(4) This would result in two negatives; therefore no conclusion could be drawn, if the minor premise were negative. _Problem: To prove that the conclusion must be particular._ _Data_: Given the form of the third figure: M ― G M ― S ――――― S ― G _Proof_: (1) The minor term, which is the predicate of the affirmative minor premise, is undistributed; because no affirmative distributes its predicate. (2) If undistributed in the premise, then the minor term must remain undistributed in the conclusion, where it is used as the subject. (3) The conclusion must, then, be particular; since all universals distribute their subjects. _Epitome._ _In the third figure, unless the minor premise be affirmative, there can be no conclusion; since a negative minor would necessitate a negative major. An affirmative minor compels a particular conclusion, in order that the minor term, in the conclusion, may remain undistributed._ _Canons of the fourth figure._ (1) If the major premise is affirmative, the minor premise must be universal. (2) If the minor premise is affirmative, the conclusion must be particular. (3) If either premise is negative, the major must be universal. _Problem: To prove that if the major is affirmative, the minor must be universal._ _Data_: Given the form of the fourth figure: G ― M M ― S ――――― S ― G _Proof_: (1) If the major premise is affirmative, then its predicate which is the middle term, M, is undistributed; for no affirmative distributes its predicate. (2) The middle term must then be distributed in the “minor” according to rule 3. (3) Then the “minor” must be universal; since only universals distribute their subjects. _Problem: To prove that if the minor is affirmative, the conclusion must be particular._ _Data_: Given the form of the fourth figure: G ― M M ― S ――――― S ― G _Proof_: (1) If the minor premise be affirmative, then S, its predicate, must be undistributed; because no affirmative distributes its predicate. (2) Since S is undistributed in the minor premise, it must remain undistributed in the conclusion where it is used as the subject. _Problem: To prove that if either premise is negative, the major must be universal._ _Data_: Given the form of the fourth figure: G ― M M ― S ――――― S ― G _Proof_: (1) If one of the premises is negative, then the conclusion must be negative according to rule 6. (2) If the conclusion is negative, then the predicate, G, must be distributed. (3) If G is distributed in the conclusion, it must be distributed in the major premise. (4) The major premise must be universal; as G is used as its subject, and only universals distribute their subjects. _Epitome._