contestible.
3dly. The logicians have believed that the definition is good, and that the idea defined is perfectly explained when they have determined it, per genus proximum et differentiam specificam, as they say; that is to say, when they have expressed that one of its elements which constitutes it of such a genus, and the one which in this genus distinguishes it from the ideas of the neighbouring species. Now this is still false, and is only founded on the fantastical doctrine, in virtue of which they believed they were able to distribute all our ideas into different arbitrary classes called categories.
That is false, first, because these arbitrary classifications never represent nature. Our ideas are connected the one to the other by a thousand different relations. Seen under one aspect they are of one genus, and under another they are of another genus; subsequently each of them depends on an innumerable multitude of proximate ideas, by an infinity of relations, of natures so different that we cannot compare them together, to decide which is the least remote. Thus we can never, or almost never find really the proximate genus or specific difference which deserves exclusively to characterise an idea.
Moreover, if we should have found in this idea the elements which in fact determine the genus and species in which it is reasonably permitted to class it, the idea would still be far from sufficiently explained, to be well known.
These two elements might even be absolutely foreign to the decision of the question which may have given place to the definition. Assuredly when I say that gold is a metal, and the heaviest of metals except platina, I have correctly ranged gold in the genus of beings to which it belongs, and I have distinguished it by a characteristic difference from those nearest to it in that genus. Yet this does not help me to know whether the use of gold, as money, is useful to commerce, or pernicious to morality, nor even whether it is the most ductile of metals. The two first questions depend on ideas too foreign to those which fix gold in a certain place amongst metals; and though the latter may be less distant, yet we do not know the direct and necessary relation between weight and ductility.
Logicians have been mistaken respecting the nature, the effects and properties of definitions. They are incapable of answering the end which they propose to attain by their means, that of presenting the idea of which we are to judge in such a manner that we cannot avoid forming a just judgment. The only mean of attaining this is to make the best description possible of the idea, and with the precautions which we have indicated.
REMARK.
It is necessary to observe that all that we have advised in the 8th, 9th and 10th aphorisms, and also what we shall advise hereafter to be done, to know well the idea, the subject of the judgment in question is equally applicable to the idea which is the attribute of the same judgment, a knowledge of which is equally essential, and can only be acquired by the same means.
Aphorism Eleventh.
The means indicated above of knowing well the idea of which we are to judge, are the only really efficacious ones in bringing us to the formation of just judgments; but they may very possibly be insufficient to give us a certitude of having succeeded. We must therefore add subsidiary means.
Aphorism Twelfth.
The best and most useful of our secondary means is to see, on the one hand, if the judgment we are to form is not in opposition to anterior judgments, of the certitude of which we are assured; and on the other if it does not necessarily lead to consequences manifestly false.
REMARK.
The first point is that which has so strongly accredited the usage of general propositions; for, as we can confront them with a number of particular propositions, we have frequently had recourse thereto, and we have habituated ourselves to remount no further, and to believe that they are the primitive source of truth. The second is the motive of all those reasonings which consist in a reduction to what is absurd.
OBSERVATION.
The process recommended in this aphorism is a species of proof to which we submit the projected operation. It is very useful to avoid error, for if the judgment we examine is found in opposition to anterior ones which are just, or necessarily connected with false consequences, it is evidently necessary to reject it; but this same process does not lead us directly and necessarily to truth, for it may be that no determining motive for the affirmative may result from the research.
Aphorism Thirteenth.
In a case in which we want decisive reasons to determine us, no other resource is left us but to endeavour to obtain new lights, that is to say, to introduce new elements into the idea which is the subject of the judgment we are to form. This can be done in two ways only, either by seeking to collect new facts, or by endeavouring to make of those already known combinations which had not previously occurred to us, and thence to draw consequences which we had not before remarked.
OBSERVATION.
The advice contained in this aphorism, is only the developement of the first part of aphorism 9th, and it can be nothing else; for when we are assured that we are not sufficiently acquainted with a subject to judge of it, there is no other resource but to study it more.
Aphorism Fourteenth.
Finally, when the motives of determination fail us invincibly, we should know how to remain in complete doubt, and to suspend absolutely our judgment, rather than rest it on vain and confused appearances, since in these we can never be sure that there are not some false elements.
REMARK AND CONCLUSION.
This is the last and most essential of logical principles; for in following it we may possibly remain in ignorance, but we can never fall into error; all our errors arising always from admitting into that which we know elements which are not really there, and which lead us to consequences which ought not to follow from those that are there effectively.
In effect, if from our first impressions the most simple to our most general ideas, and their most complicated combinations, we have never recognized in our successive perceptions but what is there, our last combinations would be as irreproachable as the first act of our sensibility. Thus, in logical rigour, it is very certain that we ought never to form a judgment but when we see clearly that the subject includes the attributes: that is to say, that the judgment is just.
But at the same time it is also very certain that in the course of life we seldom arrive at certitude, and are frequently obliged, nevertheless, to form a resolution provisionally; to form none being often to adopt one of the most decisive character, without renouncing the principle we have just laid down, or in any manner derogating from it. It is now proper to speak of the theory of probability. It is a subject I encounter with reluctance. First, because it is very difficult, and as yet very little elucidated; next, because one cannot hope to treat it profoundly when one is not perfectly familiar with the combinations of the science of quantities, and of the language proper to them. Finally, because even with these means the nature of the subject deprives us of the hope of arriving at almost any certain result, and leaves us only that of a good calculation of chances. Let us, however, endeavour to form to ourselves an accurate and just idea of it; this will perhaps be already to contribute to its progress.
The science of probability is not a part of logic, and ought not even to be regarded as forming a supplement to it. Logic teaches us to form just judgments, and to make series of judgments: that is to say, of reasonings which are consequent. Now, properly speaking, there are no judgments or series of judgments which are probable. When we judge that an opinion or a fact is probable, we judge it positively; and this judgment is just, false, or presumptuous, according as we have perfectly or imperfectly observed the principles of the art of logic. But it will be said, that the science of probability in teaching us to estimate this probability of an opinion, teaches us to judge