Proof quotes

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Thomas_Aquinas

Reason

“Reason may be employed in two ways to establish a point: first for the purpose of furnishing sufficient proof of some principle, as in natural science, where sufficient proof can be brought to show that the movement of the heavens is always of uniform velocity. Reason is employed in another way, not as furnishing a sufficient proof of a principle, but as confirming an already established principle, by showing the congruity of its results, as in astrology the theory of eccentrics and epicycles is considered as established because thereby the sensible appearances of the heavenly movements can be explained; not, however, as if this reason were sufficient, since some other theory might explain them.”
  • Source: Saint Thomas Aquinas, Summa Theologica [1266-1273], Part I, question 32, article 2 (reply to objection 2), trans. Fathers of the English Dominican Province (i.e. L. Shapeote), revised D. J. Sullivan (1952), Vol. I, 177.

Claude_Bernard

Counterproof

“Experimenters, who see their ideas confirmed by an experiment, should still doubt and require a counterproof. Indeed, proof that a given condition always precedes or accompanies a phenomenon does not warrant concluding with certainty that a given condition is the immediate cause of that phenomenon.”
  • Source: From the book "An Introduction to the Study of Experimental Medicine" written by Claude Bernard published in French in 1865 as "Introduction à l'étude de la médecine expérimentale". Translated to English by Henry Copley Greene in 1927 and republished by Henry Shuman, Inc. in 1949. Chapter II, page 55. Available online at https://archive.org/details/b21270557 retrieved 2024.

Robert_Boyle

Good Hypothesis

“The Requisites of a good Hypothesis are:
: That It be Intelligible.
: That It neither Assume nor Suppose anything Impossible, unintelligible, or demonstrably False.
: That It be consistent with Itself.
: That It be lit and sufficient to Explicate the Phaenomena, especially the chief.
: That It be, at least, consistent, with the rest of the Phaenomena It particularly relates to, and do not contradict any other known Phaenomena of nature, or manifest Physical Truth.
 
The Qualities and Conditions of an Excellent Hypothesis are:
: That It be not Precarious, but have sufficient Grounds In the nature of the Thing Itself or at least be well recommended by some Auxiliary Proofs.
: That It be the Simplest of all the good ones we are able to frame, at least containing nothing that is superfluous or Impertinent.
: That It be the only Hypothesis that can Explicate the Phaenomena; or at least, that do's Explicate them so well.
: That it enable a skillful naturalist to foretell future Phaenomena by the Congruity or Incongruity to it; and especially the event of such experiments as are aptly devised to examine It, as Things that ought, or ought not, to be consequent to It.”
  • Source: Robert Boyle, Boyle Papers, 37. Quoted In Barbara Kaplan (ed.), Divulging of Useful Truths in Physick: The Medical Agenda of Robert Boyle (1993), 50.

Robert_N_Britcher

Requirements Testing

“Requirements testing is a subtle way of treating a nonlinear, unpredictable system as if it were a discrete symbol like a number or a word. The potential and the actual become muddled. Requirements are natural language statements, peppered in places with arithmetic. These are discrete and usually quite vague representations of the system as it might become. But the truth is that two teams writing requirements for the same system would describe them differently, and neither would get it quite right, simply because 'right' cannot be known until the system is built. ... Requirements testing is a little like trying to reduce crime in England by running a test for each line in the Magna Carta. In practice, rhetoric replaces the scientific method. As with mathematical proofs, the quest for 'true or not false' soon turns into a party - a not very cordial party - marked by endless debate over whether this sentence or that sentence has been verified by this moment of behavior or that.”
  • Source: Britcher, Robert N. (1999). The Limits of Software: People, Projects, and Perspectives. Reading, MA: Addison Wesley. ISBN 0-201-43323-0. Page 157.

Fred_Brooks

Rational Model

“Perhaps the most devastating critique of the Rational Model, although perhaps the hardest to prove, is that most experienced designers just don’t work that way.”
  • Source: Brooks Jr., F. P. (2010). The Design of Design. Upper Saddle River, NJ: Addison-Wesley. ISBN: 978-0-201-36298-5. Chapter 3, page 30.

Design Is Important

“Mediocre design provably wastes the world’s resources, corrupts the environment, affects international competitiveness. Design is important; teaching design is important.”
  • Source: Brooks Jr., F. P. (2010). The Design of Design. Upper Saddle River, NJ: Addison-Wesley. ISBN: 978-0-201-36298-5. Preface.

Christopher_Columbus

World Spherical

"I have always read that the world, both land and water, was spherical, as the authority and researches of Ptolemy and all the others who have written on this subject demonstrate and prove, as do the eclipses of the moon and other experiments that are made from east to west, and the elevation of the North Star from north to south."
  • Source: Written by Christopher Columbus in a 'Letter to the Sovereigns', Third Voyage, 1498-10-18.

Freeman_Dyson

Science Uncertain

“The fringe of physics is not a sharp boundary with truth on one side and fantasy on the other. All of science is uncertain and subject to revision. The glory of science is to imagine more than we can prove. The fringe is the unexplored territory where truth and fantasy are not yet disentangled.”
  • Source: Freeman Dyson [book/author]; “Dreams of Earth and Sky” [title]; 192 [page]; New York Review Books [publisher]; First [edition]; 2015 [pubdate]; New York, NY [publoc]; 978-1590178546 [isbn].


Michael_Faraday

Assertion Duties

“A man who makes assertions, or draws conclusions, regarding any given case, ought to be competent to investigate it. He has no right to throw the onus on others, declaring it their duly to prove him right or wrong. His duty is to demonstrate the truth of that which he asserts, or to cease from asserting. The men he calls upon to consider and judge have enough to do with themselves, in the examination, correction, or verification of their own views. The world little knows how many of the thoughts and theories which have passed through the mind of a scientific investigator have been crushed in silence and secrecy by his own severe criticism and adverse examination; that in the most successful instances not a tenth of the suggestions, the hopes, the wishes, the preliminary conclusions have been realized.”
  • Source: Lecturer=Michael Faraday; Lecture/Title=“Observations on Mental Education: A Lecture Delivered at the Royal Institution of Great Britain Before H.R.H. Prince Albert”; Date=1854-05-06; Book/Title=“Lectures on Education”; Publication/Date=1855; Book/Title=“Experimental Researches in Chemistry and Physics”; Publication/Date=1859); Page=486.

Laws of Nature

“The laws of nature, as we understand them, are the foundation of our knowledge in natural things. So much as we know of them has been developed by the successive energies of the highest intellects, exerted through many ages. After a most rigid and scrutinizing examination upon principle and trial, a definite expression has been given to them; they have become, as it were, our belief or trust. From day to day we still examine and test our expressions of them. We have no interest in their retention if erroneous. On the contrary, the greatest discovery a man could make would be to prove that one of these accepted laws was erroneous, and his greatest honour would be the discovery.”
  • Source: Book/Author=Michael Faraday; Title=“Experimental Researches in Chemistry and Physics”; Publication/Date=1859; Page=469.

Leon_Festinger

Belief

“Suppose an individual believes something with his whole heart; suppose further that he has a commitment to this belief and he has taken irrevocable actions because of it; finally, suppose that he is presented with evidence, unequivocal and undeniable evidence, that his belief is wrong: what will happen? The individual will frequently emerge, not only unshaken, but even more convinced of the truth of his beliefs than ever before. Indeed, he may even show a new fervor for convincing and converting other people to his view.”
  • Source: Leon Festinger, In When Prophecy Fails (1956), 3.

Galen

Seeks the Truth

“It would be better, I think, for the man who really seeks the truth not to ask what the poets say; rather, he should first learn the method of finding the scientific premises that I discussed in the second book; then he should train and exercise himself in this method; and when his training is sufficiently advanced, then, as he approaches each particular problem, he should enquire into the premise needed for proving it, which premise he should take from simple sense-perception, which from experience, whether drawn from life or from the arts, which from the truths clearly apprehended by the mind, in order to draw out from them the desired conclusion.”
  • Source: Galen, On the Doctrines of Hippocrates and Plato,: PHP III 8.35.1-11 translation: De Lacy, Phillip (1978- 1984) Galen, On the Doctrines of Hippocrates and Plato, Berlin. p. 233; cited in: Christopher Jon Elliott. "Galen, Rome and the Second Sophistic." p. 147-148.

Galileo

Milky Way

“The next object which I have observed is the essence or substance of the Milky Way. By the aid of a telescope anyone may behold this in a manner which so distinctly appeals to the senses that all the disputes which have tormented philosophers through so many ages are exploded at once by the irrefragable evidence of our eyes, and we are freed from wordy disputes upon this subject, for the Galaxy is nothing else but a mass of innumerable stars planted together in clusters.”
  • Source: Galileo Galilei, In the pamphlet, The Sidereal Messenger (1610), reprinted in The Sidereal Messenger of Galileo Galilei: And a Part of the Preface to the Preface to Kepler's Dioptrics Containing the Original Account of Galileo's Astronomical Discoveries (1880), 42.

Seek the Truth

“For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.”
  • Source: Galileo Galilei, Letter (4 Aug 1597) to Kepler, expressing thanks and interest in the book Kepler sent him. As quoted in translation in Jackson J. Spielvogel, Western Civilization: Alternate Volume: Since 1300 (2010), Vol. 2, 494.

Robert_Heinlein

Opinions

“A thousand reasoned opinions are never equal to one case of diving in and finding out. Galileo proved that.”
  • Source: Written by Robert A. Heinlein in the book “Time Enough for Love”, published in 1973 by Putnam's Sons, ISBN: 0-399-11151-4. Prelude I, page 9. Character: Lazarus Long.

Scientific Method

“There are but two ways of forming an opinion in science. One is the scientific method; the other, the scholastic. One can judge from experiment, or one can blindly accept authority. To the scientific mind, experimental proof is all important and theory is merely a convenience in description, to be junked when it no longer fits. To the academic mind, authority is everything and facts are junked when they do not fit theory laid down by authority.”.
  • Source: Written by Robert A. Heinlein in the short story “Life-Line” originally published in the 1939-08 edition of “Astounding Science Fiction” magazine, page 83. Character: Dr. Pinero. Retrieved 2024-05-05 from https://www.luminist.org/archives/SF/AST.htm.

Nelson_Goodman

Simple Theories

“For if as scientists we seek simplicity, then obviously we try the simplest surviving theory first, and retreat from it only when it proves false. Not this course, but any other, requires explanation. If you want to go somewhere quickly, and several alternate routes are equally likely to be open, no one asks why you take the shortest. The simplest theory is to be chosen not because it is the most likely to be true but because it is scientifically the most rewarding among equally likely alternatives. We aim at simplicity and hope for truth.”
  • Source: Nelson Goodman, Problems and Projects (1972), 352.

John_Gribbin

Scientific Method

“The Big Idea that had been developed in the seventeenth century ... is now known as the scientific method. It says that the way to proceed when investigating how the world works is to first carry out experiments and/or make observations of the natural world. Then, develop hypotheses to explain these observations, and (crucially) use the hypothesis to make predictions about the future outcome of future experiments and/or observations. After comparing the results of those new observations with the predictions of the hypotheses, discard those hypotheses which make false predictions, and retain (at least, for the time being) any hypothesis that makes accurate predictions, elevating it to the status of a theory. Note that a theory can never be proved right. The best that can be said is that it has passed all the tests applied so far.”
  • Source: John R. Gribbin. In The Fellowship: the Story of a Revolution (2005), 275.

Edwin_Hubble

Scientific Judgments

“Science deals with judgments on which it is possible to obtain universal agreement. These judgments do not concern individual facts and events, but the invariable association of facts and events known as the laws of science. Agreement is secured by observation and experiment — impartial courts of appeal to which all men must submit if they wish to survive. The laws are grouped and explained by theories of ever increasing generality. The theories at first are ex post facto — merely plausible interpretations of existing bodies of data. However, they frequently lead to predictions that can be tested by experiments and observations in new fields, and, if the interpretations are verified, the theories are accepted as working hypotheses until they prove untenable. The essential requirements are agreement on the subject matter and the verification of predictions. These features insure a body of positive knowledge that can be transmitted from person to person, and that accumulates from generation to generation.”
  • Source: Edwin Powell Hubble. From manuscript on English Science in the Renaissance (1937), Edwin Hubble collection, Box 2, Huntington Library, San Marino, California. As cited by Norriss S. Hetherington in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 41. (Hetherington comments parenthetically that the references to court, judgment and appeal may be attributable to his prior experiences as a Rhodes Scholar reading Roman law at Oxford, and to a year's practice as an attorney in Louisville, Kentucky.)

Byron_K_Jennings

Crows

“While seeing any number of black crows does not prove all the crows are black, seeing one white crow disproves it. Thus science proceeds not by proving models correct but by discarding false ones or improving incomplete ones.”
  • Source: Byron K. Jennings, In 'On the Nature of Science', Physics in Canada (Jan/Feb 2007), 63, No. 1, 7.

Carl_Jung

Materialism

“Despite the materialistic tendency to understand the psyche as a mere reflection or imprint of physical and chemical processes, there is not a single proof of this hypothesis. Quite the contrary, innumerable facts prove that the psyche translates physical processes into sequences of images which have hardly any recognizable connection with the objective [i.e. physical and chemical] process. The materialistic hypothesis is much too bold and flies in the face of experience.”
  • Source: Written by Carl Jung in the book “The Archetypes and the Collective Unconscious”. Published in London, UK by Routledge. Published 1991. Page 57.

Paul_the_Apostle

Prove all Things (1 Thessalonians 5:21)

(21) “Prove all things; hold fast that which is good.”

Keywords: Certainty_quotes Proof_quotes Hold_quotes Good_quotes

Robert_M_Pirsig

An Experiment is Never a Failure

“An experiment is never a failure solely because it fails to achieve predicted results. An experiment is a failure only when it also fails adequately to test the hypothesis in question, when the data it produces don’t prove anything one way or another.”
  • Source: Zen and the Art of Motorcycle Maintenance: An Inquiry Into Values (1974), 102.

Plato

Dreaming

“(Socrates) There's a question you must often have heard people ask - the question what evidence we could offer if we were asked whether in this present instant, at this moment, we are asleep and dreaming all our thoughts, or awake and talking to each other in real life.
(Theaetetus) Yes, Socrates, it certainly is difficult to find the proof we want here. The two states seem to correspond in all their characteristics. There is nothing to prevent us from thinking when we are asleep that we are having the very same discussion that we have just had. And when we dream that we are telling the story of a dream, there is an extraordinary likeness between the two experiences.”
  • Source: Plato, 'Theaetetus' 158bc

Karl_Popper

No Conclusive Disproof

“No conclusive disproof of a theory can ever be produced; for it is always possible to say that the experimental results are not reliable.”
  • Source: Popper, K. R. (2005). The Logic of Scientific Discovery | 1935 (1935/Epub ed.). New York, NY: Routledge. Chap. 2

Strict Proof

“If you insist on strict proof (or strict disproof) in the empirical sciences, you will never benefit from experience, and never learn from it how wrong you are.”
  • Source: Popper, K. R. (2005). The Logic of Scientific Discovery | 1935 (1935/Epub ed.). New York, NY: Routledge.

Scientific Knowledge

“If the picture of the world which modern science draws comes anywhere near the truth — in other words, if we have anything like ‘scientific knowledge’ — then the conditions obtaining almost everywhere in the universe make the discovery of structural laws of the kind we are seeking — and thus the attainment of ‘scientific knowledge’ — almost impossible. For almost all regions of the universe are filled by chaotic radiation, and almost all the rest by matter in a likewise chaotic state. In spite of this, science has been miraculously successful in proceeding toward what I think should be regarded as its aim. This strange fact cannot, I think, be explained without proving too much. But it can encourage us to pursue that aim, even though we may not get any further encouragement to believe that we can actually attain it; neither from metaphysical realism nor from any other source.”
  • Source: Realism and the Aim of Science: From the Postscript to The Logic of Scientific Discovery, 1983, p. 146, ISBN 0415084008

Willard_Van_Orman_Quine

Science as a Tool

“As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries - not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience.”
  • Source: From A Logical Point of View (1953), p. 44.

Hans_Reichenbach

Picture of Scientific Method

“The picture of scientific method drafted by modern philosophy is very different from traditional conceptions. Gone is the ideal of a universe whose course follows strict rules, a predetermined cosmos that unwinds itself like an unwinding clock. Gone is the ideal of the scientist who knows the absolute truth. The happenings of nature are like rolling dice rather than like revolving stars; they are controlled by probability laws, not by causality, and the scientist resembles a gambler more than a prophet. He can tell you only his best posits — he never knows beforehand whether they will come true. He is a better gambler, though, than the man at the green table, because his statistical methods are superior. And his goal is staked higher — the goal of foretelling the rolling dice of the cosmos. If he is asked why he follows his methods, with what title he makes his predictions, he cannot answer that he has an irrefutable knowledge of the future; he can only lay his best bets. But he can prove that they are best bets, that making them is the best he can do — and if a man does his best, what else can you ask of him?”
  • Source: Hans Reichenbach, The Rise of Scientific Philosophy (1951, 1973), 248-9. Collected in James Louis Jarrett and Sterling M. McMurrin (eds.), Contemporary Philosophy: A Book of Readings (1954), 376.

Alfred_Russel_Wallace

Truth Proof

“There is no more convincing proof of the truth of a comprehensive theory than its power of absorbing and finding a place for new facts, and its capability of interpreting phenomena which had been previously looked upon as unaccountable anomalies. It is thus that the law of universal gravitation and the undulatory theory of light have become established and universally accepted by men of science. Fact after fact has been brought forward as being apparently inconsistent with them, and one after another these very facts have been shown to be the consequences of the laws they were at first supposed to disprove. A false theory will never stand this test. Advancing knowledge brings to light whole groups of facts which it cannot deal with, and its advocates steadily decrease in numbers, notwithstanding the ability and scientific skill with which it may have been supported.”
  • Source: Alfred Russel Wallace, From a review of four books on the subject 'Mimicry, and Other Protective Resemblances Among Animals', in The Westminster Review (Jul 1867), 88, 1. Wallace is identified as the author within the article as reprinted in William Beebe, The Book of Naturalists: An Anthology of the Best Natural History (1988), 108.

Gerald_Weinberg

Egoless Programming and Cognitive Dissonance

“Now, what cognitive dissonance has to do with our programming conflict should be vividly clear. A programmer who truly sees his program as an extension of his own ego is not going to be trying to find all the errors in that program. On the contrary, he is going to be trying to prove that the program is correct — even if this means the oversight of errors which are monstrous to another eye.”
  • Source: Chapter 4. Weinberg, G. M. (2011). The Psychology of Computer Programming (Silver anniversary edition) | 1971. Weinberg & Weinberg.

Ellis_Leon_Yochelson

Scientists Make Predictions

“Scientists are supposed to make predictions, probably to prove they are human and can be as mistaken as anyone else. Long-range predictions are better to make because the audience to whom the prediction was made is no longer around to ask questions. The alternative... is to make conflicting predictions, so that one prediction may prove right.”
  • Source: Ellis Leon Yochelson. 'Fossils—The How and Why of Collecting and Storing', Proceedings of the Biological Society of Washington (1969), 82, 597.