People are smarter than you think. Give them a chance to prove themselves.
You have heard of the new chemical nomenclature endeavored to be introduced by Lavoisier, Fourcroy, &c. Other chemists of this country, of equal note, reject it, and prove in my opinion that it is premature, insufficient and false. These latter are joined by the British chemists; and upon the whole, I think the new nomenclature will be rejected, after doing more harm than good. There are some good publications in it, which must be translated into the ordinary chemical language before they will be useful.
God pity the man of science who believes in nothing but what he can prove by scientific methods; for if ever a human being needed divine pity, he does.
The mind can proceed only so far upon what it knows and can prove. There comes a point where the mind takes a higher plane of knowledge, but can never prove how it got there. All great discoveries have involved such a leap
The regularity with which we conclude that further advances in a particular field are impossible seems equaled only by the regularity with which events prove that we are of too limited vision. And it always seems to be those who have the fullest opportunity to know who are the most limited in view. What, then, is the trouble? I think that one answer should be: we do not realize sufficiently that the unknown is absolutely infinite, and that new knowledge is always being produced.
"I should have more faith," he said; "I ought to know by this time that when a fact appears opposed to a long train of deductions it invariably proves to be capable of bearing some other interpretation."
As our own species is in the process of proving, one cannot have superior science and inferior morals. The combination is unstable and self-destroying.
I have said that science is impossible without faith. ... Inductive logic, the logic of Bacon, is rather something on which we can act than something which we can prove, and to act on it is a supreme assertion of faith ... Science is a way of life which can only fluorish when men are free to have faith.
Science, by itself, cannot supply us with an ethic. It can show us how to achieve a given end, and it may show us that some ends cannot be achieved. But among ends that can be achieved our choice must be decided by other than purely scientific considerations. If a man were to say, "I hate the human race, and I think it would be a good thing if it were exterminated," we could say, "Well, my dear sir, let us begin the process with you." But this is hardly argument, and no amount of science could prove such a man mistaken.
Detest it as lewd intercourse, it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life. Having himself spent a lifetime unsuccessfully trying to prove Euclid's postulate that parallel lines do not meet, Farkas discouraged his son János from any further attempt.
That is the way of the scientist. He will spend thirty years in building up a mountain range of facts with the intent to prove a certain theory; then he is so happy with his achievement that as a rule he overlooks the main chief fact of all-that all his accumulation proves an entirely different thing.
The vortex theory [of the atom] is only a dream. Itself unproven, it can prove nothing, and any speculations founded upon it are mere dreams about dreams.
I approached the bulk of my schoolwork as a chore rather than an intellectual adventure. The tedium was relieved by a few courses that seem to be qualitatively different. Geometry was the first exciting course I remember. Instead of memorizing facts, we were asked to think in clear, logical steps. Beginning from a few intuitive postulates, far reaching consequences could be derived, and I took immediately to the sport of proving theorems.
If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.
It is not enough to discover and prove a useful truth previously unknown, but that it is necessary also to be able to propagate it and get it recognized.
It is very different to make a practical system and to introduce it. A few experiments in the laboratory would prove the practicability of system long before it could be brought into general use. You can take a pipe and put a little coal in it, close it up, heat it and light the gas that comes out of the stem, but that is not introducing gas lighting. I'll bet that if it were discovered to-morrow in New York that gas could be made out of coal it would be at least five years before the system would be in general use.
My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments: In order to which, I shall premise the following Definitions and Axioms.
There is more evidence to prove that saltness [of the sea] is due to the admixture of some substance, besides that which we have adduced. Make a vessel of wax and put it in the sea, fastening its mouth in such a way as to prevent any water getting in. Then the water that percolates through the wax sides of the vessel is sweet, the earthy stuff, the admixture of which makes the water salt, being separated off as it were by a filter.
There is one experiment which I always like to try, because it proves something whichever way it goes. A solution of iodine in water is shaken with bone-black, filtered and tested with starch paste. If the colorless solution does not turn the starch blue, the experiment shows how completely charcoal extracts iodine from aqueous solution. If the starch turns blue, the experiment shows that the solution, though apparently colorless, still contains iodine which can be detected by means of a sensitive starch test.
Guessing before proving! Need I remind you that it is so that all important discoveries have been made?
[This] may prove to be the beginning of some embracing generalization, which will throw light, not only on radioactive processes, but on elements in general and the Periodic Law.... Chemical homogeneity is no longer a guarantee that any supposed element is not a mixture of several of different atomic weights, or that any atomic weight is not merely a mean number.
As history proves abundantly, mathematical achievement, whatever its intrinsic worth, is the most enduring of all.
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations.
If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.
The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.
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