26 On Definition
26: On Definition Besides the foregoing terms of second intention, many other terms of second intention and second imposition are in common use. Students can be hindered by an ignorance of these terms; therefore, to instruct the novice I shall examine some of the relevant terms.
Some terms that logicians use are common to all universals; others are proper only to some universals. Again some apply to universals only when they are taken together; whereas others apply to one universal with respect to another. Terms which apply to several universals taken together include 'definition' and 'description'.
But 'definition' has two senses. In one sense of the word we speak of essential definitions (definitions expressing what a thing is) and, in another sense we speak of nominal definitions (definitions expressing what a word means).
'Essential definition' has two senses. In the broad sense it covers not only strict but descriptive definition. In the narrow sense, however, a definition is a complex expression signifying the whole nature of a thing without indicating any thing extrinsic to the object defined. This can happen in two ways. Sometimes the complex expression will include expressions in one or more of the oblique cases; these constituent expressions will signify essential parts of the thing. Thus, if we define man as a substance composed of body and intellective soul, the oblique forms 'body' and 'intellective soul' express parts of man.
A definition of this sort is called a natural definition.
In another form of essential definition no expression is in an oblique case; both genus and difference are in the nominative case. Here the difference expresses a part of the thing defined, but only in the way in which 'white' expresses whiteness. 'White' expresses whiteness, but it does not supposit for whiteness; it supposits, rather, for the subject of whiteness. Similarly, although differences express parts of the things they define, they do not supposit for those parts but for the whole composed of those parts. When we define man as rational animal or animated, sensing, and rational substance, the terms 'animated', 'sensing', and 'rational' supposit for man because man is rational, animated, and sensing. Nevertheless, these terms designate a part of man. Their abstract counterparts also designate a part of man but not in the same manner.
A definition of this sort is called a metaphysical definition because the metaphysician defines man in this way.
Besides these two forms of definition, no other is possible except perhaps that form of definition where the parts express more and the whole, the same.
On Definition Thus, it is wrong to claim that man, for example, has a logical, natural and metaphysical definition; for the logician, since he does not treat of men (indeed, he does not treat of things that are not signs at all), has no reason to define man. His task is rather to teach how the different sciences treating of man are to define man. Therefore the logician ought not assign any definition of man. He may, of course, use examples, but then his examples ought to include only natural and metaphysical definitions.
Just as it is wrong to divide definitions into the natural, metaphysical, and logical, it is wrong to speak of three men—the natural, the metaphysical, and the logical. Similarly, although one can say that because of the diversity of their constituent expressions, definitions are to be divided into the natural and metaphysical, it is absurd to say that there is a natural man and a metaphysical man. Such a claim must mean either that there is some truly substantial thing outside the soul that is natural man and some other substance that is metaphysical man or that there is some concept of the mind or some word that is natural man and some other concept or word that is metaphysical man. The first alternative can be rejected; for how are these men, both of which are substances, to be distinguished? Either one is a part of the other, or they are wholes which are distinct, or something is a part of both (but not everything that is a part of one is a part of the other). The first and second options clearly are not possible. Nor is the third alternative a viable option; for since natural man is composed only of matter and form, it would be necessary that either his matter or his form not be a part of metaphysical man and then either metaphysical man or natural man would be cither cxclusively matter or exclusively form; but both possibilities are absurd.
Nor will it do to say that since the metaphysician and the natural philosopher consider man in different ways, man considered by the metaphysician is different from man considered by the natural philosopher. Although it is true that each considers man differently, it does not follow that there would be one man, metaphysical man, and another, natural man. What follows on the contrary, is only that there are diverse considerations of one and the same man. Suppose that Socrates sees Plato clearly while Sortes sees him obscurely. The seeing is different but Plato who is seen is not something different in the two cases.
Similarly, the metaphysical and natural considerations of man are different, but the man who is considered is the same. There are not then two different things—natural man and metaphysical man. Nor can it be said that there is a different concept or word in the two cases. The concept is identical either with the definition, a part of the definition, or with something else that is predicated of man; but whichever of these options we take. it is clear that the desired conclusion is not achieved.
It should be clear then that definitions can be different where the thing defined is the same. Although these two definitions differ, they signify the same thing; and whatever is signified by one or by a part of one is signified by the other or by a part of the other. Nonetheless, the parts will differ in mode of signification, since the corresponding parts of the metaphysical and natu ral definitions will be in different cases.
It should be noted that when, significatively taken, a definition is predicated of something, the corresponding definitum, significatively taken, is also predicated of that thing and vice versa. Further, a proposition composed of a definition and a definitum that is hypothetical, possible, or the equivalent of either of these is a necessary proposition. The following, for example, are both necessary: 'If man is, rational animal is' (and vice versa); and 'Every man can be a rational animal' (where the subject stands for what can be). Nevertheless, no such affirmative proposition which is merely de inesse or de presenti is ever necessary. Thus, the simple propositions 'Man is a rational animal' and 'Man is a substance composed of body and intellective soul' are not necessary. The reason is that if there were no men, the propositions would be false. Aristotle, however, who claims that propositions like 'Man is an animal' and 'Donkey is an animal' are necessary, would disagree here.
From the aforesaid it is clear that a definition is not identical with the definitum. According to everyone, a definition is a complex expression either mental, vocal, or written; but it cannot be the same as any simple expression.
Nevertheless, a definition signifies the same thing as its definitum, and this is what is meant by those who say that the definition and the definitum are really the same thing; they mean that the two signify the same thing.
It should be noted that if we take 'definition' in the strict sense, the only thing that can be expressed by a definition is substance; and if we use the word
'definitum' to mean the term convertible with a definition, only names can be definita. Verbs and other parts of speech cannot.
But a definition in the broader sense, a nominal definition, is an expression explicitly indicating what is designated by an expression. Someone who wants to teach another individual what is meant by the name 'white' says something like "Something having whiteness." Not only names of which 'exists' is predicable are susceptible of this sort of definition, but also expressions of which such predication is impossible. Thus,'vacuum', 'non-entity', 'impossibility', 'infinity', and 'goat-stay' have definitions; that is, there are expressions corresponding to these names which signify the same thing as the names in question. It follows that in this sense of 'definition', it is sometimes impossible, using the verb 'to be' to predicate a definition ofits definitum; and this impossibility exists even where both definitions and definitum are significatively taken. 'Chimaera is an animal composed of a goat and a cow', for example, is not true; it carries the false implication that something actually is composed of a goat and a cow. Nevertheless, the proposition in which the terms supposit materially (*""Chimaera" and "animal composed of goat and cow" signify the same thing') is true. People