name is given to it in this manner: I call every number divisible equally by two, an even number.
This is a geometrical definition; because after having clearly designated a thing, namely, every member divisible equally by two, we give it a name divested of every other meaning, if it has any, in order to give it that of the thing designated.
Hence it appears that definitions are very arbitrary, and that they are never subject to contradiction; for nothing is more permissible than to give to a thing which has been clearly designated, whatever name we choose. It is only necessary to take care not to abuse the liberty that we possess of imposing names, by giving the same to two different things.
Not that this may not be permissible, provided we do not confound the consequences, and do not extend them from the one to the other.
But if we fall into this error, we can oppose to it a sure and infallible remedy: that of mentally substituting the definition in the place of the thing defined, and of having the definition always so present, that every time we speak, for example, of an even number, we mean precisely that which is divisible into two equal parts, and that these two things should be in such a degree joined and inseparable in thought, that as soon as the discourse expresses the one, the mind attaches it immediately to the other. For geometricians, and all those who proceed methodically, only impose names on things to abbreviate discourse, and not to diminish or change the idea of the things of which they are discoursing. And they pretend that the mind always supplies the full definition to the concise terms, which they only employ to avoid the confusion occasioned by the multitude of words.
Nothing more promptly and more effectually removes the captious cavils of sophists than this method, which it is necessary to have always present, and which alone suffices to banish all kinds of difficulties and equivocations.
These things being well understood, I return to the explanation of the true order, which consists, as I have said, in defining every thing and in proving every thing.
This method would certainly be beautiful, but it is abso-
