case may be designated by a letter of the alphabet, the peculiar significance of which is, that it stands for any Matter whatever, and not for any one in particular. Thus, A is B, is the Form of an affirmative judgment, wherein A and B stand for any two Concepts whatever. Hence, whatever is true of the general formula, A is B, will be true also of any such particular instances, as Iron is malleable, Trees are plants, &c., wherein the Form is associated with some particular Matter. In saying, then, that Logic is concerned only with the Forms of Thought, or Pure Thought, or Thought in the abstract, for all these expressions signify the same thing, we mean only, that what is Material in Thought is extralogical, and, as logicians, we have nothing to do with it; just as the geometer has nothing to do with the particular diagram on the paper before him, except so far as it is a symbol, or universal Form, of all possible figures of the same general character. As Hamilton remarks: "The objects (the Matter) of thought are infinite; no one science can embrace them all, and therefore to suppose Logic conversant about the Matter of thought in general, is to say that Logic is another name for the encyclopædiathe omne scibile of human knowledge. The absurdity of this supposition is apparent. But if it be impossible for Logic to treat of all the objects of thought, it cannot be supposed that it treats of any; for no reason can be given why it should limit its consideration to some, to the exclusion of others. As Logic cannot, therefore, possibly include all objects, and as it cannot possibly be shown why it should include only some, it follows that it must exclude from its domain the consideration of the Matter of thought altogether; and as, apart from the Matter of thought, there only remains the Form, it follows that Logic, as a special science of thought, must be viewed as conversant exclusively about the Form of thought."

Again, the definition of Logic assumes that the process

of Thinking, like every other operation in nature, does not take place at random, but according to certain fixed Laws or invariable modes of procedure. There could be no communication of Thought from one mind to another, if the process of Thinking in all minds were not subject to the same general rules. We follow these laws for the most part unconsciously, as a distinct recognition of them is not by any means necessary for correct thinking; just so, many persons speak and write correctly without any knowledge of the grammarian's rules. But they can be discovered through analysis of their results, and the business of the logician is to search them out and arrange them in order, just as the grammarian's duty is to set forth those secondary laws of Thought which control the formation and the use of Language. Logic, says Dr. Thomson, "like philosophy, of which it is a part, arises from a reflection of the mind upon its own processes; a logician is not one who thinks, but one who can declare how he thinks.'

But here a distinction is to be made, for Logic takes cognizance not of the contingent, but only of the necessary and universal, laws of Thought. Psychology, as the science of the mental phenomena in general, includes, of course, the procedures of Pure Thought; but it includes them only in their contingent and phenomenal character, as actually existing now and then, but not as necessarily existing at all times. Logic does not consider the subsidiary processes, such as Perception, Memory, and Imagination, through which we collect the materials for thinking. The operations of the Thinking Faculty are also contingently modified by the coexistence of other powers and affections of the mind; they are obstructed by indolence, and warped by prejudice and passion. Logic does not regard these accidental perversions of the Understanding, but takes into view only those fundamental and absolute principles, to which all Thought is necessarily subject, and which shine by their

own light, as they cannot be transgressed except by the idiot or the madman. A violation of one of these Laws is not so much an error in Thinking, as a negation of Thought. They are axiomatic in character; that is, they cannot be proved or deduced from higher principles, for such proof or deduction would be itself an act of Thought, and therefore would presuppose the validity of the very principles which it was intended to guarantee. These Laws cannot be proved, but they can be enunciated and explained; when understood, their truth is self-evident, for they rest upon the immediate testimony of consciousness. As necessary and universally known, they are never consciously broken; but we may be betrayed into an apparent transgression of one or more of them, through an incautious yoking together of certain words or formulas of expression, without sufficiently thinking of what they denote. Some Hibernicisms, as they are termed, are of this character. The judge, who, when puzzled by the ingenuity of two lawyers who were pleading a cause before him, exclaimed in a pet, "I believe you are both right," really violated that universal Law of Pure Thought, called the Principle of Excluded Middle, which declares that, of two contradictory propositions, one must be true, and the other false. Logic, as it proceeds from axiomatic principles, and derives none of its materials from experience, but considers only those laws which underlie all experience and first render it possible, is a purely demonstrative science, like algebra or geometry. It treats of those arguments only which are certain and irrefutable; or if it indirectly, considers some of those forms which come short of perfect demonstration, such as Analogy, Imperfect Induction, and Example, it is only for the purpose of testing them by a reference to the standard forms the validity of which they presuppose, and which they endeavor, as it were, to approximate.

Universal Logic considers the Laws of Thought in their

application, not to this or that special class of objects, but to all objects whatsoever. This is the Logica docens of the Schoolmen, and contains the abstract theory of the science in its widest sense, without any of the limitations that arise from any special purpose or study which the thinker may have in view. It corresponds to the science of Universal Grammar, which treats only of those principles which belong to language as such, and therefore are exemplified in all languages, putting aside altogether the peculiarities of Hebrew, Greek, German, or any other particular tongue. On the other hand, Special Logic, or the Logica utens of the Schools, is the Logic of Mathematics, or the Logic of History, or of any other particular science; consequently, it involves a consideration of the Laws of Thought so far only as they are exemplified or involved in the processes of this one science. Herein Logic becomes subsidiary to the objects of the special inquiry which it is intended to promote or regulate. It presupposes a knowledge of those objects, and it forms an introduction to that inquiry. Hence, it is no longer Logic considered for its own sake, but it is Geometry, History, or some other science, considered in a logical point of view. The discussion of it is therefore relegated to treatises on that science of which it forms a part, and for which it is a special preparatory study. Legal Logic is a part of the science of Law. Mathematical Logic is an introduction or an appendage to pure Mathematics. But, in what now lies before us, it is evident that we have to do only with Universal Logic, which is one, while Special Logic is multiform; which is independent, while that requires an acquaintance with other objects of study and other modes of investigation; which is a part of the Philosophy of Mind, or of Philosophy itself in its wider sense, while that is a portion of a comparatively narrow

science.

There are certain other portions of what has usually

ucts

been called Logic, which, though they do not properly belong to the science itself, yet, as they are generally discussed, often at great length, in most treatises upon it, may properly be defined and explained here, while a full consideration of them may be regarded as an appendix to the body of the work. Properly speaking, Pure Logic terminates with the consideration of the three classes of prodnamely, Concepts, Judgments, and Reasonings which are the elements into which all Thought is resolved. But Thought itself is subsidiary to the attainment of knowledge, that is, to Science. The question remains, then, after we have fully treated of Concepts, Judgments, and Reasonings, taken separately or considered in themselves alone, what use is to be made of them, taken together, in the construction of Science. A full answer to this question, as it would involve a study of the objects of Science, —that is, of the matter of the special sciences, evidently falls outside of the province of Logic. But a partial answer to it, regarding Science in its relation, not to the objects known, but to the knowing mind, may be considered as a natural appendage to Logic, as it embraces the conditions not merely of possible, but of perfect, Thought. Such an answer is usually called the Doctrine of Method, or Logical Methodology. Pure Logic considers only the Necessary Laws to which all Thought must conform; the Doctrine of Method regards those rules and principles to which all Thought ought to conform in order to obtain its end, which is the advancement of Science. Pure Logic treats merely of the elements of Thought, while Logical Methodology regards the proper arrangement of these elements into an harmonious whole. All Method is a well-defined progress towards some end; and the end in this case is the attainment of truth. Practically speaking, the Doctrine of Method is a body of rules or precepts looking to the proper regulation of the Thinking Faculty in the pursuit