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Habitual Knowledge two-fold.
      §9. Of habitual Knowledge, there are also, vulgarly speaking,
two degrees:
      First, The one is of such Truths laid up in the Memory, as whenever
they occur to the Mind, it actually perceives the Relation is between those
Ideas. And this is in all those Truths, whereof we have an intuitive
Knowledge, where the Ideas themselves, by an immediate view, dis-
cover their Agreement or Disagreement one with another.
      Secondly, The other is of such Truths, whereof the Mind having been
convinced, it retains the Memory of the Conviction, without the Proofs. Thus
a Man that remembers certainly, that he once perceived the
Demonstration, that the three Angles of a Triangle are equal to two
right ones, is certain that he knows it, because he cannot doubt of
the truth of it. In his adherence to a Truth, where the Demon-
stration, by which it was at first known, is forgot, though a Man
may be thought rather to believe his Memory, than really to know,
and this way of entertaining a Truth seem’d formerly to me like
something between Opinion and Knowledge, a sort of Assurance
which exceeds bare Belief, for that relies on the Testimony of
another; Yet upon a due examination I find it comes not short of
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perfect certainty, and is in effect true Knowledge. That which is
apt to mislead our first Thoughts into a mistake in this Matter is,
that the Agreement or Disagreement of the Ideas in this Case is not
perceived, as it was at first, by an actual view of all the inter-
mediate Ideas whereby the Agreement or Disagreement of those in
the Proposition was at first perceived; but by other intermediate
Ideas, that shew the Agreement or Disagreement of the Ideas con-
tained in the Proposition whose certainty we remember. For
Example in this Proposition, that the three Angles of a Triangle are
equal to two right ones, one, who has seen and clearly perceived
the Demonstration of this Truth, knows it to be true, when that
Demonstration is gone out of his Mind; so that at present it is not
actually in view, and possibly cannot be recollected: But he knows
it in a different way, from what he did before. The Agreement of
the two Ideas join’d in that Proposition is perceived, but it is by the
intervention of other Ideas than those which at first produced that
Perception. He remembers, i.e. he knows (for remembrance is but
the reviving of some past knowledge) that he was once certain of
the truth of this Proposition, that the three Angles of a Triangle are
equal to two right ones. The immutability of the same relations
between the same immutable things, is now the Idea that shews
him, that if the three Angles of a Triangle were once equal to two
right ones, they will always be equal to two right ones. And hence
he comes to be certain, that what was once true in the case is
always true; what Ideas once agreed will always agree; and con-
sequently what he once knew to be true he will always know to
be true, as long as he can remember that he once knew it. Upon
this ground it is, that particular demonstrations in Mathematicks
afford general Knowledge. If then the Perception that the same
Ideas will eternally have the same Habitudes and Relations be not
a sufficient ground of Knowledge, there could be no knowledge
of general Propositions in Mathematicks, for no mathematical
Demonstration would be any other than particular: And when a
man had demonstrated any Proposition concerning one Triangle or
Circle, his Knowledge would not reach beyond that particular
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Diagram. If he would extend it farther, he must renew his Demon-
stration in another instance, before he could know it to be true in
another like Triangle, and so on: by which means one could never
come to the knowledge of any general Propositions. No Body, I
think, can deny that Mr. Newton certainly knows any Proposition,
that he now at any time reads in his Book, to be true, though he has
not in actual view that admirable Chain of intermediate Ideas,
whereby he at first discovered it to be true. Such a Memory is that,
able to retain such a train of Particulars, may be well thought
beyond the reach of humane Faculties. When the very Discovery,
Perception, and laying together that wonderful connection of Ideas
is found to surpass most Readers Comprehension. But yet ’tis
evident, the Author himself knows the Proposition to be true,
remembring he once saw the connection of those Ideas, as certainly
as he knows such a Man wounded another, remembring that he
saw him run him through. But because the Memory is not always
so clear as actual Perception, and does in all Men more or less
decay in length of time, this amongst other Differences is one,
which shews, that demonstrative Knowledge, is much more imperfect
than intuitive, as we shall see in the following Chapter.
Locke Hum IV, 1, §9, pp. 528-529-530