Bad reasoning as well as good reasoning is possible; and this fact is the foundation of the practical side of logic.

The method of authority will always govern the mass of mankind; and those who wield the various forms of organized force in the state will never be convinced that dangerous reasoning ought not to be suppressed in some way.

... and it is probably that there is some secret here which remains to be discovered.

If we are to define science, ... it does not consist so much in knowing, nor even in "organized knowledge," as it does in diligent inquiry into truth for truth's sake, without any sort of axe to grind, nor for the sake of the delight of contemplating it, but from an impulse to penetrate into the reason of things.

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.

It is impossible not to envy the man who can dismiss reason, although we know how it must turn out at last.

Another characteristic of mathematical thought is that it can have no success where it cannot generalize.