Hypothetical syllogism
In logic, a hypothetical syllogism is a valid argument of the following form:
:P → Q.
:Q → R.
:Therefore, P → R. In logical operator notation
:
:
: 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
Other forms of syllogism: categorical syllogism, disjunctive syllogism.
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