Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

To assign defects in consequences, note that since consequence is twofold only—induction and syllogism—defects can be assigned either as proper to each of them or as common to both. Proper defects occur when some rule among those given and required for a good induction or syllogism is omitted. Common defects occur when there is a defect in some logical property, such as supposition, restriction, ampliation, appellation, opposition, or conversion; these properties are common to induction and syllogism.

We shall therefore briefly set out all the defects here, both proper and common, although we have already treated almost all of them in various places in the preceding discussion.

CONCERNING INDUCTION.

A defect is committed in induction:

First, if an affirmative conjunctive ascent is made without sufficiently enumerating the singulars, it is not a formal consequence, because an objection can be made from the cases not enumerated—unless the matter is necessary, in which case it is a good consequence only materially. See below, question 8, article 2.

Second, an affirmative conjunctive descent without an existence condition establishing the individuals under which one descends is not a formal consequence. For example, if you say, “Every man was a sinner, for example Peter, and that man was a sinner,” etc. You must add: “And this man, for example Peter, is or was,” which establishes the required existence condition; therefore Peter was a sinner. Otherwise, if you designate an individual that does not yet exist but will exist in the future, the consequence admits a counterexample.

Third, defects can occur if the rules given above concerning ascent and descent in chapter 3 of this book are omitted: for example, if disjunctive ascent and descent are not assigned to a term supposing determinately, conjunctive ascent and descent to a term supposing distributively, or disjunctive or conjunctive ascent and descent to a term supposing confusedly only. Likewise, it is a defect if complete conjunctive descent and ascent are assigned to a term that does not suppose distributively in a complete way; for if it distributes incompletely, descent too must be incomplete. For example, “Every animal was in Noah’s ark” does not entail “therefore this animal and that animal,” pointing to individuals, but it does if one points to species.

Fourth, there is a defect in the very order of resolving terms when several occur in the same proposition, if they are not resolved in their proper order and not all with equal immediacy. The order of resolution, or ascent by way of induction, as we said in the chapter on induction,¹ is this: first ascend under the term supposing determinately, second under the term supposing distributively, and third under the term supposing confusedly. If one ascends under a term supposing distributively before ascending under a term supposing determinately, there is a defect called “from several determinates to a single determinate.” For example, if you make this ascent: “A man is not this rational thing, and a man is not this rational thing, etc.; therefore a man is not rational,” the consequence is invalid. For the term “man” in that proposition supposes determinately with respect to several singulars, which are several determinates (for all singulars are determinate), whereas in the consequent it does not suppose with respect to several determinates but to one thing in common. This defect sometimes occurs in theology, as when it is said: “A man can do this good work, and he can do that one, etc.; therefore he can do every good work.” However, if all the terms in a proposition suppose either determinately or distributively, each can be resolved with equal immediacy.

Fifth, there is a defect in descent if one first descends disjunctively under a term supposing confusedly only, rather than under a term supposing distributively. Thus this does not follow: “Every man is an animal; therefore every man is this animal.” This defect is called “arguing from one distribution to several,” because one descends under a term that is not distributed as though it were distributed.

Here, however, arises the difficulty concerning propositions composed of a complex of a straight case and an oblique case, such as “A man’s horse runs,” or “A man’s horse does not run.” The genitive functions as a determination and the straight case as what is determined, because the genitive as it were restricts the straight case to standing for a possessed horse. Many sophisms, not very useful, are made concerning the order of resolving these terms; we shall touch on some below, question 7, article 2, argument 5. For now we briefly observe that the resolution Magister Bañez gives in book 4 of the Summulae, treatise 1, chapter 3, is easier. When the whole complex is taken in a single sense—that is, when the genitive, which is the determination, follows after what is determined—the same resolution and supposition are due to both terms, because the genitive is equivalent to an adjective. For “a man’s horse” means the same as “a horse possessed by a man,” and therefore it supposes and is resolved like a complex composed of a noun and adjective, since it is held with the same supposition. Just as, if one says “a white horse runs,” “white” supposes as “horse” does, so if one says “a possessed horse” or “a man’s horse,” “possessed” and “man’s” suppose as “horse” does. Thus, if you say “Every horse belonging to a man runs,” you can immediately descend under “man’s” by saying “Every horse of this man (that is, the possessor) runs,” provided you add or understand the existence condition “And this man possesses a horse.” For the term does not distribute absolutely for every one, but for every possessor of a horse, just as “every horse” there does not distribute absolutely, but for every possessed horse. Hence “man’s” does not suppose confusedly there, but distributively for possessors.

If, however, the whole complex is taken in several senses, because the genitive precedes, then each term is due its own separate resolution according to its supposition and the signs affecting it, so that priority is given to determinate supposition, then distributive, then confused supposition. You will recognize which term supposes determinately and which distributively from the rules in chapter 10 of book 2 on supposition.²

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.

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