In his Institutes of Oratory, the rhetorician Quintilian, in discussing the value of learning logic, mentions the “horn” problem, which evidently was this tricky syllogism:

“You have what you have not lost. You have not lost horns. Therefore you have horns.”

Initially I supposed that this was invalid, until I put it into categorical form:

All things you have not lost are things you have.
All horns are things you have not lost.
∴  All horns are things you have.

This is an AAA-1, and is thus valid. It could just as readily be written as modus ponens: Continue reading Watch your assumptions! →