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.
Difference between infinity of space, and space infinite.§ 7. Though our idea of infinity arise from the contemplation of quantity, and the endless increase the mind is able to make in quantity, by the repeated additions of what portions thereof it pleases; yet I guess we cause great confusion in our thoughts, when we join infinity to any supposed idea in quantity the mind can be thought to have, and so discourse or reason about an infinite quantity, viz. an infinite space,
