“A scientific theory is usually felt to be better than its predecessors not only in the sense that it is a better instrument for discovering and solving puzzles but also because it is somehow a better representation of what nature is really like. One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently generalizations like that refer not to the puzzle-solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is “really there.””

— Thomas Kuhn , book The Structure of Scientific Revolutions

Perhaps there is some other way of salvaging the notion of ‘truth’ for application to whole theories, but this one will not do. There is, I think, no theory-independent way to reconstruct phrases like ‘really there’; the notion of a match between the ontology of a theory and its “real” counterpart in nature now seems to me illusive in principle. Besides, as a historian, I am impressed with the implausability of the view. I do not doubt, for example, that Newton’s mechanics improves on Aristotle’s and that Einstein’s improves on Newton’s as instruments for puzzle-solving. But I can see in their succession no coherent direction of ontological development. On the contrary, in some important respects, though by no means in all, Einstein’s general theory of relativity is closer to Aristotle’s than either of them is to Newton’s.
The Structure of Scientific Revolutions (1962), Postscript (1969)

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American historian, physicist and philosopher 1922–1996

Ivar Ekeland (1944) French mathematician

Source: The Best of All Possible Worlds (2006), Chapter 3, The Least Action Principle, p. 48.

“This fact, that all charges are integral multiples of a fundamental unit, is still one of the unexplained puzzles of fundamental physics. It does not in any way contradict electromagnetic theory, but it is not predicted by it, and until we have a more fundamental theory that explains it, we shall not feel that we really understand electromagnetic phenomena thoroughly. Presumably its explanation will not come until we understand quantum theory more thoroughly than we do at present.”

John C. Slater (1900–1976) American physicist

[John Clarke Slater, Nathaniel Herman Frank, Electromagnetism, Courier Dover Publications, 1969, 0486622630, 11]

“Schizophrenia--its nature, etiology, and the kind of therapy to use for it--remains one of the most puzzling of the mental illnesses. The theory of schizophrenia presented here is based on communications analysis, and specifically on the Theory of Logical Types. From this theory and from observations of schizophrenic patients is derived a description, and the necessary conditions for, a situation called the "double bind"--a situation in which no matter what a person does, he "can't win."”

Gregory Bateson (1904–1980) English anthropologist, social scientist, linguist, visual anthropologist, semiotician and cyberneticist

It is hypothesized that a person caught in the double bind may develop schizophrenic symptoms.
Gregory Bateson, Don D. Jackson, Jay Haley, and John Weakland (1956) " Towards a theory of Schizophrenia http://www.psychodyssey.net/wp-content/uploads/2012/05/TOWARD-A-THEORY-OF-SCHIZOPHRENIA-2.pdf" In: Behavioral Science (1956) Vol 1, nr.4, pp.251-254

“The theory is the result of listening to the problem. When the theory acquires a life of its own because some people like it more than the real world, all kinds of uninspiring, uninteresting things happen, so the key is both to listen to the problem and to study the theory. But always remember that just as much theory is bunk as there are buggy solutions. There is nothing more wrong with "theory" than "solutions" – both their quality and their applicability are orthogonal to their existence.”

Erik Naggum (1965–2009) Norwegian computer programmer

Re: "Choose the Right Language" in "Tutorial" by Norvig and Pitman http://groups.google.com/group/comp.lang.lisp/msg/99d41ab4a42978b1 (Usenet article).
Usenet articles, Miscellaneous

“"Groping" and "muddling through" is usually described as a solution by trial and error…. a series of trials, each of which attempts to correct the error committed by the preceding and, on the whole, the errors diminished as we proceed and the successive trials come closer and closer to the desired final result…. we may wish a better characterization…"successive trials" or "successive corrections" or "successive approximations."… You use successive approximations when… looking for a word in the dictionary… A mathematician may apply the term… to a highly sophisticated procedure… to treat some very advanced problem… that he cannot treat otherwise. The term even applies to science as a whole; the scientific theories which succeed each other, each claiming a better explanation… may appear as successive approximations to the truth.
Therefore, the teacher should not discourage his students from using trial and error—on the contrary, he should encourage the intelligent use of the fundamental method of successive approximations. Yet he should convincingly show that for… many… situations, straightforward algebra is more efficient than successive approximations.”

George Pólya (1887–1985) Hungarian mathematician

George Pólya, Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (1962)

“Normal science, the puzzle-solving activity we have just examined, is a highly cumulative enterprise, eminently successful in its aim, the steady extension of the scope and precision of scientific knowledge. In all these respects it fits with great precision the most usual image of scientific work. Yet one standard product of the scientific enterprise is missing. Normal science does not aim at novelties of fact or theory and, when successful, finds none.”

Thomas Kuhn book The Structure of Scientific Revolutions

Source: The Structure of Scientific Revolutions (1962), VI. Anomaly and the Emergence of Scientific Discoveries, p. 52

“A new theory by the author has been added, which draws the physical inferences consequent on the extension of the foundations of geometry beyond Reimann… and represents an attempt to derive from world-geometry not only gravitational but also electromagnetic phenomena. Even if this theory is still only in its infant stage, I feel convinced that it contains no less truth than Einstein's Theory of Gravitation—whether this amount of truth is unlimited or, what is more probable, is bounded by the Quantum Theory.”

Hermann Weyl (1885–1955) German mathematician

From the Author's Preface to Third Edition (1919)
Space—Time—Matter (1952)

“Rather like the Bible is for many Christians, the General Theory is the essential economics reference which few economists have ever read.”

Steve Keen (1953) Australian economist

Source: Debunking Economics - The Naked Emperor Of The Social Sciences (2001), Chapter 9, The Sum Of The Parts, p. 199

“The monkeys solved the puzzle simply because they found it gratifying to solve puzzles. They enjoyed it. The joy of the task was its own reward.”

Daniel H. Pink book Drive: The Surprising Truth About What Motivates Us

Source: Drive: The Surprising Truth About What Motivates Us

“A theory is only as good as its assumptions. If the premises are false, the theory has no real scientific value. The only scientific criterion for judging the validity of a scientific theory is a confrontation with the data of experience.”

Maurice Allais (1911–2010) French economist; 1988 winner of the Nobel Memorial Prize in Economics

L'anisotropie de l'espace. La nécessaire révision de certains postulats des théories contemporaines. Les données de l'expérience (1997), p. 591

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