Thus, by science I mean, first of all, a worldview giving primacy to reason and observation and a methodology aimed at acquiring accurate knowledge of the natural and social world. This methodology is characterized, above all else, by the critical spirit: namely, the commitment to the incessant testing of assertions through observations and/or experiments — the more stringent the tests, the better — and to revising or discarding those theories that fail the test. One corollary of the critical spirit is fallibilism: namely, the understanding that all our empirical knowledge is tentative, incomplete and open to revision in the light of new evidence or cogent new arguments (though, of course, the most well-established aspects of scientific knowledge are unlikely to be discarded entirely).. . . I stress that my use of the term 'science' is not limited to the natural sciences, but includes investigations aimed at acquiring accurate knowledge of factual matters relating to any aspect of the world by using rational empirical methods analogous to those employed in the natural sciences. (Please note the limitation to questions of fact. I intentionally exclude from my purview questions of ethics, aesthetics, ultimate purpose, and so forth.) Thus, 'science' (as I use the term) is routinely practiced not only by physicists, chemists and biologists, but also by historians, detectives, plumbers and indeed all human beings in (some aspects of) our daily lives. (Of course, the fact that we all practice science from time to time does not mean that we all practice it equally well, or that we practice it equally well in all areas of our lives.)

~ Alan Sokal

The real difference is this: the Christian says that he has knowledge; the Agnostic admits that he has none; and yet the Christian accuses the Agnostic of arrogance, and asks him how he has the impudence to admit the limitations of his mind. To the Agnostic every fact is a torch, and by this light, and this light only, he walks.The Agnostic knows that the testimony of man is not sufficient to establish what is known as the miraculous. We would not believe to-day the testimony of millions to the effect that the dead had been raised. The church itself would be the first to attack such testimony. If we cannot believe those whom we know, why should we believe witnesses who have been dead thousands of years, and about whom we know nothing?The Agnostic takes the ground that human experience is the basis of morality. Consequently, it is of no importance who wrote the gospels, or who vouched or vouches for the genuineness of the miracles. In his scheme of life these things are utterly unimportant. He is satisfied that “the miraculous” is the impossible. He knows that the witnesses were wholly incapable of examining the questions involved, that credulity had possession of their minds, that 'the miraculous' was expected, that it was their daily food.

~ Robert G. Ingersoll

Agnosticism, in fact, is not a creed, but a method, the essence of which lies in the rigorous application of a single principle. That principle is of great antiquity; it is as old as Socrates; as old as the writer who said, 'Try all things, hold fast by that which is good'; it is the foundation of the Reformation, which simply illustrated the axiom that every man should be able to give a reason for the faith that is in him, it is the great principle of Descartes; it is the fundamental axiom of modern science. Positively the principle may be expressed: In matters of the intellect, follow your reason as far as it will take you, without regard to any other consideration. And negatively: In matters of the intellect, do not pretend that conclusions are certain which are not demonstrated or demonstrable. That I take to be the agnostic position, which if a man keep whole and undefiled, he shall not be ashamed to look the universe in the face, whatever the future may have in store for him.The results of the working out of the agnostic principle will vary according to individual knowledge and capacity, and according to the general condition of science. That which is unproved today may be proved, by the help of new discoveries, tomorrow. The only negative fixed points will be those negations which flow from the demonstrable limitation of our faculties. And the only obligation accepted is to have the mind always open to conviction.That it is wrong for a man to say he is certain of the objective truth of a proposition unless he can provide evidence which logically justifies that certainty. This is what agnosticism asserts and in my opinion, is all that is essential to agnosticism.

~ Thomas Henry Huxley