11.  III.  Thirdly, Because we perceive not intermediate Ideas to show conclusions.

Our reason is often at a stand, because it perceives not those ideas, which could serve to show the certain or probable agreement or disagreement of any other two ideas:  and in this some men’s faculties far outgo others.  Till algebra, that great instrument and instance of human sagacity, was discovered, men with amazement looked on several of the demonstrations of ancient mathematicians, and could scarce forbear to think the finding several of those proofs to be something more than human.

12.  IV.  Fourthly, Because we often proceed upon wrong Principles.

The mind, by proceeding upon false principles, is often engaged in absurdities and difficulties, brought into straits and contradictions, without knowing how to free itself:  and in that case it is in vain to implore the help of reason, unless it be to discover the falsehood and reject the influence of those wrong principles.  Reason is so far from clearing the difficulties which the building upon false foundations brings a man into, that if he will pursue it, it entangles him the more, and engages him deeper in perplexities.

13.  V. Fifthly, Because we often employ doubtful Terms.

As obscure and imperfect ideas often involve our reason, so, upon the same ground, do dubious words and uncertain signs, often, in discourses and arguings, when not warily attended to, puzzle men’s reason, and bring them to a nonplus.  But these two latter are our fault, and not the fault of reason.  But yet the consequences of them are nevertheless obvious; and the perplexities or errors they fill men’s minds with are everywhere observable.

14.  Our highest Degree of Knowledge is intuitive, without Reasoning.

Some of the ideas that are in the mind, are so there, that they can be by themselves immediately compared one with another:  and in these the mind is able to perceive that they agree or disagree as clearly as that it has them.  Thus the mind perceives, that an arch of a circle is less than the whole circle, as clearly as it does the idea of a circle:  and this, therefore, as has been said, I call intuitive knowledge; which is certain, beyond all doubt, and needs no probation, nor can have any; this being the highest of all human certainty.  In this consists the evidence of all those maxims which nobody has any doubt about, but every man (does not, as is said, only assent to, but) knows to be true, as soon as ever they are proposed to his understanding.  In the discovery of and assent to these truths, there is no use of the discursive faculty, no need of reasoning, but they are known by a superior and higher degree of evidence.  And such, if I may guess at things unknown, I am apt to think that angels have now, and the spirits of just men made perfect shall have, in a future state, of thousands of things which now either wholly escape our apprehensions, or which our short-sighted reason having got some faint glimpse of, we, in the dark, grope after.