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A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.
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"On Denoting", Mind, Vol. 14, No. 56 (October 1905), pp. 479–493; as reprinted in Logic and Knowledge: Essays, 1901–1950, (1956).

 

Bertrand Russell

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What is very important to me is two points: A theory should be internally consistent and it should have some contact with observation. Well, I’m told by all the experts that this theory [String theory] is internally consistent, although they think up new interpretations every time I turn my back. But contact with reality? Nobody’s given me anything. I just watch. I’m somewhat unhappy that so many people are working on it. To me, as a physicist, it’s sort of sad that so many people at the same time work at something that doesn’t seem to have any contact with experiment. But that, to some extent, is due to the fact that we don’t have any great experimental puzzle to be thinking about. We have to supply the puzzles, and there aren’t that many puzzles right now.

 

Valentine Telegdi

 

Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory. As philosopher of science Karl Popper has emphasized, a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation. Each time new experiments are observed to agree with the predictions the theory survives, and our confidence in it is increased; but if ever a new observation is found to disagree, we have to abandon or modify the theory.

 

Stephen Hawking

 

Common Logic is the Grammar of the higher Speech, that is, of Thought; it examines merely the relations of ideas to one another, the Mechanics of Thought, the pure Physiology of ideas. Now logical ideas stand related to one another, like words without thoughts. Logic occupies itself with the mere dead Body of the Science of Thinking. — Metaphysics, again, is the Dynamics of Thought; treats of the primary Powers of Thought; occupies itself with the mere Soul of the Science of Thinking. Metaphysical ideas stand related to one another, like thoughts without words. Men often wondered at the stubborn Incompletibility of these two Sciences; each followed its own business by itself; there was a want everywhere, nothing would suit rightly with either. From the very first, attempts were made to unite them, as everything about them indicated relationship; but every attempt failed; the one or the other Science still suffered in these attempts, and lost its essential character. We had to abide by metaphysical Logic, and logical Metaphysic, but neither of them was as it should be.

 

Novalis

 

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

 

To say that prediction is the purpose of a scientific theory is to confuse means with ends. It is like saying that the purpose of a spaceship is to burn fuel. ... Passing experimental tests is only one of many things a theory has to do to achieve the real purpose of science, which is to explain the world. (Ch. 1)

 

David Deutsch