Hypothetical Syllogism

HYPOTHETICAL SYLLOGISM

The hypothetical syllogism is made up of three conditional statements: one in each of the two premises and one in the conclusion. This is also known as the chain argument because it links together all components of the premises and conclusion. For example:

If I move to the Bay Area, then I will need an income. If I need an income, then I will need a job. So, if I move to the Bay Area, then I will need a job.

The symbolic form of the hypothetical syllogism is as follows:

If A then B. If B then C. So, if A then C.

This argument form is quite easy to recognize because it consists entirely of conditional statements. Like the other valid argument forms, the hypothetical syllogism always provides an argument with good structure, but not necessarily true content. The following examples need checks of both form and content. In particular, a chain must use the same intervening proposition in both premises.

1. If community colleges continue to cut classes, then fewer Americans will have access to education. If fewer Americans have access to education, then poverty will increase. Therefore, if community colleges continue to cut classes, poverty will increase.

2. If I rob the bank, then I may kill someone. If I kill someone, then there is a possibility that I will spend my life in prison. So, if I rob the bank, then there is a possibility that I will spend my life in prison.

As written, this is not a direct instance of the stated form: possibly killing someone and actually killing someone are different propositions. A valid treatment of the possibilities would require additional assumptions.

3. If the atheists are correct, then there is no God. If there is no God, then intelligent design is false. Therefore, if the atheists are correct, then intelligent design is false.