1. The word "definition" signifies the specification of the limits of a thing. Limits make clear the unity of a thing—what it is, what it is not.
2. We can distinguish between the definitions of things and the definitions of terms. The definition of a thing marks out the limits of a thing. The definition of a term marks out the limits of a term.
3. Terms are obviously just another kind of thing.
4. The kind of definition appropriate for a thing will depend on the manner of its existence: is it a substance, a quantity, a quality, place, time, relation, position, habit, passion, action? In each case, what is required to mark out the limits of a thing will be different.
5. The more a thing has being in itself, the more a the specification of its limits will tend to capture what is formally distinct about it. Thus places and times, relations, positions, habits, passions, and actions are defined relatively and with a degree of indeterminacy. Their determinacy comes from the substances relative to which they are defined.
6. Terms have an accidental existence. They exist as features of thinking and speaking agents, and as means by which the minds of those thinkers and speakers maintain a real relation to the things referenced by the terms. To say that they have an accidental existence does not mean that they are not real, or that they cannot be spoken of without reference to any particular agent, but that it belongs to them to exist in a subject distinct from them: terms do not form an abstract set of things apart from the people who think and speak by means of them. Insofar as they exist, terms always exist in people.
7. What is a term, then? A term is a form abstracted from things, held in the mind, and associated with a particular verbal sign.
8. What is a sign? A sign is anything that directs our attention beyond itself. Terms differ from signs in that a term does not simply direct one's attention, but is a means by which we reference a thing. The term stands for the thing.
9. In terms, the verbal sign directs our attention to the idea immediately, so that in practice the sign and the idea become indistinguishable. The association between the two is formed by habit.
10. Because in terms the idea and the sign are always joined together (except in moments of forgetfulness, when we cannot remember the word), the use of terms exists in a mutual causal relationship with natural language. (Much more could be said about this)
11. How do we come to possess terms? How are they formed? Most terms are acquired by the observation or indication of some formal aspect of things. We notice something about things and ask "what is the word for that", we encounter a word and inquire after its meaning, or perhaps we invent a word to express some idea we have come upon by ourselves. (Much more could be said about this as well.)
12. It should be noted that the "things" abstracted from need not be outside the mind: they can be phantasms of the imagination, or constructed ideas based on forms already held by the mind from experience.
13. Though every term must refer back somehow to something abstracted from things outside the mind, a particular term need not stand for anything real. It is in the power of the mind to combine the apprehended aspects of things in ways not yet apprehended. We combine certain aspects of goats with certain aspects of men, and construct in our minds an idea, which we name "satyr".
14. A definition specifies the limits of a thing, of what it is, but by what means? If I draw a line around my property is that a definition? Not exactly. A definition employs terms to specify the limits of what it defines. A definition expresses the form of one thing in other terms.
15. Definitions are principles: they are attempts to grasp first of all what sort of thing is being discussed. But they are principles not in that they found the subject of discourse, but because they are the first attempt, on which much of what follows depends.
16. An incorrect definition will not necessarily corrupt every element of one's discourse on the subject of the definition, but it indicates error and will tend to produce errors as one goes on. (Parvus error in principio, magnus est in fine.)
17. If one errs in the definition, then one's grasp of the subject is wrong: the idea does not conform to the reality. And this lack of conformity will continue to manifest itself as things proceed.
18. So what makes a true definition? A definition expresses the form of one thing in other terms. This is to say that we do not define a rose by saying, "It is a rose." We define it in terms of something else, something more general, and then proceed to distinguish it from other variants of that more general form by giving a difference specific to what is being defined. Thus "genus" and "difference" determine a species.
19. Definitions always take the form of a categorical judgment: "A is B." "[Thing Defined] is [Genus] with [Difference]." In the genus/difference predicate, the difference modifies the genus, so that the generic form stands for the substance of what is being defined, and the difference acts as an accidental form added to the genus, even though often this is not the case.
20. Because to be a thing is to be one, in every definition of a thing, there is something which stands in for the substance of what is defined. In other words, it is impossible to produce an adequate definition which reduces a real thing entirely to qualities.
21. This was Berkeley's difficulty: by choosing to admit only qualities in his analysis of things, he became incapable of accounting for their substance, and was forced to reduce their unity to the one substance he could not easily deny: himself.
22. Definitions of things seek to reduce the essence of things to terms. Definitions of terms reduce the essences of terms to other terms. When defining natures outside the mind, one always has the thing itself to get in the way of error; but terms in the mind are mutable and shifting: when brought into relations, they shift in order to accommodate each other.
23. If the purpose of terms is to more readily direct the mind to forms and aspects of forms in reality, then a terminological system will be better the more it grasps different forms under different aspects. Our lexicon of terms must be at least as diverse as the real forms we attempt to reference with them.
25. In order to bring various terms and forms into proper relationship with each other, their distinctness must be preserved. In order to form a true (i.e. correct) hierarchy of forms in thought, one needs to give individual forms room for dissimilitude from any primary term. This space of dissimilitude is provided by analogy.
26. Without analogy the only legitimate connections drawn between terms are univocal. In this case, one tries to unify all the objects one encounters under whatever aspect can account for everything univocally.
27. Of all the aspects of a thing, quantity abstracts most perfectly from what it is. This is why mathematics proceeds so effectively without the use of experience.
28. How do we define things? We define them by what they are, what they do, what they tend to become, what they are made of, and where they come from. But especially the first two.
29. Each thing is united in what it is, its act. To define a thing is to specify those features of its act which cannot be removed without the destruction of the thing—those features which preserve its unity, which give reason to the acts of all its parts.
30. Quantity always presupposes a unity (this is because quantity is an accidental feature of things). Quantity always presupposes a kind or form. If someone says, "there are 43.5" this means nothing without specification of a form, or unity of kind.
31. We observe this when we try to define a particular quantity. What is "two"? Russell's famous definition is "the set of all dual sets" or "The set of all sets S such that S contains two non-identical elements." But what is an element? And by what are these elements non-identical? Two itself is identical in all its instances, since it is a mere quantity, and yet whatever it is by which there are two of anything seems not to be a quantity. And if not, what is it?