HOW A NUMBER MAY BE CALLED INFINITE.42
Project Gutenberg EPUB3 edition
Plotinus and Guthrie, Kenneth Sylvan
17. As the reasons here advanced would seem to imply that every number is limited, we may ask in which sense may a number be said to be infinite? This conclusion is right, for it is against the nature of number to be infinite. Why do people then often speak of a number as infinite? Is it in the same sense that one calls a line infinite? A line is said to be infinite, not that there really exists an infinite line of this kind, but to imply the conception of a line as great as possible, greater than any given line. Similarly with number. When we know which is the number (of certain objects), we can double it by thought, without, on that account, adding any other number to the first. How indeed would it be possible to add to exterior objects the conception of our imagination, a conception that exists in ourselves exclusively? We shall therefore say that, among intelligible entities, a line is infinite; otherwise, the intelligible line would be a simple quantative expression. If however the intelligible line be not this, it must be infinite in number; but we then understand the word "infinite" in a sense other than that of having no limits that could not be transcended. In what sense then is the word "infinite" here used? In the sense that the conception of a limit is not implied in the being of a line in itself.