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These are the limits of the scientific method and of logic itself, insofar as they must rely on language. Our words are built on the objects of our experience. They have acquired their effectiveness by adapting themselves to the occurrences of our everyday world. But when we approach realities of another scale, these words can become obstacles.
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Hubert Reeves (1984) Atoms of silence: an exploration of cosmic evolution Massachusetts Institute of Technology. p. 37

 

Hubert Reeves

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Now, it is unquestionable that language, and consequently the system of concepts which it translates, is the product of a collective elaboration. What it expresses is the manner in which society as a whole represents the facts of experience. The ideas which correspond to the diverse elements of language are thus collective representations. Even their contents bear witness to the same fact. In fact, there are scarcely any words among those which we usually employ whose meaning does not pass, to a greater or less extent, the limits of our personal experience. Very frequently a term expresses things which we have never perceived or experiences which we have never had or of which we have never been the witness. Even when we know some of the objects which it concerns, it is only as particular examples that serve to illustrate the idea which they would never have been able to form by themselves. Thus there is a great deal of knowledge condensed in the word which I never collected, and which is not individual; it even surpasses me to such an extent that I cannot even completely appropriate all its results. Which of us knows all the words of the language he speaks and the entire signification of each?

 

Emile Durkheim

 

You had to form for yourself a lucid language for the world, to overcome the battering of experience, to replace everyday life’s pain and harshness and wretched dreariness with — no not with certainty but with an ignorance you could live with. Deep ignorance, but still a kind that knew its limits. The limits were crucial.

 

Gregory Benford

 

Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.

 

Bertrand Russell

 

Logic pervades the world: the limits of the world are also its limits. So we cannot say in logic, "The world has this in it, and this, but not that." For that would appear to presuppose that we were excluding certain possibilities, and this cannot be the case, since it would require that logic should go beyond the limits of the world; for only in that way could it view those limits from the other side as well. We cannot think what we cannot think; so what we cannot think we cannot say either. (5.61)

 

Ludwig Wittgenstein

 

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.

 

Charles Darwin