Sidenote: Priority of Concepts.]

Sect. 78. But a more important logical development has been due to the
recent analysis of definite accredited systems of knowledge. The study
of the fundamental conceptions of mathematics and mechanics, together
with an examination of the systematic structure of these sciences,
furnishes the most notable cases. There are two senses in which such
studies may be regarded as logical. In the first place, in so far as
they bring to light the inner coherence of any body of truth, the kind
of evidence upon which it rests, and the type of formal perfection which
it seeks, they differ from formal logic only in that they derive their
criteria from cases, rather than from the direct analysis of the
procedure of thought. And since formal logic must itself make
experiments, this difference is not a radical one. The study of cases
tends chiefly to enrich _methodology_, or the knowledge of the special
criteria of special sciences. In the second place, such studies serve to
define the relatively few simple truths which are common to the
relatively many complex truths. A study of the foundations of arithmetic
reveals more elementary conceptions, such as _class_ and _order_, that
must be employed in the very definition of number itself, and so are
implied in every numerical calculation. It appears similarly that the
axioms of geometry are special axioms which involve the acceptance of
more general axioms or indefinables.[189:8] Logic in this sense, then,
is the enumeration of conceptions and principles in the order of their
indispensableness to knowledge. And while it must be observed that the
most general conceptions and principles of knowledge are not necessarily
those most significant for the existent world, nevertheless the careful
analysis which such an enumeration involves is scarcely less fruitful
for metaphysics than for logic.

[Sidenote: Aesthetics Deals with the Most General Conditions of Beauty.
Subjectivistic and Formalistic Tendencies.]

Sect. 79. _Aesthetics is the formulation, as independently as possible
of special subject-matter, of that which conditions beauty._ As logic
commonly refers to a judgment of truth, so aesthetics at any rate
_refers_ to a judgment implied in appreciation. But while it is
generally admitted that truth itself is by no means limited to the form
of the judgment, the contrary is frequently maintained with reference
to beauty. The aphorism, _De gustibus non est