Thus the mind perceives that white is not black, that a circle is not a triangle, that three are more than two and equal to one and two. He that demands a greater certainty than this, demands he knows not what, and shows only that he has a mind to be a sceptic, without being able to be so. Certainty depends so wholly on this intuition, that, in the next degree of knowledge which I call demonstrative, this intuition is necessary in all the connexions of the intermediate ideas, without which we cannot attain knowledge and certainty. The next degree of knowledge is, where the mind perceives the agreement or disagreement of any ideas, but not immediately. The reason why the mind cannot always perceive presently the agreement or disagreement of two ideas, is, because those ideas, concerning whose agreement or disagreement the inquiry is made, cannot by the mind be so put together as to show it.
Demonstration depends on clearly perceived proofs.
As certain, but not so easy and ready as intuitive knowledge. This knowledge, by intervening proofs, though it be certain, yet the evidence of it is not altogether so clear and bright, nor the assent so ready, as in intuitive knowledge. The demonstrated conclusion not without doubt, precedent to the demonstration. If the eyes have lost the faculty of seeing, or the mind of perceiving, we in vain inquire after the quickness of sight in one, or clearness of perception in the other. Not so clear as intuitive knowledge.