On the contrary, the propositions of the Science of Economy are rigorous and necessary. "Granted that soils of different degrees of fertility are cultivated, their possessors will all obtain, besides the absolute rent, a differential rent, with the exception of the possessor of the least fertile soil" (Ricardo's law). "Bad money drives out good" (Gresham's law). Now, it is not conceivable in any case that soils of different fertility, all of them cultivated, should not give a differential rent. It will be said that the State can confiscate the differential rent, or that the possessor, owing to his bad cultivation or to his bad administration, may lose it; but the proposition does not remain less sound on this account. Nor is it possible that, when an unchangeable paper money is in circulation, gold coins should also circulate indifferently and on a par with it, when the total of the money in circulation lowers the value of the monetary unit beneath the metallic value of the better money. A madman who might be in possession of a hoard of gold pieces at the time of the circulation of the declining paper money (which causes poverty) would perhaps give it in exchange for the inferior money; but the wise man will keep it in his safe. The economic proposition expresses the rational necessity, not the madness, which is irrational. Those propositions, like all the others of economic science, are therefore certainly not descriptions, but _theorems._ [Sidenote: _Their mathematical nature._] The denomination "theorems" makes us think at once of the mathematical disciplines, among which alone can economic Science find a place. The propositions of that science being excluded from philosophical, historical, or naturalistic science, there remains nothing that they can be, save _mathematical._ Yes, they are mathematical, but not pure mathematics, for in that case they would be nothing but arithmetic, algebra, or the calculus, that is, they would belong to the kind of mathematical disciplines called _applied,_ because they introduce into the paradigms of the calculus certain data taken from reality, that is to say, taken from without the purely numerical conception. Economic Science, then, is a mathematic applied to the concept of human action and to its sub-species. It does not inquire what human action is; but having posited certain concepts of action, it creates formulæ for the prompt recognition of the necessary connections. [Sidenote: _Its principles; their character of arbitrary postulates and definitions. Their utility._]