Aphorism Fourth.
When we form a judgment of an idea, when we see in it a new element, one of these four things must necessarily happen:
Either the judgment which we now form is consequent to a just idea, in which case it is just; and the idea without changing its nature has only developed and extended itself.
Or it is inconsequent to a just idea, in which case it is false; and the idea is changed, and is become false.
Or it is consequent to an idea already false, then it is false, but the idea is not changed; it is when it has become false previously, that it has changed in relation to what it was primitively.
Or it is inconsequent to a false idea, then it may be just or false; but never certain, for the idea is changed. But it may have become just, such as it was originally, or false, in a manner different from the preceding.
OBSERVATION.
Remark always, that an idea infected with false elements, and consequently meriting the name of false, taken in mass, may also contain many true elements. We may form then, in consequence of these true elements, just judgments, and then they will be completely true; as we may also form from them false judgments, which shall be completely false; but these judgments will not be formed from that idea, inasmuch as it is false, and in consequence of that which it has of falsity; they ought therefore to be considered as formed from a true idea, and enter into what we have said of these.
This is what most frequently happens to us, so few compound ideas have we which are perfectly pure, and without mixture of imperfection. Perhaps we have none. Perhaps it would suffice for us to have one alone, to render all our others the same, by the sole force of their relations and combinations, proximate or remote.
Aphorism Fifth.
Thus all our perceptions are originally just and true, and error is only introduced to them at the moment when we admit an element which is opposed to them. That is to say, which denaturalises and changes them, without our perceiving it.
Aphorism Sixth.
This would never happen to us, if we had always present to the mind, that which the idea comports, of which we judge. Thus all our errors really come from this: that we represent the idea imperfectly to ourselves.
Aphorism Seventh.
What precedes not appertaining to any circumstance peculiar to any one of our perceptions rather than to another, agrees generally with all.
COROLLARY.
Hence it follows, 1st. That our manner of proceeding is the same for our ideas of every kind.
2dly. That all our errors originate from the basis of our ideas, and not from the form of our reasonings.
3dly. That all the rules which can be prescribed for the forms of these reasonings, can contribute nothing to avoid error; or at least can contribute to it but accidentally.
Aphorism Eighth.
We have then no other effectual means of avoiding error, but to assure ourselves well of the comprehension of the idea of which we judge, that is to say, of the elements of which it is composed.
OBSERVATION.
That is not possible, unless we commence by well determining the extension of this idea, for it contains many elements in certain degrees of its extension, which it does not in others, that is to say, it is not exactly similar to itself, it is not rigorously the same idea in their different degrees of extension.
Aphorism Ninth.
This general and only method embraces several others, and first that of studying with care the object, or objects, from which the idea in question emanates, and afterwards that of guarding ourselves with the same care from the affections, passions, prejudices, dispositions, habits and manners of being, by which the idea could be altered.
OBSERVATION.
These two precautions are necessary, the first to assemble, as far as possible, all the elements which really appertain to the idea in question, the second to separate from it in like manner all those which are foreign to it, and which might mingle themselves with it, and alter it, without our perceiving it.
Aphorism Tenth.
After these two necessary preliminaries, if we are still in doubt as to the judgment we are to form, the most useful expedient of which we can avail ourselves, is to make an enumeration the most complete possible of the elements composing the idea, which is the subject of the judgment, and principally of those which have relation to the idea which we propose to attribute to it, that is to say, to the attribute of the contemplated judgment.
OBSERVATION.
The effect of this operation is to recall to ourselves, or to those whom we wish to convince of the truth or falsity of a proposition, the elements of the subject which implicitly comprehend the proposed attribute, or which on the contrary may exclude it.
It is the object which the logicians propose to attain by what they call definitions; but in my opinion they fall into several errors relatively to definitions, and they greatly mistake their effects and properties.
1st. They believe that there are definitions of words, and definitions of things, while in truth there are none but definitions of ideas. When I explain the sense of a word, I do nothing but explain the idea which I have when I pronounce that word, and when I explain what a being is, I still do nothing but explain the idea I have of that being, and which I express when I pronounce its name.
2d. They aver that definitions are principles, and that we cannot dispute about definitions. These two assertions are contraries, and yet both of them false.
In the first place they are contradictory, for if definitions are principles, we can and we ought frequently to question their truth, as we ought never to recognise any principle as true without a previous examination, and if we cannot contest definitions, they cannot be principles, since every principle should be proved before it is admitted.
Again, these two assertions are both false. definitions are not principles; for facts are the only true principles; and definitions are not facts, but simple explanations founded on facts, as all our other propositions whatsoever. Now we may contest a definition, as every other proposition; for when I explain the idea that I have of a being, I do not pretend to say merely that I have this idea; I pretend also to affirm that this idea agrees with that being, and that we may so conceive it without error; now this is what may be false, and what may be contested. So also when I explain the idea which I have of the sense of a word, I do not solely pretend that I have this idea, I pretend further that it does not affect the real relations of this word with an infinity of others, that we may employ it in this sense without inconvenience and without inconsequence; now this is what again may be contested with reason. In fine, if I should pretend by a definition only to explain the complex and compound idea that I have actually in my head, yet it should always be allowed to show me that this idea is badly formed, that it is composed of judgments inconsequent the one to the other, and that it includes contradictory elements.
Then definitions never are principles, and yet they always are