ideas of the more compound beings, which include several co-existent qualities:-for example, the mind having observed, that Peter, James, John, &c., resemble each other in certain common agreements of shape, and other qualities, leaves out of the complex or compounded idea it has of Peter, James, &c., that which is peculiar to each, retaining only what is common to all; and so makes an abstract idea wherein the particulars equally partake, abstracting entirely, and cutting off all those circumstances and differences which might determine it, to any particular existence. And after this manner it is said, we come by the abstract idea of man, or if you please humanity, or human nature; 'tis true, there is included colour, because there is no man but has some colour, but then it can be neither white nor black, nor any particular colour, because there is no one particular colour, wherein all men partake; so there is included stature, but then it is neither tall stature, nor low stature, nor yet middle stature, but something abstracted from all these; and so of the rest. Moreover, there being a great variety of other creatures that partake in some parts, not all, of the complex idea, man, the mind leaving out those parts which are peculiar to men, and retaining those only which are common to all living creatures, frames the idea of animals, which abstracts not only from all particular men, but also, all birds, beasts, fishes, and insects. By Body is meant body without any particular shape, or figure, there being no one shape or figure common to all animals, without covering of hair, feathers, or scales, &c. nor yet naked; hair, feathers, scales, and nakedness, being the distinguishing properties of particular animals, and for that reason left out of the abstract idea; upon the same account the spontaneous motion must be neither in walking, nor flying, nor creeping, it is nevertheless a motion, but what that motion is, it is not easy to conceive.'

Whether others have this wonderful faculty of abstracting their ideas, they best can tell: for myself I dare be confident I have it not. I have a faculty of imagining or representing to myself the ideas of those particular things I have perceived, and of variously compounding and dividing them. I can imagine a man with two heads or the upper part of a man joined to the body of a horse; I can consider the hand, the eye, the nose, each by itself, abstracted or separated from the rest of the body. But then, whatever hand or eye, I imagine, it must have some particular shape, and colour. Likewise, the idea of man that I frame to myself must be either of a white, or a black, or a tawny; a strait, or a crooked; a tall, or a low, or a middle sized man. I cannot by any effort of thought conceive the abstract idea above-described: and it is equally impossible for me to form the abstract idea of motion distinct from the body moving, and

sensible that we can only discover those relations, and not what the things truly are.'

Berkeley handled his subjects with little tenderness, and he has perfectly anatomised this subject of abstract ideas. In choosing to answer the objections to this doctrine as stated by him, I shall not be accused of wishing to encounter a mean adversary. I can only trust to the goodness of my cause. I hope I shall be excused for going at some length into the argument, because it is one of the most difficult and complicated in itself, and is of the most extensive application to other questions relating to the human understanding. If we can come to any satisfactory issue to it, it will be worth the pains of enquiry.

It is agreed on all hands,' says this author, that the quantities or modes of things do never really exist in each of them, apart by itself, and separated from all others, but are mixed, as it were, and blended together, several in the same object. But we are told the mind being able to consider each quality singly, or abstracted from those other qualities with which it is united, does by that means frame to itself abstract ideas. For example, there is perceived by sight, an object, extended, coloured, and moved. This mixed idea the mind resolving into its simple constituent parts, and viewing each by itself exclusive of the rest, does frame the abstract ideas of extension, colour, and motion. Not that it is possible for colour or motion to exist without extension, but only that the mind can frame to itself by abstraction the idea of colour, exclusive of extension, and of motion exclusive both of colour and extension. Again, the mind having observed that in the particular extensions perceived by sense, there is something common and alike in all, and some other things peculiar, as this or that figure, or magnitude, which distinguish them one from another, it considers apart, or singles out by itself that which is most common, making thereof a most abstract idea of extension, line, surface, or solid, nor has any figure or magnitude, but is an idea prescinded from all these. So likewise the mind by leaving out of the particular colours perceived by sense, that which distinguishes them one from another, and retaining that which only is common to all, makes an idea of colour in abstract, which is neither red, nor blue, not white, &c. And in like manner by considering motion abstractedly, not only the body moved, but likewise from the figure it describes, and all particular directions and velocities, the abstract idea of motion is framed, which equally corresponds to all particular motions whatsoever that may be perceived by sense.

'And as the mind frames to itself abstract ideas of qualities, or modes, so does it by the precision or mental separation, attain abstract

or general line, but of all particular right lines that may possibly exist, so the latter must be thought to derive its generality from the same cause, namely, the various particular lines which it indifferently denotes.'

To give the reader a clearer view of the nature of abstract ideas, and the uses they are thought necessary to, I shall add one more passage out of the Essay on Human Understanding, which is as follows:-"Abstract ideas are not so obvious or easy to children, or the yet unexercised mind as particular ones. If they seem so to grown men, it is only by constant and familiar use they are made so. For when we nicely reflect upon them, we shall find that general ideas are fictions and contrivances of the mind, that carry difficulty with them, and do not so easily offer themselves as we are apt to imagine. For example, does it not require some skill and pains to form the general idea of a triangle (which is yet none of the abstract, comprehensive, and difficult), for it must be neither oblique nor rectangle, neither equilateral, equicrural, nor scalenon, but all and none of these at once. In effect it is something imperfect that cannot exist, an idea wherein some parts of different and inconsistent ideas are put together. 'Tis true the mind in this imperfect state has need of such ideas, and makes all the haste it can to them, for the convenience of communication and enlargement of knowledge, to both of which it is naturally very much inclined. But yet one has reason to suspect such ideas are marks of our imperfections, at least this is enough to show that the most abstract and general ideas are not those that the mind is first and most easily acquainted with, nor such as its earliest knowledge is conversant about.". -After laughing at this description of the general idea of a triangle, which is neither oblique nor rectangle, equilateral, equicrural, nor scalenon, but all and none of these at once, Berkeley adds,much is here said of the difficulty that abstract ideas carry with them, and the pains and skill requisite to the forming of them. And it is on all hands agreed that there is need of great toil and labour of mind, to emancipate our thoughts from particular objects, and raise them to those sublime speculations that are conversant about abstract ideas. From all which the natural consequences should seem to be, that so difficult a thing as forming abstract ideas was not necessary for communication, which is so familiar to all sorts of men. But, we are told, if they seem obvious and easy to grown men, it is only because by constant and familiar use they are made so. Now I would fain know at what time it is, men are employed in surmounting that difficulty and furnishing themselves with those necessary helps for discourse. It cannot be when they are grown up, for then it seems they are not conscious of any such pains-taking; it therefore

remains to be the business of their childhood. And surely the great and multiplied labour of framing abstract notions will be found a hard task for that tender age. Is it not a hard thing to imagine that a couple of children cannot prate of their sugar plums, and rattles, and the rest of their little trinkets, till they have first packed together numberless inconsistencies, and so framed in their minds general abstract ideas, and annexed them to every common name they make use of.

It is I know a point much insisted on that all knowledge and demonstration are about universal notions, to which I fully assent. But then it does not appear to me that those notions are formed by abstraction, in the manner premised; universality, so far as I can comprehend, not consisting in the absolute, positive nature and conception of any thing, but in the relation it bears to the particulars signified, or represented by it. But here it will be demanded, how we can know any proposition to be true of all particular triangles, except we have seen it first demonstrated of the abstract idea of a triangle which equally agrees to all?

For because a property may be demonstrated to agree to some particular triangle, it will not thence follow that it equally belongs to every other with it. For example, having demonstrated that the three angles of an isosceles, rectangular triangle, are equal to two right ones, I cannot therefore conclude this affection argues to all other triangles, which have neither a right angle, nor two equal sides. It seems, therefore, that to be certain this proposition is universally true we must either make a particular demonstration for every particular triangle, which is impossible, or once for all demonstrate it of the abstract idea of a triangle, in which all the particulars do indifferently partake, and by which they are all equally represented.' To which I answer, that though the idea I have in view, whilst I make the demonstration, be, for instance, that of an isosceles, not a regular triangle, whose sides are of a determinate length, I may nevertheless be certain it extends to all other rectilinear triangles of what sort or bigness soever. And that neither because the right angle, nor the equality, nor determinate length of the sides are at all concerned in the demonstration. It is true, the diagram I have in view includes all these particulars, but then there is not the least mention made of them in the proofs of the proposition. It is not said the three angles are equal to two right ones, because one of these is a right angle, or because the sides comprehending it are of the same length. Which sufficiently shews that the right angle might have been oblique and the sides unequal, and for all the others the demonstrations have held good. And for this reason it is that I conclude that to be true of

any oblique angular, or scalenon, which I had demonstrated of a particular right angled, equicrural, triangle, and not because I demonstrated the proposition of the abstract idea of a triangle.' The author then adds some further remarks on the use of abstract terms, and concludes- May we not, for example, be affected with the promise of a good thing, though we have not an idea of what it is or is not the being threatened with danger sufficient to excite a dread, though we think not of a particular evil likely to befal us, and yet frame to ourselves an idea of danger in abstract?' Introduction to Principles of Human Knowledge, p. 31.

Hume, who has taken up Berkeley's arguments on this subject, and affirms that the doctrine of abstract ideas applies the flattest of all contradictions, that it is possible for the same thing to be and not to be, has enlarged a good deal on this last topic of the manner in which words may be supposed to excite general ideas. His words are these: Where we have found a resemblance between any two objects that often occur to us, we apply the same name to all of them, whatever differences we may observe in the degrees of their quantity and quality, and whatever differences may appear among them. After we have acquired a custom of this kind, the hearing of that name revives the idea of one of these objects, and makes the imagination conceive it with its particular circumstances and proportions. But as the same word is supposed to have been frequently applied to other individuals that are different in many respects from the idea which is immediately present to the mind, the word not being able to revive the idea of all these individuals, only touches the soul, if I may be allowed so to speak, and revives that custom, which we have acquired by surveying them. They are not in reality present to the mind, but only in power, nor do we draw them out distinctly in the imagination, but keep ourselves in readiness to survey any of them, as we may be prompted by a present design or necessity. The word raises up an individual idea, along with a certain custom; and that custom produces any other individual one, for which we may have occasion.' Treatise of Human Nature, p. 43, 4. The author afterwards adds, with his usual candour, that this account does not perfectly satisfy him, but he relies principally on the logical demonstration of the impossibilities of abstract ideas just before given.

I confess it does not seem an easy matter to recover the argument in this state of it; however, I will attempt it. What I shall endeavour will not be so much to answer the foregoing reasoning as to prove that in a strict sense all ideas whatever are mere abstractions and can be nothing else; that some of the most clear, distinct, and positive ideas of particular objects are made up of numberless incon