13. Now, such principles are nothing but definitions, whereof there are two sorts; one of names, that signify such things as have some conceivable cause, and another of such names as signify things of which we can conceive no cause at all. Names of the former kind are, body, or matter, quantity, or extension, motion, and whatsoever is common to all matter. Of the second kind, are such a body, such and so great motion, so great magnitude, such figure, and whatsoever we can distinguish one body from another by. And names of the former kind are well enough defined, when, by speech as short as may be, we raise in the mind of the hearer perfect and clear ideas or conceptions of the things named, as when we define motion to be the leaving of one place, and the acquiring of another continually; for though no thing moved, nor any cause of motion be in that definition, yet, at the hearing of that speech, there will come into the mind of the hearer an idea of motion clear enough. But definitions of things, which may be understood to have some cause, must consist of such names as express the cause or manner of their generation, as when we define a circle to be a figure made by the circumduction of a straight line in a plane, &c. Besides definitions, there is no other proposition that ought to be called primary, or (according to severe truth) be received into the number of principles. For those axioms of Euclid, seeing they may be demonstrated, are no principles of demonstration, though they have by the consent of all men gotten the authority of principles, because they need not be demonstrated. Also, those petitions, or postulata, (as they call them) though they be principles, yet they are not principles of demonstration, but of construction only; that is, not of science, but of power; or (which is all one) not of theorems, which are speculations, but of problems, which belong to practice, or the doing of something. But as for those common received opinions, Nature abhors vacuity, Nature doth nothing in vain, and the like, which are neither evident in themselves, nor at all to be demonstrated, and which are oftener false than true, they are much less to be acknowledged for principles.
To return, therefore, to definitions; the reason why I say that the cause and generation of such things, as have any cause or generation, ought to enter into their definitions, is this. The end of science is the demonstration of the causes and generations of things; which if they be not in the definitions, they cannot be found in the conclusion of the first syllogism, that is made from those definitions; and if they be not in the first conclusion, they will not be found in any further conclusion deduced from that; and, therefore, by proceeding in this manner, we shall never come to science; which is against the scope and intention of demonstration.
The nature & definition of a definition.
14. Now, seeing definitions (as I have said) are principles, or primary propositions, they are therefore speeches; and seeing they are used for the raising of an idea of some thing in the mind of the learner, whensoever that thing has a name, the definition of it can be nothing but the explication of that name by speech; and if that name be given it for some compounded conception, the definition is nothing but a resolution of that name into its most universal parts. As when we define man, saying man is a body animated, sentient, rational, those names, body animated, &c. are parts of that whole name man; so that definitions of this kind always consist of genus and difference; the former names being all, till the last, general; and the last of all, difference. But if any name be the most universal in its kind, then the definition of it cannot consist of genus and difference, but is to be made by such circumlocution, as best explicateth the force of that name. Again, it is possible, and happens often, that the genus and difference are put together, and yet make no definition; as these words, a straight line, contain both the genus and difference; but are not a definition, unless we should think a straight line may be thus defined, a straight line is a straight line: and yet if there were added another name, consisting of different words, but signifying the same thing which these signify, then these might be the definition of that name. From what has been said, it may be understood how a definition ought to be defined, namely, that it is a proposition, whose predicate resolves the subject, when it may; and when it may not, it exemplifies the same.
Properties of a definition.
15. The properties of a definition are:
First, that it takes away equivocation, as also all that multitude of distinctions, which are used by such as think they may learn philosophy by disputation. For the nature of a definition is to define, that is, to determine the signification of the defined name, and to pare from it all other signification besides what is contained in the definition itself; and therefore one definition does as much, as all the distinctions (how many soever) that can be used about the name defined.
Secondly, that it gives an universal notion of the thing defined, representing a certain universal picture thereof, not to the eye, but to the mind. For as when one paints a man, he paints the image of some man; so he, that defines the name man, makes a representation of some man to the mind.
Thirdly, that it is not necessary to dispute whether definitions are to be admitted or no. For when a master is instructing his scholar, if the scholar understand all the parts of the thing defined, which are resolved in the definition, and yet will not admit of the definition, there needs no further controversy betwixt them, it being all one as if he refused to be taught. But if he understand nothing, then certainly the definition is faulty; for the nature of a definition consists in this, that it exhibit a clear idea of the thing defined; and principles are either known by themselves, or else they are not principles.
Fourthly, that, in philosophy, definitions are before defined names. For in teaching philosophy, the first beginning is from definitions; and all progression in the same, till we come to the knowledge of the thing compounded, is compositive. Seeing, therefore, definition is the explication of a compounded name by resolution, and the progression is from the parts to the compound, definitions must be understood before compounded names; nay, when the names of the parts of any speech be explicated, it is not necessary that the definition should be a name compounded of them. For example, when these names, equilateral, quadrilateral, right-angled, are sufficiently understood, it is not necessary in geometry that there should be at all such a name as square; for defined names are received in philosophy for brevity's sake only.