Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

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.