On Knowledge (1875-1899)

"[…] it must be noticed that these diagrams do not naturally harmonize with the propositions of ordinary life or ordinary logic. […] The great bulk of the propositions which we commonly meet with are founded, and rightly founded, on an imperfect knowledge of the actual mutual relations of the implied classes to one another. […] one very marked characteristic about these circular diagrams is that they forbid the natural expression of such uncertainty, and are therefore only directly applicable to a very small number of such propositions as we commonly meet with." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"Science is the observation of things possible, whether present or past; prescience is the knowledge of things which may come to pass, though but slowly." (Leonardo da Vinci, "The Notebooks of Leonardo da Vinci", 1883)

"[…] when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of science." (William T Kelvin, "Electrical Units of Measurement", 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)

"Just as, in the map of a half-explored country, we see detached bits of rivers, isolated mountains, and undefined plains, not connected into any complete plan, so a new branch of knowledge consists of groups of facts, each group standing apart, so as not to allow us to reason from one to another." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1887)

"We say it is ‘explanation’ but it is only in ‘description’ that we are in advance of the older stages of knowledge and science. We describe better we explain just as little as our predecessors." (Friedrich W Nietzsche, "The Joyful Wisdom", 1887)

"The smallest group of facts, if properly classified and logically dealt with, will form a stone which has its proper place in the great building of knowledge, wholly independent of the individual workman who has shaped it." (Karl Pearson, "The Grammar of Science", 1892)

"The true aim of the teacher must be to impart an appreciation of method and not a knowledge of facts." (Karl Pearson, "The Grammar of Science", 1892)

"There is no short cut to truth, no way to gain a knowledge of the universe except through the gateway of scientific method." (Karl Pearson, "The Grammar of Science", 1892)

"Facts are not much use, considered as facts. They bewilder by their number and their apparent incoherency. Let them be digested into theory, however, and brought into mutual harmony, and it is another matter. Theory is of the essence of facts. Without theory scientific knowledge would be only worthy of the mad house." (Oliver Heaviside, "Electromagnetic Theory", 1893)

"Mature knowledge regards logical clearness as of prime importance: only logically clear images does it test as to correctness; only correct images does it compare as to appropriateness. By pressure of circumstances the process is often reversed. Images are found to be suitable for a certain purpose; are next tested as to their correctness ; and only in the last place purged of implied contradictions." (Heinrich Hertz, "The Principles of Mechanics Presented in a New Form", 1894)

"Without a theory all our knowledge of nature would be reduced to a mere inventory of the results of observation. Every scientific theory must be regarded as an effort of the human mind to grasp the truth, and as long as it is consistent with the facts, it forms a chain by which they are linked together and woven into harmony." (Thomas Preston, "The Theory of Heat", 1894)

"It is they who hold the secret of the mysterious property of the mind by which error ministers to truth, and truth slowly but irrevocably prevails. Theirs is the logic of discovery, the demonstration of the advance of knowledge and the development of ideas, which as the earthly wants and passions of men remain almost unchanged, are the charter of progress, and the vital spark in history." (Lord John Acton, "The Study of History", [lecture delivered at Cambridge] 1895)

"In order to comprehend and fully control arithmetical concepts and methods of proof, a high degree of abstraction is necessary, and this condition has at times been charged against arithmetic as a fault. I am of the opinion that all other fields of knowledge require at least an equally high degree of abstraction as mathematics, - provided, that in these fields the foundations are also everywhere examined with the rigour and completeness which is actually necessary." (David Hilbert, "Die Theorie der algebraischen Zahlkorper", 1897)