(7) Since the minor premise cannot be negative, it must be affirmative. _Problem: To prove that the major premise must be universal._ _Data_: Given the form of the first figure: M ― G S ― M ――――― S ― G _Proof_: (1) The predicate of the minor premise, M, which is the middle term, is undistributed; because no affirmative proposition distributes its predicate. (2) The middle term must be distributed in the major premise; since in any syllogism the middle term must be distributed at least once. (3) As the middle term, M, used as the subject of the major premise, must be distributed, then the major premise must be universal; because only universals distribute their subjects. _Epitome._ _In the first figure, the minor premise must be affirmative, since making it negative necessitates making the major premise negative also; the major premise must be universal in order to distribute the middle term at least once._ _Special canons of the second figure._ (1) One premise must be negative. (2) The major premise must be universal. _Problem: To prove that one premise must be negative._ _Data_: Given the form of the second figure: G ― M S ― M ――――― S ― G _Proof_: (1) The middle term, M, is the predicate of both premises. (2) The middle term must be distributed at least once, according to rule 3. (3) Hence one premise must be negative; since only negatives distribute their predicates. _Problem: To prove that the major premise must be universal._ _Data_: Given the form of the second figure: G ― M S ― M ――――― S ― G _Proof_: (1) As one premise must be negative, it follows that the conclusion must be negative according to rule 6. (2) If the conclusion is negative, then its predicate, G, the major term, must be distributed; since all negatives distribute their predicates. (3) When distributed in the conclusion, the major term, G, must also be distributed in the major premise, where it is used as the subject. See rule 4. (4) Hence the major premise must be universal; for only universals distribute their subjects. _Epitome._ _In the second figure one premise must be negative in order to distribute the middle term at least once; and the major premise must be universal that the major term, which is distributed in the conclusion, may be distributed in the premise where it occurs._ _Canons of the third figure._ (1) The minor premise must be affirmative. (2) The conclusion must be particular. _Problem: To prove that the minor premise must be affirmative._ _Data_: Given the form of the third figure, which is, M ― G M ― S ――――― S ― G _Proof_: (1) Suppose the minor premise were negative, then the conclusion would have to be negative, and this would distribute the predicate G. (2) A distributed predicate would necessitate its being distributed in the major premise. (3) But G, being the conclusion of the major premise, could be distributed only by a negative proposition.