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THERE is no part of the doctrines of Logic to which I would more urgently request the attention of the reader than to that which I will endeavour to explain clearly in the present Lesson. I speak of the double meaning which is possessed by most logical terms—the meaning in extension, and the meaning in intension. I believe that the reader who once acquires a thorough apprehension of the difference of these meanings, and learns to bear it always in mind, will experience but little further difficulty in the study of logic.

The meaning of a term in extension consists of the objects to which the term may be applied; its meaning in intension consists of the qualities which are necessarily possessed by objects bearing that name. A simple example will make this distinction most apparent. What is the meaning of the name “metal”? The first and most obvious answer is that metal means either gold, or silver, or iron, or copper, or aluminium, or some other of the 48 substances known to chemists, and considered to have a metallic nature. These substances then form the plain and common meaning of the name, which is the meaning in extension. But if it be asked why the name is applied to all these substances and these only, the answer must be—Because they possess certain qualities which belong to the nature of metal. We cannot, therefore, know to what substances. we may apply the name, or to what we

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may not, unless we know the qualities which are indispensable to the character of a metal. Now chemists lay these down to be somewhat as follows:-(1) A metal must be an element or simple substance incapable of decomposition or separation into simpler substances by any known means. (2) It must be a good conductor of heat and electricity. (3) It must possess a great and peculiar reflective power known as metallic lustre*.

These properties are common to all metals, or nearly all metals, and are what mark out and distinguish a metal from other substances. Hence they form in a certain way the meaning of the name metal, the meaning in intension, as it is called, to distinguish it from the former kind of meaning.

In a similar manner almost any other common name has a double meaning. “Steamship” denotes in extension the Great Eastern, the Persia, the Himalaya, or any one of the thousands of steamships existing or which have existed; in intension it means “a vessel propelled by steam-power.” Monarch is the name of Queen Victoria, Victor Emmanuel, Louis Napoleon, or any one of a considerable number of persons who rule singly over countries; the persons themselves form the meaning in extension; the quality of ruling alone forms the intensive meaning of the name. Animal is the name in extension of any one of billions of existing creatures and of indefinitely greater numbers of other creatures that have existed or will exist; in intension it implies in all those creatures the existence of a certain animal life and sense, or at least the power of digesting food and exerting force, which are the marks of animal nature.

It is doubtfully true that all metals possess metallic lustre, and chemists would find it very difficult to give any consistent explanation of their use of the name ; but the statements in the text are sufficiently true to furnish an example.



It is desirable to state here that this distinction of extension and intension has been explained by logicians under various forms of expression. It is the peculiar misfortune of the science of logic to have a superfluity of names or synonyms for the same idea. Thus the intension of a term is synonymous with its comprehension, or connotation, or depth; while the extension is synonymous with the denotation or breadth. This may be most clearly stated in the form of a scheme:

The extension, extent, The intension, intent, breadth, denotation, do- depth, connotation, or immain, sphere or application plication of a of a name consists of the sists of the qualities the individual things to which possession of which by those the name applies.

things is implied. Of these words, denotation and connotation are employed chiefly by Mr J. S. Mill among modern logical writers, and are very apt for the purpose. To denote is to mark down, and the name marks the things to which it may

be applied or affixed; thus metal denotes gold, silver, copper, &c. To connote is to mark along with (Latin con, together; notare, to mark), and the connotation accordingly consists of the qualities before described, the possession of which is implied by the use of the name metal

When we compare different but related terms we may observe that they differ in the quantity of their extension and intension. Thus the term element has a greater extension of meaning than metal, because it includes in its meaning all metals and other substances as well. But it has at the same time less intension of meaning; for among the qualities of a metallic substance must be found the qualities of an element, besides the other qualities peculiar to a metal. If again we compare the terms metal and malleable metal, it is apparent that the

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latter term does not include the metals antimony, arsenic, and bismuth, which are brittle substances. Hence malleable metal is a term of narrower meaning in extension than metal; but it has also deeper meaning in intension, because it connotes or implies the quality of malleability in addition to the general qualities of a metal. White malleable metal is again a narrower term in extension because it does not include gold and copper ; and I can go on narrowing the meaning by the use of qualifying adjectives until only a single metal should be denoted by the term.

The reader will now see clearly that a general law of great importance connects the quantity of extension and the quantity of intension, viz.—As the intension of a term is increased the extension is decreased. It must not be supposed, indeed, that there is any exact proportion between the degree in which one meaning is increased and the other decreased. Thus if we join the adjective red to metal we narrow the meaning much more than if we join the adjective white, for there are at least twelve times as many white metals as red. Again, the term white man includes a considerable fraction of the meaning of the term man as regards extension, but the term blind man only a small fraction of the meaning. Thus it is obvious that in increasing the intension of a term we may decrease the extension in any degree.

In understanding this law we must carefully discrimi. nate the cases where there is only an apparent increase of the intension of a term, from those where the increase is real. If I add the term elementary to metal, I shall not really alter the extension of meaning, for all the metals are elements; and the elementary metals are neither more nor less numerous than the metals. But then the intension of the term is really unaltered at the same time; for the quality of an element is really found among the

qualities of metal, and it is superfluous to specify it over again. A quality which belongs invariably to the whole of a class of things is commonly called a property of the class (see Lesson XI.), and we cannot qualify or restrict a term by its own property.

This is a convenient place to notice a distinction between terms into those which are connotative and those which are non-connotative, the latter consisting of the terms which simply denote things without implying any knowledge of their qualities. As Mr Mill considers this distinction to be one of great importance, it will be well to quote his own words*:

“A non-connotative term is one which signifies a sub- * ject only, or an attribute only. A connotative term is one which denotes a subject, and implies an attribute. By a subject is here meant anything which possesses attributes. Thus John, or London, or England, are names which signify a subject only. Whiteness, length, virtue, signify an attribute only. None of these names, therefore, are connotative. But white, long, virtuous, are connotative. The word white denotes all white things, as snow, paper, the foam of the sea, &c., and implies, or, as it was termed by the schoolmen, connotes the attribute whiteness. The word white is not predicated of the attribute, but of the subjects, snow, &c. ; but when we predicate it of them, we imply, or connote, that the attribute whiteness belongs to them......

“All concrete general names are connotative. The word man, for example, denotes Peter, James, John, and an indefinite number of other individuals, of whom, taken as a class, it is the name. But it is applied to them, because they possess, and to signify that they possess, cer

System of Logic, Vol. I. p. 31, 6th ed. Book I. Chap. II.

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