monstrative. Indeed, in respect of their demonstrative character, "Logic and Mathematics stand alone among the sciences, and their peculiar certainty flows from the same source. Both are conversant about the relations of certain a priori forms of intelligence-Mathematics about the necessary forms of imagination, Logic about the necessary forms of understanding. Both are thus demonstrative or absolutely certain sciences, each developing what is given as necessary in the mind itself."" Hence Kant, followed by Esser, who in turn is followed by Hamilton, defines Logic to be the science of the necessary forms of thought.'

16

Such is the definition of Pure Logic. It excludes Psychology. We have already seen that it excludes Applied Logic. If we adhere to it, we must reject also Modified Logic as not properly any part of the science. For Modified Logic considers thought "not as determined by its necessary and universal laws, but as contingently affected by the empirical conditions under which thought is actually exerted, showing what these conditions are, how they impede, and, in general, modify the act of thinking; and how, in fine, their influence may be counteracted." Treatises on Concrete or Applied Logic, and on Modified Logic, may be valuable appendices to works on Logic, but they constitute no part of the pure science.1

99 17

18

§ 6. As an expressive synonym for Logic we have adopted the phrase "Theory of Thought." Theory is properly opposed to practice. Theory is mere knowledge; practice is the application of it."

15 Hamilton's Logic, p. 31.

16 It will be seen hereafter that the "necessary forms of thought" corresponds to the old logical phrase "second intentions." Hence an excellent definition of Logic, were not the phrase obscure, would be "the science of second intentions." See pt. ii, ch. iv, § 8.

17 Hamilton's Logic, p. 43.

18 On the title-page occurs the phrase "Deductive Logic,” to indicate the absence of any treatment of Induction in the present work. The importance of Induction cannot be overestimated, but it calls for a distinct treatise. We often hear the phrase "Inductive Logic." But induction is not correctly, etymology apart, opposed to Deduction, and all Logic proper is Deductive Logic.

"With Plato 0εwptiv is applied to a deep contemplation of the truth. By Aristotle it is always opposed to párтe, and to Tour, so that he makes philosophy theoretical, practical, and artistical. The Latins and Boethius rendered Owpɛiv by speculari.-Trendelenburg's Element. Log. Arist. p. 76. See also, on theory and practice, Hamilton's Metaphysics, p. 120.

Theory denotes the most general laws to which certain facts can be reduced. It is a collection of the inferences drawn from facts and compressed into principles; it is a systematized explanation of facts demonstrably true. Logic is such a systematized collection of the laws that govern thinking, and it is occupied with demonstrating their validity from certain axioms. It is, therefore, properly called the Theory of Thought.

§ 7. It is evident that a work strictly limited by the definition of pure Logic would be very abstract and difficult. Being a discussion of forms, it could offer no examples; for since a pure abstract form cannot be realized in consciousness apart from matter, much less can it be expressed. Even in general expressions by algebraic symbols, the symbols themselves are a species of matter that is extralogical.

Again, if the treatise be kept strictly apart from Psychology, it will admit of no reference to actual thinking. It will tell us nothing of how the mind does actually proceed in its efforts to systematize its knowledge, nothing of the nature of the thinking act as giving rise to the logical product, nothing of the phenomena of illegitimate thinking. Thus our science would be shorn of its rays.

Consequently, few, if any, writers have allowed themselves to be rigidly bound by the definition. In the present treatise, while we make pure, abstract Logic its basis, while developing systematically the Theory of Thought, and keeping this prime object constantly in view, we shall freely transgress the limits of the definition whenever it seems desirable. We shall consider not merely how the mind must think, but how it does think. We shall give copious concrete illustrations, and analyze and exhibit actual exercises of thought, appealing to observation and to the experience of consciousness to corroborate the theory, just as the astronomer turns to the stars to observe the fulfilment of the laws of the Mécanique Céleste.

II. PRIMARY LAWS.

§ 1. In the study of Psychology we find by subjective analysis that there are certain modes of intelligence to which the mind is necessitated by virtue of its essential and original constitution. Among others are certain forms of thought determined or necessitated by the nature of the thinking subject itself. The chief of these necessary forms are, the concept, the judgment, the reasoning. By saying that these forms are necessary is meant that the mind cannot truly think except in them. But since they are native and necessary, they must be universal, both in the sense that they are found in every human mind, and in the sense that all the thoughts of each mind are always determined in them. For it cannot be that a form is necessary on some occasions and not on others. If so, it would be merely contingent, which contradicts our notion of necessity. Now, the forms being necessary and universal, we may view them as governed by necessary laws. These laws will be an expression of the general abstract principles common to the forms, and, as the result of a complete analysis, will be ultimate and axiomatic. When evolved and enunciated, they are known as Logical Principles, or as the Primary or Fundamental Laws of Thought."

Again, if, preliminary to pure Logic, products of thought viewed objectively as embodied in language are subjected to a critical analysis, they are found to exhibit general or universal forms. In other words, if from the various manifestations of thought in speech and literature we abstract the matter and all differences characterizing them, we discover a residuum common to all, a mode, a manner, having certain forms that belong to all, that interpenetrate all. These forms, being universal, are considered as governed by laws; and these laws, when enunciated, are found to be the same as those obtained by subjective analysis. Thus the two processes are mutually corroborative.

This complement of laws is assumed by Logic as its punctum saliens, and it proceeds to demonstrate synthetically from them as

For the history of these laws, see Hamilton's Logic, pp. 62-68.

axioms the secondary or special laws of the concept, the judgment, the reasoning. The whole of pure Logic is only an articulate development of these Primary Laws, and of the various modes in which they are applied.

To say that these self-evident laws are necessary, is to say that the contradictory of each is inconceivable. It is not that they are inviolable, not that the mind is constrained of necessity to obey them, as a planet is blindly constrained to obey the laws of gravitation, inertia, etc. They are violable in the sense that we may wilfully or unconsciously disregard them; but the result is fallacy, inconsequence; or, rather, the mental process is then suicidal or absolutely null and void. All consequent thinking must be legitimate; i. e., it necessarily conforms to these laws, advertently or inadvertently. They are the primary conditions of the possibility of valid thought."

The reader must not be offended to find these axiomatic laws so obvious as to seem mere truisms. When stated, they appear to have been always known, being implied in every thought we have ever experienced or observed, though until stated we are as unconscious of them as we are of the laws that govern our breathing. Being the widest generalities, penetrating every science, and, indeed, governing every mental movement that comprehends anything, they seem of all things the most familiar and trite. Their very truth requires that they contain nothing new. Standing related to the axioms of geometry as these are related to elaborate propositions, they at first appear singularly meagre, barren of significance, and even frivolous. But if these laws are really the code by which all human thought is actually regulated, then their study is not futile; so far from being barren, they are the most wonderfully productive of principles; so far from being frivolous, they have the profoundest significance.

§ 2. The Primary Laws of thought are three. The first is the Law of Identity. It is the principle of all logical affirmation. It is variously enunciated: e. g., Whatever is, is, or Omne ens est ens; Everything is equal to itself; Every object of thought is conceived as itself; A thing is what it is; Conceptions which agree can be united in thought, or affirmed of the same subject at the same time. The formula is AA; or A=a'+a"+a"

The following are examples: "4=4;" "4=2x2;" "2+2= 2×2;" "4=3+1," etc.; "According to Plato, The Idea is equal to itself;" "Man's a man for a' that;" "Saltpetre is nitrate of potash ;" "Francis Bacon was Baron Verulam ;" "Francis Bacon was the father of inductive philosophy;" "Man is rational and animal;" "Man is the last creation;" "Man is the only being that laughs;" "A habit is a habit;" What I have written, I have written."

Hamilton extends this law to include the relation of partial identity or sameness in which a concept stands to each of its constituents, as expressed in the second formula. E. g., "Man is rational," i. e. my notion "Man" comprehends the notion "rational" as one of its constituents;-similarly, "Man is animal." We may go further, to the part of a part. E. g., The notion animal comprehends the notion corporeal, and we may say, "Man is corporeal." In this extension of the law, the predicate is only a part of what is implicated in the subject.

To affirm that a thing is itself seems to be solemn trifling, and is ridiculed by Locke. Nulla propositio est verior illa in qua idem prædicatur de seipso." When, however, we consider that every object of thought has definite characteristics by which it is marked off and distinguished from all others as being itself and nothing else, it is evident that every concept may be viewed in relation to these characteristics, and that these two several aspects must be affirmed of each other. The law then declares the necessity of thinking the concept and its constituent characters as the same. A better expression of it would perhaps be: A notion and its constituents are the same. This is a more general expression of the axiom: A whole is equal to the sum of its parts. In the predicate, the whole is contained explicitly which in the subject is contained implicitly.

It is obvious that this law enjoins self-consistency; or, rather, it is the necessity for self-consistency in thought that is formulated in this law. Whatever be the aspects of a thing, whatever be the modes of statement concerning it, they must be equivalent; the thought underlying each must be the same.

§ 3. The second is the Law of Contradiction. It is the principle of all logical negation. Enunciations are: The same attribute. cannot be at the same time affirmed and denied of the same sub