespective of the fact that its hypothesis is false. Similarly, the implication, “If Rome was built in one day, then life is a walking shadow” is also true. It is a hard reality to acknowledge. Right?
A lot of people fail to be well-versed with this very basic fact about the truth value of an implication and accordingly they misuse language. Not knowing it is simply akin to playing ducks and drakes with language.
Having understood what implications are and having grasped what constitutes their truth value, the next thing to gulp down is the notion of the inverse of an implication.
Given the conditional statement “If p, then q”, the conditional statement “If not p, then not q” is called the inverse of the given conditional statement. For example, the inverse of “If the Sun is a star, then the Moon is a satellite” is “If the Sun is not a star, then the Moon is not a satellite”. A lot of people pass the inverse of an implication for the original implication. Some others do acknowledge that an implication is not to be passed for its inverse, yet they consider the two logically equivalent, meaning that one of the two provides sufficient ground for determining the truth value of the other. This is, however, far from being a fact.
The inverse of an implication may be true of false irrespective of the truth value of the original implication. For example, “If two is a number, then five is a number” is true, and its inverse “If two is not a number, then five is not a number” is also true because the hypothesis of the latter is false, as discussed before.
One cannot estimate the amount of despair and anger that one, versed with logic, has to absorb in a world where logic is thrown to the wind and interpreted as per one’s own wishes and whims. Seeing the misuse of implications in diurnal matters is both agonizing and devastating as the same time.
Although this write-up may not be good enough to incite the readers to become well-versed with the correct use of implications and their inverses, yet it seems fit enough as a caveat. It should act as a deterrent every time the reader things of implications and their misuses. Go and grab some sources and learn the basics of implications. Go and save the misuse of language, in general and that of implications, in particular.

The writer is Assistant Professor at Government Degree College Sopore. [email protected]


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