intensive (or compreHaving adopted the

Note. The distinction between the denotation and connotation of a term is often otherwise expressed, as that between the extension and intension (or comprehension), or the extensive and hensive) capacity, of a notion. phraseology which designates the simplest product of thought as a term, instead of a notion, we shall speak of the extensive and intensive (or comprehensive) capacity of a term. The extensive capacity of a term is measured by the number of individuals which it designates (denotes), the intensive or comprehensive capacity of a term by the number of attributes which it includes or suggests (connotes). It is plain that in a series of common terms, standing to one another in a relation of subordination, the denotation and connotation, or the extensive and intensive capacities, of the term are so related, that as the one increases the other decreases, and vice versâ. Thus, if we arrange in order any series of common terms, as flower, rose, moss-rose, we see that 'flower,' which implies the smallest number of attributes, is applicable to the largest number of individuals ; 'moss-rose,' which is applicable to the smallest number of individuals, implies the largest number of attributes: and generally in any series of common terms arranged in subordination, the larger the denotation or extensive capacity, the smaller is the connotation or intensive capacity, and vice versâ. In conformity with this principle, the singular term which stands for the individual and is smallest in denotation, is, when we refer it to

the various common terms which may be predicated of it, and so assign to it mediately an intensive capacity, the largest in connotation. Thus the term Socrates, when I regard it as expressing one who was a philosopher, a teacher, a martyr, a soldier, an Athenian citizen, &c., &c., suggests to me far more attributes than any one of these common terms singly.

PART II.-THE PROPOSITION.

CHAPTER I.

On the Subject and Predicate.

A PROPOSITION, as the result of comparison, asserts or denies some word or combination of words of some other word or combination of words, as e. g. 'James is the man I saw yesterday;' 'No rectilineal figure is contained by less than three lines;' 'Some stars are not planets.' As before stated, the words or combinations of words thus employed are called terms, the term affirmed or denied is called the predicate, the term of which it is affirmed or denied the subject, the connecting verb, whether qualified or not by the negative particle, the copula, and the predicate is said to be predicated of the subject. In the above examples, 'the man I saw yesterday,' 'contained by less than three straight lines,' and 'planets' are predicates and are predicated respectively of 'James,' 'all rectilineal figures,' and 'some stars' as subjects. In the first case the predicate is predicated affirmatively, a fact which is expressed by the copula 'is;' in the two last negatively, a fact which is

expressed by the copula 'is not.' These remarks may appear inconsistent with the form of the second example, but no rectilineal figure is &c.' is really an abbreviated and unambiguous mode of stating the longer and ambiguous proposition 'All rectilineal figures are not, &c.'

The word 'predicated,' as equivalent to asserted or denied,' is here used in a wider than its ordinary signification. In common language, we say such and such an attribute cannot be predicated of such and such a term, using 'predicated' as equivalent to 'asserted' and as opposed to 'denied.' All ambiguity may be avoided by speaking of the predicate as predicated affirmatively or predicated negatively of the subject.

CHAPTER II.

On the Copula.

THE Logical Copula, it being its office simply to serve as a sign of predication, is limited to the present tense of the verb 'to be,' with or without the addition of the negative particle, according as the proposition is negative or affirmative. This follows from the fact that it is simply the office of the proposition to express my present judgment as to the compatibility or incompatibility of two terms. Hence all reference to time, past or future, and even to time present, as respects the terms themselves, and not my judgment as to their compatibility, must be expressed in the predicate and not in the copula. I may, for brevity's sake, say 'fire burns,' 'Alexander was the son of Philip,' 'The guns will be fired to-morrow,' and, in conversation or discussion, it would undoubtedly be pedantic to express these propositions otherwise; but formally, for the purpose of being estimated logically, I must resolve them into their logical elements, and say 'Fire is burning,' 'Alexander is a person who was son of Philip,' 'The firing of the guns is an event which will take place to-morrow.'

Not only does the logical copula convey no notion of