Sigwart does not indeed shrink from this and greater absurdities; he reduces the first figure to the modus ponens and the second to the modus tollens of the hypothetical syllogism, and then, finding no place for the third figure, denies that it can infer necessity; whereas it really infers the necessary consequence of particular conclusions.
Two forms are possible (i.) modus ponens (which establishes the consequent set down in the major premise): if A is B, it is C (or C is D); A is B; therefore A is C (or C is D), and (ii.) modus tollens (which disproves the antecedent): if A is B, it is C (or C is D); A is not C (or C is not D); therefore it is not B (or A is not B).
Again two forms occur: (i.) modus ponendo tollens which by the affirmation of one alternative denies the other (A is either B or C; A is B; therefore it is not C: or either A is B, or C is D; A is B; therefore C is not D: or either A or B is C; A is C; therefore B is not C); (ii.) modus tollendo ponens which by the denial of the one, establishes the validity of the other alternative (A is either B or C; A is not B; therefore it is C: or either A or B is C; A is not C; therefore B is C: or either A is B, or C is D; A is not B; therefore C is D).