§ [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.
Æsthetics Deals with the Most General Conditions of Beauty. Subjectivistic and Formalistic Tendencies.
§ [79]. Æsthetics 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 æsthetics 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 disputandum, expresses a common opinion to the effect that beauty is not a property belonging to the object of which it is predicated, but a property generated by the appreciative consciousness. According to this opinion there can be no beauty except in the case of an object's presence in an individual experience. Investigators must of necessity refuse to leave individual caprice in complete possession of the field, but they have in many cases occupied themselves entirely with the state of æsthetic enjoyment in the hope of discovering its constant factors. The opposing tendency defines certain formal characters which the beautiful object must possess. Evidently the latter school will attribute a more profound philosophical importance to the conception of beauty, since for them it is a principle that obtains in the world of being. This was the first notable contention, that of Plato. But even with the emphasis laid upon the subjective aspect of the æsthetic experience, great metaphysical importance may be attached to it, where, as in the case of the German Romanticists, reality is deliberately construed as a spiritual life which is to be appreciated rather than understood.
As in the case of logic, a strong impulse has manifested itself in æsthetics to deal with groups of objects that lie within its province, rather than directly with its concepts and principles. The first special treatise on æsthetics, the "Poetics" of Aristotle, belongs to this type of inquiry, as does all criticism of art in so far as it aims at the formulation of general principles.
Ethics Deals with the Most General Conditions of Moral Goodness.
§ [80]. Ethics, the oldest and most popular of the normative sciences, is the formulation, as independently as possible of special subject-matter, of that which conditions goodness of conduct. Ethics is commonly concerned with goodness only in so far as it is predicated of conduct, or of character, which is a more or less permanent disposition to conduct. Since conduct, in so far as good, is said to constitute moral goodness, ethics may be defined as the formulation of the general principles of morality. The principles so formulated would be those virtually employed to justify conduct, or to disprove the imputation of immorality.
Conceptions of the Good. Hedonism.
§ [81]. The student of this science is confronted with a very considerable diversity of method and differentiation of problems. The earliest and most profound opposition of doctrine in ethics arose from the differences of interpretation of which the teaching of Socrates is capable. His doctrine is, as we have seen, verbally expressed in the proposition, virtue is knowledge. Socrates was primarily concerned to show that there is no real living without an understanding of the significance of life. To live well is to know the end of life, the good of it all, and to govern action with reference to that end. Virtue is therefore the practical wisdom that enables one to live consistently with his real intention. But what is the real intention, the end or good of life? In the "Protagoras," where Plato represents Socrates as expounding his position, virtue is interpreted to mean prudence, or foresight of pleasurable and painful consequences. He who knows, possesses all virtue in that he is qualified to adapt himself to the real situation and to gain the end of pleasure. All men, indeed, seek pleasure, but only virtuous men seek it wisely and well.
"And do you, Protagoras, like the rest of the world, call some pleasant things evil and some painful things good?—for I am rather disposed to say that things are good in as far as they are pleasant, if they have no consequences of another sort, and in as far as they are painful they are bad."[192:9]
According to this view painful things are good only when they lead eventually to pleasure, and pleasant things evil only when their painful consequences outweigh their pleasantness. Hence moral differences reduce to differences of skill in the universal quest for pleasure, and sensible gratification is the ultimate standard of moral value. This ancient doctrine, known as hedonism, expressing as it does a part of life that will not suffer itself for long to be denied, is one of the great perennial tendencies of ethical thought. In the course of many centuries it has passed through a number of phases, varying its conception of pleasure from the tranquillity of the wise man to the sensuous titillations of the sybarite, and from the individualism of the latter to the universalism of the humanitarian. But in every case it shows a respect for the natural man, praising morality for its disciplinary and instrumental value in the service of such human wants as are the outgrowth of the animal instinct of self-preservation.