seems to have maintained it from what he says in many parts of his 'Elements", nevertheless what he really meant is, that Logic does not treat of reasoning apart from, but only as expressed in, language. "If any process of reasoning," says he, "can take place in the mind without any employment of language, orally or mentally, such a process does not come within the province of the science here treated of 2." Whately really adopted the subject-matter of the first view, and only the phraseology of the third. This is also evident from his definition of Logic 'as the science and also as the art of reasoning.'

§ 5. Hamilton adopts the first view, and defines Logic as "the science of the laws of thought as thought, or the science of the formal laws of thought, or the science of the laws of the form of thought," that is, as the science of those universal laws or principles to which thought must conform in order that its products, viz., concepts, judgments, and reasonings, may be valid. Hamilton uses the word valid to mean free from inconsistency or self-contradiction, and by laws of thought he means only the fundamental principles of consistency, that is (1) the Principle of Identity, (2) the Principle of Contradiction, and (3) the Principle of Excluded Middle. The first means that A is A, that a thing is what it is, that while 'A' is 'A,' it cannot be anything else. The second means that A cannot be both B and not-B, at the same time, in the same place, and in the same respect. If the proposition 'A' is 'B' be true, then the proposition “A is

1 Whately writes, for example:-"Logic is entirely conversant about language." Again, "It (Logic) is, therefore (when regarded as an art), the art of employing language properly for the purpose of reasoning and of distinguishing what is properly and truly an argument from spurious imitations of it.”—Elements, 9th Edition, p. 37. 2 Whately's Elements, 9th Edition, p. 37.

3 Lectures, Vol. ш. pp. 25, 26. See also pp. 4, 17, 24. On p. 24 Hamilton defines Logic as 'the science of the necessary forms of thought,' and afterwards developes this definition into the expression given in the text. By 'thought as thought' Hamilton means 'the form of thought to the exclusion of the matter' (p. 15).

not-B" cannot be true. If a thing be red, it cannot at the same time be not-red. It may lose redness afterwards, or, it may not be red in all its parts; but if any part of it be red, that same part cannot be not-red at the same time, The third means that one or other of two contradictory terms must be true of one and the same thing, the middle or the mean between them being excluded. A is either B or not-B'. Here'B' and' not-B' are two contradictory terms, and A must be one or other of the two. It cannot be neither. "This thing is either red or not-red'; this proposition means that the thing must be one or the other, 'red' or 'not-red'-i. e. if not 'not-red' then 'red'; and if not 'red,' then 'not-red.' It cannot be anything else than either 'red' or 'not-red.' The two concepts, 'red' and 'not-red' cover the whole sphere of thought and existence; and every possible as well as real object must be one or the other. It is evident that the concept 'not-red' is so indefinite, that it, in fact, includes every thing real or imaginary except 'red'.

According to Hamilton, if a thought does not violate any of the above three laws of thought, then it is valid; and the science of Logic is entirely conversant about the forms or the uniform and constant modes of thinking in conformity to those laws, to the entire exclusion of the matter of thought. He does not require that the products of thought must agree with actual realities; the only condition which they must fulfil, according to him, is that they must be free from self-contradiction or inconsistency.

§ 6. In his Examination of Hamilton's Philosophy, Mill adopts the first view with the qualification that the products of thought must not only be formally valid, but true or objectively real. He defines Logic as "the art of thinking, which means of correct thinking, and the science of the conditions of correct thinking," that is, "the science of the conditions on which right concepts, judgments, and reasonings depend."

The products of thought, according to Mill, should be not only free from inconsistency or self-contradiction, i. e., valid in Hamilton's sense, but must also be true, i. e., 'agree with the

reality of things.' A concept 'must be a concept of something real, and must agree with the real fact which it endeavours to represent, that is, the collection of attributes composing the concept must really exist in the objects marked by the classname.' A judgment must be a true judgment, that is, the objects judged of 'must really possess the attributes predicated of them.' A reasoning 'must conduct to a true conclusion1.'

In the work referred to Mill thus really adopts the subjectmatter of the second view, and only the phraseology of the first. The qualification introduced by him into the first view as noticed above has really the effect of changing it into the second2.

In his System of Logic Mill adopts the phraseology of the third view, but always refers to the second for the real import or meaning of his names, propositions, and arguments. He, in fact, holds the second view, and takes the subject-matter of Logic to be what it is according to that view, though in his treatment of the science he freely uses the phraseology of the third2.

§ 7. Herbert Spencer adopts the second view, and defines Logic as the science which "formulates the most general laws of correlation among existences considered as objective," as the science which "contemplates in its propositions certain connexions predicated, which are necessarily involved with certain other connexions given; regarding all these connexions as existing in the Non ego-not it may be, under the form in which we know them, but in some form3."

§ 8. We shall not confine ourselves to any of these views. But regarding Logic as primarily or immediately concerned with thought, and, secondarily, or as a means to an end, with language in which thought is expressed, and ultimately with attributes and things, mental or material, real or imaginary, the objectmatter of all thought, we shall freely adopt the phraseology of any or all of them, whenever this seems desirable for purposes of explanation and illustration.

1 Mill's Examination of Hamilton's Philosophy, 4th ed. pp. 564, 470. 2 See Appendix E.

3 Spencer's Principles of Psychology, 2nd ed. Vol. 11. p. 87.

§ 9. The relation of Logic to the other sciences is shown in the following tabular views :

In the first table the mental and the material sciences are placed in two separate series, and Logic and Mathematics are

placed above both, as their principles are equally applicable to the sciences in the two series. Logic is placed above Mathematics, as it is the most general and abstract of all sciences, as its principles are applicable to Mathematics as well as to the other sciences.

In the second table the same relation is shown by placing Logic at the top, and Mathematics next to it. The other sciences are arranged in order of generality, the one lying above being more general than the one lying below. Thus Mathematics is more general than Physics, the latter more general than Chemistry, and so forth. The relation of Logic as a Practical Science dependent upon the Psychology of Cognition is shown in the second table.

§ 10. The end of Logic as defined here is the attainment of truth so far as truth can be obtained by thinking, that is, by the processes of naming, definition, classification, generalization, inference, &c., employed upon the data, or materials, supplied by direct observation, experiment, perception, or intuition. Some logicians (Ueberweg, for example) have indeed made all truth the end of Logic, and defined it as "the science of the regulative principles of human knowledge1," that is, of all knowledge both intuitive and inferential, immediate and mediate. But, following the British Logicians in general, I have defined Logic so as to exclude intuitive truth from its scope and province. According to Ueberweg, perception and percepts are as much a part of Logic as conception, judgment, and reasoning, while all British Logicians, whatever their differences may be on other points, agree in excluding intuition and intuitive truth from the jurisdiction of Logic 2.

Truth is the agreement of thought with its object, and is said to be either formal or real. It is real when the object of thought actually exists,—is something either material or mental. It is

1 Ueberweg's Logic, English Translation, p. 1.

2 See Ueberweg's Logic, pp. 1, 17, 77, 78; and Mill's Logic, Vol. I. pp. 5, 6, 8.