Syllogisms ?

Syllogism is a word which everybody has heard of or even had to use in practice. This modern form of logical reasoning is almost always associated with intelligent tests and assessment trainings nowadays. But what is the origin of this word, what does syllogisms mean and more important how to solve it?

History of Syllogisms

Aristotle (384-322 BC) can be seen as the founder of today’s form of logical reasoning e.g. syllogisms. He was the first in his time to divert with the correctness and validity of logical reasoning. A lot of his work from those days unfortunately has gone lost. The few remains however of his work were bundled in books called “The Organon”. These books, consisting out of 6 parts, contain a lot of his works and documents concerning logical reasoning and as a part of that syllogisms. Until the dark ages these books were the only useful concerning matter of logic. Later on in history Boole and Frege followed with respectively their PROPOSITION LOGIC and PREDICATE LOGIC, both documents concerning a modern way of interpreting logical reasoning and connected to that syllogisms.

Aristotle’s was interested among others in syllogisms, a form of logical reasoning. A syllogism always consists out of 3 parts, namely the subject, the predicate and the middle term. The subject stands for, as the word already indicates, the central theme in the syllogism. This is the keyword of the syllogism. Predicate is another word for a specific feature connected to the subject. The last part is the middle term which consists out of all the remaining information in a syllogism. Each syllogism can be classified using these three terms, resulting in a valid or invalid conclusion of the syllogism.

Solving Syllogisms

Syllogisms can be solved in many ways, however the most frequently used method is by using the so called Venn diagrams. Venn diagrams show all possible and hypothetically logical relations between a collection of finite and infinite statements. By means of an overlap between some certain assumptions conclusions can be made using the (in)finite statements. Next a few syllogism examples will follow in which words will be classified and the syllogism will be checked on validity.

Syllogism Example:

1. All Canadians are right handed
2. All right handed are opticians
3. Conclusion: Some opticians are Canadian

To check the validity of this statement first the different terms are appointed.

Subject:          Optician

Predicate:       Canadian

Middle term:   Right handed

Since the two premises (a and b) from the example are valid, the conclusion must be valid two, since it is not possible for the premises to be true and the conclusion to be false.

Syllogism Example 2:

1. All mortals die
2. All men are mortals
3. Conclusion: All men die

To check the validity of this statement first the different terms are appointed.

Subject:          Men

Predicate:       Die

Middle term:   Mortal

Again it can be concluded that the two premises (a and b) are valid and so is the conclusion. This is in general always the case with syllogisms, which is a form of logical reasoning of the deductive reasoning type. For more information about different types of syllogisms, you can take a look at our related pages shown below.