Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Defects common to every consequence, whether syllogistic or inductive, are those that arise from a defect in some logical property, such as supposition, ampliation, etc.

In supposition, the first defect is when the kind of supposition is varied in some consequence. I say “kind,” because the species can be varied, as when one infers determinate or particular supposition from distributive supposition. But the kind of supposition cannot be varied, for example, by changing simple supposition into personal supposition, or material supposition into personal supposition, etc. Because of this defect, the following consequences are invalid: “Man is a species; Peter is a man; therefore Peter is a species.” “Man is a word; every man is an animal; therefore some animal is a word.”

The second defect is that a consequence from undistributed supposition to distributed supposition is invalid, though the converse is valid. Thus this does not follow: “Some man runs; therefore every man runs.”

The third defect is that a consequence from supposition that is confused only, not distributed, to determinate supposition is invalid, though the converse, from determinate to confused, is valid. Thus this does not follow: “Every man is an animal; therefore some animal is every man,” though the converse is valid.

In ampliation and restriction, the second logical property, there are rules of ampliation from which the defects of consequences also follow. Therefore, when we proceed from an amplified to a non-amplified term without distributing the amplified term, the consequence is invalid.

The second defect occurs if we proceed affirmatively from an amplified to a non-amplified term, even with the amplified term distributed, but without constancy. For example, if you say “Every man is white,” you cannot immediately infer “therefore Peter is white” unless you add the constant “and Peter exists”; otherwise, if Peter does not exist, a falsehood is inferred. We say deliberately “with the amplified term distributed,” because if the amplified term is not distributed, the consequence is invalid even when constancy is posited. For example: “Man is possibly white,” or “Every man is possibly white,” and Peter exists; therefore Peter is white.” Although “possibly” amplifies, it does not distribute to less amplified terms except under the very account of possibility. Thus one should infer “therefore Peter is possibly white”; otherwise, one argues affirmatively from potency to act. This is shown by the fact that if “impossibly” or “necessarily” is posited, which are modes that distribute, the following is valid: “A man is impossibly white; therefore Peter is not white.”

The third defect occurs if we proceed from a non-amplified to an amplified term with distribution of the amplified term. This is to argue from what is not distributed to what is distributed, which is always a defect. The defect of proceeding from incomplete universality to complete universality, or from complete particularity to incomplete particularity, is also reduced to this defect, since in each case one argues, at least equivalently, from what is not distributed to what is distributed. We call universality incomplete when it is not distributed perfectly, and complete when it is distributed perfectly. Conversely, particularity is complete when it is particularized perfectly, so that none of the universality remains; it is incomplete when it is not particularized perfectly, but retains some universality. For example, “Some animal was not in Noah’s ark” is incomplete particularity, that is, “No animal of some species was there”; “Neither of the two men runs” means “Neither one of some pair [runs].” In each case some universality is joined to the particularity.

In appellation, another logical property, all defects are reduced to one: whenever appellation is varied, the consequence is invalid, whether the appellation is real or of reason, or concerns terms signifying acts of the soul. Thus these do not follow: “Peter is a great logician; therefore he is great”; “Man is a species; therefore Peter, who is a man, is a species”; “Whiteness is intense; therefore the likeness, which is whiteness, is intense”; “I know someone coming; therefore I know Peter, who is coming.” For acts of the soul are always directed toward their objects under the precise formal aspect under which they are such acts. Thus this does not follow: “I see the one who is coming; therefore I see him coming”; “I saw the Pope; therefore I saw him as Pope.” Nor does the converse follow, unless in both cases the term “insofar as he is coming” or “insofar as he is the Pope” is taken under the same appellation, that is, under the same account of knowing, and not under another. Otherwise, by varying the formal accounts of knowing, many deceptions are made possible. Those who say that one may infer from an appellative to a non-appellative term in cases involving terms signifying acts of the soul do not thereby say that the inference holds with appellation varied; rather, it holds from the formal to the material, while the latter still falls under the formal, and in this sense it is true.

In oppositions, the first rule is: In contradictories, given the truth of one, the falsity of the other follows, and conversely.

The second rule is: In contraries, the falsity of one follows from the truth of the other. But the converse, from the falsity of one to the truth of the other, is a bad consequence, because both can be false, though they cannot both be true.

The third rule is: In subcontraries, the truth of one follows from the falsity of the other. But the converse is a bad consequence, because both can be true at the same time.

In equipollences there is no defect; a good consequence always holds from one equipollent to another.

In conversion, the first rule is: From the converted proposition to the converting proposition, the consequence is always good, as in “Every man is an animal; therefore some animal is a man.”

The second rule is: There is no good mutual consequence in conversion except in simple conversions, not in conversions per accidens. A mutual consequence is one that holds not only from the converted to the converting proposition, but also conversely, from the converting to the converted proposition. Thus this does not follow: “Some white thing is a man; therefore every man is white.” This is from the converting to the converted proposition in the conversion per accidens of a universal affirmative; the converse, however, is valid.

In exponibles, or resolvable propositions, the first rule is: From an exponible proposition to all its exponents, or from a resolvable proposition to all its resolving propositions, and conversely, the consequence is good, because it is between equipollents.

The second rule is: From an exponible or resolvable proposition to any one of its exponents taken conjunctively, the consequence is good; conversely, however, there is a defect from any one exponent to the resolvable proposition, because the first is from a conjunctive proposition to a part, the second from a part to a conjunctive proposition.

The third rule is: From any one disjunctive exponent to its exponible proposition, the consequence is good, but the converse is invalid. This is clear from the rule for disjunctive propositions. See what we said in the chapter on exponible and hypothetical propositions concerning each of the places of argument.¹