Hypothetical Syllogism

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Normally there are two conditional premises where the antecedent of one is the consequent of the other and the conclusion is a conditional relating the two UNCOMMON parts of the premises.

For example:

If YOU STUDY LOGIC, then you will understand logic.

If you understand logic, then YOU WILL PASS THIS COURSE.

So, if YOU STUDY LOGIC, then YOU WILL PASS THIS COURSE.

In Chapter 1, ANY two premise argument with a conditional premise is called a hypothetical syllogism. In Chapters 6, 7 and 8, both premises will have to be conditional.