As is evident, we first have to deal with the three great groups of the
formal, the physical, and the biological sciences. The formal sciences
treat of characteristics belonging to all experiences, characteristics,
consequently, that enter into every known phase of life, and so affect
science in the broadest sense. In order immediately to overcome a
widespread error, I emphasize the fact that these sciences are to be
considered just as experiential or empirical as the sciences of the
other two groups, as to which there is no doubt that they are empirical.
But because the concepts dealt with by the first group are so extremely
wide, and the experiences corresponding to them, therefore, are the most
general of all experiences, we easily forget that we are dealing with
experiences at all; and our very firmly rooted consciousness of the
unqualified similarity of these experiences causes them to seem native
qualities of the mind, or _a priori_ judgments. Nevertheless,
mathematics has been proved to be an empirical science by the fact that
in certain of its branches (the theory of numbers) laws are known which
have been found empirically and the "deductive" proof of which we have
as yet not succeeded in obtaining. The most general concept expressed
and operative in these sciences is the concept of order, of _conjugacy_
or _function_, the content and significance of which will become clear
later in a more thorough study of the special sciences.
In the second group, the physical sciences, the arbitrariness of the
classification becomes very apparent, since these sciences are among the
best known. We are perfectly justified in regarding mechanics as a part
of physics; and in our day physical chemistry, which in the last twenty
years suddenly developed into an extended and important special science,
thrust itself between physics and chemistry.
The most general concept of the physical sciences is that of _energy_,
which does not appear in the formal sciences. To be sure it is not a
fundamental concept. On the contrary, its characteristic is undoubtedly
that of compositeness, or, rather, complexity.
The third group comprehends all the relations of living beings. Their
most general concept, accordingly, is that of _life_. By physiology is
understood the entire science dealing with non-psychic life phenomena.
It therefore embraces what is called, in the present often chance
arrangement of scientific activities, botany, zoology, and physiology of
the plants, animals, and man. Psychology is the science of mental
phenomena. As such, it is not limited to man, even though for many
reasons he claims by far the preponderating part of it for himself.
Sociology is the science which deals with the peculiarities of the human
race. It may therefore be called anthropology, but in a far wider sense
than the word is now applied.
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