studies of a University, and which within a few years it has wellnigh reclaimed, is vindicated by the great value of the effort which is necessary to master it, considered simply as a vigorous exercise of the understanding. Indeed, its chief function is disciplinary, for the effort to acquire it may be said to equal or surpass in value the subsequent use to be made of the acquisition. It is not of so much importance to know, as it is to have strengthened and developed all the faculties in learning to know. No other study taxes so severely the power of abstract thought, and hence no one furnishes better preparatory training for the pursuit of all the sciences which do not consist mainly in accumulating facts and registering the materials thus obtained.

Little needs to be said of the intrinsic dignity of the subject. "Admitting," says Heinrich Richter, as translated by Hamilton, "that this science teaches nothing new, that it neither extends the boundaries of knowledge, nor unfolds the mysteries which lie beyond the compass of our reflective intellect, and that it only investigates the immutable laws to which the mind in thinking is subjected, still, inasmuch as it develops the application of these laws, it bestows on us, to a certain extent, a dominion over our thoughts themselves. And is it nothing to watch the secret workshop in which nature fabricates cognitions and thoughts, and to penetrate into the sanctuary of self-consciousness, to the end that, having learnt to know ourselves, we may be qualified rightly to understand all else? Is it nothing to seize the helm of thought, and to be able to turn it at our will? For through a research into the laws of thinking, Logic gives us, in a certain sense, a possession of the thoughts themselves. It is true, indeed, that the mind of man is, like the universe of matter, governed by eternal laws, and follows, even without consciousness, the invariable canons of its nature. But to know and understand itself, and out of the boundless chaos of phenomena presented to the senses to

form Concepts, through Concepts to reduce that chaos to harmony and arrangement, and thus to establish the dominion of intelligence over the universe of existence,—it is this alone which constitutes man's grand and distinctive pre-eminence." "Our whole dignity," says Pascal, "consists in thought."

It is also argued by Sir William Hamilton, with great force, that "Logic is further useful as affording a Nomenclature of the laws by which legitimate thinking is governed, and of the violation of these laws, through which thought becomes vicious or null.

and it may be safely confessed that this is one of the principal utilities of Rhetoric. A mere knowledge of the rules of Rhetoric can no more enable us to compose well, than a mere knowledge of the rules of Logic can enable us to think well. There is required from nature, in both, the faculty; but this faculty must, in both departments, be cultivated by an assiduous and also a well-directed exercise; that is, in the one, the powers of Comparison must be exercised according to the rules of a sound Rhetoric, in the other, according to the rules of a sound Logic. In so far, therefore, the utility of either science is something more than a mere naming of their tools. But the naming of their tools, though in itself of little value, is valuable as the condition of an important function, which, without this, could not be performed. Words do not give thoughts; but without words, thoughts could not be fixed, limited, and expressed. They are, therefore, in general, the essential condition of all thinking worthy of the name. Now, what is true of human thought in general, is true of Logic and Rhetoric in particular. The nomenclature in these sciences

is the nomenclature of certain general analyses and distinctions, which express to the initiated, in a single word, what the uninitiated could (supposing—what is not probable that he could perform the relative processes) neither understand nor express without a tedious and vague periphrasis; while, in his hands, it would assume only the appearance of a particular observation, instead of a particular instance of a general and acknowledged rule. To take a very simple example: there is in Logic a certain sophism, or act of illegal inference, by which two things are, perhaps in a very concealed and circuitous manner, made to prove each other. Now, the man unacquainted with Logic may perhaps detect and be convinced of the fallacy; but how will he expose it? He must enter upon a long statement and explanation, and, after much labor to himself and others, he probably does not make his objection clear and demonstrative after all. But between those acquainted with Logic, the whole matter would be settled in two words. It would be enough to say and show, that the inference in question involved a circulus in concludendo, and the refutation is at once understood and admitted. It is in like manner that one lawyer will express to another the ratio decidendi of a case in a single technical expression; while their clients will only perplex themselves and others in their attempts to set forth the merits of their cause. Now, if Logic did nothing more than establish a certain number of decided and decisive rules in reasoning, and afford us brief and precise expressions by which to bring particular cases under these general rules, it would confer on all who in any way employ their intellect that is, on the cultivators of every human science -the most important obligation. For it is only in the possession of such established rules, and of such a technical nomenclature, that we can accomplish, with facility, and to an adequate extent, a criticism of any work of reasoning. Logical language is thus, to the general reasoner,

what the notation of Arithmetic, and still more of Algebra, is to the mathematician. Both enable us to comprehend and express, in a few significant symbols, what would otherwise overpower us by their complexity; and thus it is, that nothing would contribute more to facilitate and extend the faculty of reasoning, than a general acquaintance with the rules and language of Logic,—an advantage extending indeed to every department of knowledge, but more especially of importance to those professions which are occupied in inference, and conversant with abstract matter, such as Theology and Law."

CHAPTER III.

THE PRIMARY AXIOMS OF PURE THOUGHT.

HA

AVING defined Logic to be the Science of the Necessary Laws of Pure Thought, our first object must be to ascertain what are the Fundamental and Universal Laws, here called Primary Axioms, to which all Thought, as such, is subject. In the separate consideration, which will come afterwards, of the three classes of Thoughts, namely, Concepts, Judgments, and Reasonings, we may expect

to find Special Laws or Rules which are applicable only to one or two of these divisions. Such Special Rules may or may not be derivative in character; that is, they may be either immediate inferences from the Primary Axioms which govern all the products of the Thinking Faculty, or they may be independent, as resting upon their own evidence. Of this hereafter. But our first inquiry must be, whether there are any Axioms of universal applicability, which underlie and govern every act and product of the human Understanding; and, if there are such, to determine their character and significance.

If there are such Axioms, they must be few, meagre in import, not susceptible of proof, and recognizable by all as familiar truisms, which have always implicitly directed their thoughts, though perhaps, on account of their very obviousness, they have never been explicitly stated or drawn out into distinct consciousness. They must have these characteristics, because they concern only the Forms of Thought, or the manner of thinking irrespective of what