Hypothetical syllogism
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In logic, a hypothetical syllogism is a valid argument of the following form:
- P → Q.
- Q → R.
- Therefore, P → R.
In logical operator notation
- <math> p \rightarrow q <math>
- <math> q \rightarrow r, <math>
- <math> \vdash p \rightarrow r <math>
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. he:סילוגיזם_היפותטי