Note 75:1 — Chapter II

"If we take as the utmost bounds of this system the orbit Uranus, we shall find that it occupies a portion of space not less than three thousand six hundred millions of miles in extent. The mind fails to form an exact notion of a portion of space so immense; but some faint idea of it may be obtained from the fact, that, if the swiftest race-horse ever known, had begun to traverse it at full speed, at the time of the birth of Moses, he could only as yet have accomplished half his journey."—Vestiges of the Natural History of Creation, pp. 1-2. Here an attempt is made to give a conception of abstract numbers, by calling up in the mind the ideas deposited there from actual impressions. Hume had, in the application of his theory to mathematics, to struggle with the fact that no truths had a clearer and more distinct existence in the mind than the abstract truths of the exact sciences; and feeling the difficulty he thus had to encounter, he did not recur in his subsequent works to this part of the sceptical theory. Kant seems to have filled up the blank for him, by treating those truths as synthetical intuitions anterior to experience in their abstract existence, though depending on experience in the knowledge of their concrete application; but it may be observed, that at the beginning of sect. 4. of his Inquiry, Hume seems to have nearly anticipated some such principle.