A Quote by Carl Gustav Hempel
A geometrical theory in physical interpretation can never be validated with mathematical certainty ... ; like any other theory of empirical science, it can acquire only a more or less high degree of confirmation.
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The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena. The verbal interpretation, on the other hand - i.e., the metaphysics of quantum theory - is on far less solid ground. In fact, in more than forty years physicists have not been able to provide a clear metaphysical model.
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.
It is clear that Economics, if it is to be a science at all, must be a mathematical science ... simply because it deals with quantities... As the complete theory of almost every other science involves the use of calculus, so we cannot have a true theory of Economics without its aid.
Science may be weird and incomprehensible--more weird and less comprehensible than any theology--but science works. It gets results. It can fly you to Saturn, slingshotting you around Venus and Jupiter on the way. We may not understand quantum theory (heaven knows, I don't), but a theory that predicts the real world to ten decimal places cannot in any straightforward sense be wrong.
Belief Systems contradict both science and ordinary "common sense." B.S. contradicts science, because it claims certitude and science can never achieve certitude: it can only say, "This model"- or theory, or interpretation of the data- "fits more of the facts known at this date than any rival model." We can never know if the model will fit the facts that might come to light in the next millennium or even in the next week.
A hypothesis is empirical or scientific only if it can be tested by experience. A hypothesis or theory which cannot be, at least in principle, falsified by empirical observations and experiments does not belong to the realm of science.
An old French mathematician said: "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.
It must be conceded that a theory has an important advantage if its basic concepts and fundamental hypotheses are 'close to experience,' and greater confidence in such a theory is certainly justified. There is less danger of going completely astray, particularly since it takes so much less time and effort to disprove such theories by experience. Yet more and more, as the depth of our knowledge increases, we must give up this advantage in our quest for logical simplicity in the foundations of physical theory.
There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.
Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has.
There was a time, before I was in graduate school, when political philosophy pretty much ceased to exist. The positivists thought there were only two things you could do: conceptual analysis or empirical investigation. Any kind of political theory or even ethical theory was nonsense.
I like to think that Einstein would look at string theory’s journey and smile, enjoying the theory’s remarkable geometrical features while feeling kinship with fellow travelers on the long and winding road toward unification.
No fairer destiny could be allotted to any physical theory than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.
Some claim evolution is just a theory. As if it were merely an opinion. The theory of evolution, like the theory of gravity, is a scientific fact. Evolution really happened. Accepting our kinship with all life on Earth is not only solid science. In my view, it’s also a soaring spiritual experience.
String theory has had a long and wonderful history. It originated as a technique to try to understand the strong force. It was a calculational mechanism, a way of approaching a mathematical problem that was too difficult, and it was a promising way, but it was only a technique. It was a mathematical technique rather than a theory in itself.
Those who are enamoured of practice without science are like a pilot who goes into a ship without rudder or compass and never has any certainty of where he is going. Practice should always be based upon a sound knowledge of theory.
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