13. The secondary qualities of things not discovered by
demonstration. Not knowing, therefore, what number of particles, nor
what motion of them, is fit to produce any precise degree of
whiteness, we cannot demonstrate the certain equality of any two
degrees of whiteness; because we have no certain standard to measure
them by, nor means to distinguish every the least real difference, the
only help we have being from our senses, which in this point fail
us. But where the difference is so great as to produce in the mind
clearly distinct ideas, whose differences can be perfectly retained,
there these ideas or colours, as we see in different kinds, as blue
and red, are as capable of demonstration as ideas of number and
extension. What I have here said of whiteness and colours, I think
holds true in all secondary qualities and their modes.
14. Sensitive knowledge of the particular existence of finite beings
without us. These two, viz. intuition and demonstration, are the
degrees of our knowledge; whatever comes short of one of these, with
what assurance soever embraced, is but faith or opinion, but not
knowledge, at least in all general truths. There is, indeed, another
perception of the mind, employed about the particular existence of
finite beings without us, which, going beyond bare probability, and
yet not reaching perfectly to either of the foregoing degrees of
certainty, passes under the name of knowledge.
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