"Metaphysics. The science to which ignorance goes to learn its knowledge, and knowledge to learn its ignorance. On which all men agree that it is the key, but no two upon how it is to be put into the lock." (Augustus De Morgan, [letter to Dr. Whewell] 1850)
"Nothing can be more puerile than the complaints sometimes made by certain cultivators of a science, that it is very difficult to make discoveries now that the soil has been exhausted, whereas they were so easily made when the ground was first broken. It is an error begotten by ignorance out of indolence. The first discovery did not drop upon the expectant idler who, with placid equanimity waited for the goods the gods might send, but was heavily obtained by patient, systematic, and intelligent labour; and, beyond all question, the same labour of the same mind which made the first discoveries in the new science, would now succeed in making many more, trampled though the field may be by the restless feet of those unmethodical inquirers who, running to and fro, anxiously exclaim, 'Who will show us any good thing?'" (George Gore, "Psychological Inquiries", Journal of Mental Science, 1862)
"It has often been said that, to make discoveries, one must be ignorant. This opinion, mistaken in itself, nevertheless conceals a truth. It means that it is better to know nothing than to keep in mind fixed ideas based on theories whose confirmation we constantly seek, neglecting meanwhile everything that fails to agree with them." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)
"Nevertheless so profound is our ignorance, and so high our presumption, that we marvel when we hear of the extinction of an organic being; and as we do not see the cause, we invoke cataclysms to desolate the world, or invent laws on the duration of the forms of life!" (Charles Darwin, "On the Origin of Species by Means of Natural Selection", 1866)
"[T]he notion of a negative magnitude has become quite a familiar one […] But it is far otherwise with the notion which is really the fundamental one (and I cannot too strongly emphasize the assertion) underlying and pervading the whole of modern analysis and geometry, that of imaginary magnitude in analysis and of imaginary space (or space as a locus in quo of imaginary points and figures) in geometry: I use in each case the word imaginary as including real. This has not been, so far as I am aware, a subject of philosophical discussion or inquiry. […] considering the prominent position which the notion occupies-say even that the conclusion were that the notion belongs to mere technical mathematics, or has reference to nonentities in regard to which no science is possible, still it seems to me that (as a subject of philosophical discussion) the notion ought not to be thus ignored; it should at least be shown that there is a right to ignore it." (Arthur Cayley, [address before the meeting of the British Association at Southport] 1870)
"You cannot and need not expect to disturb the public in the possession of its medical superstitions. A man’s ignorance is as much his private property, and as precious in his own eyes, as his family Bible." (Oliver W Holmes, "The Young Practitioner", [speech] 1871)
"A wise man only remembers his ignorance in order to destroy it." (Clifford W Kingdon, "Aims and Instruments of Scientific Thought", The Popular Science Monthly Vol. 2, 1872)
"There are no limits in mathematics, and those that assert there are, are infinite ruffians, ignorant, lying blackguards. There is no differential calculus, no Taylor's theorem, no calculus of variations, [...] in mathematics. There is no quackery whatever in mathematics." (Augustus De Morgan, "A Budget of Paradoxes", 1872)
"You may read any quantity of books, and you may be almost as ignorant as you were at starting, if you don’t have, at the back of your minds, the change for words in definite images which can only be acquired through the operation of your observing faculties on the phenomena of nature." (Thomas H Huxley, "Science and Education", 1877)
"Dazzling source of light and heat, of motion, life, and beauty, the inimitable sun has in all ages received the earnest and grateful homage of mortals. The ignorant admire it because they feel the effects of its power and its value; the savant appreciates it because he has learned its unique importance in the system of the world; the artist salutes it because he sees in its splendor the virtual cause of all harmonies." (Camille Flammarion, Popular Astronomy: A General Description of the Heavens, 1880)
"You must not know too much, or be too precise or scientific about birds and trees and flowers and watercraft; a certain free margin, and even vagueness - perhaps ignorance, credulity - helps your enjoyment of these things." (Walt Whitman, "Specimen Days", 1882)
"Our task is only that of sending out a few pickets under the starry flag of science to the edge of that dark domain where the ensigns of the obstinate rebel, Ignorance, are flying undisputed." (Oliver W Holmes, "Medical Essays 1842–1882", 1883)
"I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them on the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge, - knowledge mingled with ignorance, producing doubt." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1887)
"Our science is a drop, our ignorance a sea. Whatever else be certain, this at least is certain - that the world of our present natural knowledge is enveloped in a larger world of some sort whose residual properties [about which] we at present can frame no positive idea." (William James, "Is Life Worth Living?", 1895)
"Round about the accredited and orderly facts of every science there ever fl oats a sort of dust-cloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to […]" (William James, "The Will to Believe", 1896)
"Theory helps us to bear our ignorance of facts." (George Santayana, "The Sense of Beauty", 1896)
"The history of civilization proves beyond doubt just how sterile the repeated attempts of metaphysics to guess at nature’s laws have been. Instead, there is every reason to believe that when the human intellect ignores reality and concentrates within, it can no longer explain the simplest inner workings of life’s machinery or of the world around us." (Santiago Ramón y Cajal, "Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad", 1897)
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