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There cannot be a doubt that the method of inquiry which Mr. Darwin has adopted is not only rigorously in accordance with the canons of scientific logic, but that it is the only adequate method. Critics exclusively trained in classics or in mathematics, who have never determined a scientific fact in their lives by induction from experiment or observation, prate learnedly about Mr. Darwin's method, which is not inductive enough, not Baconian enough, forsooth, for them. But even if practical acquaintance with the process of scientific investigation is denied them, they may learn, by the perusal of Mr. Mill's admirable chapter "On the Deductive Method," that there are multitudes of scientific inquiries in which the method of pure induction helps the investigator but a very little way.
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Thomas Henry Huxley, "Darwin on the Origin of Species," Westminster Review, 1860, volume 17 (new series) pages 541-570, at page 566
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(Note that Denton's objections, made in 1986, had already been answered by Huxley in 1860!)

 

Charles Darwin

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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.

 

Karl Popper

 

Induction was shown to be untenable as a scientific method by Popper in The Logic of Scientific Discovery (1959). Instead, advances in scientific understanding come ideally from hypothetico-deductivism: firstly, development of a hypothesis in relation to a problem situation, and secondly, its testing in relation to all relevant knowledge and furthermore by its great explanatory power.

 

John Carew Eccles

 

The chronological method which begins with the experience of the learner and develops from that the proper modes of scientific treatment is often called the "psychological" method in distinction from the logical method of the expert or specialist. The apparent loss of time involved is more than made up for by the superior understanding and vital interest secured. What the pupil learns he at least understands. Moreover by following, in connection with problems selected from the material of ordinary acquaintance, the methods by which scientific men have reached their perfected knowledge, he gains independent power to deal with material within his range, and avoids the mental confusion and intellectual distaste attendant upon studying matter whose meaning is only symbolic. Since the mass of pupils are never going to become scientific specialists, it is much more important that they should get some insight into what scientific method means than that they should copy at long range and second hand the results which scientific men have reached. Students will not go so far, perhaps, in the "ground covered," but they will be sure and intelligent as far as they do go. And it is safe to say that the few who go on to be scientific experts will have a better preparation than if they had been swamped with a large mass of purely technical and symbolically stated information. In fact, those who do become successful men of science are those who by their own power manage to avoid the pitfalls of a traditional scholastic introduction into it.

 

John Dewey

 

In this complex world, science, the scientific method, and the consequences of the scientific method are central to everything the human race is doing and to wherever we are going. If we blow ourselves up we will do it by misapplication of science; if we manage to keep from blowing ourselves up, it will be through intelligent application of science.

 

Robert A. Heinlein

 

"The issue of 'science' does not intrude itself directly upon the occasion of the performance of a musical work, at least a non-electronically produced work, since—as has been said—there is at least a question as to whether the question as to whether musical composition is to be regarded as a science or not is indeed really a question; but there is no doubt that the question as to whether musical discourse or—more precisely—the theory of music should be subject to the methodological criteria of scientific method and the attendant scientific language is a question, except that the question is really not the normative one of whether it 'should be' or 'must be,' but the factual one that it is, not because of the nature of musical theory, but because of the nature and scope of scientific method and language, whose domain of application is such that if it is not extensible to musical theory, then musical theory is not a theory in any sense in which the term ever has been employed. This should sound neither contentious nor portentous, rather it should be obvious to the point of virtual tautology.”

 

Milton Babbitt