All men are mortal, because all men die,
Socrates was a man, because he was a rational animal,
∴ Socrates was mortal.
It is obvious that supporting each premise with a reason lends strength to the argument. This justifies the use of the epicheirema.
3. POLYSYLLOGISM.
A polysyllogism is a series of syllogisms in which the conclusion of a preceding syllogism becomes a premise of a succeeding one.
The syllogism in the series whose conclusion becomes a premise of the succeeding syllogism is termed a prosyllogism; while the syllogism which uses as one of its premises the conclusion of the preceding syllogism is called an episyllogism.
Illustrations.
| Polysyllogism |  | A quadruped is an animal, |  | Prosyllogism | |
| A dog is a quadruped, | |||||
| ∴ A dog is an animal. | | ||||
| Fido is a dog, | Episyllogism | ||||
| ∴ Fido is an animal. | |||||
| Polysyllogism | | All who libel an associate are unprofessional, | | Prosyllogism | |
| This teacher has libelled her associate, | |||||
| ∴ This teacher is unprofessional. | | ||||
| All who are unprofessional should be disciplined, | Episyllogism | ||||
| ∴ This teacher should be disciplined. |