All Science is necessarily prophetic, so truly so, that the power of prophecy is the test, the infallible criterion, by which any presumed Science is ascertained to be actually & verily science. The Ptolemaic Astronomy was barely able to prognosticate a lunar eclipse; with Kepler and Newton came Science and Prophecy.

An infallible Remedy for the Tooth-ach, viz Wash the Root of an aching Tooth, in Elder Vinegar, and let it dry half an hour in the Sun; after which it will never ach more; Probatum est.

And as to the faculties of the mind, setting aside the arts grounded upon words, and especially that skill of proceeding upon generall, and infallible rules, called Science; which very few have, and but in few things; as being not a native faculty, born within us; nor attained, (as Prudence,) while we look after somewhat else.

By far the most important books for geology students were the quarries and clay pits, the cliffs and creek beds, the road and railroad cuts in woods and fields. Our words and letters were the imprints of plants and animals in stone, the minerals and crystals, and our vast, inexhaustible, incorruptible, and infallible library was nature itself.

For the saving the long progression of the thoughts to remote and first principles in every case, the mind should provide itself several stages; that is to say, intermediate principles, which it might have recourse to in the examining those positions that come in its way. These, though they are not self-evident principles, yet, if they have been made out from them by a wary and unquestionable deduction, may be depended on as certain and infallible truths, and serve as unquestionable truths to prove other points depending upon them, by a nearer and shorter view than remote and general maxims. … And thus mathematicians do, who do not in every new problem run it back to the first axioms through all the whole train of intermediate propositions. Certain theorems that they have settled to themselves upon sure demonstration, serve to resolve to them multitudes of propositions which depend on them, and are as firmly made out from thence as if the mind went afresh over every link of the whole chain that tie them to first self-evident principles.

Genius-worship is the infallible sign of an uncreative age.

I was appalled to find that the first referee recommended that part A be omitted and B condensed while the second referee recommended that B should be omitted and A condensed! Perceiving that even referees were not infallible, I decided to persist, and after a lot of bother to myself and to other referees I got both parts published.

In other words then, if a machine is expected to be infallible, it cannot also be intelligent.

It is perplexing to see the flexibility of the so-called 'exact sciences' which by cast-iron laws of logic and by the infallible help of mathematics can lead to conclusions which are diametrically opposite to one another.

Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight.

Much as I venerate the name of Newton, I am not therefore obliged to believe that he was infallible. I see … with regret that he was liable to err, and that his authority has, perhaps, sometimes even retarded the progress of science.

Nature could not err, but knew exactly and infallibly. Our function was to ask her questions, to listen patiently to the answers, and to understand them correctly.
And to this end we went out into the field, time and time again. Often at brief intervals we returned to the same outcrop where our Pythia, nature, opened her mouth from time to time to utter her equivocal oracles. Time and again we studied the same stratification, or the same interpenetration of rocks, and yet each time advanced one step further, because of what we had learned on the last visit, because the previous impression had had time to settle, or because this time our eyes were a little keener and now observed what hitherto had escaped them.

Occasionally and frequently the exercise of the judgment ought to end in absolute reservation. It may be very distasteful, and great fatigue, to suspend a conclusion; but as we are not infallible, so we ought to be cautious; we shall eventually find our advantage, for the man who rests in his position is not so far from right as he who, proceeding in a wrong direction, is ever increasing his distance.

Physical science is like simple addition: it is either infallible or it is false.

Such pretensions to nicety in experiments of this nature, are truly laughable! They will be telling us some day of the WEIGHT of the MOON, even to drams, scruples and grains—nay, to the very fraction of a grain!—I wish there were infallible experiments to ascertain the quantum of brains each man possesses, and every man's integrity and candour:—This is a desideratum in science which is most of all wanted.

The reasoning of mathematicians is founded on certain and infallible principles. Every word they use conveys a determinate idea, and by accurate definitions they excite the same ideas in the mind of the reader that were in the mind of the writer. When they have defined the terms they intend to make use of, they premise a few axioms, or self-evident principles, that every one must assent to as soon as proposed. They then take for granted certain postulates, that no one can deny them, such as, that a right line may be drawn from any given point to another, and from these plain, simple principles they have raised most astonishing speculations, and proved the extent of the human mind to be more spacious and capacious than any other science.

The reputation of science which ought to be the most lasting, as synonymous with truth, is often the least so. One discovery supersedes another; and the progress of light throws the past into obscurity. What is become of the Blacks, the Lavoisiers, the Priestleys, in chemistry? … When any set of men think theirs the only science worth studying, and themselves the only infallible persons in it, it is a sign how frail the traces are of past excellence in it.

Well, it [evolution] is a theory, it is a scientific theory only, and it has in recent years been challenged in the world of science and is not yet believed in the scientific community to be as infallible as it once was believed. But if it was going to be taught in the schools, then I think that also the biblical theory of creation, which is not a theory but the biblical story of creation, should also be taught.