The beliefs which we have most warrant for, have no safeguard to rest on, but a standing invitation to the whole world to prove them unfounded.

Lord, enlighten thou our enemies. Sharpen their wits, give acuteness to their perceptions, and consecutiveness and clearness to their reasoning powers: we are in danger from their folly, not from their wisdom; their weakness is what fills us with apprehension, not their strength.

On religion in particular, the time appears to me to have come, when it is a duty of all who, being qualified in point of knowledge, have, on mature consideration, satisfied themselves that the current opinions are not only false, but hurtful, to make their dissent known.

The process of tracing regularity in any complicated, and at first sight confused, set of appearances, is necessarily tentative; we begin by making any supposition, even a false one, to see what consequences will follow from it ; and by observing how these differ from the real phenomena, we learn what corrections to make in our assumption.

The pupil who is never required to do what he cannot do, never does what he can do.

The natural tendency of representative government, as of modern civilisation, is towards collective mediocrity: and this tendency is increased by all reductions and extensions of the franchise, their effect being to place the principal power in the hands of classes more and more below the highest level of instruction in the community.

The application of algebra to geometry ... has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.