denied of every thing belonging to that class; or, "what belongs to a higher class belongs to a lower." Some logicians maintain that it can be deduced from the three Laws of Thought, while others regard it as an independent axiom incapable of deduction from those laws.

(6) The fundamental axioms or canons of Syllogism as given by different logicians (Mill, Martineau, Thompson, Lambert, Whately, &c.1).

(7) The Mathematical Axioms :-(1) that of Argumentum à fortiori, namely, that “a thing which is greater than a second, which is greater than a third, is greater than the third"; (2) the axiom that "two things equal to the same thing are equal to each other"; and other axioms of a similar nature.

1 See below, Appendix A.

PART I-TERMS.

CHAPTER I.

THE VARIOUS DIVISIONS OF TERMS.

§ 1. A name may be defined as a sign for a thing or things. More accurately, it is a word, or a combination of words, signifying some object of thought, or something real or imaginary, mental or material, substantive or attributive, phenomenal or nöumenal. For example, the words 'animal,' 'plant,' 'flower,' 'table,' 'paper,' 'chair' are names of real things, while the words 'centaur,' 'golden mountain,' &c., are names standing for imaginary objects; the words 'mind,' 'soul,' 'spirit,' 'self,' &c., are names signifying mental things or substances, while the words 'gold,' 'silver,' 'mineral,' 'copper,' &c., are names standing for material things; the words 'sensation,' 'pleasure,' 'pain,' 'perception,' 'imagination,' 'memory,' &c., are names expressing attributes of mind, while 'solidity,' 'colour,' 'figure,' 'hardness,' &c., are words signifying attributes of matter; the words 'thinking,' 'perceiving,' 'feeling,' 'wishing,' 'hoping,' &c., are names expressing acts or phenomena of mind, while the words 'moving,' 'melting,' 'expanding,' 'cooling,' &c., are words signifying phenomena or changes of bodies; the words 'thing-in-itself,' 'matter-in-itself,' 'mind-in-itself,' are names expressing nöumena or realities which are believed to underlie all phenomena; and the

words 'substance,' 'substratum,' those in which attributes are supposed to be inherent.

A concept is the product of comparing two or more individual objects or things with a view to find out the attribute or attributes in which they all agree. Regarded objectively, it is an attribute, or a collection of attributes, which is possessed in common by a number of individual things; and, regarded subjectively, it is an idea or notion corresponding to that attribute or collection of attributes, It is signified or expressed in language by a word, or combination of words, called a name or term.' It may be symbolized by any sign whatever. For example, any letter of the alphabet, or any other sign, may be made to stand for any concept. Conception usually means the process of forming concepts; but it is sometimes used for the product also, and is, then, taken by some logicians to signify an idea corresponding to an individual thing as well as an idea corresponding to an attribute or a group of attributes common to a number of individuals. The former is called by them an individual conception, and the latter a general conception, or notion. For example, an idea corresponding to an individual thing, such as a particular man, animal, tree, or flower, is an individual conception, while an idea corresponding to an attribute or collection of

attributes possessed in common by a number of individual things, such as men, animals, trees, or flowers, is a general conception. Objectively regarded, an individual conception is an individual thing itself, while, subjectively, it is an idea of the thing.

The process of forming concepts may be regarded as consisting of the following steps: (1) the observation of individuals; (2) the analysis of each of them into its constituent attributes; (3) the comparison of them with one another, in order to find out the attributes in which they all agree, and to separate these from those in which they differ; (4) the mental unification, if possible, of these common attributes, that is, the thinking of them together or the making of the aggregate of them a single object of thought; (5) the expression or symbolization of this aggregate, or single object of thought, by an audible, visible, or other sign, usually by a word or combinatian of words, called a name or term. For example, in forming the concept 'metal,' (1) different individual metals, such as gold, silver, copper, mercury, platinum, &c., must be observed and experimented upon; (2) the attributes of each of them must be found out by physical and chemical methods;' . (3) they must be compared with one another in order to find out the attributes in which they agree; (4) these attributes, when found out, must be thought of together; and (5) symbolized for reference afterwards as well as for communication to others, by a word, or some other sign. The concepts 'man,' 'horse,' 'plant,' 'animal,' 'book,' 'table,' 'element,' 'flower,' &c., are formed in the same manner.

A term, in the wider sense, is a name. It is the expression in language of a concept or of an individual or individuals. In the narrower sense, it is the subject or the predicate of a proposition, that is, that of which something is said, or that which is said about something, in a sentence or proposition. For example; the words 'man,' 'horse,' 'plant,' 'flower,' and the combinations of words 'flowering plant,' 'elementary substance,' 'elements that conduct heat and electricity,' 'animals that live in water,' 'the smell of a flower,' are terms in the wider sense, but not in the narrower sense, in which they must be either the subject or

the predicate in a proposition, that is, either they must be affirmed or denied of something, or something must be affirmed or denied of them; in other words, a term, in the narrower sense, is a part of a sentence, while, in the wider sense, it is a name, whether part of a sentence or not. Every term or name, though it may not actually form, is capable of forming either the subject or the predicate of a proposition, that is, something may be affirmed or denied of it, or it may be affirmed or denied of something; and this is the best test by which a term or name may be distinguished from a mere word or combination of words. Terms are divided by logicians into certain broad divisions, which are given below in a tabular form :—

§ 2. The first division of terms is into single-worded and many-worded. A single-worded term consists of a single word, while a many-worded term consists of a combination of words. For example, the terms 'man,' 'metal,' 'animal,' 'paper,' are single-worded; while the terms 'wise man,' 'rational animal,' 'white paper,' 'yellow flower,' are many-worded. A many-worded term may consist of any number of words from two upwards. It may consist of nearly the whole of a sentence or paragraph, provided that it expresses some object of thought, or something of which something may be affirmed or denied, or which may be