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Induction is the glory of science and the scandal of philosophy.
--
Concluding words of his commemorative address on the occasion of The Bacon Tercentenary (5 October 1926), as quoted in Argument and Analysis: An Introduction to Philosophy (1992) by Martin Curd, p. 470

 

C. D. Broad

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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

 

It seems to me that science has a much greater likelihood of being true in the main than any philosophy hitherto advanced (I do not, of course, except my own). In science there are many matters about which people are agreed; in philosophy there are none. Therefore, although each proposition in a science may be false, and it is practically certain that there are some that are false, yet we shall be wise to build our philosophy upon science, because the risk of error in philosophy is pretty sure to be greater than in science. If we could hope for certainty in philosophy, the matter would be otherwise, but so far as I can see such a hope would be chimerical.

 

Bertrand Russell

 

Never was there a time, in the history of the world, when moral heroes were more needed. The world waits for such, the providence of God has commanded science to labor and prepare the way for such. For them she is laying her iron tracks, and stretching her wires, and bridging the oceans. But where are they? Who shall breathe into our civil and political relations the breath of a higher life? Who shall touch the eyes of a paganized science, and of a pantheistic philosophy, that they may see God? Who shall consecrate to the glory of God, the triumphs of science? Who shall bear the life-boat to the stranded and perishing nations?

 

Mark (educator) Hopkins

 

In every science, after having analysed the ideas, expressing the more complicated by means of the more simple, one finds a certain number that cannot be reduced among them, and that one can define no further. These are the primitive ideas of the science; it is necessary to acquire them through experience, or through induction; it is impossible to explain them by deduction.

 

Giuseppe Peano

 

I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.

 

Isaac Newton