Berkeley, Principles of Human Knowledge

But we are told by locke replying to this point if

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Unformatted text preview: lve abstract ideas. It would seem to follow that the forming of abstract ideas is too difficult to be necessary for communication, which is so easy and familiar for all sorts of people. But, we are told ·by Locke, replying to this point·, if adults find abstract ideas easy to form, that is only because they have become good at it through long practice. Well, I would like to know when it is that people are busy overcoming that difficulty and equipping themselves with what they need for communication! It can’t be when they are grown up, for by then ·they can communicate, so that· it seems the difficulty is behind them; so it has to be something they do in their childhood. But surely the labour of forming abstract notions - with so many to be formed, and each of them so difficult - is too hard a task for that tender age. Who could believe that a couple of children cannot chatter about sugar-plums and toys until they have first tacked together numberless inconsistencies and so formed abstract general ideas in their minds, attaching them to every common name they make use of? 7 15 intro. Abstract ideas are no more needed, in my opinion, for the growth of knowledge than they are for communication. I entirely agree with the widespread belief that all knowledge and demonstration concerns universal notions; but I cannot see that those are formed by abstraction. The only kind of universality that I can grasp does not belong to anything’s intrinsic nature; a thing’s universality consists how it relates to the particulars that it signifies or represents. That is how things, names, or notions that are intrinsically particular are made to be universal ·through their relation to the many particulars that they represent·. When I prove a proposition about triangles, for instance, I am of course employing the universal idea of a triangle; but that doesn’t involve me in thinking of a triangle that is neither equilateral nor scalenon nor equicrural! All it means is that the particular triangle I have in mind, no matter what kind of triangle it may be, is ‘universal’ in the sense that it equally stands for and represents all triangles whatsoever. All this seems to be straightforward and free of difficulties. 16 intro. You may want to make this objection: How can we know any proposition to be true of all particular triangles unless we first see it demonstrated of the abstract idea of a triangle that fits all the particular ones? Just because a property can be demonstrated to belong to some one particular triangle, it doesn’t follow that it equally belongs to any other triangle that differs in some way from the first one. For example, having demonstrated of an isosceles right-angled triangle that its three angles are equal to two right ones, I cannot conclude from this that the same holds for all other triangles that don’t have a right angle and two equal sides. If we are to be certain that this proposition is universally true, it seems, we must either Ÿprove it for every particular triangle (which is impossible) or Ÿprove it once and for all of the abstract idea of a triangle, in which all the particulars are involved and by which they are all equally represented. To this I answer that although the idea I have in view while I make the demonstration may be (for instance) that of an isosceles right-angled triangle whose sides are of a determinate length, I can still be certain that it applies also to all other triangles, no matter what their sort or size. I can be sure of this because neither the right angle nor the equality of sides nor length of the sides has any role in the demonstration. It is true that the diagram I have in view ·in the proof· includes all these details, but they are not mentioned in the proof of the proposition. It is not said that the three angles are equal to two right ones because one of them is a right angle, or because the sides that form it are of the same length. This shows that the demonstration could have held good even if the right angle had been oblique and the sides unequal. That is why I conclude that the proposition holds for all triangles, having Ÿdemonstrated it ·in a certain way· to hold for a particular right-angled isosceles triangle - not because I Ÿdemonstrated it to hold for the abstract idea of a triangle! I do not deny that a man can abstract in that he can consider a figure merely as triangular, without attending to the particular qualities of the angles or relations of the sides. But that doesn’t show that he can form an abstract general inconsistent idea of a triangle. Similarly, because all that is perceived is not considered, we may think about Peter considered as a man, or considered as an animal, without framing the abstract idea of man or of animal. 8 17 intro. It would be an endless and a useless task to trace the scholastic philosophers [that is, mediaeval followers of Aristotle], those great masters of abstraction, through all the tangling labyrinths of error and dispute that their doctrine of abstract natures and notions seem...
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