While Aristotle focused on many different subjects, one of his most significant contributions to the world of philosophy and Western thought was his creation of logic. To Aristotle, the process of learning could be placed into three distinct categories: theoretical, practical, and productive. Logic, however, did not belong to any one of these categories.
Instead, logic was a tool used to attain knowledge, and was, therefore, the very first step in the learning process. Logic enables us to discover errors and establish truths.
In his book, Prior Analytics, Aristotle introduced the notion of the syllogism, which turned out to be one of the most important contributions to the field of logic. A syllogism is a type of reasoning whereby a conclusion can be deduced based on a series of specific premises or assumptions.
For example:
- All Greek people are human.
- All humans are mortal.
- Therefore, all Greek people are mortal.
To further break down what a syllogism is, one can summarize it in the following way:
- If all X are Y, and all Y are Z, then all X are Z.
Syllogisms are made up of three propositions: the first two are premises; the last is the conclusion. Premises can either be universal (using words like every, all, or no) or particular (for example, using the word some), and they can also be affirmative or negative.
Aristotle then set out to create a set of rules that would produce a valid inference. One classic example is:
- At least one premise has to be universal.
- At least one premise has to be affirmative.
- If one of the premises is negative, the conclusion will be negative.
For example:
- No dogs are birds.
- Parrots are birds.
- Therefore, no dogs are parrots.
Aristotle believed three rules applied to all valid thoughts:
- The law of identity: This law states that X is X, and this holds true because X has certain characteristics. A tree is a tree because we can see the leaves, the trunk, the branches, and so on. A tree does not have another identity other than a tree. Therefore, everything that exists has its own characteristics true to itself.
- The law of noncontradiction: This law states X can’t be X and not X simultaneously. A statement can never be true and false at the exact same time. If this were the case, a contradiction would arise. If you were to say you fed the cat yesterday and then say you did not feed the cat yesterday, there is a contradiction.
The law of the excluded middle: This law claims a statement can be either true or false; there cannot be middle ground. This law also claims something has to either be true or be false. If you say your hair is blond, the statement is either true or false. However, later philosophers and mathematicians would dispute this law.