an indefinite extent of logical arguments immediately deducible from the principle of substitution of which the ancient syllogism forms but a small and not even the most important part.

The Logic of Relatives.

There is a difficult and important branch of logic which may be called the Logic of Relatives. If I argue, for instance, that because Daniel Bernoulli was the son of John, and John the brother of James, therefore Daniel was the nephew of James, it is not possible to prove this conclusion by any simple logical process. We require at any rate to assume that the son of a brother is a nephew. A simple logical relation is that which exists between properties and circumstances of the same object or class. But objects and classes of objects may also be related according to all the properties of time and space. I believe it may be shown, indeed, that where an inference concerning such relations is drawn, a process of substitution is really employed and an identity must exist; but I will not undertake to prove the assertion in this work. The relations of time and space are logical relations of a complicated character demanding much abstract and difficult investigation. The subject has been treated with such great ability by Professors Peirce, De Morgan, Ellis', and Harley, that I will not in the

Description of a Notation for the Logic of Relatives, resulting from an Amplification of the Conceptions of Boole's Calculus of Logic.' By C. S. Peirce.Memoirs of the American Academy,' vol. ix. Cambridge, U.S., 1870.

y On the Syllogism, No. IV, and on the Logic of Relations.' By Augustus De Morgan. 'Transactions of the Cambridge Philosophical Society,' vol. x. part ii. 1860.

z 'Observations on Boole's Laws of Thought.' By the late R. Leslie Ellis; communicated by the Rev. Robert Harley, F.R.S. 'Report

present work attempt any review of their writings, but merely refer to the publications in which they are to be found.

of the British Association,' 1870. 'Report of Sections,' p. 12. Also, 'On Boole's Laws of Thought.' By the Rev. Robert Harley, F.R.S., ibid. p. 14.

CHAPTER II.

TERMS.

EVERY proposition expresses the resemblance or difference of the things denoted by its terms. As reasoning or inference treats of the relation between two or more propositions, so a proposition consists in a relation between two or more terms. In the portion of this work which treats of deduction it will be convenient to follow the usual order of exposition, and consider in succession the various kinds of terms, propositions, and arguments, and we commence in this chapter with terms.

The simplest and most palpable meaning which can belong to a term consists of some single material object, such as Westminster Abbey, the Sun, Sirius, Stonehenge, &c. It is probable that in the earliest stages of intellect only concrete and palpable things are the objects of thought. The youngest child knows the difference between a hot and a cold body. The dog can recognise his master among a hundred other persons, and animals of much lower intelligence know and discriminate their haunts. In all such acts there is judgment concerning the likeness or unlikeness of physical objects, but there is little or no power of analysing each object and regarding it as a group of qualities or circumstances.

The dignity of intellect begins with the power of separating points of agreement from those of difference. Comparison of two objects may lead us to perceive that

they are at once like and unlike. Two fragments of rock may differ entirely in outward form, yet they may have the same colour, hardness, and texture. Flowers which agree in colour may differ in odour. The mind learns to regard each object as an aggregate of qualities, and acquires the power of dwelling at will upon one or other of those qualities to the exclusion of the rest. Logical abstraction, in short, comes into play, and the mind becomes capable of reasoning, not merely about objects which are physically complete and concrete, but about things which may be thought of separately in the mind though they exist not separately in nature. We can think of the hardness of a rock, or the colour of a flower, and thus produce abstract notions, denoted by abstract terms which will form a subject for further consideration.

At the same time arise general notions and classes of objects. We cannot fail to observe that the quality hardness exists in many objects, for instance in many fragments of rock; and mentally joining these we create the class hard object, which will include, not only the actual objects examined, but all others which may happen to agree with them as they agree with each other. As our senses cannot possibly report to us all the contents of space, we cannot usually set any limits to the number of objects which may fall into any such class. At this point we begin to perceive the power and generality of thought which enables us at once to treat of indefinitely or even infinitely numerous objects. We can safely assert that whatever is true of any one object coming under a general notion or class is true of any of the other objects so far as they possess the common qualities implied in their belonging to the class. We must not place an individual thing in a class unless we are prepared to believe of it all that is believed of the

class in general; but it remains as a matter of important consideration how far and in what manner we can safely undertake thus to assign the place of objects in that general system of classification which constitutes the whole body of science.

Twofold Meaning of General Names.

Etymologically the meaning of a name is what we are caused to think of when the name is used. Now every general name causes us to think of some one or more of the objects belonging to a class; it may also cause us to think of the common qualities possessed by those objects. A name is said to denote the distinct object of thought to which it may be applied; it implies at the same time the possession of certain qualities or circumstances. The number of objects denoted forms the extent of meaning of the term; the number of qualities implied forms the intent of meaning. Crystal is the name of any substance of which the molecules are arranged in a regular geometrical manner. The substances or objects in question form the extent of meaning; the circumstance of having the molecules so arranged forms the intent of meaning.

When we compare a variety of general terms it may often be found that the meaning of one is included in the meaning of another. Thus all crystals are included among material substances, and all opaque crystals are included among crystals: here the inclusion is in extension. We may also have inclusion of meaning in regard to intension. For as all crystals are material substances, the qualities implied by the term material substance must be among those implied by crystal. Again, it is obvious that while in extension of meaning opaque crystals are but a part of crystals, in intension of meaning