Locke: Number


„The SIMPLE MODES of NUMBER are of all other the most distinct; every the least variation, which is an unit, making each combination as clearly different from that which approacheth nearest to it, as the most remote; two being as distinct from one, as two hundred; and the idea of two as distinct from the idea of three, as the magnitude of the whole earth is from that of a mite. This is not so in other simple modes, in which it is not so easy, nor perhaps possible for us to distinguish betwixt two approaching ideas, which yet are really different. For who will undertake to find a difference between the white of this paper and that of the next degree to it: or can form distinct ideas of every the least excess in extension?“ (Book II, Chap. XVI, §3) #Locke #number

Locke, John, An Essay Concerning Human Understanding. Oxford: Clarendon Press 1979.

Berkeley: Number


„Number is so visibly relative, and dependent on Mens Understanding, that it is strange to think how any one shou’d give it an absolute Existence without the Mind.“ (Of the Principles of Human Knowledge, §12) #Berkeley #number #mind

Berkeley, George, A Treatise Concerning the Principles of Human Knowlege: Part I. Wherein the Chief Causes of Error and Difficulty in the Sciences, with the Grounds of Scepticism, Atheism, and Irreligion, are Inquir’d Into. Dublin 1710.

Mill: Number and Space


„In the laws of number, then, and in those of space, we recognize in the most unqualified manner, the rigorous universality of which we are in quest. Those laws have been in all ages the type of certainty, the standard of comparison for all inferior degrees of evidence. Their invariability is so perfect, that it renders us unable even to conceive any exception to them; and philosophers have been led, though (as I have endeavored to show) erroneously, to consider their evidence as lying not in experience, but in the original constitution of the intellect.“ (Chap. V, § 1) #Mill #number #space

Mill, John Stuart, A System of Logic, Ratiocinative and Inductive Being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation. New York: Harper & Brothers 81882.