Please improve this article if you can. (February 2007)
In logic, a hypothetical syllogism has two uses. In propositional logic it expresses a rule of inference, while in the history of logic, it is a short-hand for the theory of consequence.
Propositional logic
Hypothetical syllogism is one of the proof rules in classical logic that may or may not be available in a non-classical logic. The hypothetical syllogism (abbr. H.S.) is a valid argument of the following form:
P → Q. Q → R. Therefore, P → R.Symbolically, this is expressed:
In other words, this kind of argument states that if one implies another, and that other implies a third, then the first implies the third. An example hypothetical syllogism:
If I do not wake up, then I cannot go to work. If I cannot go to work, then I will not get paid. Therefore, if I do not wake up, then I will not get paid.Hypothetical syllogisms have the advantage that they can be counterfactual: they can be true even if the premises suppose propositions known to be false.
Example counterfactual premises which could be used in a valid hypothetical syllogism:
- If George Washington had a beard, he would look distinguished.
- If Yogi Berra had hit 800 home runs, that would be amazing.