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Essay Writing Guide: Explanatory / Expository Essay
§ 6. For the mind having a power to repeat the idea of any length directly stretched out, and join it to another in the same direction, which is to double the length of that straight line, or else join another with what inclination it thinks fit, and so make what sort of angle it pleases; and being able also to shorten any line it imagines, by taking from it one half, or one fourth, or what part it pleases, without being able to come to an end of any such divisions, it can make an angle of any bigness: so also the lines that are its sides, of what length it pleases; which joining again to other lines of different lengths, and at different angles, till it has wholly inclosed any space, it is evident, that it can multiply figures both in their shape and capacity, in infinitum; all which are but so many different simple modes of space.
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§ 6. If it be so, that our idea of infinity be got from the power we observe in ourselves of repeating without end our own ideas; it may be demanded, “why we do not attribute infinite to other ideas, as well as those of space and duration;” since they may be as easily, and as often repeated in our minds, as the other; and yet nobody ever thinks of infinite sweetness, or infinite whiteness, though he can repeat the idea of sweet or white, as frequently as those of a yard, or a day? To which I answer, all the ideas that are considered as having parts, and are capable of increase by the addition of any equal or less parts, afford us by their repetition the idea of infinity; because with this endless repetition, there is continued an enlargement, of which there can be no end. But in other ideas it is not so; for to the largest idea of extension or duration that I at present have, the addition of any the least part makes an increase; but to the perfectest idea I have of the whitest whiteness, if I add another of a less or equal whiteness, (and of a whiter than I have, I cannot add the idea) it makes no increase, and enlarges not my idea at all: and therefore the different ideas of whiteness, &c. are called degrees. For those ideas that consist of parts are capable of being augmented by every addition of the least part; but if you take the idea of white, which one parcel of snow yielded yesterday to our sight, and another idea of white from another parcel of snow you see to-day, and put them together in your mind, they embody, as it were, and run into one, and the idea of whiteness is not at all increased; and if we add a less degree of whiteness to a greater, we are so far from increasing that we diminish it. Those ideas that consist not of parts cannot be augmented to what proportion men please, or be stretched beyond what they have received by their senses; but space, duration, and number, being capable of increase by repetition, leave in the mind an idea of endless room for more: nor can we conceive any where a stop to a farther addition or progression, and so those ideas alone lead our minds towards the thought of infinity.