Prove Quotes (91 quotes)

Proved Quotes, Proving Quotes

Proved Quotes, Proving Quotes

A fateful process is set in motion when the individual is released “to the freedom of his own impotence” and left to justify his existence by his own efforts. The autonomous individual, striving to realize himself and prove his worth, has created all that is great in literature, art, music, science and technology. The autonomous individual, also, when he can neither realize himself nor justify his existence by his own efforts, is a breeding call of frustration, and the seed of the convulsions which shake our world to its foundations.

A Frenchman who arrives in London, will find Philosophy, like every Thing else, very much chang’d there. He had left the World a

*plenum*, and he now finds it a*vacuum*. At*Paris*the Universe is seen, compos’d of Vortices of subtile Matter; but nothing like it is seen in*London*. In*France*, ‘tis the Pressure of the Moon that causes the Tides; but in*England*‘tis the Sea that gravitates towards the Moon; so what when you think that the Moon should make it flood with us, those Gentlemen fancy it should be Ebb, which, very unluckily, cannot be prov’d. For to be able to do this, ‘tis necessary the Moon and the Tides should have been enquir’d into, at the very instant of the Creation.
All the experiments which have been hitherto carried out, and those that are still being daily performed, concur in proving that between different bodies, whether principles or compounds, there is an agreement, relation, affinity or attraction (if you will have it so), which disposes certain bodies to unite with one another, while with others they are unable to contract any union: it is this effect, whatever be its cause, which will help us to give a reason for all the phenomena furnished by chemistry, and to tie them together.

Concepts that have proven useful in ordering thi ngs easily achieve such authority over us that we forget their earthly origins and accept them as unalterable givens.

Einstein’s results again turned the tables and now very few philosophers or scientists still think that scientific knowledge is, or can be, proven knowledge.

Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have ‘proved’ that it involves no contradiction either in its terms or with the truths previously admitted.

Far must thy researches go

Wouldst thou learn the world to know;

Thou must tempt the dark abyss

Wouldst thou prove what

Naught but firmness gains the prize,—

Naught but fullness makes us wise,—

Buried deep truth ever lies!

Wouldst thou learn the world to know;

Thou must tempt the dark abyss

Wouldst thou prove what

*Being*is;Naught but firmness gains the prize,—

Naught but fullness makes us wise,—

Buried deep truth ever lies!

For it is too bad that there are so few who seek the truth and so few who do not follow a mistaken method in philosophy. This is not, however, the place to lament the misery of our century, but to rejoice with you over such beautiful ideas for proving the truth. So I add only, and I promise, that I shall read your book at leisure; for I am certain that I shall find the noblest things in it. And this I shall do the more gladly, because I accepted the view of Copernicus many years ago, and from this standpoint I have discovered from their origins many natural phenomena, which doubtless cannot be explained on the basis of the more commonly accepted hypothesis.

Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it is the truth.

Gödel proved that the world of pure mathematics is inexhaustible; no finite set of axioms and rules of inference can ever encompass the whole of mathematics; given any finite set of axioms, we can find meaningful mathematical questions which the axioms leave unanswered. I hope that an analogous Situation exists in the physical world. If my view of the future is correct, it means that the world of physics and astronomy is also inexhaustible; no matter how far we go into the future, there will always be new things happening, new information coming in, new worlds to explore, a constantly expanding domain of life, consciousness, and memory.

He made an instrument to know If the moon shine at full or no;

That would, as soon as e’er she shone straight,

Whether ‘twere day or night demonstrate;

Tell what her d’ameter to an inch is,

And prove that she’s not made of green cheese.

That would, as soon as e’er she shone straight,

Whether ‘twere day or night demonstrate;

Tell what her d’ameter to an inch is,

And prove that she’s not made of green cheese.

He thought he saw an Argument

That proved he was the Pope:

He looked again and found it was

A Bar of Mottled Soap.

“A fact so dread.” he faintly said,

“Extinguishes all hope!”

That proved he was the Pope:

He looked again and found it was

A Bar of Mottled Soap.

“A fact so dread.” he faintly said,

“Extinguishes all hope!”

However, if we consider that all the characteristics which have been cited are only differences in degree of structure, may we not suppose that this special condition of organization of man

*has been gradually acquired at the close of a long period of time, with the aid of circumstances which have proved favorable?*What a subject for reflection for those who have the courage to enter into it!
I am coming more and more to the conviction that the necessity of our geometry cannot be proved, at least neither by, nor for, the

*human*intelligence … One would have to rank geometry not with arithmetic, which stands a priori, but approximately with mechanics.
I am more fond of achieving than striving. My theories must prove to be facts or be discarded as worthless. My efforts must soon be crowned with success, or discontinued.

I believe in an immortal soul. science has proved that nothing disintegrates into nothingness. Life and soul, therefore, cannot disintegrate into nothingness, and so are immortal.

I believe that the science of chemistry alone almost proves the existence of an intelligent creator.

I can’t recall a single problem in my life, of any sort, that I ever started on that I didn't solve, or prove that I couldn’t solve it. I never let up, until I had done everything that I could think of, no matter how absurd it might seem as a means to the end I was after.

I confess that Fermat’s Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.

I have been arranging certain experiments in reference to the notion that Gravity itself may be practically and directly related by experiment to the other powers of matter and this morning proceeded to make them. It was almost with a feeling of awe that I went to work, for if the hope should prove well founded, how great and mighty and sublime in its hitherto unchangeable character is the force I am trying to deal with, and how large may be the new domain of knowledge that may be opened up to the mind of man.

I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the “Law of Frequency of Error.” The law would have been personified by the Greeks and deified, if they had known of it. It reigns with serenity and in complete self-effacement, amidst the wildest confusion. The huger the mob, and the greater the apparent anarchy, the more perfect is its sway. It is the supreme law of Unreason. Whenever a large sample of chaotic elements are taken in hand and marshaled in the order of their magnitude, an unsuspected and most beautiful form of regularity proves to have been latent all along.

I ought to call myself an agnostic; but, for all practical purposes, I am an atheist. I do not think the existence of the Christian God any more probable than the existence of the Gods of Olympus or Valhalla. To take another illustration: nobody can prove that there is not between the Earth and Mars a china teapot revolving in an elliptical orbit, but nobody thinks this sufficiently likely to be taken into account in practice. I think the Christian God just as unlikely.

If anyone could prove to me that Christ is outside the truth, and if the truth really did exclude Christ, I should prefer to stay with Christ and not with truth.

If basketball was going to enable Bradley to make friends, to prove that a banker’s son is as good as the next fellow, to prove that he could do without being the greatest-end-ever at Missouri, to prove that he was not chicken, and to live up to his mother’s championship standards, and if he was going to have some moments left over to savor his delight in the game, he obviously needed considerable practice, so he borrowed keys to the gym and set a schedule for himself that he adhereded to for four full years—in the school year, three and a half hours every day after school, nine to five on Saturday, one-thirty to five on Sunday, and, in the summer, about three hours a day.

If Einstein’s theory [of relativity] should prove to be correct, as I expect it will, he will be considered the Copernicus of the twentieth century.

If finally, the science should prove that society at a certain time revert to the church and recover its old foundation of absolute faith in a personal providence and a revealed religion, it commits suicide.

If I set out to prove something, I am no real scientist—I have to learn to follow where the facts lead me—I have to learn to whip my prejudices.

If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?

If you were going to risk all that, not just risk the hardship and the pain but risk your life. Put everything on line for a dream, for something that’s worth nothing, that can’t be proved to anybody. You just have the transient moment on a summit and when you come back down to the valley it goes. It is actually a completely illogical thing to do. It is not justifiable by any rational terms. That’s probably why you do it.

If [in a rain forest] the traveler notices a particular species and wishes to find more like it, he must often turn his eyes in vain in every direction. Trees of varied forms, dimensions, and colors are around him, but he rarely sees any of them repeated. Time after time he goes towards a tree which looks like the one he seeks, but a closer examination proves it to be distinct.

In teaching man, experimental science results in lessening his pride more and more by proving to him every day that primary causes, like the objective reality of things, will be hidden from him forever and that he can only know relations.

In the same sense that our judicial system presumes us to be innocent until proven guilty, a medical care system may work best if it starts with the presumption that most people are healthy. Left to themselves, computers may try to do it in the opposite way, taking it as given that some sort of direct, continual, professional intervention is required all the time, in order to maintain the health of each citizen, and we will end up spending all our money on nothing but this.

In the summer of 1937, … I told Banach about an expression Johnny [von Neumann] had once used in conversation with me in Princeton before stating some non-Jewish mathematician’s result, “Die Goim haben den folgendenSatzbewiesen” (The goys have proved the following theorem). Banach, who was pure goy, thought it was one of the funniest sayings he had ever heard. He was enchanted by its implication that if the goys could do it, Johnny and I ought to be able to do it better. Johnny did not invent this joke, but he liked it and we started using it.

Induction may be defined, the operation of discovering and proving general propositions.

It is one of the chief merits of proofs that they instil a certain scepticism as to the result proved.

It is through science that we prove, but through intuition that we discover.

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.

It usually develops that after much laborious and frustrating effort the investigator of environmental physiology succeeds in proving that the animal in question can actually exist where it lives. It is always somewhat discouraging for an investigator to realize that his efforts can be made to appear so trite, but this statement does not belittle the ecological physiologist. If his data assist the understanding of the ways in which an animal manages to live where it does, he makes an important contribution to the study of distribution, for the present is necessarily a key to the past.”

It was said round 1912 that it gave him [Edmund Landau] the same pleasure when someone else proved a good theorem as if he had done it himself.

Keep some souvenirs of your past, or how will you ever prove it wasn’t all a dream?

Logicians have but ill defined

As rational the human mind;

Reason, they say, belongs to man,

But let them prove it if they can.

As rational the human mind;

Reason, they say, belongs to man,

But let them prove it if they can.

Many orthodox people speak as though it were the business of sceptics to disprove received dogmas rather than of dogmatists to prove them. This is, of course, a mistake.

Mathematical proofs are essentially of three different types: pre-formal; formal; post-formal. Roughly the first and third prove something about that sometimes clear and empirical, sometimes vague and ‘quasi-empirical’ stuff, which is the real though rather evasive subject of mathematics.

Mathematics as a science commenced when first someone, probably a Greek, proved propositions about

*any*things or about*some*things, without specification of definite particular things. These propositions were first enunciated by the Greeks for geometry; and, accordingly, geometry was the great Greek mathematical science.
Metaphysics: An attempt to prove the incredible by an appeal to the unintelligible.

No experience whatsoever could prove that the heavens rotate daily and not the earth.

No science doth make known the first principles whereon it buildeth; but they are always taken as plain and manifest in themselves, or as proved and granted already, some former knowledge having made them evident.

Noise proves nothing. Often a hen who has merely laid an egg cackles as if she laid an asteroid. — Pudd’nhead Wilson’s New Calendar

Not long ago the head of what should be a strictly scientific department in one of the major universities commented on the odd (and ominous) phenomenon that persons who can claim to be scientists on the basis of the technical training that won them the degree of Ph.D. are now found certifying the authenticity of the painted rag that is called the “Turin Shroud” or adducing “scientific” arguments to support hoaxes about the “paranormal” or an antiquated religiosity. “You can hire a scientist [sic],” he said, “to prove anything.” He did not adduce himself as proof of his generalization, but he did boast of his cleverness in confining his own research to areas in which the results would not perturb the Establishment or any vociferous gang of shyster-led fanatics. If such is indeed the status of science and scholarship in our darkling age, Send not to ask for whom the bell tolls.

Nothing can so quickly blur and distort the facts as desire—the wish to use the facts for some purpose of your own—and nothing can so surely destroy the truth. As soon as the witness wants to prove something he is no longer impartial and his evidence is no longer to be trusted.

Of possible quadruple algebras the one that had seemed to him by far the most beautiful and remarkable was practically identical with quaternions, and that he thought it most interesting that a calculus which so strongly appealed to the human mind by its intrinsic beauty and symmetry should prove to be especially adapted to the study of natural phenomena. The mind of man and that of Nature’s God must work in the same channels.

One of the principal results of civilization is to reduce more and more the limits within which the different elements of society fluctuate. The more intelligence increases the more these limits are reduced, and the nearer we approach the beautiful and the good. The perfectibility of the human species results as a necessary consequence of all our researches. Physical defects and monstrosities are gradually disappearing; the frequency and severity of diseases are resisted more successfully by the progress of modern science; the moral qualities of man are proving themselves not less capable of improvement; and the more we advance, the less we shall have need to fear those great political convulsions and wars and their attendant results, which are the scourges of mankind.

Our world is not an optimal place, fine tuned by omnipotent forces of selection. It is a quirky mass of imperfections, working well enough (often admirably); a jury-rigged set of adaptations built of curious parts made available by past histories in different contexts ... A world optimally adapted to current environments is a world without history, and a world without history might have been created as we find it. History matters; it confounds perfection and proves that current life transformed its own past.

Prove all things; hold fast that which is good.

— Bible

Psychoanalysis is a science conducted by lunatics for lunatics. They are generally concerned with proving that people are irresponsible; and they certainly succeed in proving that some people are.

Science is often regarded as the most objective and truth-directed of human enterprises, and since direct observation is supposed to be the favored route to factuality, many people equate respectable science with visual scrutiny–just the facts ma’am, and palpably before my eyes. But science is a battery of observational and inferential methods, all directed to the testing of propositions that can, in principle, be definitely proven false ... At all scales, from smallest to largest, quickest to slowest, many well-documented conclusions of science lie beyond the strictly limited domain of direct observation. No one has ever seen an electron or a black hole, the events of a picosecond or a geological eon.

Science is really in the business of disproving current models or changing them to conform to new information. In essence, we are constantly proving our latest ideas wrong.

Since the examination of consistency is a task that cannot be avoided, it appears necessary to axiomatize logic itself and to prove that number theory and set theory are only parts of logic. This method was prepared long ago (not least by Frege’s profound investigations); it has been most successfully explained by the acute mathematician and logician Russell. One could regard the completion of this magnificent Russellian enterprise of the

*axiomatization of logic*as the crowning achievement of the work of axiomatization as a whole.
Some of the men stood talking in this room, and at the right of the door a little knot had formed round a small table, the center of which was the mathematics student, who was eagerly talking. He had made the assertion that one could draw through a given point more than one parallel to a straight line; Frau Hagenström had cried out that this was impossible, and he had gone on to prove it so conclusively that his hearers were constrained to behave as though they understood.

The average gambler will say “The player who stakes his whole fortune on a single play is a fool, and the science of mathematics can not prove him to be otherwise.” The reply is obvious: “The science of mathematics never attempts the impossible, it merely shows that other players are greater fools.”

The existence of trousers proves that God meant us to be bipeds.

The fact that man produces a concept ‘I’ besides the totality of his mental and emotional experiences or perceptions does not prove that there must be any specific existence behind such a concept. We are succumbing to illusions produced by our self-created language, without reaching a better understanding of anything. Most of so-called philosophy is due to this kind of fallacy.

The fact that your patient gets well does not prove that your diagnosis was correct.

The facts proved by geology are briefly these: that during an immense, but unknown period, the surface of the earth has undergone successive changes; land has sunk beneath the ocean, while fresh land has risen up from it; mountain chains have been elevated; islands have been formed into continents, and continents submerged till they have become islands; and these changes have taken place, not once merely, but perhaps hundreds, perhaps thousands of times.

The individual on his own is stable only so long as he is possessed of self-esteem. The maintenance of self-esteem is a continuous task which taxes all of the individual’s powers and inner resources. We have to prove our worth and justify our existence anew each day. When, for whatever reason, self-esteem is unattainable, the autonomous individual becomes a highly explosive entity. He turns away from an unpromising self and plunges into the pursuit of pride—the explosive substitute for self-esteem. All social disturbances and upheavals have their roots in crises of individual self-esteem, and the great endeavor in which the masses most readily unite is basically a search for pride.

The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several of them have tried to prove the impossibility of it. However, if I am not mistaken, they have not as yet succeeded. I therefore dare hope that the mathematicians will receive this memoir with good will, for its purpose is to fill this gap in the theory of algebraic equations.

The motto in the pursuit of knowledge, of whatever kind, has always been, “Hope all things;—Prove all things.”

The oceans are the planet’s last great living wilderness, man’s only remaining frontier on Earth, and perhaps his last chance to prove himself as a rational species.

The one quality that seems to be so universal among eccentrics is … so subjective as to be incapable of being proved or disproved, yet … eccentrics appear to be happier than the rest of us.

The professor may choose familiar topics as a starting point. The students collect material, work problems, observe regularities, frame hypotheses, discover and prove theorems for themselves. … the student knows what he is doing and where he is going; he is secure in his mastery of the subject, strengthened in confidence of himself. He has had the experience of discovering mathematics. He no longer thinks of mathematics as static dogma learned by rote. He sees mathematics as something growing and developing, mathematical concepts as something continually revised and enriched in the light of new knowledge. The course may have covered a very limited region, but it should leave the student ready to explore further on his own.

The proving power of the intellect or the senses was questioned by the skeptics more than two thousand years ago; but they were browbeaten into confusion by the glory of Newtonian physics.

The rainbow, “the bridge of the gods,” proved to be the bridge to our understanding of light—much more important.

The story of a theory’s failure often strikes readers as sad and unsatisfying. Since science thrives on self-correction, we who practice this most challenging of human arts do not share such a feeling. We may be unhappy if a favored hypothesis loses or chagrined if theories that we proposed prove inadequate. But refutation almost always contains positive lessons that overwhelm disappointment, even when no new and comprehensive theory has yet filled the void.

The Synthesis consists in assuming the Causes discovered and established as Principles, and by them explaining the Phænomena proceeding from them, and proving the Explanations.

The whole history of physics proves that a new discovery is quite likely lurking at the next decimal place.

The work of Planck and Einstein proved that light behaved as particles in some ways and that the ether therefore was not needed for light to travel through a vacuum. When this was done, the ether was no longer useful and it was dropped with a glad cry. The ether has never been required since. It does not exist now; in fact, it never existed.

Things sweet to taste prove in digestion sour.

This alleged damage which the small radioactivity is causing—supposedly cancer and leukemia—has not been proved, to the best of my knowledge, by decent and clear statistics. It is possible that there is damage. It is even possible, to my mind, that there is no damage; and there is the possibility, further, that very small amounts of radioactivity are helpful.

Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the

*logic piano*imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.
To illustrate the apparent contrast between statistics and truth … may I quote a remark I once overheard: “There are three kinds of lies: white lies, which are justifiable; common lies—these have no justification; and statistics.” Our meaning is similar when we say: “Anything can be proved by figures”; or, modifying a well-known quotation from Goethe, with numbers “all men may contend their charming systems to defend.”

We may summarize … the fundamental characteristics and limitations of mathematics as follows: mathematics is ultimately an experimental science, for freedom from contradiction cannot be proved, but only postulated and checked by observation, and similarly existence can only be postulated and checked by observation. Furthermore, mathematics requires the fundamental device of all thought, of analyzing experience into static bits with static meanings.

We must reject the false choice between combating climate change and fostering strong economic growth. If any country can prove that, it’s the United States.

We must somehow keep the dreams of space exploration alive, for in the long run they will prove to be of far more importance to the human race than the attainment of material benefits. Like Darwin, we have set sail upon an ocean: the cosmic sea of the Universe. There can be no turning back. To do so could well prove to be a guarantee of extinction. When a nation, or a race or a planet turns its back on the future, to concentrate on the present, it cannot see what lies ahead. It can neither plan nor prepare for the future, and thus discards the vital opportunity for determining its evolutionary heritage and perhaps its survival.

What is now proved was once only imagin’d.

What is truth ? A man may prove much that has no other truth but in him, and all be a turnip lantern leading to a precipice over the sea.

What vexes me most is, that my female friends, who could bear me very well a dozen years ago, have now forsaken me, although I am not so old in proportion to them as I formerly was: which I can prove by arithmetic, for then I was double their age, which now I am not.

Whoever … proves his point and demonstrates the prime truth geometrically should be believed by all the world, for there we are captured.

X-rays will prove to be a hoax.

[Someone] remarked to me once: Physicians should not say, I have cured this man, but, This man didn’t die in my care. In physics too one might say, For such and such a phenomenon I have determined causes whose absurdity cannot finally be proved, instead of saying, I have

*explained it*.
~~[Misquoted ?]~~ It gives me the same pleasure when someone else proves a good theorem as when I do it myself.

… There can be no doubt about faith and not reason being the

*ultima ratio*. Even Euclid, who has laid himself as little open to the charge of credulity as any writer who ever lived, cannot get beyond this. He has no demonstrable first premise. He requires postulates and axioms which transcend demonstration, and without which he can do nothing. His superstructure indeed is demonstration, but his ground his faith. Nor again can he get further than telling a man he is a fool if he persists in differing from him. He says “which is absurd,” and declines to discuss the matter further. Faith and authority, therefore, prove to be as necessary for him as for anyone else.