§ 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: Æsthetics Deals with the Most General Conditions of Beauty. Subjectivistic and Formalistic Tendencies.]