Definition, in logic , is an enumeration of the principal simple ideas from which we form a composite idea; we enumerate these simple ideas to determine or explain the nature and the character of the composite idea. [1]

The Scholastic philosophers have imparted very flawed notions of definition . Some other philosophers define definition as the foremost notion or idea that we have of a thing, which serves to distinguish it from all other things, and from which we can deduce all that is known and all that is thought of that thing. But definition is still usually defined as oratio explicans quid res est , a discourse that explains what a thing is, that is, a statement that examines the attributes by which the nature of the thing is determined, for to explain is nothing other than to separately and explicitly itemize or enumerate the parts that previously were mentioned implicitly and conjointly, so that any explanation always relates to the whole.

Now, just as we can distinguish parts of a different nature in a thing, known as the physical parts, the metaphysical parts, and so on, so we can give different definitions of the same thing; and so we can define a man as an animal composed of a body and a soul or just as well as a rational animal .

There are, we may also say, two sorts of definitions : the one nominal , or of the name ; the other real , or of the thing . A definition of the name is what explains the sense or the signification allotted or assigned to a word; or, as was accurately stated by Wolff [2], it is an enumeration that we make of a certain number of marks or characteristics that suffice to distinguish the thing we define from all others, so that no doubt remains about what we intend to designate by the name. Such is the definition that we give of a square when we say that it is a figure of four equal sides that make right angles among themselves. By a definition of the name we wish to introduce either ideas that are attached to a word in ordinary usage or particular ideas that we would purposefully attach to it, that is, a particular sense in which we want a word to be understood and to be used during the rest of a conversation.

A definition of the thing is properly an enumeration that we make of the principal attributes of a thing to explain and to reveal its nature. We may thus define a circle as a figure in which all the points of the circumference are equally distant from the center . Wolff says that a definition of the thing is a distinct notion that explains the origins of a thing, that is, the way it is made or the way it generates itself. Such is the definition given of a circle when we say that a circle is a figure formed by the movement of a straight line around one of its end points . On this ground, the previous definition that we had given for a circle would not be a definition of the thing but simply a definition of the name .

The notion that we have given of definition of the thing , as taught by many philosophers, suffices to show how this notion differs from definition of the name . But although Wolff’s notion has on its side the advantage of analogy, of clarity, and of suitability, nevertheless, as Wolff’s definition of real definition is itself only a definition of the name , that is, a definition of a term , it is principally from this point of view that we should consider Wolff’s definition of the thing . We will view it as an idea arbitrarily attached to the term real definition , an attachment that Wolff preserves throughout his work. [3] But Wolff’s notion of real definition does not contain the ordinary sense or signification that we customarily give to this term. The ordinary sense is much less precise and less distinct; and it is this ordinary signification that most interests us.

Thus, although a definition of the thing is nothing more than an explanation of the word that signifies the thing, there is nevertheless a difference between definition of the thing and definition of the word . Both of these sorts of definition are actually nothing more than explanations of the meaning of a word, but a definition of the word is an explanation established by received usage, an explanation that conforms to the ideas that most people attach to a word. In contrast, a definition of the thing is an explanation of a word arbitrarily contrived, a word to which I help myself as I please, such that I attach to that word, just as it pleases me, the number and quality of ideas that I declare to have now in mind.

Thus it seems that such a definition of a word , even of an arbitrarily taken word, can in a very legitimate sense be called the nature of the defined thing because the definition then expresses perfectly the nature of the thing that I define, just as I conceive it—but what I conceive is not necessarily the actual nature of the thing.

But to understand it well, the different ideas attached to the word nature must be explained. [4] First , it signifies the collection of all things that the human mind is capable of knowing; second , the universal principle that forms those things and that guides them; third , the distinctive, innermost, and essential [5] constitution that makes each thing in particular what it is; and, fourth , the disposition that is found in things, independent of our industry and of human will—and, in that sense, what is natural is opposed to the artificial. So we say that a chute of water that falls in a cascade in the garden is artificial because it has to be disposed by human industry to fall in such a way. Finally, fifth , the word nature signifies the idea that we form for ourselves of what we deem most interior and most essential in each thing and that we express by definition ; this is what the Scholastic philosophers call metaphysical essence . See Nature.

These different senses that are given to the word nature , being thus fixed and determined, make it easy to understand which of them is the sense that the philosophers give to the nature of things when they claim to explain that nature by their definitions . As they intend to mean by the nature of things the distinctive, innermost, and essential constitution that makes each thing in particular what it is , it is evident that all their definitions on the nature of substances are vain and frivolous. Their definitions will always be defective due to the inability of these philosophers to know the essential nature of substances. They do not suspect this inability in themselves because they are predisposed to abstract ideas: they reify these abstractions and they then mistake their reifications for the very essence of things. What has encouraged the philosophers in this mistake is, first, that they have believed that, in mathematics, the notion of the thing carries knowledge of its essence. Second, they have precipitously concluded that it is the same in physics, and so they have imagined that they know the very essence of substances. Instead of occupying themselves by defining substances by their kind and their nearest difference, philosophers should instead analyze exactly the simple ideas that can be part of substances, in brief, they should develop the origin and the generation of their abstract notions. But it is far more convenient to suppose in things a reality for which we take words as true signs; to understand by these names— man , animal , and so on—an existential essence  [6] that determines and distinguishes these things than to pay attention to all the simple ideas that enter into the notions that we form from them. This way satisfies our impatience and our curiosity at the same time. There are perhaps few people, even among those who have worked the most to rid themselves of their prejudices, who do not feel some propensity to relate all names of substances to such unknown realities. See Abstraction.

This is certainly one of the biggest sources of our errors. We need only to suppose that words correspond to the reality of things; from that beginning, we then confound things with words and we then further conclude that words explain perfectly the nature of things. This is why whoever poses a question and asks what is this thing , that person believes, as Locke remarked, that he asks for something more than a name; and whoever replies to him, it is iron , that person believes as well that he tells him something more. But with such jargon there is no hypothesis, however unintelligible it might be, that cannot be supported.

It is thus very important that we not reify our abstractions. I know only one way to avoid this risk: it is to always substitute analysis for the definitions of the philosophers. Analyses are the best definitions that we can make, but this approach, as simple as it is, has been unknown to philosophers. The cause of their ignorance in this respect is the prejudice they have always had that it is necessary to begin with general ideas, for when we are forbidden to begin with particulars, it is not possible to explain the more abstract ideas from which these particulars draw their origins. And here is an example.

After having defined impossible as that which implies contradiction , possible as that which does not imply contradiction , and being as that which can exist , these philosophers [7] have not known how to give any other definition of existence than the complement of possibility . But I ask whether this definition presents any actual idea , and whether we should not show it the ridicule that we have given to some of those of Aristotle.

If the possible is that which does not imply contradiction , possibility is the non-implication of contradiction . Existence is then the complement of the non-implication of contradiction . What a way to talk! Were we to more closely observe the natural order of ideas, we would see that the notion of possibility does not arise until after the notion of existence has been formed. I think that people adopt these sorts of definitions only because they already know the things defined, and so they do not pay much attention to their definitions : their minds already impressed by some clear and precise ideas [8], they attribute the source of that clarity to those definitions , and they do not perceive that the definitions themselves are unintelligible.

But if all the definitions that we make about substances are not made from knowledge of nature, it is not the same in the sciences where we reason from archetypal ideas. According to the philosophers, given that the essence of a thing is that which constitutes what it is , it follows that we can have ideas of essences in these cases. However, we confuse the essences of things with the notions that we have of them: and so we give them names that conflate signs of essence and of notion. A space bounded by three lines may be regarded in this sense as the essence of a triangle. The name justice signifies in this way the essence of a just man; the name wisdom , the essence and the notion of the wise man, and so forth. This is perhaps one of the reasons that led the Scholastics to believe that they had only to follow analogy in language to create names that expressed the essences of substances; thus they made words such as corporality , animality , and humanity to designate the essences of the body corpus , the animal , and the human . Because such terms have become familiar to these Scholastic philosophers, it is very difficult to persuade them that these definitions are void of sense.

It should be observed that once the nature of purely ideal things is fixed, we draw from them consequences whose fabric forms a science as true as geometry, which is founded on the definition of words. All geometry begins by saying: I mean by the word point this thing, by a line this other thing. By this definition of words, which are of as many essences as the mind wants to form, we come to the most profound knowledge, to the farthest consequences, and to the most reliable and the most obvious demonstrations; but we must always remember that these are truths whose only grounds are the arbitrary abstractions we create in our minds.

Here, following Locke, [9] we can make a useful analysis of the method established by the Scholastic philosophers [10], that is, their method of defining by means of kind and of difference. The kind comprehends what the defined thing has in common with other things. The difference comprehends what the thing has in particular, and what it does not have in common with any other thing. This method is no more than a supplement to the enumeration of the various qualities of a defined thing; for example, when we say that a man is a reasoning animal , the word animal includes the qualities of living , moving  [11], and sensing . This is so true that if a particular word cannot be found to express all the qualities of a defined thing, then we must have recourse to an enumeration of these very qualities. For example, should we wish to define a pearl , we cannot do so by simply marking a kind— animal —and a precise difference— reasoning —as we marked in our definition of a man. This is because there is no single word that contains all the qualities that a pearl has in common with other beings. Thus, the method of definition by way of kind and difference is but a supplement or a summary of the enumerated qualities that we discover in a defined thing. However, what we discover is not all of the nature of a defined thing. A definition is nothing other than an explanation of the true signification of a word and of the sense that usage that has attached to it. A definition is not an explanation of the actual nature, real and total, of the thing indicated by the word.

We generally ask three things of a good definition . First, a definition should be clear , that is, it should give us a very clear and very distinct idea of the thing that is defined, and it should make us, insofar as it can, understand the nature of the defined thing. Second, a definition should be universal or comprehensive , that is, it should suit all things that are encompassed by the defined species; and, third, a definition should be appropriate or particular to the defined thing.

In general, we can make the following observations about definition .

First, truly simple ideas cannot be defined. Locke has shown this, and it is rather surprising that he would be the first person to discuss this. “There is no definition ”, says Locke, “of light or redness that is more able to excite in us any of these ideas than the sound of the word light or redness could by itself. To hope to produce an idea of light or of color by a sound, however it might be formed, is to believe that sounds can be things seen, or that colors can be things heard, and to attribute to the ears the functions of all the other senses. This is as though someone were to say that we could taste , smell , and see by the means of the ears; this sort of philosophy would be agreeable only to Sancho Panza, who had the ability to see Dulcinea by hear-say . [12] The only way then to introduce someone to the signification of words that express simple ideas is to impress on his senses the objects that embody them and to produce thus in him the ideas for which he has already learned the names.

A blind man, who loved to study, mightily worried his head on the subject of visible objects. Having consulted his books and his friends to be able to comprehend the words light and color that he often encountered in his path, he said one day with extreme confidence that he at last understood what the word scarlet signified. Upon hearing this, his friend asked him what it was. ‘It is,’ he answered, ‘ something that resembles the sound of a trumpet! ’ Whoever imagines that he will discover the meaning of the name of any other simple idea solely by a definition , or by other terms that one can use to explain it, will rightly find himself in the shoes of this blind man.” Locke, book 3, chapter 4 .

The philosophers who came before the English philosopher John Locke [13] did not distinguish ideas that should be defined from those that ought not to be defined; we can judge that by the confusions found in their writings. The Cartesians were not unaware that there are some ideas that are more clear than any definition that can be given of them, but they did not know the reason for this, however obvious this may seem to be. So they strive mightily to define very simple ideas, while they think it unnecessary to define other ideas that are quite compound. This goes to show how difficult it is to take even the smallest steps in philosophy. See Name.

Second, definitions by which one would explain the properties of things by kind and by difference are completely useless, if by kind and difference you mean only to supplement or to summarize the enumeration of qualities that are revealed only by analysis. The most effective way of extending knowledge is to study the generation of ideas in the same order in which they are formed. This method is indispensable for abstract notions: it is the only way to explain them with clarity and precision [14]. Now, this method is the distinctive feature of analysis .

Third, definitions never help us know the nature of substances, but only essences that we conflate with notions that we form of things, notions based on archetypal ideas and not on actually existing real things such as substances.

Fourth, given that definitions —both of names and of things—are nothing other than explanations of words and that they signify the senses that we attach to words, according to differences that we mark between one word and other words, it follows that definitions cannot be contested and we can take them as principles. The reason is this: one may not argue that the idea we have pointed out cannot be called by the name we have given it. However, we should not conclude from this anything more about the idea, nor believe that just because we have bestowed a name upon an idea that the word signifies something real. For example, should a philosopher say to me, “I call gravity the interior principle that makes a stone fall without anything to push it or to pull it”, I will not contest that definition . To the contrary, I will freely accept his definition because his word gravity makes me hear what he wishes to say; but I can deny that what he means by the word gravity is anything real.

Fifth, one of the major benefits of definitions is to help us definitively understand what we are talking so that we do not pointlessly argue about words, as we so often do even in ordinary conversation. Beyond this benefit, there is yet another that arises because we often cannot grasp the distinct idea of a complicated thing without using many words to designate it. Now, it would be tedious, above all in scientific work [15], to always repeat such a large suite of words to designate an idea. This is why, having reached an understanding of a thing through all its individual words, we attach the complex idea to a single word that we conceive to take the place of all the others.

So, having comprehended that there are numbers that are equally divisible by two and wanting to avoid repeating all these terms— a number that can be divided into two equal parts —, we give a name to this property by saying: “I call any number that is equally divisible by two an even number .”

This shows that whenever we use a word that we have defined, we must mentally substitute the definition in the place of the defined word, and to have this definition so present in our minds that, for example, as soon as someone calls a number an even number , we understand precisely that this a number that is divisible into two equal parts . These two things, word and definition , are so joint and inseparable in thought that, as soon as conversation expresses a defined word, the mind immediately attaches the definition to the word; and those who define terms, as mathematicians [16] do with so much care, do so primarily to shorten speech that would be made annoying by such frequent circumlocutions.

Sixth, definitions already accepted should not be changed when we have no reason to find fault with them, for it is always easier to make a word be understood when it is already sanctioned by usage to signify an idea, at least among scholars, than it must be to re-attach the word to a new idea and to remove from it the idea to which it was ordinarily joined. The reason for this observation is that people, having once attached an idea to a word, do not unbind it so easily; and thus their old idea—always echoing—makes them easily forget the new idea that you would give them by redefining that word. Thus, it would be easier to accustom people to a word that now signifies nothing than to accustom them to use a word without the idea that was first bound to it.

Those chemists who delight in changing the names of those things they talk about—without any corresponding benefits—fall into this error. They give new names to those things, names that already signify other things, names that have no real relationship with the new ideas to which these chemists reassign these names. This lays the ground for people to make ridiculous arguments like those of a certain person who deludes himself that the plague is a sickness sent by Saturn [17]. He imagines that he can cure a victim of the plague by hanging around the victim’s neck a piece of lead, which the alchemists [18] call saturn , upon which he has engraved—on a Saturday, which also carries the name of Saturn —the symbol ♄ that astronomers use to represent that planet. [19] As if these arbitrary and unreasonable relations between lead and the planet Saturn, and between that planet and the day Saturday, and the little mark that symbolizes Saturn, could have real effects that actually cure sicknesses!

Notes:

1. I wish to express my appreciation for the help I have received in preparing this translation from David J. Adams, University of Manchester; A. Sebastian Anderson, University of Illinois at Urbana-Champaign; André Bandelier; Ralf Breslau, Staatsbibliothek zu Berlin; Jeff Loveland, University of Cincinnati; Edward Rhodes, George Mason University; Glenn Roe, ARTFL Project, University of Chicago; Gordon Schochet; Christi Sumich, Mount Carmel Academy; Karl-Erik Tallmo; Nick Treuherz; Abbie Weinberg, Folger Shakespeare Library; Nuria Yanez-Bouza, University of Manchester; Richard Yeo, Griffith University; and participants in the WordReference.com forums on the French language.

2. Christian Wolff, German philosopher and student of Leibniz, in his Der Anfangs-Gründen Aller Mathematischen Wissenschaften (1710) and Elementa matheseos universae (1713).

3. I have substituted “Wolff”, the author’s name, for “l’auteur”. We know that the author is Wolff on the grounds of this context: “and which the author always denotes by that word in the course of his book.”

4. For consistency, here I translate “les êtres” as “things” rather than “beings”.

5. Here I translate “intime” as “innermost and essential”.

6. The term entité as used here is a term borrowed from Scholastic philosophy that I translate as “existential essence”.

7. I have rendered the rather generic “on n’a pas sû” more specifically as “these philosophers have not known how”. These philosophers include Leibniz and Wolff.

8. Here I translate “clarté” as “clear and precise ideas”.

9. John Locke, An Essay Concerning Humane Understanding (1690).

10. In the text, “dans les Écoles”.

11. In the text, “mourant” (dying) instead of “mouvant” (moving). I treat this as a simple typographic error.

12. Locke refers to Cervantes’s tales of Don Quixote. Sancho Panza is Don Quixote’s squire, and Dulcinea is Don Quixote’s unrequited love. This term “hear-say” is a literal translation of “oüi-dire”, which is in turn Pierre Coste’s literal translation of “hear-say” in Locke (1690). Unfortunately, Locke’s printers seem to have muddled his meaning: Locke surely intended the term to be “hear-see”.

13. I have supplied Locke’s name.

14. Here I translate “netteté” as “clarity and precision”.

15. In the text, “livres de science” (books of science); I render this as “scientific work”.

16. Here I generalize “Géometres” (geometers or geometricians) as “mathematicians”.

17. In the text, “une mal saturnin”. The word “mal” is used here in the sense of malady rather than evil .

18. Here I translate “chimistes” as “alchemists”.

19. I have supplied the symbol itself.