7. The true method of advancing knowledge is by considering our abstract ideas.
We must, therefore, if we will
proceed as reason advises, adapt our methods of inquiry to the nature of the ideas we examine, and the truth we
search after. General and certain truths are only founded in the habitudes and relations of abstract ideas. A
sagacious and methodical application of our thoughts. for the finding out these relations, is the only way to
discover all that can be put with truth and certainty concerning them into general propositions. By what steps we
are to proceed in these, is to be learned in the schools of the mathematicians, who, from very plain and easy
beginnings, by gentle degrees, and a continued chain of reasonings, proceed to the discovery and demonstration of
truths that appear at first sight beyond human capacity. The art of finding proofs, and the admirable methods they
have invented for the singling out and laying in order those intermediate ideas that demonstratively show the
equality or inequality of unapplicable quantities, is that which has carried them so far, and produced such
wonderful and unexpected discoveries: but whether something like this, in respect of other ideas, as well as those
of magnitude, may not in time be found out, I will not determine. This, I think, I may say, that if other ideas that
are the real as well as nominal essences of their species, were pursued in the way familiar to mathematicians, they
would carry our thoughts further, and with greater evidence and clearness than possibly we are apt to imagine.
