Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

The first defect in syllogisms is arguing in four terms, since the whole art of syllogism consists in connecting two terms with each other, inferred from their connection with a third. Hence there ought to be no more than two extremes and no more than one middle. Thus this is invalid: “Every human being is possibly white; an Ethiopian is a human being; therefore an Ethiopian is white,” because the middle is not only the term “human being” but also the term “possibly.” To this is reduced the requirement that the extremes be complete extremes: for if they are not complete, the argument proceeds with more than three terms.

The second defect: The middle must not be taken equivocally, but in the same sense in both premises; otherwise it could not unite the extremes with one another. Thus this is invalid: “Every dog is a barker; some star is a dog; therefore some star is a barker.”

The third defect: Nothing follows from purely particular premises. We explained this above.¹

The fourth: Nothing follows from purely negative premises. This too was explained above.²

The fifth: The middle is not completely distributed in one of the premises. Hence this is invalid: “Every animal was in Noah’s ark; Socrates is an animal; therefore Socrates was in Noah’s ark.”

The sixth: No term should be distributed in the conclusion unless it was distributed in one of the premises. This was explained above³ and coincides with the defect of arguing from the undistributed to the distributed. Also belonging here are defects involving amplification or restriction, such that the middle is not taken more broadly where it is undistributed than where it is distributed.

The seventh defect: The middle enters into the conclusion. Otherwise all syllogisms in which appellation is varied would be valid, for example, if you say: “Every human being is a creature; Christ is a human being; therefore Christ is a creature insofar as he is a human being.” “Every likeness is a quality; this quality is intense; therefore this likeness is intense insofar as it is a quality.”

The eighth defect: The particular rules for the figures of syllogisms set out above⁴ are not observed, such as that in the first figure the major proposition cannot be particular, along with the other rules explained there.