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 justly whether this opinion is or is not probable. I admit it: but it produces this effect as the science of the properties of bodies, physics, teaches us to form the judgment that such a property appertains to such a body; as the science of extension teaches us to form the judgment that such a theorem results from the properties of such a figure; as the science of quantity teaches us that such a number is the result of such a calculation; finally, as all the sciences teach us to form sound judgments of the objects, which belong to their province. Nevertheless we cannot say, and we do not say, that they are but parts of logic, nor even that they are supplements to it. They all on the contrary throw light on the subjects of which they treat only in consequence of the means and processes with which they are furnished by sound logic. This is useful to all the sciences; but none of them either aid it immediately, supply its place, make a part of it, or are supplements to it. The science of probability has in this respect no particular privileges under this aspect; it is a science similar to all the others.
But I go further; the science to which we have given the name of the science of probability, is not a science: or to explain myself more clearly, we comprehend erroneously under this collective and common name a multitude of sciences or of portions of sciences quite different among themselves, strangers to one another, and which it is impossible to unite without confounding them all. In effect, that which is called commonly the science of probability comprehends two very distinct parts, of which one is the research, and the valuation of data, the other is the calculation, or the combination of these same data.
Now the success of the research and valuation of data, if the question is on the probability of a narration, consists in a knowledge of the circumstances, proper to the fact in itself, and to all those who have spoken of it: thus it depends on and forms a part of the science of history. If the question is on the probability of a physical event, this research of data consists in acquiring a knowledge of anterior facts and of their connection: thus it appertains to physics. If the question is on the probable results of a social institution, or of the deliberations of an assembly of men, the anterior facts are the details of the social organization, or of the intellectual dispositions and operations of these men: thus it depends on social and moral science, or on Ideology. Finally, when it is only to foresee the chances of the play of cross and pile, the data would be the construction of the piece, the manner of resistance of the medium in which it moves, that of the bodies against which it may strike, the motion proper to the arm which casts it, and which are more or less easy to it. Thus these data would still depend on the physical constitution of animate and inanimate bodies. Then as to the research of data, and to the fixation of their importance, the pretended science of probability is composed of a multitude of different sciences, according to the subject on which it is employed; and consequently it is not a particular science.
As to the combination of the data once established, the science of probability is nothing, when we employ calculation therein, but the science of quantity or of calculation itself; for the difficulty does not consist in giving to abstract unity any concrete value whatever, and sometimes one and sometimes another, but in knowing all the resources which perfect calculation furnishes to make of this unity and of all its multiplied combinations the most complicated, and to connect them regularly without losing their thread.
We see then that neither in regard to the research and valuation of data, nor in regard to the combinations of these same data, the pretended science of probability is not a particular science distinct from every other.
We might rather consider it either as a branch of the science of quantities, and as an employment which we make of it in certain parts of several different sciences which are susceptible of this application, or as the reunion of scattered portions of many sciences, strangers the one to the other, which have only so much in common as to give place to such questions as can only be resolved by a very learned and very delicate employment of the admirable means of calculation furnished by the science of quantities in the state of perfection which it has at this time attained; but this is not seeing the theory of probability in its full extent, for we cannot always employ calculation in the estimation of probability. Nevertheless this manner of considering and decomposing what is called the science of probability explains to us already many of the things which concern it, and puts us in the way of forming to ourselves an accurate and complete idea of it.
We see first why it is the mathematicians who have had the idea of it, and who have, if we may so say, created and made it entirely. It is because such as they have conceived it, it consists principally in the employment of a powerful agent which was at their disposal; they have been able to push to a great length speculations which other men have been obliged to abandon in consequence of a want of means to pursue them.
We also see why these mathematicians principally and almost entirely employed themselves on subjects of which the data are very simple, such as the chances of games of hazard, and of lotteries, or the effects of the interest of money lent; it is because their principal advantage consisting in their great skill in calculation, they have with reason preferred the objects where this art is almost every thing, and where the choice and valuation of data present scarcely any difficulty; and it is in fact in cases of this kind that they have obtained a success both curious and useful.
We moreover see why it is that all the efforts of these mathematicians, even the most skilful, when they have undertaken to treat in the same manner subjects of which the data were numerous, subtile and complicated, have produced little else than witty conceits which may be called difficiles nugae, learned trifles. It is because the farther they have pursued the consequences resulting from the small number of data which they have been able to obtain, the farther they have departed from the consequences which these same data would have produced, united with all those often more important, which they have been obliged to neglect from inability to unravel and appreciate them. This is the cause why we have seen great calculators, after the most learned combinations, give us forms of balloting the most defective, not having taken into account a thousand circumstances, inherent in the nature of men and of things, attending only to the circumstance of the number of the one and of the other. It is the reason why Condorcet himself,1 when he undertook to apply the theory of probabilities to the decisions of assemblies, and particularly to the judgments of tribunals, either has not ventured to decide any thing on actual institutions, and has confined himself to reasoning on imaginary hypothesis, or has often been led to expedients absolutely impracticable, or which would have inconveniencies more serious than those he wished to avoid.
Whatever respect I bear to the great intelligence and high capacity of this truly superior and ever to be regretted man, I do not fear to pass so bold a sentence on this part of his labors, for I am in some measure authorized to do it by himself. The title of Essay which he has given to his treatise, and the motto which he has prefixed to it, prove how much he doubted of the success of such an enterprise, and what confirms it is, that in his last work, composed on the eve of an unfortunate death, in which he has traced with so firm a hand the history of the progress of the human mind, and in which he has assigned to the theory of probabilities so great a part in the future success of the
