We have already illustrated the slight perceptibility of differences (or the slight interest that we take in individual differences), as we gradually descend into what is called nature or inferior reality. On this is founded the illusion that nature is invariable and without history. And it also explains why mathematics has seemed more applicable to the _globus naturalis_ than to the _globus intellectualis,_ and in the _globus naturalis,_ to mineralogy more than to zoology, to physics more than to biology. Still, mathematics is equally applicable to the _globus intellectualis,_ as, for instance, in Economics and Statistics. And, on the other hand, it is inapplicable to both spheres, when they are considered in their effective truth and unity as the _history of nature_ or the _history of reality,_ in which nothing is repeated and therefore nothing is equal and identical. Beneath that difference of applicability there is nothing but a consideration of utility. If the grains of sand on which we tread can be considered (although they are not) equal to one another, it happens less frequently that we regard those with whom we associate and act in the same light. Hence the _decreasing utility_ of naturalistic constructions (and of mathematical calculation), as we gradually approach human life and the historical situation in which we find ourselves. Decreasing but never non-existent, for otherwise, neither empirical sciences (grammars, books on moral conduct, psychological types, etc.) nor calculations (statistics, economic calculations, etc.,) would continue in use. A constructor of machines needs little intuition, but much physics and mechanics. A leader of men needs very little mathematics, little empirical science, but much intuitive and perceptive faculty for the vices and value of the human individuals with whom he has to do. But both little and much are empirical determinations; the Spirit, which is the whole spirit in every particular man and at every particular instant of life, is never composed of measurable elements. [Footnote 1: _Introduction to Philosophy,_ Italian tr., Vidossich, p. 272.] [Footnote 2: There is a curious collection of judgments adverse to mathematics in Hamilton, _Fragments philosophiques,_ tr. Plisse, Paris, 1840, pp. 283-370.] [Footnote 3: Autobiography in _Works,_ Ferrari, 2nd edition, iv. p. 336.] VII THE CLASSIFICATION OF THE SCIENCES [Sidenote: _The theory of the forms of knowledge and the doctrine of the categories._]