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Who said: “I seem to have been only like a boy playing on the seashore, ... finding a smoother pebble or a prettier shell ... whilst the great ocean of truth lay all undiscovered before me.”
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Home > Category Index for Science Quotations > Category Index L > Category: Logical

Logical Quotes (20 quotes)

A noble, logical diagram once recorded will never die, but long after we are gone be a living thing, asserting itself with ever-growing insistency. Remember that our sons and our grandsons are going to do things that would stagger us.
(1907) As quoted in 'Closing In', Charles Moore, Daniel H. Burnham, Architect, Planner of Cities (1921), Vol. 2, 147.
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A principle of induction would be a statement with the help of which we could put inductive inferences into a logically acceptable form. In the eyes of the upholders of inductive logic, a principle of induction is of supreme importance for scientific method: “... this principle”, says Reichenbach, “determines the truth of scientific theories. To eliminate it from science would mean nothing less than to deprive science of the power to decide the truth or falsity of its theories. Without it, clearly, science would no longer have the right to distinguish its theories from the fanciful and arbitrary creations of the poet’s mind.” Now this principle of induction cannot be a purely logical truth like a tautology or an analytic statement. Indeed, if there were such a thing as a purely logical principle of induction, there would be no problem of induction; for in this case, all inductive inferences would have to be regarded as purely logical or tautological transformations, just like inferences in inductive logic. Thus the principle of induction must be a synthetic statement; that is, a statement whose negation is not self-contradictory but logically possible. So the question arises why such a principle should be accepted at all, and how we can justify its acceptance on rational grounds.
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An essential [of an inventor] is a logical mind that sees analogies. No! No! not mathematical. No man of a mathematical habit of mind ever invented anything that amounted to much. He hasn’t the imagination to do it. He sticks too close to the rules, and to the things he is mathematically sure he knows, to create anything new.
As quoted in French Strother, 'The Modern Profession of Inventing', World's Work and Play (Jul 1905), 6, No. 32, 187.
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Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have ‘proved’ that it involves no contradiction either in its terms or with the truths previously admitted.
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In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly
Geometry and the imagination (New York, 1952).
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Innovation is not the product of logical thought, even though the final product is tied to a logical structure.
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Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems—general and specific statements—can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.
Essay,'Private Games', in Lewis Wolpert, Alison Richards (eds.), A Passion for Science (1988), 53.
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Mathematics… is the set of all possible self-consistent structures, and there are vastly more logical structures than physical principles.
In 'Conclusion', Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension (1995), 328.
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My “"thinking”" time was devoted mainly to activities that were essentially clerical or mechanical: searching, calculating, plotting, transforming, determining the logical or dynamic consequences of a set of assumptions or hypotheses, preparing the way for a decision or an insight. Moreover ... the operations that fill most of the time allegedly devoted to technical thinking are operations that can be performed more effectively by machines than by men.
From article 'Man-Computer Symbiosis', in IRE Transactions on Human Factors in Electronics (Mar 1960), Vol. HFE-1, 4-11.
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Quantum mechanics and relativity, taken together, are extraordinarily restrictive, and they therefore provide us with a great logical machine. We can explore with our minds any number of possible universes consisting of all kinds of mythical particles and interactions, but all except a very few can be rejected on a priori grounds because they are not simultaneously consistent with special relativity and quantum mechanics. Hopefully in the end we will find that only one theory is consistent with both and that theory will determine the nature of our particular universe.
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Science, in its ultimate ideal, consists of a set of propositions arranged in a hierarchy, the lowest level of the hierarchy being concerned with particular facts, and the highest with some general law, governing everything in the universe. The various levels in the hierarchy have a two-fold logical connection, travelling one up, one down; the upward connection proceeds by induction, the downward by deduction.
In The Scientific Outlook (1931, 2009), 38.
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Science’s defenders have identified five hallmark moves of pseudoscientists. They argue that the scientific consensus emerges from a conspiracy to suppress dissenting views. They produce fake experts, who have views contrary to established knowledge but do not actually have a credible scientific track record. They cherry-pick the data and papers that challenge the dominant view as a means of discrediting an entire field. They deploy false analogies and other logical fallacies. And they set impossible expectations of research: when scientists produce one level of certainty, the pseudoscientists insist they achieve another.
In Commencement Address at the California Institute of Technology (10 Jun 2016). Published on the website of The New Yorker (10 Jun 2016).
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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.
In 'The Teaching of the History of Science', The Scientific Monthly (Sep 1918), 194.
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The physicist, in his study of natural phenomena, has two methods of making progress: (1) the method of experiment and observation, and (2) the method of mathematical reasoning. The former is just the collection of selected data; the latter enables one to infer results about experiments that have not been performed. There is no logical reason why the second method should be possible at all, but one has found in practice that it does work and meets with reasonable success.
From Lecture delivered on presentation of the James Scott prize, (6 Feb 1939), 'The Relation Between Mathematics And Physics', printed in Proceedings of the Royal Society of Edinburgh (1938-1939), 59, Part 2, 122.
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The scientific method is one and the same in all branches, and that method is the method of all logically trained minds.
From The Grammar of Science (1892), 13.
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There are diverse views as to what makes a science, but three constituents will be judged essential by most, viz: (1) intellectual content, (2) organization into an understandable form, (3) reliance upon the test of experience as the ultimate standard of validity. By these tests, mathematics is not a science, since its ultimate standard of validity is an agreed-upon sort of logical consistency and provability.
In 'The Future of Data Analysis', Annals of Mathematical Statistics (1962), 33, No. 1, 5-6.
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Through purely logical thinking we can attain no knowledge whatsoever of the empirical world.
In Francis Crick, The Astonishing Hypothesis: the Scientific Search for the Soul (1995), 215.
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We must learn to think not only logically, but bio-logically.
In One Life at a Time, Please (1988), 68.
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When the intensity of emotional conviction subsides, a man who is in the habit of reasoning will search for logical grounds in favor of the belief which he finds in himself.
In Mysticism and Logic (2004), 15.
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[An outsider views a scientist] as a type of unscrupulous opportunist: he appears as a realist, insofar as he seeks to describe the world independent of the act of perception; as idealist insofar as he looks upon the concepts and theories as the free inventions of the human spirit (not logically derivable from that which is empirically given); as positivist insofar as he considers his concepts and theories justified only to the extent to which they furnish a logical representation of relations among sense experiences. He may even appear as Platonist or Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research.
In 'Reply to Critcisms', Paul Arthur Schilpp (ed.), Albert Einstein: Philosopher-Scientist (1949, 1959), Vol. 2, 684.
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Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton



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