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Law of Non-Contradiction
Posted: Friday, February 07, 2014
When Aristotle wrote his fourth book on Metaphysics he introduced the Law of Non-Contradiction. Basically this states that things cannot be and not be at the same time. The law isn’t concerned with how we know what we know but with how we know what it is that we know. So the Law of Non-Contradiction isn’t to be confused with epistemology. It doesn’t make a difference how one came to know something, what matters is how one knows what it is that they know.

How does someone know what it is that they know? Well first off one would have to prove it. Most likely they would use an argument to prove what it is they are talking about. This is where Aristotle comes up with the axiom. An axiom is a statement that is true and needs no further proof, qualification or quantification. This doesn’t mean there isn’t more proof that the statement is true, it just means it’s not needed. The statement is true on its own in the form it is in.

To present an axiom to someone, Aristotle created the syllogism. This is a form of argument that, when presented correctly, is a stated axiom. So the syllogism is the way of expressing the true statement, but because the statement is non-falsifiable and needs no other proof to be true it is also an axiom. This is what Aristotle felt was the key to proving what it is that one knows – making a simple, true statement that could not be falsified and needed no other proof to be true.

The syllogism has two parts, the premise and the conclusion. The premise is broken up into three parts: the major premise (the predicate or assertion of the conclusion), the minor premise (the subject of the conclusion) and the middle premise (major and minor premise supporting facts). An example of this form of argument would be: all A’s are B’s; all B’s are C’s; since A’s and B’s are identical and since B’s and C’s are identical it is not possible for A’s and C’s to be different; therefore all A’s are C’s.

The middle premise is always excluded from a syllogism. The middle premise is a supporting statement to the major and minor premises and is not needed to quantify the statement any further. So the correct form of this argument would be: all A’s are B’s; all B’s are C’s; therefore all A’s are C’s. This is a statement in a true form that, even though it can be proven more, it doesn’t need to be.

This whole process is called deductive reasoning. Deductive logic is taking something from a general form to a precise form. This is not to be confused with inductive reasoning, which is logic that starts with something precise and expands it into something general. The most famous of all syllogisms, which Aristotle came up with to prove his development of the axiom and the syllogism, was: “All men are mortal; Socrates is a man; therefore Socrates is mortal”.