📓On Literature: On Facts (From Fiction to Science-Fiction)

"Every fact is a logarithm; one added term ramifies it until it is thoroughly transformed. In the general aspect of things, the great lines of creation take shape and arrange themselves into groups; beneath lies the unfathomable." (Victor Hugo, "The Toilers of the Sea", 1866)

'It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts." (Sir Arthur C Doyle, "The Adventures of Sherlock Holmes", 1892)

"If the fresh facts which come to our knowledge all fit themselves into the scheme, then our hypothesis may gradually become a solution." (Arthur C Doyle, "The Adventure of Wisteria Lodge", 1908)

"The facts of life do not penetrate to the sphere in which our beliefs are cherished; as it was not they that engendered those beliefs, so they are powerless to destroy them." (Marcel Proust, "In Search of Lost Time", 1913)

"The superstitions of today are the scientific facts of tomorrow." (Hamilton Deane & John L. Balderston, "Dracula", 1927)

"The point is that we are all capable of believing things which we know to be untrue, and then, when we are finally proved wrong, impudently twisting the facts so as to show that we were right. Intellectually, it is possible to carry on this process for an indefinite time: the only check on it is that sooner or later a false belief bumps up against solid reality, usually on a battlefield." (George Orwell, "In Front of Your Nose", Tribune, 1946)

"One thinks one’s something unique and wonderful at the center of the universe. But in fact one’s merely a slight delay in the ongoing march of entropy." (Aldous Huxley, "Island", 1962)

"Science fiction is, very strictly and literally, analogous to science facts. It is a convenient analog system for thinking about new scientific, social, and economic ideas - and for re-examining old ideas." (John W Campbell Jr., "Prologue to Analog", 1962)

"These dwarfs amass knowledge as others do treasure; for this reason they are called Hoarders of the Absolute. Their wisdom lies in the fact that they collect knowledge but never use it." (Stanislaw Lem, "How Erg the Self-Inducing Slew a Paleface", 1965)

"[Human] communication is rendered more complex by the use of differing sets of sound-symbols, called languages and by the fact that a given set of symbols tends to change with the passage of years to become an entirely new language." (Howard L Myers, "The Creatures of Man", 1968)

"What are the facts? Again and again and again - what are the facts? Shun wishful thinking, ignore divine revelation, forget what ‘the stars foretell,’ avoid opinion, care not what the neighbors think, never mind the unguessable ‘verdict of history', - what are the facts, and to how many decimal places? You pilot always into an unknown future; facts are your only clue. Get the facts!" (Robert A Heinlein, "Time Enough for Love", 1973)

"Many scientists deeply involved in the exploration of the solar system (myself among them) were first turned in that direction by science fiction. And the fact that some of that science fiction was not of the highest quality is irrelevant. Ten-year-olds do not read the scientific literature." (Carl Sagan, "Broca's Brain", 1979)

"The whole fabric of the space-time continuum is not merely curved, it is in fact totally bent." (Douglas N Adams, "The Restaurant at the End of the Universe", 1980)

"The fact is that thresholds exist throughout reality, and that things on their far sides are altogether different from things on their hither sides." (Poul Anderson, "The Saturn Game", 1981)

"This is an exercise in fictional science, or science fiction, if you like that better. Not for amusement: science fiction in the service of science. Or just science, if you agree that fiction is a part of it, always was, and always will be as long as our brains are only miniscule fragments of the universe, much too small to hold all the facts of the world but not too idle to speculate about them." (Valentino Braitenberg," Vehicles: Experiments in Synthetic Psychology", 1984)

"A science fiction writer is - or should be - constrained by what is, or logically might be. That can mean simple fidelity to facts (which, in science, are always more important than theories - though Lord knows the two help shape each other, undermining the convenient, complacent separation of observer and observed). To me it also means heeding the authentic, the actual and concrete. Bad fiction uses the glossy generality; good writing needs the smattering of detail, the unrelenting busy mystery of the real." (Gregory Benford, "Afterword to Exposures", [in Alien Flesh] 1986)

"In the end, each life is no more than the sum of contingent facts, a chronicle of chance intersections, of flukes, of random events that divulge nothing but their own lack of purpose." (Paul Auster, "The Locked Room", 1988)

"The rationality of our universe is best suggested by the fact that we can discover more about it from any starting point, as if it were a fabric that will unravel from any thread." (George Zebrowski, "Is Science Rational?", OMNI Magazine, 1994)

"The old knowledge had been difficult but not distressing. It had been all paradox and myth, and it had made sense. The new knowledge was all fact and reason, and it made no sense." (Ursula K Le Guin," "A Man of the People", 1995)

"Because the question for me was always whether that shape we see in our lives was there from the beginning or whether these random events are only called a pattern after the fact. Because otherwise we are nothing." (Cormac McCarthy, "All the Pretty Horses", 2010)

"Science fiction these days is only half a step ahead of science. Astrophysicists and scientists are working in the same way as science fiction writers. They’re working things out in their imagination based on the slim scientific facts that they know. Hawking imagines a black hole and then discovers the mathematics that support his theory, and new possibilities come to light. That’s the imaginative flair that scientists have to have. For me as a sci-fi writer, spinning those ideas in your mind brings you to the point where you dream in science fiction. Suddenly you think of something in the middle of the night, and it’s so vivid you don’t need to write it down because you know you’ll remember it in the morning. That’s what these books, Zero G, reflect: a vivid imagination." (William Shatner, "William Shtner on Sci-Fi, Aging and the Environment", Saturday Evening Post, [interview] 2017)

🧩Out of Context: On Facts (Definitions)

"While those whom devotion to abstract discussions has rendered unobservant of the facts are too ready to dogmatize on the basis of a few observations." (Aristotle, "De Caelo" ["On the Heavens"], cca. 350 BC)

" By observation, facts are distinctly and minutely impressed on the mind. By analogy, similar facts are connected. By experiment, new facts are discovered [...]" (Sir Humphry Davy, "Elements of Chemical Philosophy" Vol. 4, 1812)

"Facts are the mere dross of history. " (Thomas B Macaulay, "History", 1828)

"Facts are not much use, considered as facts." (Oliver Heaviside, "Electromagnetic Theory", 1893)

"Facts are carpet-tacks under the pneumatic tires of theory." (Austin O’Malley, "Keystones of Thought", 1918)

"Obvious facts are apt to be over-rated." (George Iles, "Canadian Stories", 1918)

"We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest." (Alfred N Whitehead, "The Concept of Nature", 1919)

"[…] facts are too bulky to be lugged about conveniently except on the wheels of theory." (Julian Huxley, "Essays of a Biologist", 1929)

"If our so-called facts are changing shadows, they are shadows cast by the light of constant truth." (Sir Arthur S Eddington, "Science and the Unseen World", 1929)

"Facts are the raw material of science - the bricks from which our model of the universe must be built - and we are rightly taught to search for sound and solid facts, for strong and heavy bricks that will serve us well in building foundations, for clean and polished bricks that will fi t neatly into ornamental towers. " (Marston Bates, "The Natural History of Mosquitoes", 1949)

"Facts are to the scientist what words are to the poet." (Isidor Isaac Rabi, "Faith in Science", Atlantic Monthly , Vol. 187, 1951)

"No theory ever agrees with all the facts in its domain, yet it is not always the theory that is to blame. Facts are constituted by older ideologies, and a clash between facts and theories may be proof of progress." (Paul K Feyerabend, "Against Method", 1978)

"Facts are not pure and unsullied bits of information; culture also influences what we see and how we see it." (Stephen J Gould, "The Mismeasure of Man", 1980)

"Facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data." (Stephen J Gould "Evolution as Fact and Theory", 1981)

"Mathematical facts are not isolated, they are woven into a vast spider's web of interconnections." (Gregory Chaitin "Meta Math: The Quest for Omega", 2005) 

"A fact is not novel if it has an analogue which could have some interest. A fact which does not fit in with a series of known facts is a fact which deserves particular attention." (Joseph L Gay-Lussac)

"By observation, facts are distinctly and minutely impressed in the mind; by analogy, similar facts are connected ; by experiment, new facts are discovered ; and, in the progression of knowledge, observation, guided by analogy, leads to experiment, and analogy, confirmed by experiment, becomes scientific truth." (Sir Humphry Davy)

"Facts are stubborn things, but statistics are pliable." (Mark Twain)

📁 On DIKW: On Knowledge (2000-2009)

"Storytelling is the art of unfolding knowledge in a way that makes each piece contribute to a larger truth." (Philip Gerard, "Writing a Book That Makes a Difference", 2000)

"There is a strong tendency today to narrow specialization. Because of the exponential growth of information, we can afford (in terms of both economics and time) preparation of specialists in extremely narrow fields, the various branches of science and engineering having their own particular realms. As the knowledge in these fields grows deeper and broader, the individual's field of expertise has necessarily become narrower. One result is that handling information has become more difficult and even ineffective." (Semyon D Savransky, "Engineering of Creativity", 2000)

"All human knowledge - including statistics - is created  through people's actions; everything we know is shaped by our language, culture, and society. Sociologists call this the social construction of knowledge. Saying that knowledge is socially constructed does not mean that all we know is somehow fanciful, arbitrary, flawed, or wrong. For example, scientific knowledge can be remarkably accurate, so accurate that we may forget the people and social processes that produced it." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Defined from a societal standpoint, information may be seen as an entity which reduces maladjustment between system and environment. In order to survive as a thermodynamic entity, all social systems are dependent upon an information flow. This explanation is derived from the parallel between entropy and information where the latter is regarded as negative entropy (negentropy). In more common terms information is a form of processed data or facts about objects, events or persons, which are meaningful for the receiver, inasmuch as an increase in knowledge reduces uncertainty." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"Knowledge is factual when evidence supports it and we have great confidence in its accuracy. What we call 'hard fact' is information supported by  strong, convincing evidence; this means evidence that, so far as we know, we cannot deny, however we examine or test it. Facts always can be questioned, but they hold up under questioning. How did people come by this information? How did they interpret it? Are other interpretations possible? The more satisfactory the answers to such questions, the 'harder' the facts."(Joel Best, Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists, 2001)

"Knowledge maps are node-link representations in which ideas are located in nodes and connected to other related ideas through a series of labeled links. They differ from other similar representations such as mind maps, concept maps, and graphic organizers in the deliberate use of a common set of labeled links that connect ideas. Some links are domain specific (e.g., function is very useful for some topic domains...) whereas other links (e.g., part) are more broadly used. Links have arrowheads to indicate the direction of the relationship between ideas." (Angela M. O’Donnell et al, "Knowledge Maps as Scaffolds for Cognitive Processing", Educational Psychology Review Vol. 14 (1), 2002) 

"Knowledge is encoded in models. Models are synthetic sets of rules, and pictures, and algorithms providing us with useful representations of the world of our perceptions and of their patterns." (Didier Sornette, "Why Stock Markets Crash - Critical Events in Complex Systems", 2003)

"The networked world continuously refines, reinvents, and reinterprets knowledge, often in an autonomic manner." (Donald M Morris et al, "A revolution in knowledge sharing", 2003) 

"A mental model is conceived […] as a knowledge structure possessing slots that can be filled not only with empirically gained information but also with ‘default assumptions’ resulting from prior experience. These default assumptions can be substituted by updated information so that inferences based on the model can be corrected without abandoning the model as a whole. Information is assimilated to the slots of a mental model in the form of ‘frames’ which are understood here as ‘chunks’ of knowledge with a well-defined meaning anchored in a given body of shared knowledge." (Jürgen Renn, "Before the Riemann Tensor: The Emergence of Einstein’s Double Strategy", 2005)

"Evolution moves towards greater complexity, greater elegance, greater knowledge, greater intelligence, greater beauty, greater creativity, and greater levels of subtle attributes such as love. […] Of course, even the accelerating growth of evolution never achieves an infinite level, but as it explodes exponentially it certainly moves rapidly in that direction." (Ray Kurzweil, "The Singularity is Near", 2005)

“It makes no sense to seek a single best way to represent knowledge - because each particular form of expression also brings its particular limitations. For example, logic-based systems are very precise, but they make it hard to do reasoning with analogies. Similarly, statistical systems are useful for making predictions, but do not serve well to represent the reasons why those predictions are sometimes correct.” (Marvin Minsky, "The Emotion Machine: Commonsense Thinking, Artificial Intelligence, and the Future of the Human Mind", 2006)

"Information is just bits of data. Knowledge is putting them together. Wisdom is transcending them." (Ram Dass, "One-Liners: A Mini-Manual for a Spiritual Life (ed. Harmony", 2007)

"Science is not only the enterprise of harnessing nature to serve the practical needs of humankind. It is also part of man’s unending search for knowledge about the universe and his place within it." (Henry P Stapp, "Mindful Universe: Quantum Mechanics and the Participating Observer", 2007)

"Critical thinking is essentially a questioning, challenging approach to knowledge and perceived wisdom. It involves ideas and information from an objective position and then questioning this information in the light of our own values, attitudes and personal philosophy." Brenda Judge et al, "Critical Thinking Skills for Education Students", 2009)

"Equations seem like treasures, spotted in the rough by some discerning individual, plucked and examined, placed in the grand storehouse of knowledge, passed on from generation to generation. This is so convenient a way to present scientific discovery, and so useful for textbooks, that it can be called the treasure-hunt picture of knowledge." (Robert P Crease, "The Great Equations", 2009)

"Traditional statistics is strong in devising ways of describing data and inferring distributional parameters from sample. Causal inference requires two additional ingredients: a science-friendly language for articulating causal knowledge, and a mathematical machinery for processing that knowledge, combining it with data and drawing new causal conclusions about a phenomenon."(Judea Pearl, "Causal inference in statistics: An overview", Statistics Surveys 3, 2009)

📁 On DIKW: On Knowledge (1825-1849)

"It is true that of far the greater part of things, we must content ourselves with such knowledge as description may exhibit, or analogy supply; but it is true likewise, that these ideas are always incomplete, and that at least, till we have compared them with realities, we do not know them to be just. As we see more, we become possessed of more certainties, and consequently gain more principles of reasoning, and found a wider base of analogy." (Samuel Johnson, 1825)

"The first steps in the path of discovery, and the first approximate measures, are those which add most to the existing knowledge of mankind." (Charles Babbage, "Reflections on the Decline of Science in England", 1830)

"Our knowledge of circumstances has increased, but our uncertainty, instead of having diminished, has only increased. The reason of this is, that we do not gain all our experience at once, but by degrees; so our determinations continue to be assailed incessantly by fresh experience; and the mind, if we may use the expression, must always be under arms." (Carl von Clausewitz, "On War", 1832)

"Truth in itself is rarely sufficient to make men act. Hence the step is always long from cognition to volition, from knowledge to ability. The most powerful springs of action in men lie in his emotions." (Carl von Clausewitz, "On War", 1832)

"Science and knowledge are subject, in their extension and increase, to laws quite opposite to those which regulate the material world. Unlike the forces of molecular attraction, which cease at sensible distances; or that of gravity, which decreases rapidly with the increasing distance from the point of its origin; the farther we advance from the origin of our knowledge, the larger it becomes, and the greater power it bestows upon its cultivators, to add new fields to its dominions." (Charles Babbage, "On the Economy of Machinery and Manufactures", 1832)

"The peculiar character of mathematical truth is that it is necessarily and inevitably true; and one of the most important lessons which we learn from our mathematical studies is a knowledge that there are such truths." (William Whewell, "Principles of English University Education", 1838)

"[…] in order that the facts obtained by observation and experiment may be capable of being used in furtherance of our exact and solid knowledge, they must be apprehended and analysed according to some Conception which, applied for this purpose, gives distinct and definite results, such as can be steadily taken hold of and reasoned from […]" (William Whewell, "The Philosophy of the Inductive Sciences Founded Upon their History" Vol. 2, 1840)

"But a thousand unconnected observations have no more value, as a demonstrative proof, than a single one. If we do not succeed in discovering causes by our researches, we have no right to create them by the imagination; we must not allow mere fancy to proceed beyond the bounds of our knowledge."(Justus von Liebig, "The Lancet", 1844)

"[…] there do exist among us doctrines of solid and acknowledged certainty, and truths of which the discovery has been received with universal applause. These constitute what we commonly term Sciences; and of these bodies of exact and enduring knowledge, we have within our reach so large and varied a collection, that we may examine them, and the history of their formation, with good prospect of deriving from the study such instruction as we seek." (William Whewell, "The Philosophy of the Inductive Sciences Founded upon Their History" Vol. 1, 1847)

📁 On DIKW: On Knowledge (1850-1874)

"In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data." (James C Maxwell, [Letter to Lewis Campbell] 1851) 

"Remember that accumulated knowledge, like accumulated capital, increases at compound interest: but it differs from the accumulation of capital in this; that the increase of knowledge produces a more rapid rate of progress, whilst the accumulation of capital leads to a lower rate of interest. Capital thus checks its own accumulation: knowledge thus accelerates its own advance. Each generation, therefore, to deserve comparison with its predecessor, is bound to add much more largely to the common stock than that which it immediately succeeds." (Charles Babbage, "The Exposition of 1851: Or the Views of Industry, Science and Government of England", 1851)

"All knowledge is profitable; profitable in its ennobling effect on the character, in the pleasure it imparts in its acquisition, as well as in the power it gives over the operations of mind and of matter. All knowledge is useful; every part of this complex system of nature is connected with every other. Nothing is isolated. The discovery of to-day, which appears unconnected with any useful process, may, in the course of a few years, become the fruitful source of a thousand inventions." (Joseph Henry, "Report of the Secretary" [Sixth Annual Report of the Board of Regents of the Smithsonian Institution for 1851], 1852)

"SYSTEM (σύστημα, σύν ἵστημιavu, to place together) - is a full and connected view of all the truths of some department of knowledge. An organized body of truth, or truths arranged under one and the same idea, which idea is as the life or soul which assimilates all those truths. No truth is altogether isolated. Every truth has relation to some other. And we should try to unite the facts of our knowledge so as to see them in their several bearings. This we do when we frame them into a system. To do so legitimately we must begin by analysis and end with synthesis. But system applies not only to our knowledge, but to the objects of our knowledge. Thus we speak of the planetary system, the muscular system, the nervous system. We believe that the order to which we would reduce our ideas has a foundation in the nature of things. And it is this belief that encourages us to reduce our knowledge of things into systematic order. The doing so is attended with many advantages. At the same time a spirit of systematizing may be carried too far. It is only in so far as it is in accordance with the order of nature that it can be useful or sound." (William Fleming, "Vocabulary of philosophy, mental, moral, and metaphysical; with quotations and references; for the use of students", 1857)

“The conception of the inconceivable [imaginary], this measurement of what not only does not, but cannot exist, is one of the finest achievements of the human intellect. No one can deny that such imaginings are indeed imaginary. But they lead to results grander than any which flow from the imagination of the poet. The imaginary calculus is one of the master keys to physical science. These realms of the inconceivable afford in many places our only mode of passage to the domains of positive knowledge. Light itself lay in darkness until this imaginary calculus threw light upon light. And in all modern researches into electricity, magnetism, and heat, and other subtile physical inquiries, these are the most powerful instruments.” (Thomas Hill, “The Imagination in Mathematics”, North American Review Vol. 85, 1857)

"Science asks no questions about the ontological pedigree or a priori character of a theory, but is content to judge it by its performance; and it is thus that a knowledge of nature, having all the certainty which the senses are competent to inspire, has been attained - a knowledge which maintains a strict neutrality toward all philosophical systems and concerns itself not with the genesis or a priori grounds of ideas." (Chauncey Wright, "The Philosophy of Herbert Spencer", North American Review, 1865)

"One of the greatest obstacles to the free and universal movement of human knowledge is the tendency that leads different kinds of knowledge to separate into systems." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect." (Hermann von Helmholtz, "The Aim and Progress of Physical Science", 1869)

"As systematic unity is what first raises ordinary knowledge to the rank of science, that is, makes a system out of a mere aggregate of knowledge, architectonic is the doctrine of the scientific in our knowledge, and therefore necessarily forms part of the doctrine of method." (Immanuel Kant, "Critique of Pure Reason", 1871)

"Simplification of modes of proof is not merely an indication of advance in our knowledge of a subject, but is also the surest guarantee of readiness for farther progress." (William T Kelvin, "Elements of Natural Philosophy", 1873)

"Numerical facts, like other facts, are but the raw materials of knowledge, upon which our reasoning faculties must be exerted in order to draw forth the principles of nature. [...] Numerical precision is the soul of science [...]" (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

📁 On DIKW: On Knowledge (1930-1939)

"The final truth about phenomena resides in the mathematical description of it; so long as there is no imperfection in this, our knowledge is complete. We go beyond the mathematical formula at our own risk; we may find a [nonmathematical] model or picture that helps us to understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault." (James Jeans, "The Mysterious Universe", 1930)

"Scientific discovery and scientific knowledge have been achieved only by those who have gone in pursuit of them without any practical purpose whatsoever in view." (Max Planck, "Where is Science Going?", 1932)

"As facts and knowledge accumulate, the claim of the scientist to an understanding of the world in a certain sense diminishes." (Werner K Heisenberg, "Zur Geschichte der physikalischen Naturerklärung", 1933)

"The urge to knowledge is so deeply rooted in man that it can scarcely be omitted from a list of life's important needs." (Hans Reichenbach, "Atom and Cosmos: The World of Modern Physics", 1933)

"Maximal knowledge of a total system does not necessarily include total knowledge of all its parts, not even when these are fully separated from each other and at the moment are not influencing each other at all. Thus it may be that some part of what one knows may pertain to relations […] between the two subsystems (we shall limit ourselves to two), as follows: if a particular measurement on the first system yields this result, then for a particular measurement on the second the valid expectation statistics are such and such; but if the measurement in question on the first system should have that result, then some other expectation holds for that one the second. […] In this way, any measurement process at all or, what amounts to the same, any variable at all of the second system can be tied to the not-yet-known value of any variable at all of the first, and of course vice versa also." (Erwin Schrödinger, "The Present Situation in Quantum Mechanics", 1935)

"The laws of science are the permanent contributions to knowledge - the individual pieces that are fitted together in an attempt to form a picture of the physical universe in action. As the pieces fall into place, we often catch glimpses of emerging patterns, called theories; they set us searching for the missing pieces that will fill in the gaps and complete the patterns. These theories, these provisional interpretations of the data in hand, are mere working hypotheses, and they are treated with scant respect until they can be tested by new pieces of the puzzle." (Edwin P Whipple, "Experiment and Experience", [Commencement Address, California Institute of Technology] 1938)

"We have discovered that it is actually an aid in the search for knowledge to understand the nature of the knowledge we seek." (Arthur S Eddington, "The Philosophy of Physical Science", 1938)

"[…] reality is a system, completely ordered and fully intelligible, with which thought in its advance is more and more identifying itself. We may look at the growth of knowledge […] as an attempt by our mind to return to union with things as they are in their ordered wholeness. […] and if we take this view, our notion of truth is marked out for us. Truth is the approximation of thought to reality […] Its measure is the distance thought has travelled […] toward that intelligible system […] The degree of truth of a particular proposition is to be judged in the first instance by its coherence with experience as a whole, ultimately by its coherence with that further whole, all comprehensive and fully articulated, in which thought can come to rest." (Brand Blanshard, "The Nature of Thought" Vol. II, 1939) 

"The failure of the social sciences to think through and to integrate their several responsibilities for the common problem of relating the analysis of parts to the analysis of the whole constitutes one of the major lags crippling their utility as human tools of knowledge." (Robert S Lynd, "Knowledge of What?", 1939)

📁 On DIKW: 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)

On Puzzles (- 1950)

"While the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what anyone man will be up to, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician." (Sir Arthur C Doyle, "The Sign of Four", 1890)

"Everything in nature is a puzzle until it finds its solution in man, who solves it in some way with God, and so completes the circle of creation. " (Theodore T Munger, "The Appeal to Life", 1891)

"The most ordinary things are to philosophy a source of insoluble puzzles. In order to explain our perceptions it constructs the concept of matter and then finds matter quite useless either for itself having or for causing perceptions in a mind. With infinite ingenuity it constructs a concept of space or time and then finds it absolutely impossible that there be objects in this space or that processes occur during this time [...] The source of this kind of logic lies in excessive confidence in the so-called laws of thought." (Ludwig E Boltzmann, "On Statistical Mechanics", 1904)

"The discovery which has been pointed to by theory is always one of profound interest and importance, but it is usually the close and crown of a long and fruitful period, whereas the discovery which comes as a puzzle and surprise usually marks a fresh epoch and opens a new chapter in science." (Sir Oliver J Lodge, [Becquerel Memorial Lecture] Journal of the Chemical Society, Transactions 101 (2), 1912)

"The development of mathematics is largely a natural, not a purely logical one: mathematicians are continually answering questions suggested by astronomers or physicists; many essential mathematical theories are but the reflex outgrowth from physical puzzles." (George A L Sarton, "The Teaching of the History of Science", The Scientific Monthly, 1918)

"In her manifold opportunities Nature has thus helped man to polish the mirror of [man’s] mind, and the process continues. Nature still supplies us with abundance of brain-stretching theoretical puzzles and we eagerly tackle them; there are more worlds to conquer and we do not let the sword sleep in our hand; but how does it stand with feeling? Nature is beautiful, gladdening, awesome, mysterious, wonderful, as ever, but do we feel it as our forefathers did?" (Sir John A Thomson, "The System of Animate Nature", 1920)

"[while] the traditional way is to regard the facts of science as something like the parts of a jig-saw puzzle, which can be fitted together in one and only one way, I regard them rather as the tiny pieces of a mosaic, which can be fitted together in many ways. A new theory in an old subject is, for me, a new mosaic pattern made with the pieces taken from an older pattern. [...] Theories come into fashion and theories go out of fashion, but the facts connected with them stay." (William H George, "The Scientist in Action", 1936)

"The laws of science are the permanent contributions to knowledge - the individual pieces that are fitted together in an attempt to form a picture of the physical universe in action. As the pieces fall into place, we often catch glimpses of emerging patterns, called theories; they set us searching for the missing pieces that will fill in the gaps and complete the patterns. These theories, these provisional interpretations of the data in hand, are mere working hypotheses, and they are treated with scant respect until they can be tested by new pieces of the puzzle." (Edwin P Whipple, "Experiment and Experience", [Commencement Address, California Institute of Technology] 1938)

"Even if all parts of a problem seem to fit together like the pieces of a jigsaw puzzle, one has to remember that the probable need not necessarily be the truth and the truth not always probable." (Sigmund Freud, "Moses and Monotheism", 1939)

On Paradigms II

"The realm of the particularity of each experienced item differs from the formal realm of concepts. [...] The power of paradigmatic thought is to bring order to experience by seeing individual things as belonging to a category." (Donald E Polkinghorne, “Narrative configuration in qualitative analysis", International Journal of Qualitative Studies in Education Vol. 8 (1), 1995)

"Discovery commences with the awareness of anomaly, i.e., with the recognition that nature has somehow violated the paradigm-induced expectations that govern normal science. It then continues with a more or less extended exploration of the area of anomaly. And it closes only when the paradigm theory has been adjusted so that the anomalous has become the expected. […] Until he has learned to see nature in a different way - the new fact is not quite a scientific fact at all." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1962)

"The transition from a paradigm to a new one from which a new tradition of normal science can emerge is far from a cumulative process, one achieved by an articulation or extension of the old paradigm. Rather it is a reconstruction of the field from new fundamentals, a reconstruction that changes some of the field’s most elementary theoretical generalizations as well as many of its paradigm methods and applications." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1962)

"[…] paradigms, the core of the culture of science, are transmitted and sustained just as is culture generally: scientists accept them and become committed to them as a result of training and socialization, and the commitment is maintained by a developed system of social control." (Barry Barnes, "Thomas Kuhn", 1985)

"All scientific theories, even those in the physical sciences, are developed in a particular cultural context. Although the context may help to explain the persistence of a theory in the face of apparently falsifying evidence, the fact that a theory arises from a particular context is not sufficient to condemn it. Theories and paradigms must be accepted, modified or rejected on the basis of evidence." (Richard P Bentall,  "Madness Explained: Psychosis and Human Nature", 2003)

"A paradigm is a shared mindset that represents a fundamental way of thinking about, perceiving, and understanding the world." (Richard L Daft, "The Leadership Experience" 4th Ed., 2008)

On Hypotheses (1900-1909)

"Every generalisation is a hypothesis. Hypothesis therefore plays a necessary rôle, which no one has ever contested. Only, it should always be as soon as possible submitted to verification." (Henri Poincaré, "Science and Hypothesis", 1901)

"To undertake the calculation of any probability, and even for that calculation to have any meaning at all, we must admit, as a point of departure, an hypothesis or convention which has always something arbitrary about it. In the choice of this convention we can be guided only by the principle of sufficient reason. Unfortunately, this principle is very vague and very elastic, and in the cursory examination we have just made we have seen it assume different forms. The form under which we meet it most often is the belief in continuity, a belief which it would be difficult to justify by apodeictic reasoning, but without which all science would be impossible. Finally, the problems to which the calculus of probabilities may be applied with profit are those in which the result is independent of the hypothesis made at the outset, provided only that this hypothesis satisfies the condition of continuity." (Henri Poincaré, "Science and Hypothesis", 1901)

"Treatises on mechanics do not clearly distinguish between what is experiment, what is mathematical reasoning, what is convention, and what is hypothesis." (Henri Poincaré, "Science and Hypothesis", 1901)

"Entia non sunt multiplicanda praeter necessitatem. That is to say; before you try a complicated hypothesis, you should make quite sure that no simplification of it will explain the facts equally well." (Charles S Peirce," Pragmatism and Pragmaticism", [lecture] 1903)

"Chemistry and physics are experimental sciences; and those who are engaged in attempting to enlarge the boundaries of science by experiment are generally unwilling to publish speculations; for they have learned, by long experience, that it is unsafe to anticipate events. It is true, they must make certain theories and hypotheses. They must form some kind of mental picture of the relations between the phenomena which they are trying to investigate, else their experiments would be made at random, and without connection." (William Ramsay, "Radium and Its Products", Harper’s Magazine, 1904)

"A symbolical representation of a method of calculation has the same significance for a mathematician as a model or a visualisable working hypothesis has for a physicist. The symbol, the model, the hypothesis runs parallel with the thing to be represented. But the parallelism may extend farther, or be extended farther, than was originally intended on the adoption of the symbol. Since the thing represented and the device representing are after all different, what would be concealed in the one is apparent in the other." (Ernst Mach, "Space and Geometry: In the Light of physiological, phycological and physical inquiry", 1906) 

"The physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses." (Pierre Duhem, "The Aim and Structure of Physical Theory", 1906)

"A mind exclusively bent upon the idea of utility necessarily narrows the range of the imagination. For it is the imagination which pictures to the inner eye of the investigator the indefinitely extending sphere of the possible, - that region of hypothesis and explanation, of underlying cause and controlling law. The area of suggestion and experiment is thus pushed beyond the actual field of vision." (John G Hibben, "The Paradox of Research", The North American Review 188 (634), 1908)

On Conjecture (1800-1899)

"In order to supply the defects of experience, we will have recourse to the probable conjectures of analogy, conclusions which we will bequeath to our posterity to be ascertained by new observations, which, if we augur rightly, will serve to establish our theory and to carry it gradually nearer to absolute certainty." (Johann H Lambert, "The System of the World", 1800)

"In all speculations on the origin, or agents that have produced the changes on this globe, it is probable that we ought to keep within the boundaries of the probable effects resulting from the regular operations of the great laws of nature which our experience and observation have brought within the sphere of our knowledge. When we overleap those limits, and suppose a total change in nature's laws, we embark on the sea of uncertainty, where one conjecture is perhaps as probable as another; for none of them can have any support, or derive any authority from the practical facts wherewith our experience has brought us acquainted." (William Maclure, "Observations on the Geology of the United States of America", 1817)

"The science of the mathematics performs more than it promises, but the science of metaphysics promises more than it performs. The study of the mathematics, like the Nile, begins in minuteness but ends in magnificence; but the study of metaphysics begins with a torrent of tropes, and a copious current of words, yet loses itself at last in obscurity and conjecture, like the Niger in his barren deserts of sand." (Charles C Colton, "Lacon", 1820)

"We know the effects of many things, but the causes of few; experience, therefore, is a surer guide than imagination, and inquiry than conjecture." (Charles C Colton, "Lacon", 1820)

"Let me be permitted to recall that the object of mathematics is not to investigate the causes that one can assign to natural phenomena. This science would lose both its character and credit if, renouncing the support of general well-confirmed facts, it sought within the realm of nebulous conjectures, a realm which has always been a fertile source of error for ways of satisfying the thirst fo rexplanation." (Sophie Germain, "Examen des principes qui peuvent conduire a la connaissance des lois de requilibre et du mouvement des solides elastiques", Annales de Chimie 38, 1828)

"Life is not the object of Science: we see a little, very little; And what is beyond we can only conjecture." (Samuel Johnson, "Causes Which Produce Diversity of Opinion", 1840)

"The entire annals of Observation probably do not elsewhere exhibit so extraordinary a verification of any theoretical conjecture adventured on by the human spirit!" (John P Nichol, "The Planet Neptune: An Exposition and History", 1848)

"The philosophical study of nature rises above the requirements of mere delineation, and does not consist in the sterile accumulation of isolated facts. The active and inquiring spirit of man may therefore be occasionally permitted to escape from the present into the domain of the past, to conjecture that which cannot yet be clearly determined, and thus to revel amid the ancient and ever-recurring myths of geology." (Alexander von Humboldt, "Views of Nature: Or Contemplation of the Sublime Phenomena of Creation", 1850)

"The rules of scientific investigation always require us, when we enter the domains of conjecture, to adopt that hypothesis by which the greatest number of known facts and phenomena may be reconciled." (Matthew F Maury, "The Physical Geography of the Sea", 1855)

"There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact." (Samuel L Clemens [Mark Twain], "Life on the Mississippi", 1883)

"I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain. [...] But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors." (Hermann von Helmholtz, 1891)

📁 On DIKW: On Facts (1800-1824)

"Isolated facts, those that can only be obtained by rough estimate and that require development, can only be presented in memoires; but those that can be presented in a body, with details, and on whose accuracy one can rely, may be expounded in tables." (Emmanuel Duvillard, "Memoire sur le travail du Bureau de statistique", 1806)

"The foundations of chemical philosophy are observation, experiment, and analogy. By observation, facts are distinctly and minutely impressed on the mind. By analogy, similar facts are connected. By experiment, new facts are discovered; and, in the progression of knowledge, observation, guided by analogy, lends to experiment, and analogy confirmed by experiment, becomes scientific truth." (Sir Humphry Davy, "Elements of Chemical Philosophy" Vol. 4, 1812)

"The theory of which we have just given an overview may be considered from a point of view apt to set aside the obscure in what it presents, and which seems to be the primary aim, namely: to establish new notions on imaginary quantities. Indeed, putting to one side the question of whether these notions are true or false, we may restrict ourselves to viewing this theory as a means of research, to adopt the lines in direction only as signs of the real or imaginary quantities, and to see, in the usage to which we have put them, only the simple employment of a particular notation. For that, it suffices to start by demonstrating, through the first theorems of trigonometry, the rules of multiplication and addition given above; the applications will follow, and all that will remain is to examine the question of didactics. And if the employment of this notation were to be advantageous? And if it were to open up shorter and easier paths to demonstrate certain truths? That is what fact alone can decide." (Jean-Robert Argand, "Essai sur une manière de représenter les quantités imaginaires, dans les constructions géométriques", Annales Tome IV, 1813)

"Induction, analogy, hypotheses founded upon facts and rectified continually by new observations, a happy tact given by nature and strengthened by numerous comparisons of its indications with experience, such are the principal means for arriving at truth." (Pierre-Simon Laplace, "A Philosophical Essay on Probabilities", 1814)

"The substitution of analogy for fact is the bane of chemical philosophy; the legitimate use of analogy is to connect facts together and to guide to new experiments." (Sir Humphry Davy, "Journal of Science and the Arts", 1816)

"Force is not a fact at all, but an idea embodying what is approximately the fact." (William K Clifford, "The Common Sense of the Exact Sciences", 1823)

📁 On DIKW: On Facts (1825-1849)

"Facts are the mere dross of history. It is from the abstract truth which interpenetrates them, and lies latent among them, like gold in the ore, that the mass derives its whole value: and the precious particles are generally combined with the baser in such a manner that the separation is a task of the utmost difficulty." (Thomas B Macaulay, "History", 1828)

"The domain of physics is no proper field for mathematical pastimes. The best security would be in giving a geometrical training to physicists, who need not then have recourse to mathematicians, whose tendency is to despise experimental science. By this method will that union between the abstract and the concrete be effected which will perfect the uses of mathematical, while extending the positive value of physical science. Meantime, the uses of analysis in physics is clear enough. Without it we should have no precision, and no co-ordination; and what account could we give of our study of heat, weight, light, etc.? We should have merely series of unconnected facts, in which we could foresee nothing but by constant recourse to experiment; whereas, they now have a character of rationality which fits them for purposes of prevision." (Auguste Comte, "The Positive Philosophy", 1830)

"There is nothing more difficult than a good definition, for it is scarcely possible to express, in a few words, the abstracted view of an infinite variety of facts." (Humphry Davy, "Consolations in Travel, or the Last Days of a Philosopher" , 1830)

"Whilst chemical pursuits exalt the understanding, they do not depress the imagination or weaken genuine feeling; whilst they give the mind habits of accuracy, by obliging it to attend to facts, they likewise extend its analogies; and, though conversant with the minute forms of things, they have for their ultimate end the great and magnificent objects of nature." (Sir Humphry Davy, "Consolations in Travel, or the Last Days of a Philosopher", 1830)

"A maxim is a conclusion upon observation of matters of fact, and is merely speculative; a ‘principle’ carries knowledge within itself, and is prospective." (Samuel T Coleridge, "The Table Talk and Omniana of Samuel Taylor Coleridge", 1831)

"Facts, however numerous, do not constitute a science. Like innumerable grains of sand on the sea shore, single facts appear isolated, useless, shapeless; it is only when compared, when arranged in their natural relations, when crystallised by the intellect, that they constitute the eternal truths of science." (William Farr, "Observation", Br. Ann. Med. 1, 1837)

"Statistics is a science which ought to be honourable, the basis of many most important sciences; but it is not to be carried on by steam, this science, any more than others are; a wise hand is requisite for carrying it on. Conclusive facts are inseparable from unconclusive except by a head that already understands and knows." (Thomas Carlyle, "Critical and Miscellaneous Essays", 1838)

"[…] in order that the facts obtained by observation and experiment may be capable of being used in furtherance of our exact and solid knowledge, they must be apprehended and analysed according to some Conception which, applied for this purpose, gives distinct and definite results, such as can be steadily taken hold of and reasoned from […]" (William Whewell, "The Philosophy of the Inductive Sciences Founded Upon their History" Vol. 2, 1840)

"[…] in order to observe, our mind has need of some theory or other. If in contemplating phenomena we did not immediately connect them with principles, not only would it be impossible for us to combine these isolated observations, and therefore to derive profit from them, but we should even be entirely incapable of remembering facts, which would for the most remain unnoted by us." (Auguste Comte, "Cours de Philosophie Positive", 1830-1842)

📁 On DIKW: On Facts (1850-1859)

"The Laws of Nature are merely truths or generalized facts, in regard to matter, derived by induction from experience, observation, arid experiment. The laws of mathematical science are generalized truths derived from the consideration of Number and Space." (Charles Davies, "The Logic and Utility of Mathematics", 1850)

"A human being, what is a human being? Everything and nothing. Through the power of thought it can mirror everything it experiences. Through memory and knowledge it becomes a microcosm, carrying the world within itself. A mirror of things, a mirror of facts. Each human being becomes a little universe within the universe!" (Guy de Maupassant, [in "The Journal of a Madman"] 1851)

"Every science consists in the coordination of facts; if the different observations were entirely isolated, there would be no science." (Auguste Comte, "Philosophy of Mathematics", 1851)

"From carefully compiled statistical facts more may be learned [about] the moral nature of Man than can be gathered from all the accumulated experiences of the preceding ages." (Henry Thomas Buckle, "A History of Civilization in England", 1857/1898)

"SYSTEM (to place together) - is a full and connected view of all the truths of some department of knowledge. An organized body of truth, or truths arranged under one and the same idea, which idea is as the life or soul which assimilates all those truths. No truth is altogether isolated. Every truth has relation to some other. And we should try to unite the facts of our knowledge so as to see them in their several bearings. This we do when we frame them into a system. To do so legitimately we must begin by analysis and end with synthesis. But system applies not only to our knowledge, but to the objects of our knowledge. Thus we speak of the planetary system, the muscular system, the nervous system. We believe that the order to which we would reduce our ideas has a foundation in the nature of things. And it is this belief that encourages us to reduce our knowledge of things into systematic order. The doing so is attended with many advantages. At the same time a spirit of systematizing may be carried too far. It is only in so far as it is in accordance with the order of nature that it can be useful or sound." (William Fleming, "Vocabulary of philosophy, mental, moral, and metaphysical; with quotations and references; for the use of students", 1857)

"[…] ideas may be both novel and important, and yet, if they are incorrect – if they lack the very essential support of incontrovertible fact, they are unworthy of credence. Without this, a theory may be both beautiful and grand, but must be as evanescent as it is beautiful, and as unsubstantial as it is grand." (George Brewster, "A New Philosophy of Matter", 1858)

📁 On DIKW: On Facts (1860-1869)

"Observation is so wide awake, and facts are being so rapidly added to the sum of human experience, that it appears as if the theorizer would always be in arrears, and were doomed forever to arrive at imperfect conclusion; but the power to perceive a law is equally rare in all ages of the world, and depends but little on the number of facts observed." (Henry D Thoreau, "A Week on the Concord and Merrimack Rivers", 1862)

"The discoverer and the poet are inventors; and they are so because their mental vision detects the unapparent, unsuspected facts, almost as vividly as ocular vision rests on the apparent and familiar." (George H Lewes, "Principles of Success in Literature", 1865)

"Facts can be accurately known to us only by the most rigid observation and sustained and scrutinizing skepticism […]" (James A Froude, Short Studies on Great Subjects Vol. 2, 1867)

"Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect." (Hermann von Helmholtz, "The Aim and Progress of Physical Science", 1869)

"The triumph of a theory is to embrace the greatest number and the greatest variety of facts." (Charles A Wurtz, "A History of Chemical Theory from the Age of Lavoisier to the Present Time", 1869)

📁 On DIKW: On Facts (1870-1879)

"As in the experimental sciences, truth cannot be distinguished from error as long as firm principles have not been established through the rigorous observation of facts." (Louis Pasteur, "Étude sur la maladie des vers à soie", 1870)

"Therefore, the great business of the scientific teacher is, to imprint the fundamental, irrefragable facts of his science, not only by words upon the mind, but by sensible impressions upon the eye, and ear, and touch of the student, in so complete a manner, that every term used, or law enunciated, should afterwards call up vivid images of the particular structural, or other, facts which furnished the demonstration of the law, or the illustration of the term." (Thomas H Huxley, "Lay Sermons, Addresses and Reviews", 1870)

"Modern discoveries have not been made by large collections of facts, with subsequent discussion, separation, and resulting deduction of a truth thus rendered perceptible. A few facts have suggested an hypothesis, which means a supposition, proper to explain them. The necessary results of this supposition are worked out, and then, and not till then, other facts are examined to see if their ulterior results are found in Nature." (Augustus de Morgan, "A Budget of Paradoxes", 1872)

"A law of nature, however, is not a mere logical conception that we have adopted as a kind of memoria technical to enable us to more readily remember facts. We of the present day have already sufficient insight to know that the laws of nature are not things which we can evolve by any speculative method. On the contrary, we have to discover them in the facts; we have to test them by repeated observation or experiment, in constantly new cases, under ever-varying circumstances; and in proportion only as they hold good under a constantly increasing change of conditions, in a constantly increasing number of cases with greater delicacy in the means of observation, does our confidence in their trustworthiness rise." (Hermann von Helmholtz, "Popular Lectures on Scientific Subjects", 1873)

"Summing up, then, it would seem as if the mind of the great discoverer must combine contradictory attributes. He must be fertile in theories and hypotheses, and yet full of facts and precise results of experience. He must entertain the feeblest analogies, and the merest guesses at truth, and yet he must hold them as worthless till they are verified in experiment. When there are any grounds of probability he must hold tenaciously to an old opinion, and yet he must be prepared at any moment to relinquish it when a clearly contradictory fact is encountered." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"In every physical science we have carefully to distinguish between the facts which form its subject-matter and the theories by which we attempt to explain these facts, and group them in our scientific systems." (Josiah P Cooke, "The New Chemistry", 1876)

"As long as the training of a naturalist enables him to trace the action only of a particular material system, without giving him the power of dealing with the general properties of all such systems, he must proceed by the method so often described in histories of science - he must imagine model after model of hypothetical apparatus, till he finds one which will do the required work. If this apparatus should afterwards be found capable of accounting for many of the known phenomena, and not demonstrably inconsistent with any of them, he is strongly tempted to conclude that his hypothesis is a fact, at least until an equally good rival hypothesis has been invented." (James C Maxwell, "Tait’s Thermodynamics", Nature Vol. XVII (431), 1878)

📁 On DIKW: On Facts (1880-1889)

"It is of the nature of true science to take nothing on trust or on authority. Every fact must be established by accurate observation, experiment, or calculation. Every law and principle must rest on inductive argument. The apostolic motto, ‘Prove all things, hold fast that which is good’, is thoroughly scientific. It is true that the mere reader of popular science must often be content to take that on testimony which he cannot personally verify; but it is desirable that even the most cursory reader should fully comprehend the modes in which facts are ascertained and the reasons on which the conclusions are based." (Sir John W Dawson, "The Chain of Life in Geological Time", 1880)

"The easiest and surest way of acquiring facts is to learn them in groups, in systems, and systematized knowledge is science. You can very often carry two facts fastened together more easily than one by itself, as a house-maid can carry two pails of water with a hoop more easily than one without it." (Oliver W Holmes, "Medical Essays", 1883)

"While all that we have is a relation of phenomena, a mental image, as such, in juxtaposition with or soldered to a sensation, we can not as yet have assertion or denial, a truth or a falsehood. We have mere reality, which is, but does not stand for anything, and which exists, but by no possibility could be true. […] the image is not a symbol or idea. It is itself a fact, or else the facts eject it. The real, as it appears to us in perception, connects the ideal suggestion with itself, or simply expels it from the world of reality. […] you possess explicit symbols all of which are universal and on the other side you have a mind which consists of mere individual impressions and images, grouped by the laws of a mechanical attraction." (Francis H Bradley, "Principles of Logic", 1883)

"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) 

"It is difficult to understand why statisticians commonly limit their inquiries to Averages, and do not revel in more comprehensive views. Their souls seem as dull to the charm of variety as that of the native of one of our flat English counties, whose retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once. An Average is but a solitary fact, whereas if a single other fact be added to it, an entire Normal Scheme, which nearly corresponds to the observed one, starts potentially into existence." (Sir Francis Galton, "Natural Inheritance", 1889)

"While science is pursuing a steady onward movement, it is convenient from time to time to cast a glance back on the route already traversed, and especially to consider the new conceptions which aim at discovering the general meaning of the stock of facts accumulated from day to day in our laboratories." (Dmitry Mendeleyev, "The Periodic Law of the Chemical Elements", Journal of the Chemical Society Vol. 55, 1889)

📁 On DIKW: On Facts (1890-1899)

"The study of theory must go hand in hand with that of facts: and for dealing with most modern problems it is modern facts that are of the greatest use." (Alfred Marshall, "Principles of Economics", 1890)

"The graphical method has considerable superiority for the exposition of statistical facts over the tabular. A heavy bank of figures is grievously wearisome to the eye, and the popular mind is as incapable of drawing any useful lessons from it as of extracting sunbeams from cucumbers." (Arthur B Farquhar & Henry Farquhar, "Economic and Industrial Delusions", 1891)

"All great scientists have, in a certain sense, been great artists; the man with no imagination may collect facts, but he cannot make great discoveries." (Karl Pearson, "The Grammar of Science", 1892)

"It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts." (Sir Arthur C Doyle, "The Adventures of Sherlock Holmes", 1892)

"The classification of facts, the recognition of their sequence and relative significance is the function of science, and the habit of forming a judgment upon these facts unbiased by personal feeling is characteristic of what may be termed the scientific frame of mind." (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)

"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)

"Scientific facts accumulate rapidly, and give rise to theories with almost equal rapidity. These theories are often wonderfully enticing, and one is apt to pass from one to another, from theory to theory, without taking care to establish each before passing on to the next, without assuring oneself that the foundation on which one is building is secure. Then comes the crash; the last theory breaks down utterly, and on attempting to retrace our steps to firm ground and start anew, we may find too late that one of the cards, possibly at the very foundation of the pagoda, is either faultily placed or in itself defective, and that this blemish easily remedied if detected in time has, neglected, caused the collapse of the whole structure on whose erection so much skill and perseverance have been spent." (Arthur M Marshall, 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)

"The first step, whenever a practical problem is set before a mathematician, is to form the mathematical hypothesis. It is neither needful nor practical that we should take account of the details of the structure as it will exist. We have to reason about a skeleton diagram in which bearings are reduced to points, pieces to lines, etc. and [in] which it is supposed that certain relations between motions are absolutely constrained, irrespective of forces. Some writers call such a hypothesis a fiction, and say that the mathematician does not solve the real problem, but only a fictitious one. That is one way of looking at the matter, to which I have no objection to make: only, I notice, that in precisely the same sense in which the mathematical hypothesis is 'false', so also is this statement 'false', that it is false. Namely, both representations are false in the sense that they omit subsidiary elements of the fact, provided that element of the case can be said to be subsidiary which those writers overlook, namely, that the skeleton diagram is true in the only sense in which from the nature of things any mental representation, or understanding, of the brute existent can be true. For every possible conception, by the very nature of thought, involves generalization; now generalization omits, means to omit, and professes to omit, the differences between the facts generalized." (Charles S Peirce, "Report on Live Loads", cca. 1895)

"The world is chiefly a mental fact. From mind it receives the forms of time and space, the principle of causality, color, warmth, and beauty. Were there no mind, there would be no world." (John L Spalding, "Means and Ends of Education", 1895)

"In scientific investigations, it is permitted to invent any hypothesis and, if it explains various large and independent classes of facts, it rises to the ranks of a well-grounded theory." (Charles Darwin, "The Variations of Animals and Plants Under Domestication" Vol. 1, 1896)

"Mathematics is the most abstract of all the sciences. For it makes no external observations, nor asserts anything as a real fact. When the mathematician deals with facts, they become for him mere ‘hypotheses’; for with their truth he refuses to concern himself. The whole science of mathematics is a science of hypotheses; so that nothing could be more completely abstracted from concrete reality." (Charles S Peirce, "The Regenerated Logic", The Monist Vol. 7 (1), 1896)

"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)

"Science like life feeds on its own decay. New facts burst old rules; then newly developed concepts bind old and new together into a reconciling law." (William James, "The Will to Believe and Other Essays in Popular Philosophy", 1896)

"The scientific value of truth is not, however, ultimate or absolute. It rests partly on practical, partly on aesthetic interests. As our ideas are gradually brought into conformity with the facts by the painful process of selection, - for intuition runs equally into truth and into error, and can settle nothing if not controlled by experience, - we gain vastly in our command over our environment. This is the fundamental value of natural science" (George Santayana, "The Sense of Beauty: Being the Outlines of Aesthetic Theory", 1896)

"To use an old analogy - and here we can hardly go except upon analogy - while the building of Nature is growing spontaneously from within, the model of it, which we seek to construct in our descriptive science, can only be constructed by means of scaffolding from without, a scaffolding of hypotheses. While in the real building all is continuous, in our model there are detached parts which must be connected with the rest by temporary ladders and passages, or which must be supported till we can see how to fill in the understructure. To give the hypotheses equal validity with facts is to confuse the temporary scaffolding with the building itself." (John H Poynting, 1899)

📁 On DIKW: On Facts (Unsourced)

"A fact is not novel if it has an analogue which could have some interest. A fact which does not fi t in with a series of known facts is a fact which deserves particular attention. If the mind had to retain all individual facts, it could not manage and science would not exist; but when these facts can be connected by general laws and by theories, when a large number of these facts can be represented by a single one, one can remember them more easily, one can generalise one’s ideas, one can compare one general fact with another general fact and discoveries can succeed each other. It is only when laws can be introduced into a science that it assumes the true character of science." (Joseph L Gay-Lussac)

"All the pictures which science draws of Nature, and which alone seem capable of according with observational facts, are mathematical pictures." (Sir James Jeans)

"By observation, facts are distinctly and minutely impressed in the mind; by analogy, similar facts are connected ; by experiment, new facts are discovered ; and, in the progression of knowledge, observation, guided by analogy, leads to experiment, and analogy, confirmed by experiment, becomes scientific truth." (Sir Humphry Davy)

"Cognitive psychology has shown that the mind best understands facts when they are woven into a conceptual fabric, such as a narrative, mental map, or intuitive theory. Disconnected facts in the mind are like unlinked pages on the Web: They might as well not exist." (Steven Pinker) 

"Education is not the piling on of learning, information, data, facts, skills, or abilities - that's training or instruction - but is rather making visible what is hidden as a seed." (Thomas W Moore)

"Facts and values are entangled in science. It's not because scientists are biased, not because they are partial or influenced by other kinds of interests, but because of a commitment to reason, consistency, coherence, plausibility and replicability. These are value commitments." (Alva Noë)

"Facts are stubborn things, but statistics are pliable." (Mark Twain)

"[…] facts by themselves are silent. Observation discovers nothing directly of the actions of causes, but only of sequences in time." (Alfred Marshall)

"First accumulate a mass of Facts: and then construct a Theory." (Lewis Carroll)

[Maier’s Law:] "If the facts do not conform to the theory, they must be disposed of." (Norman R F Maier)

"Imagination, as well as reason, is necessary to perfection in the philosophical mind. A rapidity of combination, a power of perceiving analogies, and of comparing them by facts, is the creative source of discovery." (Sir Humphry Davy)

"In physical science the discovery of new facts is open to every blockhead with patience, manual dexterity, and acute senses; it is less effectually promoted by genius than by co-operation, and more frequently the result of accident than of design." (John Thomson)

"In the study of Nature conjecture must be entirely put aside, and vague hypothesis carefully guarded against. The study of Nature begins with facts, ascends to laws, and raises itself, as far as the limits of man’s intellect will permit, to the knowledge of causes, by the threefold means of observation, experiment and logical deduction." (Jean Baptiste-Andre Dumas)

"No good model ever accounted for all the facts, since some data was bound to be misleading if not plain wrong." (James Dewey Watson)

"Nothing in education is so astonishing as the amount of ignorance it accumulates in the form of inert facts." (Henry B Adams)

"One might describe the mathematical quality in Nature by saying that the universe is so constituted that mathematics is a useful tool in its description. However, recent advances in physical science show that this statement of the case is too trivial. The connection between mathematics and the description of the universe goes far deeper than this, and one can get an appreciation of it only from a thorough examination of the various facts that make it up." (Paul A M Dirac)

"Science does more than collect facts; it makes sense of them. Great scientists are virtuosi of the art of discovering the meaning of what otherwise might seem barren observations." (Theodosius Dobzhansky)

"Science is not a technique or a body of knowledge, though it uses both. It is rather an attitude of inquiry, or observation and reasoning, with respect to the world. It can be developed, not by memorizing facts or juggling formulas to get an answer, but only by actual practice of scientific observation and reasoning." (Karl T Compton)

"Science is opposed to theological dogmas because science is founded on fact. To me, the universe is simply a great machine which never came into being and never will end. The human being is no exception to the natural order. Man, like the universe, is a machine." (Nikola Tesla)

"Some facts can be seen more clearly by example than by proof." (Leonard Euler)

"The aim of education is the knowledge not of facts but of values." (William R Inge)

"The arguments […] by which you support my theories, are most ingenious, but not founded on demonstrated facts; analogy is no proof." (Louis Pasteur)

"The art of observation and that of experimentation are very distinct. In the first case, the fact may either proceed from logical reasons or be mere good fortune; it is sufficient to have some penetration and a sense of truth in order to profit by it. But the art of experimentation leads from the first to the last link of the chain, without hesitation and without a blank, making successive use of Reason, which suggests an alternative, and of Experience, which decides on it, until, starting from a faint glimmer, the full blaze of light is reached." (Jean Baptiste-Andre Dumas)

"The disclosure of a new fact, the leap forward, the conquest over yesterday’s ignorance, is an act not of reason but of imagination, of intuition." (Charles Nicolle)

"The experiment serves two purposes, often independent one from the other: it allows the observation of new facts, hitherto either unsuspected, or not yet well defined; and it determines whether." (René J Dubos)

"[…] the mathematician learns early to accept no fact, to believe no statement, however apparently reasonable or obvious or trivial, until it has been proved, rigorously and totally by a series of steps proceeding from universally accepted first principles." (Alfred Adler)

"The object of education is not only to produce a man who knows, but one who does; who makes his mark in the straggle of life and succeeds well in whatever he undertakes: who can solve the problems of nature and of humanity as they arise, and who, when he knows he is right, can boldly convince the world of the fact." (Henry A Rowland)

"The present system of education is all wrong. The mind is crammed with facts before it knows how to think. Control of the mind should be taught first. It takes people a long time to learn things because they can't concentrate their minds at will." (Swami Vivekananda)

"Theory helps us to bear our ignorance of facts." (George Santayana)

"There is no drawing the line between physics and metaphysics. If you examine every day facts at all closely, you are a physicist; but if you press your physics at all home, you become a metaphysician; if you press your metaphysics at all home, you are in a fog." (Samuel Butler)

"There is nothing more deceptive than an obvious fact." (Sir Arthur C Doyle)

📁 On DIKW: On Facts (-1799)

"While those whom devotion to abstract discussions has rendered unobservant of the facts are too ready to dogmatize on the basis of a few observations." (Aristotle, "De Caelo" ["On the Heavens"], cca. 350 BC)

"Everything we hear is an opinion, not a fact. Everything we see is a perspective, not the truth." (Marcus Aurelius, "Meditations", cca. 2nd century)

"The Syllogism consists of propositions, propositions consist of words, words are symbols of notions. Therefore if the notions themselves (which is the root of the matter) are confused and over-hastily abstracted from the facts, there can be no firmness in the superstructure. Our only hope therefore lies in a true induction." (Francis Bacon, "The New Organon", 1620)

"There are two kinds of truths: those of reasoning and those of fact. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contingent and their opposites are possible." (Gottfried W Leibniz, "Monadology", 1714)

"We have three principal means: observation of nature, reflection, and experiment. Observation gathers the facts reflection combines them, experiment verifies the result of the combination. It is essential that the observation of nature be assiduous, that reflection be profound, and that experimentation be exact. Rarely does one see these abilities in combination. And so, creative geniuses are not common." (Denis Diderot, "On the Interpretation of Nature", 1753)

"Facts, observations, experiments - these are the materials of a great edifice, but in assembling them we must combine them into classes, distinguish which belongs to which order and to which part of the whole each pertains." (Antoine L Lavoisier, "Mémoires de l’Académie Royale des Sciences", 1777)

"The impossibility of separating the nomenclature of a science from the science itself is owing to this, that every branch of physical science must consist of three things: the series of facts which are the objects of the science, the ideas which represent these facts, and the words by which these ideas are expressed. Like three impressions of the same seal, the word ought to produce the idea, and the idea to be a picture of the fact." (Antoine L Lavoisier, "Elements of Chemistry in a New Systematic Order", 1790)

"We must trust to nothing but facts: These are presented to us by Nature, and cannot deceive. We ought, in every instance, to submit our reasoning to the test of experiment, and never to search for truth but by the natural road of experiment and observation." (Antoin-Laurent de Lavoisiere, "Elements of Chemistry", 1790)

"[…] the speculative propositions of mathematics do not relate to facts; […] all that we are convinced of by any demonstration in the science, is of a necessary connection subsisting between certain suppositions and certain conclusions. When we find these suppositions actually take place in a particular instance, the demonstration forces us to apply the conclusion. Thus, if I could form a triangle, the three sides of which were accurately mathematical lines, I might affirm of this individual figure, that its three angles are equal to two right angles; but as the imperfection of my senses puts it out of my power to be, in any case, certain of the exact correspondence of the diagram which I delineate, with the definitions given in the elements of geometry, I never can apply with confidence to a particular figure, a mathematical theorem." (Dugald Stewart, "Elements of the Philosophy of the Human Mind", 1792)

"It has never yet been supposed, that all the facts of nature, and all the means of acquiring precision in the computation and analysis of those facts, and all the connections of objects with each other, and all the possible combinations of ideas, can be exhausted by the human mind." (Nicolas de Condorcet, "Outlines Of An Historical View Of The Progress Of The Human Mind", 1795)