What sort of representation can subsist between one concrete stroke and every other concrete stroke? If it is straight it will not correctly represent a curve; if it is curved it will not represent a straight stroke. A stroke an inch long cannot stand for a stroke a hundred miles long; a black stroke does not properly represent a red stroke. So it is incorrect to say that 'what is demonstrated of it is demonstrated of all strokes, or, in other words, of a stroke in general.' A particular object can stand only for itself, and if general words stand for many things it is not by direct representation, but because they first suggest general ideas, which are the true substitutes of many particular things.
A reference to geometrical objects, themselves so abstract, is a doubtful mode of showing how well one concrete thing can represent others. Had Berkeley taken a more complex object as his general representative he would have seen the weakness of his argument. Suppose a biologist has to discourse on a province of animal life comprising many species, and takes an individual of one species as a representative of the whole. His sample is perhaps a hare, but he has to treat of birds and fishes. What is to prevent his hearers from concluding that birds are furred animals and fishes quadrupeds? Are they to be expected to see in the hare only the properties common to all the animals reviewed? If so they have the power denied them by nominalists of forming a pure general idea, and the hare is superfluous. The common properties could have been defined and imagined without a concrete specimen, with irrelevant attributes, being brought into the discourse.
All nominalists insist that if we think long on a general idea it becomes particular, and from this they argue that it is not, and never has been, a general idea[11].
The experiments of this sort proposed by logicians are misleading, because we are without the ordinary motives for thinking generally. In practical thought we have some sufficient reason for attending to a fraction of consciousness and excluding the rest, and the irrelevant qualities are distinctly less charged with attention than the principal quality.
The power of abstracting thought is a matter of education. It is that ruling of the spirit which is more difficult than the capture of a city. We have to master the restless energic Self and fix it down on a particular plasmic figure, or a mere point or edge of one, preventing the energy from spreading to adjacent images. That is irksome and fatiguing, but it is only a high degree of the faculty everyone possesses of distinguishing particular objects from each other. Some minds are so flaccid that you cannot hold them to one subject, even the most particular and obvious, for five minutes at a time. Training enables us to bring into the focus of attention just what we wish to observe or think about, and leave the rest in the background, however closely it may be connected with the matter that immediately interests us. But for this power much of our energy would be expended to no purpose. Abstraction is simply attention of a minute and concentrated kind—a bringing of our energy of observation or recollection to a fine point.
When abstraction need not be prolonged—when we are free to pass rapidly from one general or abstract idea to another—there is no difficulty in partial thinking. We skim over the plasmic imprints, lightly brushing the surface of each where it is most prominent and therefore most general, but not pausing to recollect particulars. It is this rapid delicate touch we oftenest use in actual thought; but when for purposes of experiment we come down heavily on an imprint, then the Self overflows to adjacent channels and particular memories are stirred up, in spite of every effort to limit our attention.
So common and easy is rapid general thought that it is constantly used as a substitute for concrete thought, when a sketchy treatment of things is all that is wanted.
'A bird has alighted on the fence.' The speaker saw a particular concrete bird, and might have tried to describe it in the concrete. But the attributes that rendered it concrete are supposed not to be of present importance, and the hearer is consequently invited to think only of bird in general. Would a nominalist affirm that in such a case the words are meaningless unless the idea is concreted—unless the general sketch is filled out in detail?
Take another example. 'The man sat by the window overlooking the river that flowed towards the city.'
Here all the nouns are general, but the picture is individual and concrete. It is also quite intelligible, as a sketch. We can think of a man without assigning to him any particular type of face, or colour of hair, or stature, or age, or clothing. Our idea is the general idea man used as a sketch of a particular man. He is in a house because he is looking through a window, but we do not stay to imagine the house as cottage, inn, or mansion. We call up the general idea house, which is definite enough for our purpose, and we cannot doubt for a moment that we have such a general idea. The river may be wide or narrow, straight or crooked, navigable or not, but we think only of the general idea river, which is water flowing between banks. And surely we can imagine a general city without giving it any definite size, or form, or nationality, or number of inhabitants!