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 form 3.”

§ 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. ш. 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 Logic2.

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.

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

It is

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

formal when the object, whether actually existing or not, is simply free from any self-contradiction. The latter is the end of what is called Formal Logic, and the former of what is called Material Logic.

In Formal Logic, the concepts, judgments, and reasonings need not be really true. It is sufficient if they conform to the fundamental principles of consistency or laws of thought, as they are called, and be free from any inner contradiction or inconsistency. In Material Logic, also called by Mill the Logic of Truth, they must be true or right, and correspond to the realities actually existing; they must be valid not only formally, but also really; they must be free not only from any self-contradiction, but also from any inconsistency with reality, that is, a concept must be an attribute or a collection of attributes actually existing in things, a judgment, a relation between two true concepts, and a reasoning must lead to a conclusion that agrees with fact.

The end of Material Logic is thus the attainment of truth in the stricter and proper sense, that is, of real truth, while the end of Formal Logic is merely consistency or freedom from selfcontradiction,

Formal Logic is often called Pure Logic, and also the Logic of Consistency. Hamilton's definition of Logic, as given above, is a definition of Formal Logic, while Mill's and Spencer's are definitions of Material Logic. In the latter we are concerned with terms, propositions, and arguments that have reference to actual existences, while in the former we are concerned not with what is actual, but with what is possible, not with what is real in Nature, but with what may be realized in Thought. Formal Logic includes in its sphere all possible notions, judgments, and reasonings, or all possible attributes, and their relations, and does not confine itself to what is actual or real in Nature.

The definition which we have given at the beginning of this chapter is that of Formal or of Material Logic according as the word valid is taken to mean mere conformity to the principles of consistency, or agreement with reality, that is, according as it means merely formally valid or really valid and true. If the

products of comparison, namely, concepts, judgments, and reasonings, are required to agree with the actually existing things and phenomena, then our definition becomes the definition of Material Logic. If, on the contrary, they are required simply to be free from self-contradiction, then our definition becomes the definition of Formal Logic.

§ 11. Logic is usually regarded as consisting of three parts,— the first part treating of the process and products of conception; the second, of judgment; and the third, of reasoning or inference. To these three parts may be added a fourth, namely, Method, treating of the arrangement or disposing of a series of reasonings in an essay or discourse. Method has been defined as "the art of disposing well a series of many thoughts, either for discovering truth when we are ignorant of it, or for proving it to others when it is already known." "Thus there are two kinds of Method, one for discovering truth, which is called analysis, or the method of resolution, and which may also be termed the method of invention; and the other for explaining it to others when we have found it, which is called synthesis, or the method of composition, and which may be also called the method of doctrine1."

"Without stepping," says Professor Robertson, "beyond the bounds of Logic conceived as a formal doctrine, a fourth department under the name of method or disposing may be added to the three departments regularly assigned-conceiving (simple apprehension), judging, reasoning; and this would consider how reasonings, when employed continuously upon any matter whatever, should be set forth to produce their combined effect upon the mind. The question is formal, being one of mere exposition, and concerns the teacher in relation to the learner. How should results, attained by continuous reasoning, be set before the mind of a learner? Upon a line representing the course by which they were actually wrought out, or always in the fixed order of following from express principles to which preliminary assent is required? If the latter, all teaching becomes synthetic, and

1 Professor Baynes' Port Royal Logic, pp. 308-9.