Third, consider the insistency of an idea. The insistency of a past idea with reference to the present is a quantity which is less, the further back that past idea is, and rises to infinity as the past idea is brought up into coincidence with the present.

A true proposition is a proposition belief which would never lead to such disappointment so long as the proposition is not understood otherwise than it was intended.

Truly, that reason upon which we plume ourselves, though it may answer for little things, yet for great decisions is hardly surer than a toss up.

It is certain that the only hope of retroductive reasoning ever reaching the truth is that there may be some natural tendency toward an agreement between the ideas which suggest themselves to the human mind and those which are concerned in the laws of nature.

The essence of belief is the establishment of a habit.

A sign, or representamen, is something which stands to somebody for something in some respect or capacity. It addresses somebody,that is, creates in the mind of that person an equivalent sign, or perhaps a more developed sign. That sign which it creates I call the interpretant of the first sign. The sign stands for something, its object. It stands for that object, not in all respects, but in reference to a sort of idea, which I have sometimes called the ground of the representamen.

Kepler's discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler-such penetrating minds as Descartes and Pascal-were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.