Aristotle’s fundamental law of thought is the law of contradiction (also referred to as the law of non-contradiction). There cannot be an intermediate between contradictories. He declared also the law of excluded middle (or the law of the excluded middle term). These two derived from the law of identity, which says whatever is is. These are called the Aristotelian laws of thought.
> Law of Identity:
With respect to things, the law says that A is A (or anything is itself). Applied to propositions, the law asserts if a proposition is true then it is true.
> Law of the Excluded Middle Term:
Applied to things, it says, anything is either A or Not A.
Applied to propositions, it says, any given proposition is either true or false. For instance, the same thing cannot both exist and not exist at a given moment.
> Law of Contradiction
Applied to things, it says, nothing can be both A and Not A.
Applied to proposition, it says, any given proposition cannot be both true and false.
Some other important things to know:
Immediate inference – The relationship between two propositions that are logically equivalent. That is either both of them are true or both of them are false. They enable us to draw an immediate inference from the truth (or falsity) of either member of the pair to the truth (or falsity) of the other.
Mediate inference – In its simplest form, what we ordinarily mean by reasoning consists of three judgments. We have two judgments expressing two separate ideas, stated in propositions called premises, and we compare each idea separately with a known third idea, resulting in a judgment which we call the conclusion. There are at least three ideas and three judgments involved in the process of reasoning. This process is called mediate inference for the following reason: the agreement or disagreement between two original ideas is inferred through the “mediation” of a third idea with which both original ideas are compared.
Now I can show two syllogisms that point out the difference
Immediate Inference: (2-step)
1. No Dogs are Felines
2. Therefore, no Felines are Dogs
Note: By stating that there are never any Dogs that are Felines, then it immediately is inferred that none of the Felines are ever Dogs. This is a 2-step process by which the inference of the conclusion is given directly in the premise without any mediating premise.
Mediate Inference: (more than 2-step)
1. All Soldiers are Men.
2. Some Heroes are Soldiers
3. Therefore, Some Heroes are Men
Note: Since Soldiers is within the realm of men exclusively and Some Heroes are within the realm of Soldiers, it follows that Some Heroes are within the realm of Men. But we did not come to this conclusion (#3) immediately, but rather through premise #2. By this, the inference has been mediated by way of the second premise and could not be inferred immediately by the first premise.
A Proposition (Universal Affirmative)-All S is P
E Proposition (Universal Negative)-No S is P
I Proposition (Particular Affirmative)-Some S is P
O Proposition (Particular Negative)-Some S is not P
So, what do you think? Was Aristotle on target in formulating his logic? Remember, noone else had done anything like this before him. He deserves, and has received, many accolades for his work on logic. Moreover, besides the Boolean square of opposition, hardly any changes have been made to the traditional square which were formed on the basis of his teachings (though there are schools of thought which do not subscribe to these rigid rules).