Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Not everyone accepts the definition given by Aristotle¹; they reject it because it seems to coincide with complex terms, or terms of a composite form. For these have parts that signify separately, and therefore the whole definition of speech seems to fit them. Hence they define speech differently, as “several expressions or terms suitably arranged,” as though this too were not found in a complex term.

Others alter Aristotle’s definition, thinking that speech must consist of a noun and a verb, or at least a verb, even if not a noun. They therefore define speech as “a significant conventional voice consisting of a noun and a verb suitably agreeing with each other, or at least of a verb and a voice, if it is not significant.”

Others accept Aristotle’s definition but take issue with what is defined in speech. They think the definition of speech belongs to a voice only denominatively, as to a subject or substitute of which it is said that it is speech. They are right if “voice” is taken in itself and absolutely. But they add that this definition belongs essentially to what results from the voice and its complex signification, as to what speech is, rather than to what is said or denominated as such; in this they proceed as they do in defining a term.

Finally, others also accept Aristotle’s definition but say that the form of speech is the grammatical union of its parts.

I SAY FIRST: The best definition of speech is the one given by the Philosopher, and it is essential and quidditative in the same way as the definition of a term and a noun given above.

This conclusion is common among Aristotle’s interpreters. To explain it, it is enough to give St. Thomas’s teaching on On Interpretation I, lect. 6,² where he explains this definition very well. Speech concerns the intellect’s second operation, or the intellect as composing, not as simply apprehending. This is evident in itself, since by speech we express something joined and composed with another, whereas by a term we express something uttered separately and simply. Therefore, speech must involve several parts or expressions not merely by way of an accumulation or confused multiplication, but by way of ordering and union—and not just any union, but one that makes and composes some whole. For the parts of a complex term are also suitably arranged; but because they compose not a whole but a part, a complex term is not speech, as we will say shortly. Since, then, the definition of speech defines a certain composed and complete artifact, it is very unsuitable to explain it by saying that it is “several expressions,” which is found in a term. 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, or a certain total sign or significant voice consisting of parts.

When the Philosopher says, “some part of which signifies separately as an expression,” St. Thomas rightly observes two things.³ First, the Philosopher did not say, “a part of which, separated, signifies something,” but “some part of which is significant.” This is because of negations, says St. Thomas, and syncategorematic terms, which do not signify something but signify in some way, and yet are parts of speech. Second, the Philosopher says that a separated part signifies “as an expression, not as an affirmation,” because it is enough for speech that one of its parts be a simple expression; it need not be an affirmation or negation, though this too can be found in some speech, namely, in hypothetical speech. Speech had to be defined here as common to all; moreover, the character of a part in itself is found only in an expression or term. A proposition, even if it composes a hypothetical proposition, is not a part in itself and primarily, but accidentally, as we said above when treating the term.⁴

From these points it follows that speech need not consist of a noun and a verb as its parts. This is also clear from complete speeches themselves, since many do not consist of a noun but of infinitive verbs, as in “to run is to move,” as St. Thomas teaches in On Interpretation I, lect. 8.⁵ Indeed, it can consist of a verb and an adverb, as in “one runs quickly,” “it is well,” and so on. Among imperfect speeches too, which St. Thomas says in lect. 6⁶ truly are speeches, although they produce an imperfect sense, there is an imperfect speech without a verb, as when I say “a just man.” St. Thomas calls this speech in On Interpretation I, lect. 4,⁷ because it has significant parts and produces an imperfect sense—that is, one suspended in the hearer’s mind. Therefore, it is an imperfect speech without a verb. On the other hand, one can also be found with a verb but no noun. Therefore, it is not of the essence of speech in general to consist of both a noun and a verb, or of either one of them in particular.

I SAY SECOND: An imperfect speech and a complex term coincide materially and differ only formally.

There are complex terms that join several incomplex terms, such as “white man.” We say that the same words can also be an imperfect speech, but they differ according to the different formal character of a whole and a part, even when the part itself is composite. Parts can be joined in one thing in two ways. First, their composition can terminate in that thing as in a whole. Second, they can compose it without stopping there, instead being ordered further to a whole that the composed part also regards. An example of the first is the way bodily parts, such as an arm or a foot, are ordered to compose an animal, which is a whole, and their union terminates there. An example of the second is the way the parts from which an organic part is constituted—for example, flesh, sinews, and the like—compose it. These parts do not compose the organic part as a whole, but as a more principal part ordered to compose the whole itself. Thus the composed part and the whole are called “composed” in different ways. A composed part has the parts of which it consists quasi-materially, not formally—that is, not under the formality of a part in relation to a whole. That formality consists in the parts being joined so that they stop at the whole itself and are not ordered to anything further. But when they compose something without stopping there, and are ordered further to a whole, that thing is said to have parts, but not under that formality of a part. Nevertheless, if the organic part itself is separated from the animal and becomes a whole, its parts are ordered to it formally as parts, that is, under the formality and relation of part to whole.

In the present case, therefore, a complex term, such as “white man,” has parts not formally but materially, like a composed part and not like a whole, because those parts are joined in the complex term in such a way that through it they are ordered to constitute some whole. But the same complex, “white man,” when separated and taken after the manner of a whole, is an imperfect speech, just as a separated organic part is a whole; while it is in the animal, it is not a whole but a composed part. Therefore, a complex term and an imperfect speech differ only by this formality of whole and part.

I SAY THIRD: What is defined in speech is neither a third thing constituted and resulting from a significant voice and the form or second intention of speech, nor the significant voice itself in itself, which merely receives the form, is its subject, and is denominated speech; rather, it is the very notion and form of speech taken concretely.

This conclusion has no difficulty other than the one common to every definition of an accident taken concretely, which was settled above when treating the definition of a term; see there.⁸

I SAY FINALLY: The essential form of speech is not the union or grammatical connection by which its parts are joined.

Some think that the form of speech is this union of parts, but they are mistaken. Union is indeed the form and act of things insofar as they are capable of union; nevertheless, it is not the form that essentially constitutes the whole, but applies and unites the essential form to its matter or subject. Therefore, union, insofar as it is union, is not the constitutive form of a composite, nor can a specific and intrinsic form constituting a whole consist in it. For in its intrinsic notion, union means a means, application, or copula of extremes; therefore, it presupposes other extremes that constitute the thing and are united through it as through a means. Hence union itself is not the form that essentially constitutes, but one that applies the constitutive form.

BUT YOU WILL SAY: What, then, is the essential form of speech? We answer that just as in a physical whole there is a partial form, such as the soul in relation to the body, and a total form, such as humanity in relation to the supposit, so in speech the partial form will be the predicate, or something in place of the predicate, in relation to the subject—or rather (since, as St. Thomas says in On Interpretation I, lect. 8,⁹ one part in speech must determine another) the determining part is the form. If the parts determine one another, each is form insofar as it determines, and matter insofar as it is determinable, as is said in the mutual contract of marriage. The total form, however, is the very composed and complex signification insofar as it takes on the intention and relation of a whole. In this way it is related, as it were, in opposition to the term itself, which is a part: just as a term signifies after the manner of an artificial part, and this is its essential notion, so speech signifies complexly after the manner of a whole, and this is its essential form.

THE OBJECTIONS ARE ANSWERED.

You will object first: The definition of speech does not distinguish speech from a term; therefore, it is not a good definition.

The antecedent is proved: It does not distinguish imperfect speech from a complex term. For a complex term too is “a significant voice whose parts signify separately,” and yet it is truly a term, while imperfect speech is truly speech. Therefore.

WE ANSWER from what was said in the second conclusion: a complex term and imperfect speech can coincide materially, but they always differ formally, as was explained there.

But you will insist: An imperfect speech, even as speech, is a part; therefore, it does not differ from a complex term.

The antecedent is proved. First, St. Thomas says in On Interpretation I, lect. 6,¹⁰ that all parts of speech are referred to complete speech, of which imperfect speech is a part, since it too has parts that signify. Therefore, imperfect speech does not function as a whole but as a part. Second, complete speech is a whole complete in the genus of speech; therefore, imperfect speech is incomplete and something less than the whole, and therefore is a part. Finally, imperfect speech still belongs to the first operation, not the second; therefore, it is a part. The antecedent is clear from St. Thomas, Opusculum 48, treatise on Enunciation, ch. 3,¹¹ who says that something is missing from the sense produced by imperfect speech, because composition and division are missing. Therefore, what pertains to the second operation is missing, since the second operation is composition and division; therefore, it remains within the limits of the first operation.

We answer by denying the antecedent. To the first proof we say that St. Thomas calls imperfect speech a part either by taking “part” broadly for that which is an imperfect whole, since for that very reason it can be ordered to a perfect whole, at least as something to be perfected in the same line and genus of whole; or, if St. Thomas takes “part” strictly and properly, imperfect speech is understood to be a part materially, not formally—that is, insofar as it coincides with a complex term.

To the second proof we say that imperfect speech is something incomplex and less than the perfect whole, but not as a part; rather, it is an imperfect whole in process of becoming, in relation to the perfect whole. Imperfect speech is, as it were, speech begun in relation to complete speech.

To the third proof we say that St. Thomas denies imperfect speech the composition and division that function as affirmation and negation removing the mind’s suspension. In this way it lacks something of perfect composition and division, which generates a complete sense. It does not, however, lack the character of the second operation, which is imperfect composition and division. Indeed, the fact that it generates a suspended and imperfect sense proves that it differs from a complex term. A term, whether complex or incomplex, generates no sense at all, not even a suspended one, but only pure apprehension—of one thing, if it is an incomplex term, or of several things and concepts. Of these it generates only simple apprehension, and so remains within the notion of a term and a part. Imperfect speech, however, generates some sense beyond apprehension, although begun and imperfect, because it begins to pass beyond apprehension toward the composition of a whole, and there suspends rather than completes the sense. Therefore, it is a sign that it belongs to the second operation, but imperfectly and inchoately; thus it does not have the character of a part but of a whole.

Second, you will object: It is not of the essence of speech that its parts be significant, or that they not signify as an expression; therefore, this is wrongly placed in the definition of speech.

The antecedent is proved from speeches made up of non-signifying voices, such as “A is not B” and “blitiri is not a noun.” The same argument applies if “A” were imposed to signify the whole clause “man is white”; then it would be speech, and yet it would have no significant parts. As to the second part, it is proved that the speech “if Peter runs, he moves” does not have expressions as its parts, but speeches, namely “Peter runs” and “Peter moves.” Therefore, the parts of speech need not signify as expressions.

The argument can be confirmed by the probable opinion that a mental proposition is a simple quality; for then it has no significant parts. Therefore, that definition is not certain and common to every opinion.

WE ANSWER by denying the antecedent. To the first proof, we said above, q. 1, a. 2, when treating the term, how it is a significant voice. Here we add that the Philosopher did not say in the definition of speech that all its parts must signify separately, but that some part of it signifies separately. Thus, a proposition or speech made up of non-signifying voices has at least some significant part, for example, the verb “is”; for even speeches involving non-signifying terms cannot be made without a verb. See what we said there.

To the second proof we answer from St. Thomas, On Interpretation I, lect. 6,¹² that when speech is said to have significant parts, they must signify as expressions; this at least must be found in every speech. If it also has parts as affirmations, so much the better. Or, second, composite speech has parts as expressions mediately, since it is ultimately resolved into them.

To the confirmation we answer, in the discussion of the proposition below,¹³ that even if a mental proposition does not have parts entitatively, it has them objectively, because it signifies something complex. It also has them presuppositively, because it is formed from several apprehensive concepts as presupposed, although it does not have them formally and entitatively, as a certain quality does.

Finally, it is argued: Speech is formally a being of reason, because it is a second logical intention; therefore, it is not well defined by a voice, which is something real.

WE ANSWER that this is common to every logical instrument, which Aristotle invariably defines by a significant voice. Briefly, there is no problem in a second intention being founded on something real in the first intention and having it as the subject of denomination. Thus, there is no problem in defining a logical intention through something real as an extrinsic subject and foundation. We do not agree with those who say that speech or a term cannot absolutely be called a real being, but must be called a being of reason because formally it is a being of reason. If that were true, it could not absolutely be called a voice or a concept, since voice and concept are real beings. This is especially so because in artifacts the matter can be predicated of the whole, since it contains its entire substance, while the artificial form adds only an accident. Hence St. Thomas says in On Interpretation I, lect. 4,¹⁴ “one must grant that ‘a bowl is shaped wood,’ and likewise ‘a noun is a significant voice,’ although one can also grant denominatively that a bowl is wooden and a noun is vocal.” When the Philosopher denies in Metaphysics VII, text 25,¹⁵ that a statue is gold or stone, he is speaking of stone as unshaped and not subject to the form of art, but taken precisely as natural substance, as can be seen in St. Thomas’s explanation there.¹⁶ Therefore, since an accident or form taken concretely supposits for its subject, when the subject is something real and the form is a being of reason, it cannot absolutely be called a being of reason, but only with the qualification “formally”; absolutely, however, it can be called a real being by reason of that for which it supposits concretely.

Definition is commonly defined as “an utterance explaining the nature of a thing or the signification of a name,” which includes both a definition of the name and a definition of the thing. As for the definition of what a thing is, this is taken from Aristotle, who often says that a definition is an utterance signifying what it is for a thing to be, as in Topics I, ch. 5,¹ and Topics VII, ch. 5,² and at length in Metaphysics VII³ and Posterior Analytics II,⁴ lect. 2,⁵ in St. Thomas’s commentary. There the holy Doctor also says that a definition is an utterance signifying what a thing is.

I SAY FIRST: The definition of definition is correctly stated as an utterance, taken as its matter; “utterance” is understood to include a complex term, and a definition can be found outside a proposition.

THE FIRST PART is commonly accepted. That “utterance” must be understood to include an imperfect utterance, which materially coincides with a complex term, is clear because a definition can be the predicate in a categorical proposition, while the role of predicate in a categorical proposition belongs only to a term. Similarly, St. Thomas often teaches that definition belongs to the intellect’s first operation, as in On Interpretation I, lect. 8,⁶ and Posterior Analytics I, lect. 5,⁷ although he said that utterance in the strict sense belongs to the intellect’s second operation in On Interpretation I, lect. 6.⁸ Finally, definition is directly a mode of knowing insofar as it makes something unknown manifest. For the character of a mode of knowing, St. Thomas rightly said in Metaphysics VII, lect. 9,⁹ it is required “that it not be one expression, because one expression does not make something manifest in the way that a less-known name is made manifest through a better-known one.” Therefore, for something to be a mode of knowing, several expressions or terms must concur to explain something unknown.

THE SECOND PART of the conclusion is taken from St. Thomas in On Interpretation I, lect. 8,¹⁰ where he says, following Aristotle, that a definition is a kind of utterance; yet if no verb or verb form is added to the character of the human being—that is, to the definition—it is not yet an enunciative utterance. And in Posterior Analytics II, lect. 2, § Quae talis est,¹¹ he says: “In a definition, something is not predicated of something as in the definition ‘A human being is a two-footed animal’; neither is animal predicated of two-footed, nor two-footed of animal.”

I SAY SECOND: Although a definition may be called good or bad, it is not said to be true or false per se, but only accidentally.

Everyone accepts that it is to be called good or bad, because this is common to every mode of knowing insofar as it makes the unknown manifest through a fitting and proper explanation. Where there is proper fittingness, something is also called good; if the fittingness is improper, it is called bad. As to whether a definition can be called true or false, some affirm it, as we said, believing that truth or falsity can also occur in simple apprehension, not as affirmed or denied, but by simple conformity or nonconformity. Others deny this, because Aristotle said that truth or falsity occurs only in an enunciation.

St. Thomas resolves the dispute in Summa theologiae I, q. 17, a. 3, where he says: “Since the falsity of the intellect is per se only about the intellect’s composition, falsity can also occur accidentally in the intellect’s operation by which it knows what a thing is, insofar as a composition of the intellect is mixed into it. This can happen in two ways: in one way, when the intellect attributes the definition of one thing to another, as if it attributed the definition of a circle to a human being; in another way, when it composes together parts of a definition that cannot be joined, for then the definition is false not only with respect to some thing, but also in itself.” So St. Thomas.

I SAY THIRD: A descriptive and a quidditative definition do not differ on the part of the thing defined, but on the part of the defining components, or the things through which the definition is given.

We state this conclusion to remove a phrase that some add to the definition, namely, that it is an utterance explaining the nature or property of a thing. For in a descriptive definition the property of a thing is not explained; rather, the property itself explains the quiddity of the thing as its accident. That is why a descriptive definition is called accidental: it is given through accidents. Therefore, the property of a thing cannot be posited as the defined thing, as if a quidditative and descriptive definition differed in that one explains the nature and the other the property. This interpretation is absurd. For how could the property be what is defined and explained, when it is that which defines and explains? In both definitions, therefore, it is the thing itself, or the nature of the thing, that is defined—sometimes through genus and specific difference, sometimes through a property in place of the specific difference. Nor is it an objection that when a human being is defined as “an animal capable of laughing,” the expression “capable of laughing” signifies the human property itself or the human being under that property. This, I say, is no objection, for the signification of a name is being conflated with the manifestation or explanation in a definition. The name “risible,” or “capable of laughing,” signifies the property of the thing, as it were by representing and signifying it; but risible itself, which is signified by the name, manifests the quiddity of a human being to us by defining it accidentally.

I SAY FINALLY: The conditions required for a good definition are assigned most aptly.

We explained them in our text, chapter on Definition,¹² and all depend on the first condition: that a definition must consist of genus and specific difference, or of something that takes their place. From this it clearly follows that a definition is clearer and more explicit than the thing defined, that it is neither redundant nor deficient, since it explains the very terms within which the defined thing is contained, and that it is convertible with what it defines.

THE OBJECTIONS ARE ANSWERED.

Against the whole definition of definition, the following common argument is usually made: it is incompatible for the same thing to be at once defined and a definition, for then it would be both better known and less known than itself. Therefore, if we define definition, that very definition will be the thing defined, since it is what is being defined. And conversely, it is a definition, because this is its nature and essence. Therefore, it is simultaneously a definition and the thing defined.

This is confirmed because a definition is said to be convertible with what it defines, but the definition just given is not convertible with definition itself; therefore, and so on. The minor premise is proved: this definition is one particular definition contained under definition in general. Therefore, it cannot be adequate to, and convertible with, definition itself, since it is something contained under it. Consequently, it also defines itself, and so the argument returns: the same thing is both defined and a definition, just as if Peter defined a human being, his definition would not be convertible with a human being, and in defining a human being he would consequently define himself as well.

WE ANSWER by denying that, formally speaking, the defined thing and the definition are the same. Rather, it is a defined thing denominatively and a definition formally, because that is its nature and essence. This is no difficulty; it is very common for one second intention to be something formally and something else denominatively. For example, a genus is formally the intention of genus, but denominatively a species of the predicables; thus the same thing is genus and species, genus formally and species denominatively. In the same way, definition is essentially and formally a definition, but denominatively the thing defined insofar as it is compared with its definition. For by reflection the intellect can use even intentions themselves as subjects and denominated things, and introduce other intentions concerning them.

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

Second, an argument is made against what is placed in the definition as its genus, namely, that it is an utterance. For definition belongs to the intellect’s first operation, as St. Thomas says in his commentary on the Sentences I, d. 19, q. 5, a. 1, ad 7,¹³ where he says that “truth and falsity are not found in the first operation or in its sign, which is a definition.” But utterance belongs to the intellect’s second operation, as we said in the preceding article from St. Thomas himself in On Interpretation I, lect. 6. Therefore, utterance is incongruously placed as its genus.

This is confirmed because the immediate genus of a definition is a mode of knowing; but a mode of knowing does not have utterance as its genus, and therefore neither does definition. The major premise is clear, since definition is an artful manifestation of something unknown, which belongs to a mode of knowing. The minor premise is proved because if utterance were the genus of a mode of knowing, the mode of knowing would be in some determinate species of utterance; otherwise, it would not be a determinate subordinate of it. But it is neither a determinate perfect nor imperfect utterance, since a mode of knowing can be found in both, and those two species divide utterance exhaustively. Therefore, it is not in any determinate species of utterance.

WE ANSWER, from what was said in the first conclusion, that “utterance” is understood to include an imperfect utterance, which materially coincides with a complex term; as we said in the chapter on the Mode of Knowing, book II,¹⁴ nothing more is required for a mode of knowing. Thus there is no incompatibility in finding definition in the intellect’s first operation, namely, if we take it in the force of a complex term, with which an imperfect utterance readily coincides. This is also appropriate to definition for another special reason: its object is something simple, not something composite, namely, the quiddity of a thing. Yet it is defined through an utterance belonging to the intellect’s second operation, both because it can also be retained in the force of an utterance if taken in the manner of a whole, and because a mode of knowing is commonly defined through an utterance, even though, when the utterance is imperfect, it materially coincides with a complex term.

To the confirmation we answer that what is formally and directly placed under a genus must be placed determinately under one of its species. But what belongs to a genus materially, or is something consequent upon it, can be placed under a genus without being placed determinately under one species; it can be placed commonly under both in which it can be found. For example, a statue is placed materially under stone and wood, because it belongs to a natural genus only materially; and white is determinately a body, but not determinately animate or inanimate. Similarly, wisdom or intelligibility belongs determinately to the character of being, but is not determinately created or uncreated, because it can follow upon either. Utterance in itself, however, is not the genus of a mode of knowing but its matter, from which it is formed through another logical art; for there is no matter other than utterance, which is formed into an artful way of making the unknown manifest.

Third, an argument is made against the first conclusion: definition and the thing defined are relatives; therefore, unless a definition actually regards and is actually compared with the thing defined, it will not actually be a definition. But when it is not predicated of the thing defined, it does not regard it in act, but only in potency; therefore, it is not actually a definition, but one in potency.

This is confirmed because a definition is not actually accidental or essential except through an actual relation and comparison with what it defines. Therefore, such an actual relation is required for it to be a definite definition in act. The antecedent is clear in the definitions “an animal capable of laughing” and “a body that disperses sight.” If “capable of laughing” is applied to the risible, the definition is essential; if applied to a human being, it is accidental. Similarly, “dispersive of sight” applied to white is an essential definition, but applied to snow it is accidental. It cannot be said that this application occurs through simple apprehension or comparison, for it clearly occurs by means of the copula “is” and by predicating the definition of the thing defined. Therefore, it occurs through enunciation or composition.

WE ANSWER that a definition actually regards what it defines even outside a proposition—not under the character of subject or predicate, but precisely under the character of what is defined. For it to regard something actually under the character of what is defined, nothing more is required than that it regard it as the object and matter of the definition, just as a name regards its signified thing even if it does not actually signify it. For it is one thing to represent in act, and another to regard in act what is signified as the object of a sign. Just as matter regards form and every potency its object, even if it does not actually exercise its causality and operation concerning that object, so a definition actually has an order to what it defines even if it is not actually predicated of it.

To the confirmation we answer that a definition is essential or accidental with respect to different things defined. It does not derive this from an actual application to this or that subject under the character of subject, but from the intrinsic relation and fittingness it has with respect to this or that thing defined, even before it is actually applied to or predicated of it; this is, as it were, through a transcendental relation.

Finally, some difficulties can be raised about the conditions of a good definition. First, it does not seem necessary that a definition consist of genus and specific difference; otherwise only a species could be defined, since only a species consists of genus and specific difference. But the consequence is false, because genera, specific differences, and properties are also defined, and even individuals, especially incorruptible ones, since there can be knowledge of them; therefore, there can also be definition, which is a principle of knowledge.

Again, it is not required that a definition be better known than what it defines, as is clear in the definition of relatives, which are defined through their correlatives. But a correlative is not better known than its relative, since they are simultaneous by nature and in cognition; what is better known is prior in cognition. Accidents, too, are defined through their subject as an addition, as is said in Metaphysics VII, text 17,¹⁵ since it is outside their essence. Therefore, something redundant can occur in a definition.

Finally, manifesting the nature of a thing also belongs to other things that are not definitions, namely, demonstration and science, which by demonstrating properties of a subject manifest its very nature, at least in the way that a descriptive definition does, which is given through its properties.

WE ANSWER the first difficulty by saying that only a species is definable in the proper sense, as St. Thomas says in Metaphysics VII, lect. 3.¹⁶ Subordinate genera are also species and are defined insofar as they are such. But supreme genera are not properly defined, because they are not properly constituted by genus and specific difference; rather, they are described, or their nature is explained through an analogous concept determined by some mode that is not contracted by a specific difference. A specific difference, property, or accident, if defined, is defined insofar as it has some nature reducible to a species. If it has only the character of a part and not of a complete nature, as a specific difference does, it is not properly defined, but simply explained or described. Individuals, in actual practice, are not definable or knowable except through the nature of their species, through which they are defined. This also applies to incorruptible individuals, although in them the specific nature coincides with the principle of individuation. Thus St. Thomas, in his commentary on Metaphysics VII, text 54, lect. 15,¹⁷ says that a singular lacks definition not only because it is corruptible and material, but also because it is singular, since it does not express a quiddity, which is the object of definition, but a modification of nature and quiddity.

To the second difficulty we say first that the whole definition is better known than what it defines. It is not required, however, that each individual part be better known; a correlative term is only one part of the definition of a relative. Or second, we say that although the correlative is not prior in cognition or positively better known than its relative, it is at least so negatively, insofar as without it the relative itself remains obscure and unknown. As to what is said about an accident, the subject is not placed in the accident’s definition as entering into its constitution, but as terminating its essential and transcendental relation. Insofar as it so belongs to the essence, it belongs to it terminatively and extrinsically; therefore, it is not something redundant, since it is not irrelevant to the essence.

To the final difficulty we say that demonstration does not manifest the quiddity of a thing, because there is no definition and demonstration of the same thing, as St. Thomas proves from the Philosopher in Posterior Analytics II, lects. 3 and 4.¹⁸ Indeed, what a thing is, or its definition, is one of the principles or things previously known for demonstration, as is said in Posterior Analytics I, ch. 1.¹⁹ Demonstration manifests that properties belong to a subject. Nor does it function in the same way as a descriptive definition, because through demonstration it is proved that properties belong or inhere in a subject. Through a descriptive definition, however, it is not proved that properties belong to a subject; rather, on the assumption that they belong to it, its nature is manifested simply through them, not by proving or demonstrating that they belong to it. In this respect a descriptive definition differs from argumentation: the latter manifests by proving, the former by simple explanation.

From what has been said it follows that one cannot say, as some wish, that the proximate defined thing is the nature itself, while the remote defined thing is the proper property joined and connected to the essence. For only that is defined which is explained and declared by a definition, since definition and what is defined are related as a mode of knowing and the thing known through it. But in an essential definition the property is not the thing defined; the nature is. In a descriptive definition the property itself is not the thing defined and made known; rather, the nature is made known through the property. Therefore, the property can never be called what is defined, even remotely, unless it is declared separately from the nature, as what that property itself is.

But you will say: even in a definition of what a name means, the name itself is not the thing defined, yet we admit that it is called the proximate defined thing. Therefore, the property itself can likewise be admitted as the remote defined thing, even if it is not the thing defined. And if you say it is enough that the name itself be declared and explained virtually, although it does not formally signify the signified thing in act and in exercise, the reply is that the property of the nature is also declared virtually when the nature is declared. Therefore, it suffices for it to be called at least the remote defined thing.

This is confirmed because the Philosopher says in Posterior Analytics II, text 7,²⁰ that a definition of what a name means and a definition of what a thing is cannot be the same. Indeed, in text 9,²¹ he separates them, since the definition of what a thing is differs from the definition of what a name means. Therefore, one and the same definition cannot define one thing as the proximate defined thing and another as the remote one. For how could one single and simple definition be predicated of both a thing and a name?

WE ANSWER that the proximate defined thing can be said to be not only that which is declared and explained as the thing immediately made manifest, but also the sign itself that represents and approximates or applies the definable matter. Nevertheless, that sign too remains declared as a consequence, because when the signified thing is defined and declared, the sign remains declared and explained. But a property of the defined thing cannot have the character of what is defined as a sign through which the very nature defined is applied to a cognitive power. On the side of the thing defined, it is not a thing declared by the force of the declaration and definition of the nature; hence it can be neither the proximate nor the remote defined thing.

As to the objection that the property also remains declared virtually and as a consequence once the nature is declared, we deny the antecedent, because a property is related to the 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 that actually and in exercise signifies it cannot remain unknown. This is the role of a property in a descriptive definition: the property is not the thing defined, but that through which it is defined.

To the confirmation we answer that Aristotle is speaking of definitions of what a thing is and what a name means, which are such per se and directly, and each explains its own defined thing. But the Philosopher 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 manner of a sign, not in the manner of the matter defined.

We shall briefly settle this matter, discussing what pertains to division more by way of questions than arguments.

First, then, you will ask whether this is a proper and quidditative definition: “Division is an expression distributing a thing or a name through its parts.”

WE REPLY that it is proper and quidditative in the same way as the definition of definition and of a mode of knowing. It is given through what is proper and quidditative to division. For “expression” is posited in place of the genus, or matter; by “expression” we understand an expression that is a mode of knowing. This is required by the phrase “distributing,” which means the same as manifesting by distribution. “Distributing through parts” explains division’s proper difference, because by distributing and distinguishing the parts it manifests the confusion of some whole. Note here that both definition and division manifest something through parts, but definition manifests constitutive parts, while division manifests parts that are, as it were, quantitative, because definition regards the totality of quiddity, whereas division regards the totality of quantity or distribution.

“A thing” is said to indicate the twofold division, one of a name and the other of a thing, which we discussed in the text.

Second, you will ask whether logical division considers only a logical whole and its division, or embraces all divisions, whether physical or metaphysical, of a name or of a thing, and so on.

Some think that it belongs to dialectic alone to set out the division of a logical whole—that is, of a predicable or universal into its inferiors. For there is a physical whole consisting of matter and form or of integral parts; a metaphysical whole consisting of metaphysical parts, genus and difference; a potestative whole consisting of different powers or potential parts; an accidental whole consisting of many accidents; and finally a logical and universal whole consisting of subjective parts of which it is predicated. Only this last seems to belong to logic.

FOR MY PART, I SAY that in all these divisions we can consider either the art and method of manifesting a division and proceeding in it, so that the intellect makes it aptly and without error, or the matter itself in which the division is made and exercised. If we consider the matter, not all divisions belong to logic, since many are physical or metaphysical divisions, or partitions of quantity, distinguished from logical division. In this respect it is true that, on the side of the matter divided, it belongs per se to logic only to consider the division of a logical or predicable whole into subjective parts, as genus into species, species into individuals, and so on. But if we speak of the art and method of dividing, which is the second intention of division, then it belongs to logic to treat every division. For even when something is divided by an accidental or physical division, that division is a mode of knowing and is made artfully; therefore it belongs to logic, just as physical, metaphysical, and descriptive definition belong to logic because it treats the art and intention involved in all of them.

Third, you will ask whether a division can be given through negative or contradictory terms, so that one member of the division is negative and the other positive.

Some deny this, first because such a division makes nothing known to us: the negative member of the division makes nothing known but purely denies, as if you said, “Animal is divided into human being and nonhuman being”; by “nonhuman” nothing is made known to me. They also argue that the divided thing must be understood in each member of the division, since the divided thing is participated in by the dividers. But “nonhuman” does not participate in the account of animal, since nonhuman extends more broadly than animal.

NEVERTHELESS, the stated division is artful and conforms to logical rules. In a good division the members must be opposed to one another; otherwise, if they were not opposed, they would not be separated by differences but would either be the same or unrelated. They need not always be relatively or contrarily opposed, however; they can therefore be contradictorily opposed. This is confirmed because a division can be made by privative terms, as when you say, “One human being sees, another is blind”; “one part of the air is dark, another bright.” Therefore division can also be made through negative terms, since privation formally is a kind of negation. It is clear that everyone commonly admits this division: “Animal is divided into rational and irrational”; yet “irrational” is negative or privative with respect to “rational.”

Accordingly, since the divided thing itself is communicated to the members of the division, a negative member is always understood as falling on that divided thing—not absolutely, but restricted to it—and thus it does not extend more broadly than what is divided. When I say, “Animal is divided into human and nonhuman,” “nonhuman” is not understood absolutely and in its full breadth, but as the animal that is not human. An animal that is not human does not extend more broadly than animal as such. Likewise, in “Animal is divided into rational and irrational,” what is understood is “animal that is irrational,” not “irrational” absolutely, as it is also found in a stone. In this way the negative term too makes something known insofar as it is conjoined to the divided thing. For “nonhuman animal” or “irrational animal” makes known to me every brute animal absolutely and confusedly, and that is a kind of knowledge.

IF YOU SAY: Genus is rightly divided by differences, as “animal is divided into rational and irrational,” and yet genus is not predicated of differences; therefore the divided thing should not be understood in the members of the division.

We reply that genus is not divided into differences, but is divided by differences into species, as St. Thomas says in Metaphysics III, lecture 8,¹ and Book X, lecture 10.² Genus is predicated of species. Thus, when “animal” is divided into rational and irrational, what is understood is “one is a rational animal, another an irrational animal,” which are species.

YOU WILL OBJECT: In a partition by which a thing is divided into integral parts, the divided thing cannot be predicated of the dividers, since the whole is not predicated of its parts. The same applies to accidental division, in which an accident is not predicated of its subjects, nor a subject of its accidents, because they are not identified.

We reply that the divided thing is predicated of the dividers when it is divided into subjective parts, whether essentially or accidentally. When it is divided into integral or potestative parts, the divided thing cannot be predicated of each part; rather, each part participates in something of the whole, not by predication but by dependence on it. In accidental division, however, the divided thing is predicated of the dividers, namely, of the subjects accidentally; there the accident is identified with the subject, or conversely, because the accident is signified concretely and thus does not signify only the form but something having the form. What has the form is identified with the subject. For this reason St. Thomas said in Summa theologiae I, q. 13, a. 12, that a human being and a white thing 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. It seems not, because the members dividing an analogate are primarily diverse, not different from one another; therefore they do not presuppose some divided thing in which they agree, except perhaps in name, as equivocal things do. In that case it would be a division of a name, not of a thing. Likewise, an analogate is not divided according to different concepts, since, for example, a lower concept dividing being does not add anything to being. For if it added something, that addition would be being, but this is already supposed to be included in being. Therefore there is only a division according to different explanations of the same concept, which is properly not a division but a different explanation of the same thing.

NEVERTHELESS, WE REPLY that analogical division is artful, belongs to logic, and pertains to a mode of knowing, because its members are really distinct from one another, as God and creature, accident and substance. They also have an agreement and are one—not absolutely and simply, but as is explained more fully in Logic q. 13 and 14. They therefore have agreement in something real that is one proportionally, and have simple difference among themselves; this suffices for an artful mode of dividing, because making a division requires some ordering.

To the reason for doubt we say that the members of a division are called primarily diverse because they do not agree in some genus or become contracted through differences added to a genus. This does not prevent them from truly dividing a higher account, as it were by contracting and dividing it through different modes and explanations, though not through added differences, as will be said in the cited places in Logic. This suffices for them to agree in some concept according to a proportional unity and to differ absolutely according to different concepts. They agree not merely in name but in the thing conceived—for example, in being, which is one proportionally but not simply, as will be said there.

Finally, you will ask whether every division must be essentially adequate, so as to exhaust the whole divided thing, or whether something can be divided essentially by several divisions.

This will be discussed below when we treat the divisions of a proposition.³ FOR NOW, WE SAY that when something is divided according to that by which it is constituted in its essence ultimately and indivisibly, it admits only one essential division. But if several formalities concur, each of which can be participated in a different way, there is no obstacle to its being divided essentially by several inadequate essential divisions. On this rule see St. Thomas, Summa theologiae I–II, q. 95, a. 4, treating the division of human law, which takes different divisions from the different principles from which it proceeds and the different ends it regards. Sins are also divided in species into carnal and spiritual sins, and according to whether they are against God or neighbor, as is said in Summa theologiae I–II, q. 72, aa. 2 and 4.