no positive idea of any space or duration which is not made up of, and commensurate to, repeated numbers of feet or yards, or days and years; which are the common measures, whereof we have the ideas in our minds, and whereby we judge of the greatness of this sort of quantities.  And therefore, since an infinite idea of space or duration must needs be made up of infinite parts, it can have no other infinity than that of number capable still of further addition; but not an actual positive idea of a number infinite.  For, I think it is evident, that the addition of finite things together (as are all lengths whereof we have the positive ideas) can never otherwise produce the idea of infinite than as number does; which consisting of additions of finite units one to another, suggests the idea of infinite, only by a power we find we have of still increasing the sum, and adding more of the same kind; without coming one jot nearer the end of such progression.

14.  How we cannot have a positive idea of infinity in Quantity.

They who would prove their idea of infinite to be positive, seem to me to do it by a pleasant argument, taken from the negation of an end; which being negative, the negation on it is positive.  He that considers that the end is, in body, but the extremity or superficies of that body, will not perhaps be forward to grant that the end is a bare negative:  and he that perceives the end of his pen is black or white, will be apt to think that the end is something more than a pure negation.  Nor is it, when applied to duration, the bare negation of existence, but more properly the last moment of it.  But as they will have the end to be nothing but the bare negation of existence, I am sure they cannot deny but the beginning of the first instant of being, and is not by any body conceived to be a bare negation; and therefore, by their own argument, the idea of eternal, À parte ante, or of a duration without a beginning, is but a negative idea.

15.  What is positive, what negative, in our Idea of infinite.

The idea of infinite has, I confess, something of positive in all those things we apply to it.  When we would think of infinite space or duration, we at first step usually make some very large idea, as perhaps of millions of ages, or miles, which possibly we double and multiply several times.  All that we thus amass together in our thoughts is positive, and the assemblage of a great number of positive ideas of space or duration.  But what still remains beyond this we have no more a positive distinct notion of than a mariner has of the depth of the sea; where, having let down a large portion of his sounding-line, he reaches no bottom.  Whereby he knows the depth to be so many fathoms, and more; but how much the more is, he hath no distinct notion at all:  and could he always supply new line, and find the plummet always sink, without ever stopping, he would be something in the posture of the mind reaching after a complete