clearness, constancy, and precision of their subdivisions are susceptible of adaptation to the divisions of the series of the names of numbers, and of figures, we can employ with great advantage, instead of the ordinary instruments of reasoning, the instruments proper to the science of the ideas of quantity, that is to say, the language of calculation, its formulas, and its signs. It is this which constitutes in respect to the conjectural part the calculation of probability. It is necessary to distinguish it carefully from the science of probability; for the one is of use in all cases in which the object is a likelihood of any kind whatsoever; it is properly the conjectural part of all other sciences, whereas the other calculation has place only in those cases in which we can employ the language of calculation; it is but an instrument, of which unhappily the science of probability cannot always avail itself.
The science of probability consists in the talent and sagacity necessary to know the data, to chuse them, to perceive their degrees of importance, to arrange them in convenient order, a talent to which it is very difficult to prescribe precise rules, because it is often the product of a multitude of unperceived judgments. On the contrary, the calculation of probability, properly so called, consists only in following correctly the general rules of the language of calculation in those cases in which it can be employed.
This calculation is often extremely useful and extremely learned; but it is necessary carefully to distinguish the occasions on which we can avail ourselves of it, for however little the ideas which we attempt to calculate are mingled with those which I have named refractory, and which are truly incalculable, we are inevitably led into the most excessive miscalculations. It is what I think has happened but too frequently to skilful men, who by their knowledge, and even by their mistakes, have put us into the way of discovering their cause.
I will limit myself to this small number of results. I perceive that it is to diffuse but little direct light on a subject, which is so much the more important and the more extensive, as unfortunately certitude is for the most part far from us. But if I have contributed to the formation of a just and clear idea of it I shall not have been useless. I have much more reason than Condorcet for saying “I have not thought that I was giving a good work, but merely a work calculated to give birth to better ones, &c.”*
Not wishing to occupy myself longer with the conjectural part of our knowledge, and not believing it necessary to add to the small number of principles which I have established before this long digression, and which embrace in my opinion every thing of importance in the logical art, such as it proceeds from true logical science; it only remains for me to endeavour to make a happy application of this art to the study of our will and its effects. It is this I am going to undertake, with a hope that my instruments being better, I may better succeed than perhaps men more skilful but not so well armed.
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