definition: that is, between a definition serving to explain a thing, of which the essence only is sought and in question, and a definition which is put forward only for purposes of inquiry. The former having a definite object ought to be true, the latter need not. For instance, if someone asks me for a description of Solomon's temple, I am bound to give him a true description, unless I want to talk nonsense with him. But if I have constructed, in my mind, a temple which I desire to build, and infer from the description of it that I must buy such and such a site and so many thousand stones and other materials, will any sane person tell me that I have drawn a wrong conclusion because my definition is possibly untrue? or will anyone ask me to prove my definition? Such a person would simply be telling me, that I had not conceived that which I had conceived, or be requiring me to prove, that I had conceived that which I had conceived; in fact, evidently trifling. Hence a definition either explains a thing, in so far as it is external to the intellect, in which case it ought to be true and only to differ from a proposition or an axiom in being concerned merely with the essences of things, or the modifications of things, whereas the latter has a wider scope and extends also to eternal truths. Or else it explains a thing, as it is conceived or can be conceived by us; and then it differs from an axiom or proposition, inasmuch as it only requires to be conceived absolutely, and not like an axiom as true. Hence a bad definition is one which is not conceived. To explain my meaning, I will take Borel's example --a man saying that two straight lines enclosing a space shall be called "figurals." If the man means by a straight line the same as the rest of the world means by a curved line, his definition is good (for by the definition would be meant some such figure as (), or the like); so long as he does not afterwards mean a square or other kind of figure. But, if he attaches the ordinary meaning to the words straight line, the thing is evidently inconceivable, and therefore there is no definition. These considerations are plainly confused by Borel, to whose opinion you incline. I give another example, the one you cite at the end of your letter. If I say that each substance has only one attribute, this is an unsupported statement and needs proof. But, if I say that I mean by substance that which consists in only one attribute, the definition will be good, so long as entities consisting of several attributes are afterwards styled by some name other than substance. When you say that I do not prove, that substance (or being) may have several attributes, you do not perhaps pay attention to the proofs given. I adduced two: --First, "that nothing is plainer to us, than that every being may be conceived by us under some attribute, and that the more reality or essence a given being has, the more attributes may be attributed to it. Hence a being absolutely infinite must be defined, &c." Secondly, and I think this is the stronger proof of the two, "the more attributes I assign to any being, the more am I compelled to assign to it existence;" in other words, the more I conceive it as true. The contrary would evidently result, if I were feigning a chimera or some such being.
abstract all your thoughts and conceptions. It is no marvel that, when you have abstracted all your thoughts and conceptions, you have nothing left for thinking with. On the general subject I think I have shown sufficiently clearly and plainly, that the intellect, although infinite, belongs to nature regarded as passive rather than nature regarded as active (ad naturam naturatam, non vero ad naturam naturantem).
substance I mean that, which is in itself and is conceived through itself; that is, of which the conception does not involve the conception of anything else. By attribute I mean the same thing, except it is called attribute with respect to the understanding, which attributes to substance the particular nature aforesaid." This definition, I repeat, explains with sufficient clearness what I wish to signify by substance or attribute. You desire, though there is no need, that I should illustrate by an example, how one and the same thing can be stamped with two names. In order not to seem miserly, I will give you two. First, I say that by Israel is meant the third patriarch; I mean the same by Jacob, the name Jacob being given, because the patriarch in question had caught hold of the heel of his brother. Secondly, by a colourless surface I mean a surface, which reflects all rays of light without altering them. I mean the same by a white surface, with this difference, that a surface is called white in reference to a man looking at it, &c.
[Note N1]: The whole beginning of this letter, till after the mention of the club, is omitted in the editions before Van Vloten's Supplementum, to make the letter agree with the altered version of Letter 26, to which it is an answer.
[Note N2]: "You" in these two places is plural, and refers to the club; so also the second "your" [following]; elsewhere "you" and "your" refer to De Vries only.