only partially so, i. e., only so far as the validity of the inference is concerned. The principles governing the former kind of ratiocination constitute what is called Apodictic; those governing the latter, Dialectic. It will be seen as we progress that Apodictic is far more extensive in its scope or use than is commonly supposed, and that it includes, in fact, not only the Mathematical Sciences, both pure and applied, but also a large part of Morality, Politics, and Jurisprudence generally. And especially, it is important to observe, it includes the subject of our present investigations. For Logic, though not so treated by modern logicians, is strictly a demonstrative science, and will be so treated in this essay.'

24. VALID RATIOCINATION ILLATIVE IN NATURE. All ratiocination, or reasoning explicitly stated, discloses at once its validity or invalidity that is to say, appears on its face to be either conclusive in its effect, or fallacious. Hence, all ratiocination, unless fallacious, is illative or conclusive, or, we may say, demonstrative in its nature. On the other

1 One of the most universal infirmities of the average mind is an incapacity to distinguish (outside the mathematics) between mere opinion and apodictic, or demonstrated truth. With regard to the latter, the man who is conscientious and accurate in his Logic may realize the fine saying of Seneca: "It is truly great to have in one the frailty of a man and the security of a god" (cited Bacon, Essays, “Of Adversity").

hand, unless explicitly stated, no reasoning, however apparently convincing, can be regarded as of this nature. Hence, from a logical point of view, reasoning in general may be regarded as either valid (i. e., illative), or as invalid; the latter of which may be either fallacious or simply inconsequent. The former may be appropriately called Logical Reasoning, the latter Non-logical or Rhetorical; by which is meant not necessarily illogical or fallacious, but either fallacious or simply inconsequent, i. e., non-illative.

$ 25. RIGHT REASONING DEFINED.-It is with the former only that Logic is directly concerned, and to it we may without impropriety give the name of Right Reasoning. For the logical quality of the reasoning does not depend upon the truth or falsity of the conclusion, but upon the rectitude of the definitions, judg ments, and inferences.

26. LOGIC THE ART OF RIGHT REASONING.- Logic, therefore, regarded as an art, may be simply defined as the Art of Right Reasoning; and it must therefore be regarded as denoting the ultimate test or criterion of truth or error. For until the reasoning is made explicit, it cannot be determined whether it is right or otherwise. It also includes the doctrine of Fallacy, or Wrong Reasoning; but as the latter has for its end simply the

avoidance of error, as a means of assuring the rectitude of our reasoning, it may be regarded simply as one of the practical aspects of the doctrine of Right Reasoning.

27. LOGIC TO BE REGARDED AS INTELLECTUAL MORALITY.-Logic must, therefore, be regarded as bearing to reasoning the same relation as Morality to conduct. It may, therefore, be appropriately called Intellectual Morality.'

1 Hence it is that Logic, like Morality, is not popular with those who disregard its precepts; among whom are to be included the large majority of writers, and especially of philosophers. The principle is as expressed in the adage:

"What thief e'er felt the halter draw

With good opinion of the Law?"

CHAPTER II

DOCTRINE OF THE TERM

I

OF THE NATURE OF THE TERM

28. TERM," NAME," AND "WORD" DISTINGUIShed and DeFINED.—These words are often used as synonymous, but the distinction between them is material and important. A word is a vocal sign, or vocable, expressing a thought, or a thought expressed by such a sign. Under the name "word" is included the substantive or noun, and also other parts of speech, as, e. g., the article, the conjunction, etc. A name (noun or substantive, which may be either simple or complex) is a word or set of words used to signify an object of thought regarded as a thing, i. e., as an existing substance or entity. The knowledge or cognition of a thing by the mind is called a notion or concept; hence a name may be otherwise defined as a word, or set of words, expressing a notion, or

as a notion thus expressed.

A notion or concept is itself a thought, but it differs from other thoughts as being the thought of a thing, i. e., of something as existing. A term is a name used as a subject or predicate of a proposition. It is therefore to be regarded merely as an element of the proposition; and the proposition as the principal subject in Logic.

8 29. "THING" DEFINED. - The term thing is used in two different senses that must be carefully distinguished. In its proper sense the term denotes an actual thing or substance, whether material or spiritual, as, l. g., mineral, vegetable, animal, gas, man, soul, God, etc. In this sense things constitute the actual universe, and all notions or concepts whatever, unless false or unreal, are ultimately derived from them. But, in another sense, the term is used to denote, not only actual existences, or, as we may call them, real things, but mere objects of thought, or things existing only in contemplation of mind, and to which there are, in fact, no real things directly corresponding.' These These may be appropriately

'All true or real notions must correspond to real or actual things, but the correspondence may be either direct between the notion and the real things signified by the term - as in the case of concrete terms, e. g., "man," "horse," etc.; or indirect-as in the case of abstract terms between the notion and the things whose attributes are signified. Thus, taking for example the term "redness," there is apparently a