John Locke

“ 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. ”

“ 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 of 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. ”

“ For, when we call them infinite, we have no other idea of this infinity but what carries with it some reflection on, and imitation of, that number or extent of the acts or objects of God’s power, wisdom, and goodness, which can never be supposed so great, or so many, which these attributes will not always surmount and exceed, let us multiply them in our thoughts as far as we can, with all the infinity of endless number. ”

“ 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 anywhere a stop to a further addition or progression : and so those ideas alone lead our minds towards the thought of infinity. ”

“ If I have dwelt pretty long on the consideration of duration, space, and number, and what arises from the contemplation of them, – Infinity, it is possibly no more than the matter requires ; there being few simple ideas whose modes give more exercise to the thoughts of men than those do. ”

“ Number affords us the clearest idea of infinity. But of all other ideas, it is number, as I have said, which I think furnishes us with the clearest and most distinct idea of infinity we are capable of. For, even in space and duration, when the mind pursues the idea of infinity, it there makes use of the ideas and repetitions of numbers, as of millions and millions of miles, or years, which are so many distinct ideas, – kept best by number from running into a confused heap, wherein the mind loses itself ”

“ It suffices to my design to show how the mind receives them, such as they are, from sensation and reflection ; and how even the idea we have of infinity, how remote soever it may seem to be from any object of sense, or operation of our mind, has, nevertheless, as all our other ideas, its original there. Some mathematicians perhaps, of advanced speculations, may have other ways to introduce into their minds ideas of infinity. ”

“ So that wherever the mind places itself by any thought, either amongst, or remote from all bodies, it can, in this uniform idea of space, nowhere find any bounds, any end ; and so must necessarily conclude it, by the very nature and idea of each part of it, to be actually infinite. ”

“ So much as the mind comprehends of any space, it has a positive idea of : but in endeavouring to make it infinite, – it being always enlarging, always advancing, – the idea is still imperfect and incomplete. So much space as the mind takes a view of in its contemplation of greatness, is a clear picture, and positive in the understanding : but infinite is still greater. 1. Then the idea of so much is positive and clear. 2. The idea of greater is also clear ; but it is but a comparative idea, the idea of so much greater as cannot be comprehended. ”

“ So that what lies beyond our positive idea towards infinity, lies in obscurity, and has the indeterminate confusion of a negative idea, wherein I know I neither do nor can comprehend all I would, it being too large for a finite and narrow capacity. ”

“ Which consequence, I conceive, is very ill collected, because the existence of matter is no ways necessary to the existence of space, no more than the existence of motion, or the sun, is necessary to duration, though duration used to be measured by it. ”

“ For, when we would consider eternity, a parte ante, what do we but, beginning from ourselves and the present time we are in, repeat in our minds the ideas of years, or ages, or any other assignable portion of duration past, with a prospect of proceeding in such addition with all the infinity of number : and when we would consider eternity, a parte post, we just after the same rate begin from ourselves, and reckon by multiplied periods yet to come, still extending that line of number as before. ”

“ 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. ”

“ If, to avoid succession in external existence, they return to the punctum stans of the schools, I suppose they will thereby very little mend the matter, or help us to a more clear and positive idea of infinite duration ; there being nothing more inconceivable to me than duration without succession. ”

“ It is true, that we cannot but be assured, that the great God, of whom and from whom are all things, is incomprehensibly infinite : but yet, when we apply to that first and supreme Being our idea of infinite, in our weak and narrow thoughts, we do it primarily in respect to his duration and ubiquity ”

“ And these two being put together, are that infinite duration we call Eternity : which, as we turn our view either way, forwards or backwards, appears infinite, because we still turn that way the infinite end of number, i.e. ”