and are affiliated in unity of fundamental doctrine. Bacon is the forerunner in that great intellectual movement to which Hamilton has communicated such a mighty energy of thought, contributed the light of such vast erudition, and adduced such stringent historical proofs of its perennial existence. It is the inductive branch of logic, with its kindred doctrines, which Sir William Hamilton has brought out into bold relief, from the subordination in which it was held by Aristotle; while, at the same time, he has so developed, and simplified by a completer analysis, the deductive branch, that the Stagyrite only retains his superior fame by being the precursor. And it is by his successful labours upon these two great branches of logic that Sir William Hamilton conciliates the philosophies of Aristotle and Bacon, and gives to modern thought a force of reasoning, through the practical application of nicer discriminations of the forms of thought, and more adequate logical expression, which elevates this century to a higher intellectual platform. All this shall sufficiently appear in the sequel.

When in the year 1833 Sir William Hamilton published in the Edinburgh Review his criticism on Whately's Logic, there was prevalent in Britain total ignorance of the higher logical philosophy. The treatise of Whately was the highest logical standard; which though in ability it is much above mediocrity, in erudition it is far below the literature of the subject. The article of Sir William elevated the views of British logicians above the level of Whately, and gave them glimpses of a higher doctrine. But the chief service rendered by this masterly criticism, was the precision with which it defined the nature and the object matter of logic, and discriminated the whole subject doctrinally and historically, in the concentrated light of its literature.

The treatise of Whately presents indistinct, ambiguous, and even contradictory views of the proper object matter of logic. Sometimes it makes the process or operation of reasoning the total matter about which logic is conversant; at other times it makes logic entirely conversant about language. Now, though it involves a manifest contradiction to say that logic is exclusively conversant about each of two opposite things, yet Whately was praised by British logicians for the clearness with which he displayed the true nature and office of logic. In the low state of logical knowledge in Britain which these facts indicate, it behoved whoever undertook to point out Whately's blunders, to enter into the most elementary discussion of logic, both name and thing. This Sir William Hamilton did in the article now under consideration.

Aristotle designated logic by no single term. He employed

different terms to designate particular parts or applications of logic; as is shown by the names of his several treatises. In fact, Aristotle did not look at logic from any central point of view. And indeed his treatises are so overladen with extralogical matter, as to show that the true theoretical view of logic, as an independent science, had not disclosed itself to its great founder. In fact, it has only been gradually that the proper view of the science has been speculatively adopted,practically it never has been; and no contribution to the literature of the subject has done so much to discriminate the true domain of logic as this article of Sir William Hamilton. It marks an era in the science. Mounting up to the father of logic himself, it shows that nineteen-twentieths of his logical treatises treat of matters that transcend logic, considered as a formal science. It is shown that the whole doctrine of the modality of syllogisms does not belong to logic for if any matter, be it demonstrative or probable, be admitted into logic, none can be excluded; and thus, with the consideration of the real truth or falsehood of propositions, the whole body of real science must come within the domain of logic, obliterating all distinction between formal and real inference.

The doctrine maintained in this article is, that logic is conversant about the laws of thought, considered merely as thought. The import of this doctrine we will now attempt to unfold. The term thought is used in several significations of very different extent. It is sometimes used to designate every mental modification of which we are conscious, including will, feeling, desire. It is sometimes used in the more limited sense of every cognitive fact, excluding will, feeling, desire. In its most limited meaning it denotes only the acts of the understanding or faculty of comparison or relation, called also the discursive or elaborative faculty. It is in this most restricted sense that the word thought is used in relation to logic. Logic supposes the materials of thought already in the mind, and only considers the manner of their elaboration. And the operation of the elaborative faculty on these materials is what is meant by thought proper. And it is the laws of thought in this, its restricted sense, about which logic is conversant.

It must be further discriminated, that logic is conversant about thought as a product, and not about the producing operation or process; this belongs to psychology. Logic, therefore, in treating of the laws of thought, treats of them in regard to thought considered as a product. What, then, is thought? in other words, what are the acts of the elaborative faculty? They are three, conception, judgment, reasoning. These are all acts of comparison-gradations of thought. Öf these as producing acts psychology treats. Logic treats of

the products of these, called respectively, a concept, a judgment, a reasoning. The most articulate enunciation, therefore, of the intrinsic nature of logic is, the science of the formal laws of thought, considered as a product, and not as a process.

But we will show still further what a form of thought is. In an act of thinking there are three things which we can discriminate in consciousness. First, there is a thinking subject; second, an object which we think, called the matter of thought; and third, the relation subsisting between the subject and object of which we are conscious-a relation always manifested in some mode or manner. This last is the form of thought. Now logic takes account only of this last-the form of thought. In so far as the form of thought is viewed in relation to the subject, as an act, operation, or energy, it belongs to psychology. It is only in reference to what is thought about, only considered as a product, that the form of the act, or operation, or energy, has relation to logic.

With this explanation, we will now enounce the laws of thought, of which logic is the science.

In treating of the conditions of the thinkable, as systematised by Sir William Hamilton, we have pointed out the fact, that it is shown that logic springs out of the condition of noncontradiction; for that this condition is brought to bear only under three phases, constituting three laws: 1st, The law of identity; 2d, The law of contradiction; 3d, The law of excluded middle; of which laws logic is the science. Of these laws we will treat in their order, and explicate the import or logical significance of each.

The principle of identity expresses the relation of total sameness in which a product of the thinking faculty, be it concept, judgment, or reasoning, stands to all, and the relation of partial sameness in which it stands to each, of its constituent characters. This principle is the special application of the absolute equivalence of the whole and its parts taken together, applied to the thinking of a thing, by the attribution of its constituent or distinctive characters. In the predicate the whole is contained explicitly, and in the subject implicitly. The logical significance of the law lies in this, that it is the principle of all logical affirmation, of all logical definition.

The second law, that of contradiction, is this: What is contradictory is unthinkable. Its principle may be thus expressed: When a concept is determined by the attribution. or affirmation of a certain character, mark, note, or quality, the concept cannot be thought to be the same when such character is denied of it. Assertions are mutually contradictory, when the one affirms that a thing possesses, or is determined by the characters which the other affirms it does not possess,

or is not determined by. The logical significance of this law consists in its being the principle of all logical negation, or distinction.

The laws of identity and contradiction are co-ordinate and reciprocally relative; and neither can be deduced from the other, for each supposes the other.

The third law, called the principle of excluded middle, embraces that condition of thought which compels us, of two contradictory notions (which cannot both exist, by the law of contradiction) to think either the one or the other as existing. By the laws of identity and contradiction, we are warranted to conclude from the truth of one contradictory to the falsehood of the other; and by the law of excluded middle, we are warranted to conclude from the falsehood of one to the truth of the other. The logical significance of this law consists in this, that it determines that, of two forms given in the laws of identity and contradiction, and by these laws affirmed as those exclusively possible, that of these two only possible forms, the one or the other must be affirmed as necessary of every object. This law is the principle of disjunctive judgments, which stand in such mutual relation, that the affirmation of the one is the denial of the other.

These three laws stand to each other in relation like the three sides of a triangle. They are not the same, not reducible to unity, yet each giving, in its own existence, that of the other. They form one principle in different aspects.

These laws are but phases of that condition of the thinkable which stipulates for the absolute absence of non-contradiction. Whatever, therefore, violates these laws is impossible, not only in thought, but in existence; and they thus determine for us the sphere of possibility and impossibility, not merely in thought, but in reality. They are therefore not wholly logical, but also metaphysical. To deny the universal application of these laws is to subvert the reality of thought; and as the subversion would be an act of thought, it annihilates itself. They are therefore insuperable.

There is a fourth law, which is a corollary of these three primary laws, called the law of reason and consequent, which is so obtrusive in our reasoning that it needs to be specially considered. The logical significance of this law lies in this, that in virtue of it, thought is constituted into a series of acts indissolubly connected, each necessarily inferring the other. The mind is necessitated to this or that determinate act of thinking, by a knowledge of something different from the thinking process itself. That which determines the mind is called the reason; that to which the mind is determined is called the consequent; and the relation between the two is called the con

sequence. By reason of our intelligent nature, there is a necessary dependence of one notion upon another, from which all logical inference results as an inevitable consequent. This inference is of two kinds. It must proceed from the whole to the parts, or from the parts to the whole. When the determining notion (the reason) is conceived as a whole containing (under it), and therefore necessitating the determined notion (the consequent) conceived as its contained part or parts, argumentation proceeds, by mental analysis, from the whole to the parts into which it is separated. When the determining notion is conceived as the parts constituting, and therefore necessitating the determined notion conceived as the constituted whole, argumentation proceeds, by mental synthesis, from the parts to the whole. The process from the whole to the parts is called deductive reasoning; the other process, from the parts to the whole, is called inductive reasoning. There is therefore in logic a deductive syllogism and an inductive syllogism. The former is governed by the rule:- What belongs (or does not belong) to the containing whole, belongs (or does not belong) to each and all of the contained parts. The latter by the rule:What belongs (or does not belong) to all the constituent parts, belongs (or does not belong) to the constituted whole. These rules exclusively determine all formal inference; whatever transcends or violates them transcends or violates logic.

Sir William Hamilton was the first to discriminate accurately the difference between the deductive and the inductive syllogism. All that had been said by logicians-except Aristotle, and he is brief, and by no means unambiguous-on logical induction, is entirely erroneous; for they all, including Whately, confound logical or formal induction with that which is philosophical, and material, and extra-logical. They consider logical induction not as governed by the necessary laws of thought, but as determined by the probabilities of the sciences from which the matter is borrowed. All inductive reasoning, logical and material, proceeds from the parts (singulars) to the whole (universal); but in the formal or subjective, the illation is different from that in the material or objective. In the former, the illation is founded on the necessary laws of thought; in the latter, on the general or particular analogies of nature. The logician knows no principle but the necessary laws of thought. His conclusions are necessitated, not presumed.

All this confusion was produced by the introduction into formal logic of various kinds of matter. Aristotle himself corrupted logic in this way; and Sir William Hamilton has been the first to expel entirely this foreign element, and to purify logic from the resulting errors, though Kant had done much towards the same result. When we reflect, that the