nition has been largely due to the great prestige in modern philosophy of the method of geometry, which was regarded by Descartes and Spinoza as the model for systems of necessary truth. Self-evidence is the principle according to which conviction of truth follows directly from an understanding of meaning. In the practice of his intellectual midwifery, Socrates presupposed that thought is capable of bringing forth its own certainties. And rationalism has at all times regarded truth as ultimately accredited by internal marks recognizable by reason. Such truth arrived at antecedent to acquaintance with instances is called a priori, as distinguished from a posteriori knowledge, or observation after the fact. There can be no principles of self-evidence, but logicians have always been more or less concerned with the enumeration of alleged self-evident principles, notably those of contradiction and identity. A philosophical interest in the mathematical method has led to a logical study of axioms, but with a view rather to their fruitfulness than their intrinsic truth. Indeed, the interest in self-evident truth has always been subordinate to the interest in systematic truth, and the discovery of first principles most commonly serves to determine the relative priority of definite concepts, or the correct point of departure for a series of inferences. common. The greater part of the famous Aristotelian logic consists in a study of inference, or the derivation of new knowledge from old knowledge. Aristotle sought to set down and classify every method of advancing from premises. The most important form of inference which he defined was the syllogism, a scheme of reasoning to a conclusion by means of two premises having one term in From the premises "all men are mortal" and "Socrates is a man," one may conclude that "Socrates is mortal." This is an instance not only of the syllogism in general, but of its most important "mood," the subsumption of a particular case under a general rule. Since the decline of Aristotle's influence in philosophy there has been a notable decrease of interest in the different forms of inference; though its fundamental importance as the very bone and sinew of reasoning or deductive thinking has never been challenged. Its loss of preeminence is in part due to the growth of empiricism, stimulated by the writings of Lord Bacon in the seventeenth century, and fostered by the subsequent development of experimental science. Observation is the fundamental logical principle of empiricism. For a radical empiricism, knowledge would consist of descriptive generalizations based upon the summation of instances. That branch of logic which deals with the advance from individual instances to general principles, is called inductive logic. It has resulted in the announcement of canons of accuracy and freedom from preconception, and in the methodological study of hypothesis, experiment, and verification. Rules for observation directed to the end of discovering causes, constitute the most famous part of the epoch-making logic of J. S. Mills." 877. There are two significant tendencies in contemporary logic. Theories of the judgment have arisen in the course of an attempt Present Theory of to define the least complexity that must the Judgment. be present in order that thought shall come within the range of truth and error. It is evident that no one either knows or is in error until he takes some attitude which lays claim to knowledge. Denoting by the term judgment this minimum of complexity in knowledge, an important question arises as to the sense in which the 'The reader can find these rules, and the detail of the traditional formal logic, in any elementary text-book, such as, e. g., Jevons: Elements of Logic. judgment involves the subject, predicate, and copula that are commonly present in its propositional form. Priority of § 78. But a more important logical develop ment has been due to the recent analysis of definite accredited systems of knowledge. The Concepts. 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 8 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. 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. Deals with the Conditions of § 79. Esthetics is the formulation, as independently as possible of special subject-matter, Aesthetics of that which conditions beauty. As Most General logic commonly refers to a judgment of truth, so æsthetics at any rate refers to and Formalis- a judgment implied in appreciation. tic Tendencies. But while it is generally admitted that truth itself is by no means limited to the form of the judgment, the contrary is frequently main Beauty. 8 What is called "the algebra of logic" seeks to obtain an unequivocal symbolic expression for these truths. |