At the heart of science is an essential balance between two seemingly contradictory attitudes—an openness to new ideas, no matter how bizarre or counterintuitive they may be, and the most ruthless skeptical scrutiny of all ideas, old and new. This is how deep truths are winnowed from deep nonsense.

Colour, Figure, Motion, Extension and the like, considered only so many Sensations in the Mind, are perfectly known, there being nothing in them which is not perceived. But if they are looked on as notes or Images, referred to Things or Archetypes existing without the Mind, then are we involved all in Scepticism.

In mathematics, … and in natural philosophy since mathematics was applied to it, we see the noblest instance of the force of the human mind, and of the sublime heights to which it may rise by cultivation. An acquaintance with such sciences naturally leads us to think well of our faculties, and to indulge sanguine expectations concerning the improvement of other parts of knowledge. To this I may add, that, as mathematical and physical truths are perfectly uninteresting in their consequences, the understanding readily yields its assent to the evidence which is presented to it; and in this way may be expected to acquire the habit of trusting to its own conclusions, which will contribute to fortify it against the weaknesses of scepticism, in the more interesting inquiries after moral truth in which it may afterwards engage.

It is one of the chief merits of proofs that they instil a certain scepticism as to the result proved.

It must, however, be confessed that this species of scepticism, when more moderate, may be understood in a very reasonable sense, and is a necessary preparative to the study of philosophy by preserving a proper impartiality in our judgments and weaning our mind from all those prejudices which we may have imbibed from education or rash opinion.

Let us not fear that the issues of natural science shall be scepticism or anarchy. Through all God's works there runs a beautiful harmony. The remotest truth in his universe is linked to that which lies nearest the Throne.

The barrenness of doubt had to make itself felt before it could be supplanted by knowledge. It was not until Hume, by carrying scepticism to its uttermost extent, had shown its unsatisfactory character and vain results, that the germs of scientific method, implanted by Bacon and Descartes, could develop and bear fruit in the positive philosophy of Comte.

The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science “more geometrico.”

The hallmark of scientific behaviour is a certain scepticism even towards one’s most cherished theories.

The history of science alone can keep the physicist from the mad ambitions of dogmatism as well as the despair of pyrrhonian scepticism.

The improver of natural knowledge absolutely refuses to acknowledge authority as such. For him, scepticism is the highest of duties, blind faith the one unpardonable sin. The man of science has learned to believe in justification, not by faith, but by verification.

The institutional goal of science is the extension of certified knowledge. The technical methods employed toward this end provide the relevant definition of knowledge: empirically confirmed and logically consistent predictions. The institutional imperatives (mores) derive from the goal and the methods. The entire structure of technical and moral norms implements the final objective. The technical norm of empirical evidence, adequate, valid and reliable, is a prerequisite for sustained true prediction; the technical norm of logical consistency, a prerequisite for systematic and valid prediction. The mores of science possess a methodologic rationale but they are binding, not only because they are procedurally efficient, but because they are believed right and good. They are moral as well as technical prescriptions. Four sets of institutional imperatives–universalism, communism, disinterestedness, organized scepticism–comprise the ethos of modern science.

The major religions on the Earth contradict each other left and right. You can’t all be correct. And what if all of you are wrong? It’s a possibility, you know. You must care about the truth, right? Well, the way to winnow through all the differing contentions is to be skeptical. I’m not any more skeptical about your religious beliefs than I am about every new scientific idea I hear about. But in my line of work, they’re called hypotheses, not inspiration and not revelation.

The privilege is not allowed even to genius in this world to inspect its own elements, and read its own destiny, and it is perhaps well for mankid that it is so. Could we lift the curtain which hides our future lives, and glance hastily at the misfortunes, the vexations, and the disappointments which await us, we should be discouraged from attempting the performance of even of such deeds as are destined eventually to crown us with honor.
In a book of his reminiscenses, Oliver Hampton Smith, years after his first meeting with Morse, described the inventor - who had by then overcome the initial scepticism over his invention, but instead needed to vigorously defend his exclusive right of property in the magnetic telegraph.

These Disciplines [mathematics] serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right Reason, and inspire us with Resolution to wrestle against the unjust Tyranny of false Prejudices. If the Fancy be unstable and fluctuating, it is to be poized by this Ballast, and steadied by this Anchor, if the Wit be blunt it is sharpened upon this Whetstone; if luxuriant it is pared by this Knife; if headstrong it is restrained by this Bridle; and if dull it is rouzed by this Spur. The Steps are guided by no Lamp more clearly through the dark Mazes of Nature, by no Thread more surely through the intricate Labyrinths of Philosophy, nor lastly is the Bottom of Truth sounded more happily by any other Line. I will not mention how plentiful a Stock of Knowledge the Mind is furnished from these, with what wholesome Food it is nourished, and what sincere Pleasure it enjoys. But if I speak farther, I shall neither be the only Person, nor the first, who affirms it; that while the Mind is abstracted and elevated from sensible Matter, distinctly views pure Forms, conceives the Beauty of Ideas, and investigates the Harmony of Proportions; the Manners themselves are sensibly corrected and improved, the Affections composed and rectified, the Fancy calmed and settled, and the Understanding raised and excited to more divine Contemplations. All which I might defend by Authority, and confirm by the Suffrages of the greatest Philosophers.

We sometimes are inclined to look into a science not our own as into a catalogue of results. In Faraday’s Diary, it becomes again what it really is, a campaign of mankind, balancing in any given moment, past experience, present speculation, and future experimentation, in a unique concoction of scepticism, faith, doubt, and expectation.

Young men, have confidence in those powerful and safe methods, of which we do not yet know all the secrets. And, whatever your career may be, do not let yourselves become tainted by a deprecating and barren skepticism … Live … until the time comes when you have the immense happiness of thinking that you have contributed in some way to the progress and to the good of humanity.