Page:Mind (Old Series) Volume 11.djvu/202

 CONCEIVABILITY AND THE INFINITE. 191 the proof of the proposition. It is not said the three angles are equal to two right ones, because one of them is a right angle, or because the sides comprehending it are of the same length. Which sufficiently shows that the right angle might have been oblique, and the sides unequal, and for all that the demonstration have held good. And for this reason it is that I conclude that to be true of any obliquangular or scalenon which I had demonstrated of a particular right-angled equi-crural triangle, and not because I demonstrated the proposition of the abstract idea of a triangle. And here it must be acknowledged that a man may consider a figure merely as triangular, without attending to the particular qualities of the angles, or relations of the sides. So far he may abstract ; but this will never prove that he can frame an abstract, general, inconsistent idea of a triangle. In like manner we may consider Peter so far forth as man, or so far forth as animal, without framing the fore-mentioned abstract idea, either of man or of animal, inasmuch as all that is perceived is not con- sidered." In the former of these two extracts Berkeley has declared himself able to abstract only so far that he can represent to himself in imagination what can exist separately in nature. He denies that he can conceive separately those qualities which it is impossible should exist separately. But when he supposes an objector to ask, How is it possible for some- thing, proved to be true of a particular triangle, to be known to be true of all triangles ? he answers that it is seen that neither the right angle, nor the equality, nor the determinate length of the sides is at all concerned in the demonstration. In other words, he admits that, so far as that demonstration goes, we have to do only with those elements in which all triangles agree. And if we can reason about certain elements to the exclusion of others ; if we can see that certain objects are alike in certain elements and unlike in others ; if we can give a name to objects simply to express the presence of these same elements, however the elements accompanying them may vary, then surely the elements of the concept have been before the mind in some way in which the others have not, and have been grasped together. Berkeley frankly admits as much in the concluding sen- tences of the latter extract, sentences which were added twenty-four years after the first publication of the essay, when mature reflection, we may suppose, had brought him to see that on his previous principles, strictly held, all comparison of objects differing in any of their qualities would be impossible. If we can consider a figure merely as triangular, without attending to the particular qualities of the angles, or relations of the sides, then we can in some sort divorce the elements included under the general word ' triangle ' from the accompanying elements, and consider