A syllogism can be defined as a three-part logical argument based on deductive reasoning. In deductive reasoning, one moves from certain statements or premises to arrive at a logically certain conclusion, one that cannot, under any circumstances, be contradicted.

Let's illustrate this point using the above example:

“All mammals are animals” (the major premise).

“All cats are mammals” (the minor premise).

“Therefore, all cats are animals” (the conclusion).

The conclusion of a syllogism must logically follow from the major and minor premises, as in the above example. If not, however, then what we have is what's called a logical fallacy. For example:

“Some bad people are lawyers” (the major premise).

“Some people with beards are bad” (the minor premise).

“Therefore, some lawyers have beards” (the conclusion).

In the above example, both of the statements contained in the major and minor premises are perfectly true. But the conclusion drawn from them, while itself also perfectly true, doesn't logically follow from the premises. Therefore, the example just given is a logical fallacy, or a mistake in logic, and not a valid syllogism. For a valid syllogism, it's not enough that all the statements it contains are true; the conclusion has to follow logically from the premises. If not, it isn't a true syllogism.