Lecture 15 — Why ideas cannot be defined

But, since there are two kinds of substance, the concrete whole and the account (and I say that the former is substance taken as the account conceived with matter, and the latter is the account in general), then all things that are called substance in the former way are subject to corruption, for these are also subject to generation.

But the account is not subject to corruption in such a way that it perishes, since it is not subject to generation; for it is not the being of house that is produced, but the being of this house.

But they both are and are not without generation and corruption, for it has been shown (1033a2) that no one generates or produces these. And for this reason, too, there is neither definition nor demonstration of singular sensible substances, because they have matter whose nature is such that it is possible for them both to be and not to be. For this reason, all singular instances of these are corruptible.

Now, demonstration is of necessary things, and definition is scientific. And just as scientific knowledge cannot sometimes be scientific knowledge and sometimes ignorance, but what is such is opinion, so too neither can it be admitted that demonstration or definition is such, but that it is opinion, then, which is concerned with something that can be otherwise than it is.

If this is true, obviously there will not be demonstration or definition of these things. For corruptible things are not evident to those having scientific knowledge, and when they have been removed from the sphere of sensory perception, even though their intelligible expressions remain the same in the mind, there will be neither demonstration nor definition of them.

And for this reason, when anyone eager for setting the limits of things defines one of these singulars, he must not ignore the fact that it is always possible to overthrow his definition. For it is not possible to define such a thing. Nor is it possible, then, to define any of the ideas, for an idea is of singular things (as they say), and is separable.

And it is necessary that the intelligible expression of a thing should be composed of words, and one who forms a definition will not coin a word (for it would be unknown), but the attributes which are posited are common to all things.

It is necessary, then, that these also apply to other things. For example, if anyone were to define you, he would say that you are an animal capable of walking or white or having some other attribute which is found in something else.

But if anyone were to say that nothing prevents all things considered separately from being in many things, but that, taken together, they are present together only in this one thing, it is first necessary to say that they belong to both—as two-footed animal belongs both to animal and to two-footed.

And this must be the case with eternal things.

It is also necessary that they be prior existents and parts of the composite. And even more, they must be separable if man is separable, for either neither or both will be such. If, then, neither is separable, a genus will not exist apart from species; if both are, so also will a difference be.

Again, because they are prior to being itself, they will therefore not be destroyed.

And again, if the ideas are composed of ideas, less composite things are the elements of others.

It will, moreover, be necessary that those things of which an idea is composed should be predicated of many things, as animal and two-footed. But if this is not true, how will they be known? For there will be an idea which cannot be predicated of more things than one. However, this does not seem to be the case, but every idea is capable of being participated.

Therefore, as was stated (1040a14), the fact that it is impossible to give definitions of eternal things, and especially of any singular instances of these (like the sun and the moon), is hidden from these people.

For people err by adding such attributes as can be removed while allowing the sun to remain—such as going around the earth or being hidden at night. For according to them, if it stands still or is visible at night, it will no longer be the sun; but, since the sun means a certain substance, it is absurd if it is not the sun.

They also err by adding attributes which are capable of belonging to something else. For example, supposing that another such thing should come into being, it would evidently be a sun.

Therefore, the definitive expression is common. But the sun was taken to be a singular thing, like Cleon and Socrates. For why do none of these thinkers offer any fixed limits of an idea? For to those attempting this it would become evident that what has been said just now is true.

1606. In this place, the Philosopher shows that the ideas, which the Platonists claimed to be separate, are incapable of being defined. And he does this because the Platonists posited ideas chiefly in order that they might apply them both to definitions and to demonstrations, which have to do with what is necessary, since all these sensible substances seemed to be in motion. In regard to this, he does two things.

First (1039b20; [1606]), he uses arguments to show that the ideas cannot be defined.

Second (1040a27; [1627]), he uses an example, at therefore, as was stated.

In the first member of this division (1039b20), he presents three arguments.

The first of these he states as follows. One kind of substance is the account, that is, the essence and form, and another is the composite of matter and form, which is the concrete whole made up of matter and form. And I say that these differ. The latter, which is substance in the sense of the concrete whole, is substance taken as something having its intelligible structure conceived with matter. The former, which is the form or intelligible structure or essence of a thing, is the intelligible structure or form in general, and this does not have individual matter connected with it.

1607. Therefore, all those things that are called substance in the sense of a composite are capable of being corrupted, for it was shown above (1033a2; [1423]) that only those things that are composed of matter and form are subject to generation. But generation and corruption belong to the same subject.

1608. And substance in the sense of the intelligible structure or whatness of a thing is incapable of being corrupted in such a way that it is corrupted in itself. For it was shown above (1033a2; [1417–23]) that this kind of substance is not generated, but only the composite. For it is not the essence of a house that is produced (as was shown above), but what is peculiar to this house, because it is this particular house and not the intelligible structure of a house that is produced. Yet forms and quiddities of this kind sometimes are and sometimes are not without generation and corruption, that is, without being generated or corrupted in themselves, for they begin to be and not to be when other things are generated and corrupted. For it was shown above (1033a2; [1420]) that, in the case of natural things, no one generates these, namely, their forms and quiddities. Nor does this happen even in the case of artificial things; but this singular agent generates and produces this singular thing.

1609. And because singular things are generated and corrupted, there can be neither definition nor demonstration of singular sensible substances, for they contain individual matter, whose nature is such that anything constituted of it is capable both of being and of not being. For matter itself, considered in itself, is in potency to form, by means of which the material thing exists, and to privation, by reason of which the material thing does not exist. Hence, all singular things included among these sensible substances whose matter is in potency to being and non-being are corruptible. However, the celestial bodies do not have that kind of matter which is in potency to being and non-being, but that which is in potency to place; therefore, they are not corruptible.

1610. Hence, if demonstration is of necessary things, as was proved in the Posterior Analytics, and definition is also scientific, that is, productive of science, because it serves as the middle term in a demonstration (which is a syllogism producing science), then, just as it is impossible for scientific knowledge sometimes to be scientific knowledge and sometimes ignorance—because what is known scientifically must always be true, but what is such, that is, what can sometimes be true and sometimes false, is opinion—in the same way, it is impossible that there should be demonstration or definition of those things that can be otherwise than they are. About contingent things of this kind, there is only opinion.

1611. If this is so, I say it is evident that there will be neither definition nor demonstration of these singular, sensible, corruptible things. For corruptible things of this kind cannot be clearly known by those who have scientific knowledge of them when they have passed outside the scope of the senses, through which they are known. Hence, even though the intelligible expressions or forms of these singular instances, by which they can be known, remain in the soul, there will be neither definition nor demonstration of them.

And for this reason, when anyone, eager for setting the limits of things, that is, the definition of anything, defines a singular thing, he must not ignore the fact that it is always possible to remove the singular, while the intelligible expression as such (which he forms in his mind) remains. And this is true because it is impossible to give a genuine definition of a singular, for in the case of those things that are truly defined, the knowledge of the thing defined remains as long as the knowledge of the definition remains in the mind.

1612. Therefore, if a singular thing cannot be defined, it is impossible to define an idea. For an idea must be a singular thing, according to those who posit ideas, since they claim that an idea is something which subsists of itself apart from all other things. This is what “singular thing” means.

1613. And it is necessary (1040a9). Then he gives the second argument, and in regard to this, he does two things.

First, he gives the argument;

second (1040a14; [1619]), he rejects an answer which avoids the question, at but if.

Now, it was necessary that he should add this argument to the foregoing one, since the argument given has already proved that the singular is not definable, since it is corruptible and material and the Platonists did not assign these two properties to the ideas. Hence, lest his proof should be rendered ineffective, he adds another argument (1040a9), and states it as follows.

1614. It is necessary that every definitive expression should be composed of several words, for one who defines a thing does not convey its meaning by giving only one word, for if he were to give only one, the thing defined would still remain unknown to us. For when a single better known word is given, it is possible to know the name of the thing defined, but not the thing defined, unless its principles are given. For it is by its principles that every thing becomes known.

1615. Now, the resolving of the thing defined into its principles—which those forming definitions intend to do—is possible only when several words are given. Therefore, he says that, if only one word is given, the thing defined will still remain unknown; but if many words are given, they must be common to all the things.

1616. For in the definition of any singular thing, if certain words are given which are proper only to that thing itself, they will be synonymous names of the same singular thing. Hence it is not the thing which will be made known when words of this kind are given, but perhaps a less well-known word. For example, if we were to ask who Tullius is, and someone were to answer, “Marcus and Cicero,” it would not be an apt definition.

1617. Therefore, if a singular thing is defined, certain words must be given which are applicable to many things. Hence the definition must fit not only the singular thing whose definition is under investigation but also other things. But this is opposed to the notion of a true definition. For example, if someone intended to define you and said that you are an animal capable of walking, or a white animal, or anything else that applies to you, this definition would fit not only you, but other things as well.

1618. It is evident, then, that a singular thing lacks a definition not only because it is corruptible and material but also because it is singular. Hence, neither is an idea defined. The reason for this is the one which the Philosopher gives here: if the words taken to define a thing express the individual in terms of the things by which it is individuated, the words will be synonymous. But if they express the nature and common attributes without individuation, the definition will not be a proper definition of the thing defined, because all forms (accidental or substantial) which do not subsist of themselves are common to many when considered in themselves. And if some are found in only one thing, like the form of the sun, this does not come from the form inasmuch as it is of itself suited to be in many things, but from the matter; for the whole matter of the species is collected in one individual. Or this comes from its final cause, because one sun is sufficient for the perfection of the universe.

1619. But if anyone (1040a14). Then he rejects a captious answer. For someone could say that, while any of those attributes given in the definition of a singular idea is proper to many individually, still, when taken together, they are proper to only one thing, namely, to the one whose definition is under investigation. He rejects this answer in two ways.

First (1040a14; [1619]), with reference to the ideas themselves;

second (1040a23; [1624]), with reference to those things of which they are the ideas, at it will, moreover.

In regard to the first, he does two things.

First, he rejects the answer mentioned above by showing that it still does not follow that the definition belongs only to the thing defined;

second (1040a17; [1620]), that it does not belong to it primarily, at it is also necessary.

Hence, he says (1040a14) that, in opposing this answer, it must first be said that the definition assigned to any idea also belongs to other ideas. For example, if the definition of the idea of man is two-footed animal, these two belong to animal and to two-footed, that is, to the idea of animal and to the idea of two-footed. For those two ideas combined would also be two-footed animal. Hence, this definition, two-footed animal, will not be proper to the idea of man. And this absurdity also follows with eternal things, that is, if we consider the definition of an idea, which is an eternal singular, from the Platonists’ point of view, and if we consider that the definition given to one idea is proper to the others.

1620. It is also (1040a17). Then he exposes the second consequence: the definition assigned to the idea of man does not belong primarily to this idea. And this is opposed to the notion of a definition, for a definition is shown to be true primarily of the thing defined. He proves this in three ways.

First, he says that it is necessary not only that the definition given to man should belong to animal and to two-footed, but also that these—animal and two-footed—should be prior to man and be his parts, inasmuch as man is composed of both.

1621. But, according to the position of the Platonists, it would rather follow that both of these—animal and two-footed—are separable from man and from other animals, if man is assumed to be separable from individuals. For just as man is above individuals, in a similar fashion, genus and difference are above man. For it is necessary either that nothing common be separable, or that both of these—animal and two-footed—be separable from man. Now, if nothing common is separable, it follows that a genus will not exist apart from its species, and thus the genus will not signify substance. But if a genus exists apart from its species, then for a like reason, a difference will also exist apart, for this is more common than a species. But if both animal and two-footed are separable from man, it follows that they are prior in the way in which the separate man is prior to the individual. And thus it further follows that the definition assigned to man belongs to certain prior things—to animal and to two-footed.

1622. Again, because (1040a21). Second, he proves the same point by means of another argument. He says it is evident that animal and two-footed are prior to man in being; for those things are prior in being which are not destroyed when other things are destroyed; but when they are destroyed other things are destroyed. For example, one is prior to two, because when one is taken away, two is destroyed, but not conversely.

And when animal and two-footed are destroyed, man is destroyed, although when man is destroyed, the former (animal and two-footed) are not destroyed. Hence animal and two-footed are evidently prior to man.

1623. And again (1040a22). He then proves the same point by a third argument. He says that the same conclusion is evident if we maintain not only that animal and two-footed are separable from man, as being ideas of man, as was proved above in the first argument (1040a14; [1621]), but also that man is composed of them, so that, in this way, a separate idea turns out to be composed of separate ideas. For it is evident that animal and two-footed, of which man is composed, would be less composite than man, who is composed of them. But what is less composite is prior. Hence it follows again that animal and two-footed are prior to man, not only because they are separate (as the first argument advanced) but also because man is composite, as this third argument advanced.

1624. It will, moreover (1040a23). Then he gives an additional argument to reject the answer given above. He says not only that it follows that the definition assigned to the idea of man is common to other prior ideas of which the idea of man is supposed to be composed (namely, to animal and to two-footed), but also that these very things (animal and two-footed) will be predicated of many things and not just of man. And this will occur not only when they are taken in themselves, as the aforesaid answer of these men stated, but also when they are taken together.

1625. For if these elements of which the idea of man is composed, animal and two-footed, are not predicated of many things, how is it known that they belong to the idea of man, as was concluded above (1037b27; [1542–50])? For it would follow that there is some idea which cannot be predicated of more things than one, since it is evident that the idea of animal can be predicated of many individuals. Hence, if these two together—animal and two-footed—can be predicated of only one thing, it follows that two-footed restricts animal to one thing, such that some idea (two-footed) is predicated of only one thing. But this does not seem to be true, since every idea is capable of being participated in by many things; for from one exemplar there arise many things that resemble that exemplar. Therefore, the foregoing answer cannot be true.

1626. Moreover, it must be understood that, by the same argument, it can also be adequately shown that no singular thing among these sensible things can be defined by any properties or united forms, whatever they may be. For any idea (and also any form) taken in itself is naturally disposed to exist in many things; thus, no matter how they may be combined, there will be an exact definition of this singular thing only accidentally, inasmuch as it is possible for all of these forms taken together to be found in only one thing. It is obvious, then, that the principle of individuation is not a collection of accidents (as some said), but designated matter, as the Philosopher has stated (1035b33; [1496]).

1627. Therefore, as was stated (1040a27). Then he gives the third and chief argument to show that ideas cannot be defined. He says that, since it has been stated above (1039b20; [1609]) that individuals cannot be defined because of their corruptibility, as the first argument advanced, and since those attributes which are included in definitions are common ones, as the second argument advanced, the truth of the statement, “it is impossible to define singulars among eternal things” is not apparent, especially in the case of those which are unique in one species (like the sun and the moon). For, since the things in question are eternal, the argument based on the corruptibility of singular things does not seem to be conclusive when applied to them. And because these things are unique in their species, the argument from the commonness of the parts of a definition does not seem to be conclusive in their regard. For in this case, all attributes proper to one species alone are proper to one individual alone.

1628. But those who think that these things are definable are deceived to such an extent that they make many errors in defining such things. They err in one respect inasmuch as they add in the definitions of these things such attributes as can be removed and let the things themselves (the sun and moon) remain.

For example, in defining the sun, they say that it is something going around the earth, that is, revolving around the earth, or hidden at night, that is, invisible during the night. For if the sun were to stand still and not revolve around the earth, or if it was not invisible at night, it would not be the sun (if it had been defined properly). However, it would be absurd if it were not the sun when these attributes were removed. For the sun signifies a substance, but these things by which it is defined are certain accidents of it.

1629. And they not only err in this way, but also make a further mistake when they define the sun by an attribute which is suited to belong to something else. For supposing that another such thing should come into being (that is, some body having such a form, or the same form and species), it is evident that it would be a sun, inasmuch as “sun” signifies a species and can be defined in this way. Hence, the definitive expression, the intelligible expression of the species “sun,” is common. But this sun would be a singular thing like Cleon or Socrates. Thus it is certain that, even though the ideas are also claimed to be eternal and unique in their species, they still cannot be defined.

1630. Hence, none of those who posit ideas reveal any fixed limits, or definition, of an idea. For if they were to give the definition of some idea, as that of man or horse, it would become evident that an idea is indefinable, as has just been said in opposition to those attempting to define an idea.