What is this Law, and why is it important for not just Muslims but every Human?
This article is a summary of an audio lecture from Sheikh Ali Al-Hakim from the Islamic College.
In classical logic, the law of non-contradiction (LNC) (or the law of contradiction (PM) or the principle of non-contradiction (PNC), or the principle of contradiction) is the second of the three classic laws of thought. It states that contradictory statements cannot both be true in the same sense at the same time, e.g. the two propositions “A is B” and “A is not B” are mutually exclusive.
This is the most used concept in our minds, and it is used in everyone’s mind, however few are formally aware of it.
So here it is in simple terms. If I say that “our fish has died”, it means that the fish has died, and it can not be alive and dead in the same context. If we say that 1+1 = 2, we can not say that it is also 3 or 4 etc, it has one or the other, it can not be both.
So basically if we know something is true in one sense, it can not be the opposite in the same sense. If we know a switch is turned on, it can not be turned off at the same time, in the same respect.
Ibn Sina, a Persian philosopher, said,
“Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.” ( Metaphysics, I.8 [sect. 12, Marmura ed.]; commenting on Aristotle, Topics I.11.105a4–5)
The law of Non Contradiction is one of the Three traditional laws of knowledge: identity, non-contradiction, excluded middle.
Are there any objections?
Dialetheism is the view that some statements can be both true and false simultaneously. It is basically a denial of the Law of Non-Contradiction. It is not based on any sound reason or logic,
A classic example of dialetheist thought are riddles and paradoxes :
“All statements are true” is a false statement
The issues with such paradoxes is not that Dialetheism is true, but rather we need to break down the statement and appreciate that we need to conceptualize it. What does that mean? It means that we must further define what we are discussing. In the above example, the concept of “all statements are true”, is false. Therefore the second portion is true. However if we take the definition of statement to be just the first portion, then we can run into some trouble.