Thirdly, As to the third sort of our
knowledge, viz. the agreement or disagreement of any of our ideas in
any other relation: this, as it is the largest field of our knowledge,
so it is hard to determine how far it may extend: because the advances
that are made in this part of knowledge, depending on our sagacity
in finding intermediate ideas, that may show the relations and
habitudes of ideas whose co-existence is not considered, it is a
hard matter to tell when we are at an end of such discoveries; and
when reason has all the helps it is capable of, for the finding of
proofs or examining the agreement or disagreement of remote ideas.
They that are ignorant of Algebra cannot imagine the wonders in this
kind are to be done by it: and what further improvements and helps
advantageous to other parts of knowledge the sagacious mind of man may
yet find out, it is not easy to determine. This at least I believe,
that the ideas of quantity are not those alone that are capable of
demonstration and knowledge; and that other, and perhaps more
useful, parts of contemplation, would afford us certainty, if vices,
passions, and domineering interest did not oppose or menace such
endeavours.
Morality capable of demonstration. The idea of a supreme Being,
infinite in power, goodness, and wisdom, whose workmanship we are, and
on whom we depend; and the idea of ourselves, as understanding,
rational creatures, being such as are clear in us, would, I suppose,
if duly considered and pursued, afford such foundations of our duty
and rules of action as might place morality amongst the sciences
capable of demonstration: wherein I doubt not but from self-evident
propositions, by necessary consequences, as incontestible as those
in mathematics, the measures of right and wrong might be made out,
to any one that will apply himself with the same indifferency and
attention to the one as he does to the other of these sciences.
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