Syllogisms

From Math2033

What is Syllogism?

• Syllogism is logic. As discussed in class, all math is logic driven. Thinking logically involves taking widely accepted concepts and applying them to life.

For example, If I let go of my pencil and it falls on the ground, it is only logical to assume it fell due to gravity. I can safely assume this because gravity is known as the force on all objects which pulls them to the center of the earth.

• In addition to logic, syllogism involves deductive reasoning. If there is no clear reason as to why something happened, by using deductive reasoning you can hone in on what the cause might be.
• Aristotle has a major impact on syllogism, with his work on logic, known as formal logic. Though his work may seem trivial, it really introduced a new kind of formal system of thought. He placed emphasis on answering logical questions and using proof.

An example would be: If all humans are mortal and all Greeks are humans, then all Greeks are mortals.

Syllogisms are interesting because they can include false statements or conclusions that appear to be true. Truth and validity in syllogisms are very different things. A syllogism can be true, but not valid in a logical sense, or vice-versa.

Types of Syllogism

There are three main types of syllogism-

1. Conditional: If A is true, then B is also true.

2. Categorical: If A is in C then B is also in C.

3. Disjunctive: If A is true, then B is false.

Conditional syllogisms have three parts- a major premise, a minor premise, and a conclusion. The first two statements are presumed true. For example, a major premise could be something like 'men like beer'. This is the "A" part of the statement. The second part is the minor premise. It could be something like 'beer tastes good'. This is the B part. The third statement is the conclusion, which combines the first two statements. 'If your a man, you enjoy drinking beer'. Neither of the first two statements mentioned that, but through the combination of the first two statements, it is an easy conclusion to reach. Here is another example- imagine you are at a barber shop.

           You're hair looks bad.
           I am qualified to cut and style hair.
           I can make your hair look good.

This is a silly example, but it does the job. When the barber says your hair looks bad, that is ok, because he is about to make your hair look good again. However, something that must be taken into consideration is that conditional syllogisms are rarely completed with all three sentences. Most often only the first two parts are needed and sometimes even the first part will do the trick. The listener should infer the meaning of the conditional syllogism on their own, i.e. commercials. Name brand medicines aren't neccesarily better than their generic counterparts, but we tend to think so because they lead people to believe they can do the job better.

Catagorical syllogisms tend to be more cut and dry, although somewhat similar to conditional syllogisms. They too include a major premise, a minor premise, and a conclusion. An example of a catagorical syllogism would be 'All men are mortal'. This is assumed to be true. The second statement would say something like 'Jim is a man.' This is also assumed true. The conclusion would state 'Jim is mortal'. Through the combination of the first two parts, another easy conclusion is reached. All men are mortal, and since Jim is a man, he must be mortal. It should be noted that categorical syllogisms must follow these six premises-

Last but not least we have disjunctive syllogism. It only has two parts, a major premise and a minor premise. They cannot both be true at once. That is to say, if A is true, then B is false. If B is true, A is false. An example would be a politician saying "Vote for me or vote for higher taxes". The alternative is bleak, but it is stated in such a way that would give you no option than to vote for that politician.