The Valid Syllogisms
| 1st figure | 2nd figure | 3rd figure | 4th figure |
|
AAA (Barbara) AII (Darii) EAE (Celarent) EIO (Ferio) |
AEE (Camestres) AOO (Baroco) EAE (Cesare) EIO (Festino) |
AII (Datisi) EIO (Ferison) OAO (Bocardo) IAI (Disamis) |
AEE (Camenes) EIO (Fresison) IAI (Dimaris) |
|
1st figure ¬? ∀x (Mx → ¬? Qx) ¬? ∀x (Rx → ¬? Mx) ¬? ∀x (Rx → ¬? Qx) |
2nd figure ¬? ∀x (Qx → ¬? Mx) ¬? ∀x (Rx → ¬? Mx) ¬? ∀x (Rx → ¬? Qx) |
3rd figure ¬? ∀x (Mx → ¬? Qx) ¬? ∀x (Mx → ¬? Rx) ¬? ∀x (Rx → ¬? Qx) |
4th figure ¬? ∀x (Qx → ¬? Mx) ¬? ∀x (Mx → ¬? Rx) ¬? ∀x (Rx → ¬? Qx) |
| affirmative gen. | negative gen. | |||
| affirmed | A: | ∀x (ρx → θx) | E: | ∀x (ρx → ¬ θx) |
| negated | O: | ¬ ∀x (ρx → θx) | I: | ¬ ∀x (ρx → ¬ θx) |