ing relation to these subjects, as General Abstract ideas. And they are no less numerous than the multiplied varieties of objects, which are found to exist every where around us. It is thus, that we form the general notions of animal and of all the subordinate species of animals; of tree and its numerous varieties; of earths, and minerals, and whatever else is capable of being arranged into classes.

to criticism, and in

We may apply these views not only to natural objects, but to forms and relations of a very different character. The word Triangle is the name of a general abstract idea. Great exceptions however have been taken to certain incautious expressions of Mr. Locke on this point. Ile assets, that it requires some pains and skill to form the general idea of a triangle, and gives the following reason; "for it must be neither oblique, nor rectangle, neither equilateral, equicrural, nor scalenon, but all and none of these at once," &c. This language is undoubtedly open truth has not failed to receive a full share. The correct view seems to be this. The word TRIANGLE is not only the name of a class, but of a very general class; it is the name of a Genus, embracing all those figures, which agree in the circumstance of being bounded by three straight lines meeting one another so as to form three angles. A figure4aving any other form, (in other words not exhibiting a resemblance or similarity in this respect,) is excluded from the Genus; but it is still so extensive, taken in the sense just now mentioned, as to include all figures whatever of that name. Now there are embraced within the genus, as in numerous other cases, subordinate classes, which are distinguished by their appropriate names, viz, the class of acute-angled triangles, that of right-angled triangles, of obtuse-angled triangles,&c.

But it is to be noticed, that the general idea, whatever objects it may be founded upon, does not embrace every particular, which makes a part of such objects. When we look at a number of men, we find them all differing in some respects, in height, size, colour, tone of the voice, and in other particulars. The mind fixes only up

on those traits or properties, with which it can combine the notion of resemblance; that is to say, those traits, qualities, or properties, in which the individuals are perceived to be like, or to resemble each other.The coinplex mental state, which embraces these qualities and properties, and nothing more, (with the exception of the superadded notion of other bodies having resembling qualities,) is a General Abstract idea.

And hence the name. Such notions are called ABSTRACT, because, while embracing many individuals in certain respects, they detach and leave out altogether a variety of particulars, in which those individuals disagree. If there were not this discrimination and leaving out of certain parts, we never could consider these notions, regarded as wholes, as otherwise than individual or particular. They are called GENERAL, because, in consequence of the discrimination and selection which has just been mentioned, they embrace such qualities and properties as exist not in one merely, but in many.

The difference, therefore, between the complex notion, which we form of any particular object, and the general complex feeling now under consideration is truly this; the latter combines together fewer particulars, but unites with such, as it does combine together, the additional notion of resemblance, which implies as its basis the comparison of a number of objects, and is perhaps the distinguishing circumstance.--Hence it must be allowed, that there is no outward object precisely corresponding to the GENERAL NOTION, which we form. The mind takes into view only a division or part of any one object, combining with this select view the notion of other objects, and the relation of resemblance, in respect to such division or part.

If it should be asked, By virtue of what principle is this discovery of a resembling relation made? The answer is, (and it is the only one, which can be given,) that there is in the mind an original tendency or susceptibility, by means of which, whenever we perceive different objects together, we are instantly, without the intervention of any

other mental process, sensible of their relation in certain respects.

§. 232. Objection sometimes made to the existence of gener

al notions.

It should not, however, be objected, as is sometimes done, that we can have no such general notion at all, because there is nothing outward, which it precisely corresponds to. Such an objection,, although it appears to have been frequently made, goes too far; it would seem even to lead to the conclusion, that we can have no complex idea of any kind, neither particular nor general. It cannot be pretended, that even our notions of particular objects correspond precisely to those objects; the ideas, which we form of a particular house, tree, or plant, or any other individual object, are often erroneous in some respects, and probably always imperfect. But they are not, for that reason, to be regarded as false and chimerical, and to be rejected as having no foundation in nature.

We will suppose ourselves to have been acquainted in former years with a particular elm; we have looked upon it a thousand times; and it is familiar to us as any of our most cherished remembrances. At this great distance of time and place we form an idea, a conception, a notion of it, but it cannot be presumed to be a perfect or complete one. It cannot be pretended, that we have a notion not only of the trunk, but of every leaf and of the form of every leaf, of every branch and its intertwinings with every other branch; that it exists in our minds precisely, and in every respect, the same as it exists on the spot, where it grows. If therefore general abstract ideas are to be rejected, because they embrace only parts of those objects, which are ranked under them, we must on the same grounds reject and deny also our complex notions of individual objects; but this probably no one is prepared to do.

Take another obvious illustration in reproof of the objection, that, because general abstract ideas are purely mental, and have no outward and corresponding reality, they therefore do not exist.-We have an idea of God. We

presume to say, that it will be readily admitted, that we have such a notion; not many men are without it, even among the most degraded Savages. But evidently the same objection might be raised against the existence of any such idea, as has been raised against the existence of general abstractions. If general abstract ideas are not outwardly represented, so that of the Supreme Being, which is particular though complex, is also not outwardly represented; it is impossible, that it should be so. There is nothing we behold in heaven, or on earth, or under the earth, that is like Him. If every object in the universe were transformed into so many letters of light, to set forth his attributes and glory, they could not do it. Still we

have the idea of God; and it has as real an existence as the mind has itself.

§. 233. Of the power of general abstraction in connection with numbers, &c.

The ability, which the mind possesses of forming general abstract ideas, is of much practical importance; but whether it be the characteristical attribute of a rational nature or not, as some have supposed, it is not necessary now to inquire. It is not easy to estimate the increase of power, which is thus given to the action of the human mind, particularly in reasoning. By means of general abstract propositions, we are able to state volumes in a few sentences; that is to say, the truths, stated and illustrated in a few general propositions, would fill volumes in their particular applications. But it is enough here to refer to a single circumstance in illustration of the uses of this power.

Without the ability of forming general notions, we should not be able to number, even in the smallest degree. Before we can consider objects as forming a multitude, or are able to number them, it seems necessary to be able to apply to them a common name. This we cannot do, until we have reduced them to a genus; and the formation of a genus implies the power, (or process rather,) of abstraction. Consequently, we should be unable without such power to number. How great then is the practical importance

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of that intellectual process, by which general abstractions are formed!-Without the ability to number, we should be at loss in all investigations where this ability is requir ed; without the power to classify, all our speculations must be be limited to particulars, and we should be capable of no general reasoning.

§. 234. Of general abstract truths or principles.

There are not only general abstract ideas, but abstract truths or principles also of a general nature, which are deserving of some attention, especially in a practical point of view. Although enough has perhaps already been said to show the importance of abstraction, it may yet be desirable to have a more full view of its applications.

The process, in forming general truths or principles of an abstract nature, seems to be this. We must begin undoubtedly with the examination and study of particulars; with individual objects and characters, and with insulated We subsequently confirm the truth of whatever has been ascertained in such inquiry, by an observation of other like bodies and events. We proceed from one individual to another, till no doubt remains.

events.

Having in this way arrived at some general fact or principle, we thenceforward throw aside the consideration of the particular objects on which it is founded, and make it alone, exclusively and abstractly, the subject of our mental contemplations. We repeat this process again and again, till the mind, instead of being wholly taken up with a multitude of particulars, is stored with truths of a general kind. These truths it subsequently combines in trains of reasoning, compares together and deduces from them others of still wider application. And the number of such general truths is the greater, because, in ascertaining them we are not restricted to our own personal experience in respect to the individuals coming under examination, but may often safely avail ourselves of that of others.

§. 235. Of the speculations of philosophers and others. What has been said leads us to observe, that there is a