Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Not everyone accepts Aristotle’s definition,¹ but some reject it because it seems to coincide with the complex term, which also has separately significant parts. They therefore define an utterance differently, saying that “an utterance is several expressions or terms suitably related,” as though this were not also found in a complex term. Others define an utterance as follows: “An utterance is a significant vocal expression by convention, consisting of a noun and a verb suitably related to one another, or at least of a verb and a vocal expression, if the latter is not significant.” Still others accept Aristotle’s definition but say that the form of an utterance is the grammatical union of its parts.

FIRST CONCLUSION: The best definition of an utterance is the one given by Aristotle, namely: “An utterance is a significant vocal expression by convention, whose separated parts signify as an expression, not as an affirmation or negation”; and it is essential and quidditative in the same way as the definition of a term or a name.

This assertion is common, and its only proof is the EXPLANATION OF THE DEFINITION itself. St. Thomas gives it in the first book of the Perihermeneias, lecture 6.² We reduce it to this form: a whole in general is best defined as that which has parts, or is composed of parts; therefore such a whole in particular is best defined as that which has such parts, or is composed of such parts. But an utterance is a certain logical significant whole, that is, a certain composite whole. Therefore it is best defined as “a significant vocal expression by convention, whose parts when separated, etc.”

The consequent is evident, because this definition explains everything that belongs essentially to this composite, which is an utterance: what its parts must have, the parts of which it is composed, and that by which it differs from other things from which the defined thing differs.

The minor is proved: an utterance belongs to the intellect’s second operation, which is composition, because through an utterance we express something joined and composed with another thing, just as through a term we express something uttered separately and simply. Therefore an utterance, which is a certain logical and significant whole, is best defined as that whose separated parts signify as an expression.

St. Thomas noted that Aristotle did not say “whose parts signify something,” but simply “signify,” because of negations and syncategorematic terms, which do not signify something but signify in some way; yet they are parts of an utterance, in which at least one part must signify something, that is, be a noun or a verb, even if the others signify in some way. He also said “as an expression, not as an affirmation,” because the parts of an utterance must at least signify as an expression; for this must be found in every utterance. If, however, it also has parts as affirmations, that is better, as in a hypothetical proposition. Besides, the character of being a part in its own right is found only in an expression or term; a proposition, even if it composes a hypothetical proposition, is not a part in its own right and primarily, but accidentally, as we said above.

FROM WHAT HAS BEEN SAID IT FOLLOWS that the other definitions are not good, and that Aristotle should not be abandoned for their sake. To say that an utterance is “several expressions suitably related” is not only also applicable to a complex term, but does not explain its essence well, which consists in its being a certain composed, total, and unified whole. A composite thing is not aptly defined by saying that it “is several parts,” but by saying that it is one thing composed of parts. — We are even less satisfied with saying that an utterance is a vocal expression consisting of a noun and a verb. For many complete utterances do not consist of a noun: for example, “To run is to move.” Indeed, an utterance may consist of a verb and an adverb, as “One runs quickly,” or “It is well.” An imperfect utterance is also given—which truly is an utterance, although it produces an imperfect sense—without a verb, as “A just man,” which St. Thomas affirms to be an utterance in the first book of the Perihermeneias, lecture 4.³ Therefore it is not of the essence of an utterance in general that it consist of a noun and a verb.

SECOND CONCLUSION: The essential form of an utterance is not the grammatical union of its parts, but the predicate terms, if we speak of its partial form; or else its complex and composite signification itself, insofar as it takes on the character and intention of a whole, if we speak of its total formal aspect.

THE FIRST PART IS PROVED, because a union is the conjunction and application of things that can be united; for by union a form is applied to its matter or subject. Therefore union, insofar as it is union, is not the form constituting a composite, but the means or bond of the extremes. Therefore it presupposes the constitutive extremes, one of which—the one that is the form—is applied through union in order to constitute the composite; just as, in a human being, the constitutive form is not the union but the application of the soul, which is the constitutive form. Thus, just as a physical whole has a partial form, which is the soul with respect to the body, and a total form, which is humanity with respect to the supposit, so in an utterance the partial form is the predicate or, rather, the predicated term—because, as St. Thomas says in the first book of the Perihermeneias, lecture 8,⁴ in an utterance one part must determine the other. The determining part is the form; and if they determine one another, each is a form with respect to the other: the form insofar as it determines, the matter insofar as it is determined. So, in a marriage contract, it is customary to say that the words of the contracting parties are form and matter in relation to one another. The total form, however, is the total and complex signification of the utterance, insofar as it takes on the relation and character of a whole; in this way it is, as it were, relatively opposed to a term, which is a part. Just as a term has its essence in its character as a part, so an utterance has its essence in complex signification by way of a whole.

As to the defined thing of an utterance, one must say that it is the form of the utterance in the concrete, in accordance with what was said above about the definition of a term; this must always be said of the defined thing of any accidental concrete.

OBJECTIONS ARE ANSWERED.

First objection: A complex term too has parts that signify as expressions, etc.; therefore the whole definition of an utterance also applies to a complex term; therefore it is not a good definition. — The antecedent is clear from the definition of a term.

THE ANSWER IS: The antecedent is distinguished: that a complex term has parts formally is denied; materially, it is granted.

That is called a part formally which composes under the formal character of a part. The formal character of a part, however, lies in its order to a whole, which it concerns and composes by stopping in it, so that it is not ordered further to something else. But when parts compose something in such a way that they do not stop in it but are ordered further to a whole, then that thing is said to have parts materially, and not under the formal character of a part. Thus parts can be joined into one thing in two ways: in one way, their composition terminates in that thing as a certain whole; in another, they compose it without stopping in it, but by being ordered further to a whole that the thing composed of those parts also concerns.

You have an example in an arm or a foot. For these parts are ordered to compose an animal, which is a whole, and their union terminates and stops there. The animal is said to be composed of parts formally, or under the formal character of parts—that is, of parts that concern it as the whole they compose and in which they stop. But flesh, nerves, and bones, of which an arm is composed, are parts materially, because they do not compose the arm as a certain whole in which they stop, but as a more principal and composite part (for in wholes there are both simple parts and parts composed of other parts), which is ordered to compose the animal itself. Nevertheless, if an arm or another organic part is separated from the animal and made into a certain whole, its parts will be ordered to it as parts formally, that is, under the formality and relation of parts to a whole.

Therefore an utterance or proposition is a certain whole consisting of parts. Some parts of this whole are simple, such as incomplex terms; others are composite, such as a complex expression, which is, as it were, the arm of an utterance, or a composite part and not a whole, even though it has parts. For its parts are joined in a complex term in such a way that through that term they are ordered to compose some further whole, namely, an utterance. But the same complex expression “a white man,” if separated and taken by way of a whole (like an arm separated from an animal), becomes an imperfect utterance; whereas, when it is in an utterance, it is a composite part. Hence an imperfect utterance and a complex term coincide materially, but differ formally, because a complex expression is always a part, even if composed of parts, whereas an utterance, even an imperfect one, is always a whole.

OBJECTION AGAINST THIS: An imperfect utterance too, even as an utterance, is a part; therefore the whole solution collapses.

The antecedent is proved first from St. Thomas, first book of the Perihermeneias, lecture 6,⁵ who says that an imperfect utterance is a part of a perfect utterance. Also, in Opusculum 48, treatise on the Enunciation, chapter 3,⁶ the same holy Doctor holds that an imperfect utterance belongs to the intellect’s first operation and not its second. For he says there “that something is lacking to the sense produced by an imperfect utterance, namely, composition and division.” Therefore it lacks what belongs to the second operation; therefore it remains within the bounds of the first; therefore it falls within the account of a part, since whatever belongs to the first operation is a part with respect to other things.

Second: A perfect utterance is a complete whole in the genus of utterance; therefore, since an imperfect utterance is something incomplete, it is less than the whole itself; therefore it is a part.

The antecedent is denied. To the first proof from St. Thomas it is answered that the holy Doctor called an imperfect utterance a part either by taking “part” broadly for that which is an imperfect whole—for whatever in a genus does not attain perfection is called its beginning or part—or, if he takes “part” strictly and properly, he is speaking of an imperfect utterance materially, that is, as a complex term, and not of it formally, as an utterance and a whole.

To the second proof from the same holy Doctor, it is answered that an imperfect utterance lacks composition and division insofar as these are like affirmation and negation that remove the mind’s suspension; thus it lacks the composition and division that produce a perfect sense, but it does not lack the account of the second operation, which is imperfect composition and division. Indeed, from the fact that it produces a suspended and imperfect sense, it is shown to differ from a complex term: the latter produces a simple apprehension of several things or concepts, but makes no sense, even a suspended one, and so remains within the account of a term and a part. An imperfect utterance, by contrast, goes beyond the account of apprehension and produces a certain sense, although one that is incipient and imperfect, because it begins to pass into the composition of a whole—as when, for example, I utter “A white man”—and intends to say something further; yet it stops there and does not complete the sense. Therefore it belongs to the second operation, even if imperfectly and incipiently, and so is not a part but a whole.

To the second proof from reason, it is answered: the consequent is distinguished: “Therefore an imperfect utterance is less than the whole itself within the genus of a whole,” that is, an imperfect whole, is granted; “outside the genus of a whole, so that it is a part,” is denied. An imperfect utterance is like an utterance begun with respect to a perfect utterance, or like becoming with respect to a perfect whole; because it is suspended, it does not proceed further or attain the character of perfection.

Second argument: If the letter A were imposed to signify the clause “a man is white,” then A would be an utterance and would not have parts that signify; therefore this is not required for an utterance. Also, according to a probable opinion, a mental proposition is a simple quality; therefore an utterance then does not have parts that signify.

THE ANSWER IS that in that case A would have parts that signify virtually or equivalently, although not formally, because it would be subordinated to several concepts.

To the second proof it is answered, in keeping with that opinion, that although a proposition or utterance does not have parts entitatively, it nevertheless has them objectively, because it signifies something complex. It also has them presuppositionally, because it is formed from several concepts apprehended as its presuppositions.

You will ask: How are an utterance, a term, and the other logical instruments, since they are formally beings of reason, defined by “vocal expression” (an utterance is a “vocal expression,” a term is a “vocal expression,” etc.), which is something real?

THE ANSWER IS: All the aforesaid things are defined by “vocal expression” as by an extrinsic subject and foundation in which a second intention of reason is grounded. Thus St. Thomas, in the first book of the Perihermeneias, lecture 4,⁷ said “that this should be granted: ‘A dish is shaped wood,’ and likewise, ‘A name is a significant vocal expression,’ although it can also be granted denominatively that a dish is wooden and a name is vocal.” For in artifacts the matter can be predicated of the whole, because it contains its entire substance, while the artificial form adds only an accident. And when Aristotle, in the seventh book of the Metaphysics, text 25,⁸ denies that a statue is gold or stone, he is speaking of stone as unshaped and not subject to the form of an art, but taken precisely as a natural substance, as the holy Doctor explains there.⁹ Hence, because an accident or form in the concrete supposes for its subject, when the subject is something real and the form a being of reason, one cannot say absolutely that it is a being of reason, but only with an added qualification, namely, “formally”; absolutely, however, it can be called a real being on account of that for which it supposes in the concrete.

For p. 136 b 13.

OBJECTIONS ARE RESOLVED.

A common argument is usually made against the whole definition of definition: the same thing cannot at once be defined and be a definition, for then it would be more known and less known than itself. Therefore, if we define definition, the definition itself will be the defined thing, since it is what is defined. And again it is a definition, since this is its nature and essence; therefore it is at once a definition and the defined thing.

It is confirmed because a definition is said to be convertible with its defined thing, but the definition given here is not convertible with definition; therefore. The minor is proved: this definition is a particular definition contained under definition in general; therefore it cannot equal and be convertible with that general definition, since it is something contained under it. Consequently, it defines itself, and thus the argument returns: the defined thing and the definition are the same, just as if Peter were to define a human being, his definition would not be said to be convertible with a human being.

I ANSWER: Distinguish the proposition “The defined thing and the definition are formally the same”: denied. “The definition is formally the same thing (because this is its essence), and the defined thing is the same denominatively (insofar as it is compared with its definition)”: granted. For it is very common for one second intention to be such formally and to be another denominatively. For example, genus is formally the intention of genus, and denominatively a species of the predicables, as we shall say in Logic.

To the confirmation, the answer is that the definition of definition is said to be convertible with its defined thing formally, insofar as it is what is defined by it; but insofar as it regards definition in general as its genus, it is not convertible with it, but is contained under it. Peter, however, does not regard a human being as what he defines, but precisely as a superior species.

Second argument: Definition belongs to the first operation of the intellect, but an expression belongs to the second, as we said in the preceding article; therefore, “expression” is incongruously posited as its genus.

The major is established by Thomas, Sentences I, d. 19, q. 5, a. 1, ad 7, who says that “truth and falsity are not found in the first operation and its sign, which is a definition.”¹

It is confirmed: A definition is a mode of knowing; a mode of knowing does not have an expression as its genus; therefore, neither does definition.

The minor is proved: what is placed under some genus must be placed determinately under one of its species; but a mode of knowing is not in any determinate species of expression; therefore, it does not have expression as its genus. The major is proved: a mode of knowing can be found in both a perfect and an imperfect expression; therefore, it is not determinately in any one species of expression.

I ANSWER that “expression” is understood to include an imperfect expression, which materially coincides with a complex term; for nothing more is required for a mode of knowing, as was said above. Thus, it is not contradictory for a definition to be found in the first operation of the intellect, namely, when it is taken in the force of a complex term, and because its object is something simple, the quiddity of a thing, although it is explained compositionally. It is nevertheless defined through an expression because it is a mode of knowing, and a mode of knowing is commonly defined through an expression; also, definition can be held in the force of an expression if it is taken in the mode of a whole, although, when taken in the force of a complex term, it pertains to the first operation.

To the confirmation, the response is that the major of the second syllogism is distinguished: “What is placed formally and directly under a genus must be placed determinately under one of its species”: the major is granted. “What pertains to a genus only materially or consequently”: denied. For example, a statue is placed materially in stone or wood, because it belongs to a natural genus only materially, that is, as made from it. It does not follow that it must be constituted determinately in this stone or that wood, because it does not regard stone or wood as its genus, but as its matter; thus it can be made from any stone or any wood without any determination. Similarly, white is determinately a body, but not determinately animate or inanimate; wisdom or intelligibility is determinately a being, but is not determinately created or uncreated, because it can follow upon either. Therefore, expression is not the genus of a mode of knowing, but the matter from which it is formed under another logical art, namely, as an artificial mode of making the unknown manifest.

Third argument: Definition cannot be found outside a proposition; therefore, the first conclusion is false.

The antecedent is proved: Definition and the defined thing are relatives; therefore, definition must actually regard and be compared with the defined thing in order to be a definition. But when it is not predicated of the defined thing, it does not regard it in act, but in potency; therefore, it is not actually a definition.

It is confirmed: A definition is not actually accidental or essential except through an actual comparison with such a defined thing; therefore, it is not absolutely a definition except through a comparison with the defined thing. The antecedent is proved: this definition, “an animal apt to laugh,” is essential if applied to what is capable of laughter, but accidental if applied to a human being. Therefore.

I ANSWER the argument: The consequence of the second enthymeme is distinguished: “It must actually regard and be compared with the defined thing under the aspect of subject or predicate”: denied; “under the precise aspect of what is defined”: granted. In this way, a definition regards its defined thing even when it is not actually predicated of it. So a name regards what it signifies, matter regards form, and every potency its object, even if it does not actually exercise its causality and operation upon it. For actually regarding is one thing, actually causing or predicating another. Outside a proposition, a definition regards what it defines; from this it has the character of a definition even if it is not actually predicated.

To the confirmation, the answer is in the same way: a definition is essential or accidental not through predicative application to what it defines in the role of subject or predicate, but through the simple regard and relation it has to it as what is defined, which is found outside a proposition.

OBJECTIONS AGAINST THE CONDITIONS OF DEFINITION.

First: Genera, differences, property, and individuals, especially incorruptible ones, are defined by their own definitions; therefore, it is not necessary for a definition to consist of genus and difference.

The consequence is proved: if this were necessary, only a species would be definable, since only a species consists of genus and difference; but all the things listed above are defined; therefore.

I ANSWER by absolutely denying the antecedent. For only a species is properly definable, as Thomas teaches in Metaphysics VII, lect. 3.² If genera are supreme, they are not defined but described through a determinate analogous concept, not through a difference but through a mode. If they are subordinate, they are also species, and insofar as they are such, they are defined. Difference, property, and accident are defined only insofar as they have some nature that is reduced to a species. But if they are taken as parts, not as complete natures—as differences are—they are not defined, but described. Individuals as such, formally and in their actual exercise, are not definable or knowable, even if incorruptible, formally as individuals. If they are defined, it is through the nature of their species or by taking individuation in general. Hence Thomas, in the cited place, lect. 15,³ asserts that the singular lacks a definition not only because it is corruptible and material, but because it is singular: as such, it does not express a quiddity, which is the object of definition, but a mode or modification of quiddity.

Again: Relatives are simultaneous in nature and cognition; therefore, one is not better known than the other, since what is better known is prior in cognition. Yet one relative is defined through the other; therefore, it is not required that a definition be better known than what it defines.

I ANSWER IN TWO WAYS: First, it is not required that each part of a definition be better known than what it defines, but that the whole definition taken together be so; a relative, however, is only one part in the definition of a relative. Second, grant that the parts too must be better known; then explain that they are either positively or negatively better known. A relative is not positively better known or prior to its correlative, but it is negatively better known, insofar as without it the relative itself remains obscure and unknown.

Finally, demonstration and science manifest the nature of a thing; therefore, the definition of definition belongs to other things as well. If you say that demonstration proves properties or attributes, against this: therefore, it will manifest the nature at least in the way that a descriptive definition does, since the latter concerns properties.

I ANSWER: The antecedent is denied. For definition is one of the principles or items of prior knowledge for demonstration, as is said in Posterior Analytics I, ch. 1.⁴ Demonstration manifests that attributes belong to a subject, but it does not do so in the manner of a descriptive definition: the latter does not prove that attributes belong to a subject, but, presupposing this, explains it in a simple way through those attributes and manifests its nature accidentally, without proving or demonstrating it.

WHAT THE PROXIMATE AND REMOTE DEFINED THING ARE.

In the text we said that the name of the thing defined can be called the proximate defined thing, while the thing signified by it can be called the remote defined thing. The reason is that the name is a sign that represents and brings near, or applies, the matter that can be defined. This sign, in turn, remains declared consequently: when the thing defined and the signified thing have been declared, the sign is also declared and explained. Hence the name, in this respect, can be called the proximate defined thing, even if it is not the thing most immediately manifested.

Others add that the quiddity or nature defined can be called the proximate defined thing, while the attribute connected and joined to the essence can be called the remote defined thing. But they assert this falsely, because only that is a defined thing which is explained and declared by a definition; for the defined thing and the definition are related. But in an essential definition the attribute is not the thing defined; rather, it is the nature. Likewise, in a descriptive definition the attribute is not the thing that is defined and made known; rather, the nature is made known through the attribute. Therefore, an attribute can never be called what is defined except when it is defined separately from the nature.

If it is objected that the name, too, is not the thing defined, yet it is called the proximate defined thing, you will say that the name itself is declared and explained at least virtually, though not formally.

Against this: When the nature is declared, its attribute is also declared virtually; therefore, this suffices for it to be called the defined thing, at least remotely. Again, the Philosopher, Posterior Analytics II, text 7,⁵ asserts that a definition of the name and a definition of the thing cannot be the same; therefore, by one and the same definition one thing cannot be defined as the proximate defined thing and another as the remote one.

TO THE ARGUMENT: The answer there was sound. To the reply: the antecedent is denied; an attribute is related to a nature as an effect that follows it, not as a sign representing it, as a name does. When the nature of a cause is declared, its effect can still remain unknown; but when the signified thing is declared, the sign cannot remain unknown, since it actually and in the exercise of signifying represents the thing signified. To the Philosopher, the answer is that he is speaking of a definition of the thing and a definition of the name, which are such in themselves and directly, and each explains its own defined thing. Aristotle does not deny that, once the thing itself has been defined, the name itself can consequently and indirectly be explained as the proximate defined thing in the mode of a sign, not in the mode of matter being defined.

We will resolve questions concerning division by means of questions rather than arguments. Is this the quidditative and proper definition of division: “a discourse, namely, that distributes a thing or a name through its parts”? We answer affirmatively. It is given through what is proper and quidditative to division. “Discourse” is put in place of the genus, or as the matter, by which we also understand a complex term. Like definition, division can have the role of a predicate in a categorical proposition and therefore the role of a complex term, and it can belong to the first operation. “Distributing” means “by distributing and manifesting”; this explains the specific and differentiating character of the mode of knowing proper to division, since by distributing and distinguishing the parts it manifests the confusion of the whole. For both definition and division manifest something through parts: definition manifests constitutive parts, while division manifests quasi-quantitative parts. Definition regards the totality of quiddity, whereas division regards the totality of quantity or distribution. Having parts belongs to quiddity and quantity, though in different ways. Thus definition explains what is defined through parts by constituting it, not by distributing it; division distributes and removes the confusion of what is divided through distribution and, as it were, enumeration of the parts. “A thing or a name” is said to indicate the twofold division of a name and of a thing, which we treated in the text.

Second, you will ask whether logical division treats and distributes only a logical whole, or also extends to physical, metaphysical, nominal, real, and other divisions.

For the resolution, note that there is a logical whole, that is, a predicable or universal in relation to its inferiors; a physical whole, that is, a composite of matter and form or of integral parts; a metaphysical whole, that is, a composite of genus and specific difference; a potential whole, that is, something consisting of diverse powers or potential parts; and an accidental whole, that is, something consisting of many accidents. Some therefore say that it belongs only to dialectic to teach the division of a logical whole.

We must say, however, that in all these divisions one can consider the matter in which division is exercised, or the form, namely, the technique or manner of manifesting and carrying out division. As to its matter, not all divisions belong to logic, since many are physical or metaphysical. Thus, materially, it belongs per se to logic only to consider division of the logical whole, namely, a universal or predicable, into subjective parts, as a genus into species, a species into individuals, and so forth. But as to the form, or technique or manner of dividing—which is the second intention of division—it belongs to logic to treat every division, because whether physical or metaphysical, such division is a mode of knowing and is performed in a methodical way. Physical or metaphysical definition likewise belongs to logic, since logic treats the technique and intention of all definitions.

Third, you will ask whether division can be given by negative or contradictory terms, for example: “An animal is either a man or a non-man.”

Some deny this, both because such a division gives us no information—the negative member gives no information but merely negates—and because the divided thing is understood in each member and shared by the dividing members. But “non-man” is broader than animal and does not share the notion of animal.

Nevertheless, it must be said that the proposed division is methodical and conforms to logical rules. It is proved because in a good division the members must be opposed to one another; otherwise they would not be separated by differences, but would either be identical or disparate. They need not, however, be relatively or contrarily opposed; therefore they can be contradictorily opposed. This is confirmed: “A man is either seeing or blind,” “air is either dark or bright,” and “an animal is either rational or irrational” are good divisions, one member of each being negative or privative, yet they are commonly accepted. Therefore the proposed division is good.

To the reasons for doubt we reply that the negative member is not taken absolutely, but as falling upon and restricted to the divided item; thus it is not broader than what is divided. Hence when I say, “An animal is either a man or a non-man,” “non-man” is not understood absolutely and in its whole extension, but as an animal that is not a man; thus it is no broader than animal as such. Likewise, in “irrational,” animal is understood, not “irrational” absolutely as it is found in a stone. In this way the negative member, as applied to this divided thing, gives information and manifests something, namely, every irrational animal, every brute animal, and so on.

Objection: A genus is rightly divided by differences, as animal into rational and irrational; yet the genus is not predicated of the differences. Therefore the divided thing should not be understood in the dividing members.

We reply that a genus is not divided into differences, but divided by differences into species; the genus is predicated of the species. Thus, when animal is divided into rational and irrational, what is understood is: “One animal is rational, another animal is irrational,” and these are species.

You will object: In partition, by which a thing is divided into integral parts, the divided thing cannot be predicated of the dividing members, since the divided thing is a whole and the dividing items are parts, and a whole is not predicated of a part. In accidental division, too, an accident is not predicated of the subjects themselves, nor the subject of the accidents, since they are not identical. Therefore.

We reply that in the first case the divided item is not predicated of each part; rather, each part shares something of the whole, not by predication but by dependence on it. In the second case the divided item is predicated of the dividing members, namely, of subjects accidentally; there the accident is identified with the subject and conversely, because the accident is signified concretely. Thus it does not signify the form alone, but something having the form, and what has the form is identified with the subject. Hence St. Thomas says, ST I, q. 13, a. 12, body, that man and white are the same in subject but differ in account, that is, in form and quiddity.

Fourth, you will ask whether analogical division is included in this mode of knowing.

Some deny it, saying that in analogical division there is no divided item in which the dividing members agree, except for a name, and there are no differences by which the division is made.

NEVERTHELESS, THE ANSWER MUST BE AFFIRMATIVE, because analogical division is methodical and belongs to a mode of knowing: its dividing members are really distinct from one another, as God and creature, accident and substance, yet they agree in something one—not simply or by univocal unity, but proportionally and analogically. Although the analogical item has no differences, it has modes by which it can be divided. This suffices for a methodical way of dividing, since division requires some order in its execution, and this belongs to logic.

Finally, you will ask whether something can be divided by several essential divisions, or whether every division must be adequate, so that it completely exhausts what is divided and leaves no room for another division.

THE ANSWER IS that when something is divided according to that by which it is ultimately and indivisibly constituted in its essence, it admits only one essential division. But if several formal aspects concur, each of which can be participated in a different way, it can then be divided by several essential divisions, though they are inadequate. Thus St. Thomas, ST I-II, q. 95, a. 4, takes different divisions of human law from the different principles from which it proceeds and the different ends it regards. Sins, too, are divided in species into carnal and spiritual, and according as they are against God or neighbor. See also the cited place and ST I-II, q. 72, aa. 2 and 4, and our later treatment of divisions of propositions.