Here is a passage from chapter 12 of Antoine Arnauld's book Logic, or The Art of Thinking where he explains the difference between a nominal definition, definitio nominis, and a real definition, definitio rei.

Arnauld's definition differs both from the definition given by the scholastic philosophers such as Ockham, and from other early modern philosophers such as Locke.

According to Arnauld, the distinction is between the definition of sounds which we have arbitrarily assigned a meaning in order to make our ideas clearer, which is a nominal definition, and between a definition which attempts to explicate the ideas connected with a word as it is ordinarily used, which is a real definition. Thus we cannot argue about nominal definitions, for you cannot deny that someone has given a sound the meaning he said he would give it, though we can argue about real definitions, since they can be false. For example, you can say that the word 'parallelogram' means a triangle, you are not wrong to do so, as long as I use it in only this way. But if you keep the ordinary meaning of the word (a figure with parallel sides), and say that a parallelogram is a figure with three sides, that would then be a real definition, and it would be false, since it is impossible for a figure with three sides to have parallel sides.

For the scholastic philosophers, by contrast, a real definition explicates the real nature or essence of a thing, whereas a nominal definition is simply of the meaning of a word.

See here for links to other etexts in this series.

The translation is by Jill Vance Buroker (Cambridge 1996).

The best way to avoid the confusion in words encountered in ordinary language is to create a new language and new words that are connected only to the ideas we want them to represent. But in order to do that it is not necessary to create new sounds, because we can avail ourselves of those already in use, viewing them as if they had no meaning. Then we can give them the meaning we want them to have, designating the idea we want them to express by other simple words that are not at all equivocal. Suppose, for example, I want to prove that the soul is immortal. Since the word 'soul' is equivocal, as we have shown, it could easily cause confusion in what I want to say. To avoid this confusion I will view the word 'soul' as if it were a sound that does not yet have a meaning, and I will apply it uniquely to the principle of thought in us, saying 'By "soul" I mean the principle of thought in us'.

This is called a nominal definition, definitio nominis, which geometers use so frequently, and which must be clearly distinguished from a real definition, definitio rei.

For in a real definition, perhaps such as these: 'Man is a rational animal', or 'Time is the measure of motion', we leave the term being defined, such as 'man' or 'time', its usual idea, which we claim contains other ideas, such as rational animal, and measure of motion. Whereas in a nominal definition, as we said previously, we consider only the sound, and then determine this sound to be the sign of an idea we designate by other words.

We must be also be careful not to confuse the nominal definition we are discussing here with what some philosophers speak of, who mean the explanation of a word's meaning according to ordinary linguistic practice or etymology. We will discuss this elsewhere. Here, however, we are concerned only with the particular way the person defining the word wants us to take it in order to conceive his thought clearly, without taking the trouble to see if others understand it in the same sense.

From this it follows, first, that nominal definitions are arbitrary, and real definitions are not. Since each sound is indifferent in itself and by its nature able to signify all sorts of ideas, I am permitted for my own particular use, provided I warn others, to determine a sound to signify precisely one certain thing, without mingling it with anything else. But it is entirely otherwise with real definitions. For whether ideas contain what people want them to contain does not depend at all on our wills. So if in trying to define them we attribute to these ideas something they do not contain, we are necessarily mistaken.

So, to give some examples of each: if I strip the word 'parallelogram' of all meaning and use it to signify a triangle, this is permitted and I commit no error in doing so, as long as I use it in only this way. I could then say that a parallelogram has three angles equal to two right angles. But suppose I leave this word its ordinary meaning and idea, which signifies a figure with parallel sides and I go on to say that a parallelogram is a figure of three lines. Since that would then be a real definition, it would be quite false, because it is impossible for a figure of three lines to have parallel sides.

Second, it follows from their arbitrariness that nominal definitions cannot be contested. For you cannot deny that people have given a sound the meaning they said they gave it, nor that the sound has this meaning only in their use of it, once they have warned us about it. But we often have the right to contest real definitions, since they can be false, as we have shown.

It follows, third, that every nominal definition can be taken for a principle, since it is not contestable, whereas real definitions can never be taken for principles, and are genuine propositions which can be denied by anyone who finds some obscurity in them. Consequently, they need to be proved like other propositions, and should never be assumed unless they are in themselves as clear as axioms.

Nevertheless, I need to explain what I just said, that nominal definitions can be taken as principles. For this is true only because we should not deny that a designated idea can be called by the name someone has given it. But nothing further should be concluded to the advantage of this idea, nor should we believe that merely because someone has given it a name, it signifies something real. I can define the word 'chimera', for example, by saying 'I call a chimera whatever implies a contradiction'. It does not follow from this, however, that a chimera is something. Similarly, if a philosopher tells me, 'I call weight the internal principle which causes a rock to fall without being pushed by anything,' I will not dispute this definition. On the contrary, I will welcome it because it makes me understand what he means. But I will deny that what he means by the word 'weight' is something real, because there is no such principle in rocks.

I wanted to explain this at some length, because in ordinary philosophy two important abuses are committed on this subject. The first is confusing a real definition with a nominal definition, and attributing to the first what belongs only to the second. For philosophers have capriciously created a hundred definitions, not of names but of things, that are quite false and not at all explain the real nature of things or the ideas we have of them. Subsequently they wished to have these definitions considered as principles that could not be contradicted. If someone does deny them, since they are highly questionable, they claim that it is not worth discussing.

The second abuse is leaving these names in confusion, since people hardly ever use nominal definitions to remove the obscurity from names and to fix them to certain clearly designated ideas. As a result, the majority of their disagreements are only verbal. Further, they use what is clear and true in confused ideas to establish something obscure and false, which would be easily recognised if the names had been defined. Thus philosophers usually believe that the clearest thing in the world is that fire is hot and a rock is heavy, and that it would be foolish to deny it. Indeed, they would convince everyone of this as long as the names are not defined. But once they are defined, we easily discover whether what is denied on the subject is clear or obscure. For we must ask them what they mean by the words 'hot' and 'heavy'. If they reply that by 'hot' they mean only what properly speaking causes the sensation of heat in us, and by 'heavy' whatever falls when not supported in any way, they are right to say that it would be unreasonable to deny that fire is hot and that a rock is heavy. But if they mean by 'hot' what has in it a quality similar to what we imagine when we feel heat, and by 'heavy' whatever has an internal principle making it move towards the centre of the earth without being pushed by anything whatever, then it will be easy to show them that it is not denying something clear but very obscure, not to say quite false, to deny that fire is hot and a rock is heavy in the senses just mentioned. For it is quite clear that fire causes us to have the sensation of heat by the impression it makes on the body, but it is not at all obvious that fire has anything in it resembling what we feel when we are near the fire. Likewise, clearly a rock falls when it is dropped, but it is not at all clear that it falls by itself without anything pushing it down.

Here, therefore, is the great utility of nominal definitions, to make the matter clearly understood in order to avoid useless disputes over words that one person understands one way and another in another way, as so often happens even in ordinary speech.

But besides this advantage, there is yet another. Often we can have a distinct idea of something only by using many words to designate it. Now it would be inconvenient, especially in scientific texts, to repeat constantly this long series of words. This is why, once we have explained something by means of all these words, we connect the idea we have conceived to a single word, which thereby takes the place of all the others. Thus, when we understand that some numbers are divisible into two equal parts, we give a name to this property to avoid repeating all these terms frequently, saying: 'I call every number which is divisible into two equal parts an even number'. This shows that every time we use a word we have defined, we mentally have to substitute the definition for the defined word, and to have this definition present. As soon as we call a number even, for example, we will understand precisely that it is divisible into two equal parts, and that these two things are so connected and inseparable in thought that as soon as one is expressed, the mind immediately connects it to the other. Those who define terms, as geometers do so carefully, do it only to abbreviate their discourse, which would be irritating if it included so many circumlocutions. Ne assidue circumloquendo moras faciamus [we make work tiresome by circumlocution], as St Augustine said*. But they do not do it to abbreviate the ideas of the things they are discussing, because they claim that the mind supplies the entire definition to the shortened expression, which they use only to avoid the complication produced by a great many words.

* The literal meaning of Genesis, Bk XII, c. 7, 16 vol. 2.

THE LOGIC MUSEUM Copyright (introduction) © E.D.Buckner 2006.