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# Are all deductive arguments syllogisms?

Premise 1: All syllogisms are deductive arguments with premises concerning class-relations and a conclusion concerning class relations.

Premise 2: Some deductive arguments do not concern class relationships, and some do not have two premises.

Conclusion: Some deductive arguments are not syllogisms.

Explanation: A deductive argument is one such that, if the premises are true, then the conclusion supposedly cannot possibly fail to be true. A valid deductive argument is a deductive argument that actually goes through, meaning that the premises, if true, do in fact provide a 100% guarantee of the truth of the conclusion. Here are some examples of valid deductive arguments:

Jim has 2 cars. Therefore, Jim has more than one car.

John is rich. Therefore, John is either rich or smart.

John is a lawyer. If John is a lawyer, then John went to law school. Therefore, John went to law school.

If John is a lawyer, then John went to law school. John did not go to law school. Therefore, John is not a lawyer.

If Jim can read, then Jim is animate.

If the membership of a class can be bijected with the class of real numbers, it has a higher cardinality than a class that can be bijected with the class of even numbers less than 100.

All police officers work for the state. All people who work for the state are paid out of taxes. Therefore, all police officers are paid out of taxes.

All of these are valid deductive arguments, but only the last one is a syllogism. A syllogism is a deductive argument such that (i) it has two premises and a conclusion and (ii) the premises and the conclusion all concern class-relationships, i.e. they concern degrees of overlap or non-overlap between classes (sets of objects.)

Here are other examples of syllogisms.

• All mammals have fur. No lizards have fur. Therefore, no mammals are lizards.

• All mammals are warm blooded. Some bipeds are mammals. Therefore, some bipeds are warm-blooded.

• All computer-technicians are at least moderately intelligent. Some people with blond hair are computer technicians. Therefore, some people with blond hair are at least moderately intelligent.

To sum up, deductive arguments do not have to concern class-relationships, and they also don't have to have exactly two premises. But syllogisms do have to have exactly two premises and also concern class relationships.