Proof Theory Quotes & Sayings

Paul Erdos has a theory that God has a book containing all the theorems of mathematics with their absolutely most beautiful proofs, and when he wants to express particular appreciation of a proof he exclaims, "This is from the book!" — Ross Honsberger

In the first quarter of the nineteenth century the experimental proof for the interdependence of the composition and properties of chemical compounds resulted in the theory that they are mutually related, so that like composition governs like properties, and conversely. — Wilhelm, Ostwald

Reincarnation is not an exclusively Hindu or Buddhist concept, but it is part of the history of human origin. It is proof of the mindstream's capacity to retain knowledge of physical and mental activities. It is related to the theory of interdependent origination and to the law of cause and effect. — Dalai Lama

The aim was to regulate the value of money by increasing or diminishing the quantity of it. The effects of these measures appeared to provide an inductive proof of the correctness of this superficial version of the Quantity Theory, and incidentally concealed the weaknesses of its logic. — Ludwig Von Mises

The word 'proof' should strictly only be used when we are dealing with deductive inferences.... Popper claimed that scientists only need to use deductive inferences.... So if a scientist is only interested in demonstrating that a given theory is false, she may be able to accomplish her goal without the use of inductive inferences.... When a scientist collects experimental data, her aim might be to show that a particular theory...is false. She will have to resort to inductive reasoning.... So Popper's attempt to show that science can get by without induction does not succeed. — Samir Okasha

In point of fact, no conclusive disproof of a theory can ever be produced; for it is always possible to say that the experimental results are not reliable or that the discrepancies which are asserted to exist between the experimental results and the theory are only apparent and that they will disappear with the advance of our understanding. If you insist on strict proof (or strict disproof) in the empirical sciences, you will never benefit from experience, and never learn from it how wrong you are. — Karl Popper

On the unfalsifiable theory of global warming:Evidence that contradicts the global warming theory, climate kooks enlist as evidence for the correctness of their theory; every permutation in weather patterns warm or cold is said to be a consequence of that warming or proof of it. — Ilana Mercer

Whereas a novice makes moves until he gets checkmated (proof), a Grand Master realizes 20 moves in advance that it's futile to continue playing (conceptualizing). — Bill Gaede

The sense of alienation that inspires wonder, awe and fear in us is enough of a proof that life does not belong to the planet Earth. — Raheel Farooq

The treatment of the indeterminacy principle as absolute and final can then be criticized as constituting an arbitrary restriction on scientific theories, since it does not follow from the quantum theory as such, but rather from the assumption of the unlimited validity of certain of its features, an assumption that can in no way ever be subjected to experimental proof. — David Bohm

I think that there is something that happens, a phenomenon that happens around a conspiracy theory, where if you believe in a conspiracy theory, then every critique of that theory is simply more proof that the conspiracy exists. And I think that that's something that goes on in the person of Donald Trump. — Ben Domenech

What never fails inside the mind of an intellectual never works outside the confines of his head. The world's stubborn refusal to vindicate the intellectual's theories serves as proof of humanity's irrationality, not his own. Thus, the true believer retrenches rather than rethinks; he launches a war on the world, denying reality because it fails to conform to his theories. If intellectuals are not prepared to reconcile theory and practice, then why do they bother to venture outside the ivory tower or the coffeehouse? Why not stay in the world of abstractions and fantasy? — Daniel J. Flynn

In order to disprove the assertion that all crows are black, one white crow is sufficient. — William James

Operational proof ... it's all theory until you see for yourself whether or not something works. — Julia Child

With this definition of "evil" in mind, it is the purpose of this book to show that many laws and governmental practices are impregnated with it, and to trace this wholesale infringement of our rights to the power acquired by the federal government in 1913 to tax our incomes - the Sixteenth Amendment. That is the "root." Furthermore, proof will be offered to support the proposition that the "evil" has reached the point where the doctrine of natural rights has been all but abrogated in fact, if not in theory. As a consequence, the kind of government we are acquiring is distinctly different from that envisaged by the Founding Fathers; it is fast becoming a government that conceives itself to be the source of rights, which it gives and can recall at its own pleasure. The transformation is not yet complete, but it will be seen as we go along that completion is not far off - if nothing is done to prevent it. — Frank Chodorov

The highway looked different to him now, as they drove on. In theory it was the same stretch of tarmac, bounded by the same traffic paraphernalia and flimsy metal fences, but it had been transformed by their own intent. It was no longer a straight line to an airport, it was a mysterious hinterland of shadowy detours and hidey-holes. Proof, once again, that reality was not objective, but always waiting to be reshaped and redefined by one's attitude. Of course, everybody on earth had the power to reshape reality. It was one of the things Peter and Beatrice talked about a lot. The challenge of getting people to grasp that life was only as grim and confining as you perceived it to be. The challenge of getting people to see that the immutable facts of existence were not so immutable after all. The challenge of finding a simpler word for immutable than immutable. — Michel Faber

No theory ever agrees with all the facts in its domain, yet it is not always the theory that is to blame. Facts are constituted by older ideologies, and a clash between facts and theories may be proof of progress. It is also a first step in our attempt to find the principles implicit in familiar observational notions. — Paul Feyerabend

Do you see this egg? With this you can topple every theological theory, every church or temple in the world. — Denis Diderot

Theory without practice is of little value, whereas practice is the proof of theory.Theory is the knowledge, practice the ability. — Alois Podhajsky

There are two ways of forming an opinion. One is the scientific method; the other, the scholastic. To the scientific mind, experimental proof is all-important, and theory is merely a convenience in description, to be junked when it no longer fits. To the academic mind, authority is everything, and facts are junked when they do not fit theory. — Robert A. Heinlein

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts. — Adrien-Marie Legendre

Certainly in order to understand the natural world one needs clarity, logic, and the capacity for theory building. But that understanding tends to improve because and to the extent that it is provisional, hypothetical, when it looks for disconfirmation in the particular rather than final proof as a universal. — Talal Asad

Here departs from his master, and holds that the spheres and the intellects had a beginning, and were brought into existence by the will of the Creator. He does not attempt to give a positive proof of his doctrine; all he contends is that the theory of the creatio ex nihilo is, from a philosophical point of view, not inferior to the doctrine which asserts the eternity of the universe, and that he can refute all objections advanced against his theory (ch. xiii.-xxviii.). — Maimonides

People needed proof that Utopia was nothing more than a theory, an illusion read in fictional stories. — Soroosh Shahrivar

In the vestibule of the Manchester Town Hall are placed two life-sized marble statues facing each other. One of these is that of John Dalton ... the other that of James Prescott Joule ... Thus the honour is done to Manchester's two greatest sons - to Dalton, the founder of modern Chemistry and of the atomic theory, and the laws of chemical-combining proportions; to Joule, the founder of modern physics and the discoverer of the Law of Conservation of Energy.
One gave to the world the final proof ... that in every kind of chemical change no loss of matter occurs; the other proved that in all the varied modes of physical change, no loss of energy takes place. — Henry Enfield Roscoe

Science proceeds by inference, rather than by the deduction of mathematical proof. A series of observations is accumulated, forcing the deeper question: What must be true if we are to explain what is observed? What "big picture" of reality offers the best fit to what is actually observed in our experience? American scientist and philosopher Charles S. Peirce used the term "abduction" to refer to the way in which scientists generate theories that might offer the best explanation of things. The method is now more often referred to as "inference to the best explanation." It is now widely agreed to be the philosophy of investigation of the world characteristic of the natural sciences. — Alister E. McGrath

These forays into the real world sharpened his view that scientists needed the widest possible education. He used to say, "How can you design for people if you don't know history and psychology? You can't. Because your mathematical formulas may be perfect, but the people will screw it up. And if that happens, it means you screwed it up." He peppered his lectures with quotations from Plato, Chaka Zulu, Emerson, and Chang-tzu.

But as a professor who was popular with his students - and who advocated general education - Thorne found himself swimming against the tide. The academic world was marching toward ever more specialized knowledge, expressed in ever more dense jargon. In this climate, being liked by your students was a sign of shallowness; and interest in real-world problems was proof of intellectual poverty and a distressing indifference to theory. — Michael Crichton

Proof' is the hallmark of religion. — Bill Gaede

I am now convinced that we have recently become possessed of experimental evidence of the discrete or grained nature of matter, which the atomic hypothesis sought in vain for hundreds and thousands of years. The isolation and counting of gaseous ions, on the one hand, which have crowned with success the long and brilliant researches of J.J. Thomson, and, on the other, agreement of the Brownian movement with the requirements of the kinetic hypothesis, established by many investigators and most conclusively by J. Perrin, justify the most cautious scientist in now speaking of the experimental proof of the atomic nature of matter, The atomic hypothesis is thus raised to the position of a scientifically well-founded theory, and can claim a place in a text-book intended for use as an introduction to the present state of our knowledge of General Chemistry. — Wilhelm, Ostwald

So far Unitarian realism claiming to possess positive knowledge about Ultimate Reality has succeeded only by excluding large areas of phenomena or by declaring, without proof, that they could be reduced to basic theory, which, in this connection, means elementary particle physics. — Paul Feyerabend

People talk about getting lucky breaks in their careers. I'm living proof that the 'lucky breaks' theory is simply wrong. You get to make your own luck ... The world is run by those who show up ... not those who wait to be asked. — Steve Blank

Homosexuality is the most beautiful aspect of humanity. For its existence is proof that altruism is natural; it is to demonstrate that the theory of the "survival of the fittest" can only apply to the species as a whole, and that reproduction is insufficient to secure our place in the great jungle of life, which means being nice is a more stable evolutionary strategy than making kids; and if the homosexual is attracted to religion or to art - or, in smaller societies, to shamanism or caring for other people's children - is this not due to his or her search for purpose? If so, then what we call purpose must be something that encompasses all modes of life. What we call love must be greater than child rearing or caring for a mate. — Anthony Marais

The fact of evolution is the backbone of biology, and biology is thus in the peculiar position of being a science founded on an unproved theory -is it then a science or a faith? Belief in the theory of evolution is thus exactly parallel to belief in special creation - both are concepts which believers know to be true but neither, up to the present, has been capable of proof. — L. Harrison Matthews

Taking experimental results and observations for granted and putting the burden of proof on the theory means taking the observational ideology for granted without having ever examined it. — Paul Feyerabend

Few things in life are certain, and one of them is that you can turn on the television at three in the morning and someone will be singing and dancing on the Indian channel. Proof of Nietzsche's theory of eternal recurrence. — Jessica Zafra

I don't believe anything till I have seen the proof. For anything without proof, I think we should believe the theory that gives us peace. It doesn't matter whether the theory is true or not. — Amish Tripathi

(T)he most important reason American leftists love France is that French elites say bad things about America. French intellectuals call us racist, stupid, imperialistic, simplistic, etc. ' and that alone is proof of their intellectualism. So long as you call America "racist," you could add that an enema is as good as a toothbrush and some professor of "communications theory" would applaud. — Jonah Goldberg

Einstein's prediction of light deflection could not be tested immediately in 1915, because the First World War was in progress, and it was not until 1919 that a British expedition, observing an eclipse from West Africa, showed that light was indeed deflected by the sun, just as predicted by the theory. This proof of a German theory by British scientists was hailed as a great act of reconciliation between the two countries after the war. — Stephen Hawking

Osteopath
One who argues that all human ills are caused by the pressure of hard bone upon soft tissue. The proof of his theory isto be found in the heads of those who believe it. — H.L. Mencken

Now I'm no biologist, but it seems to make a lot of sense that slow lives, as well as being enjoyable, are long lives. One only has to think of the example of the tortoise for proof of this theory from the animal world. — Tom Hodgkinson

Properly a theory about knowledge, not about religion. A theist and a Christian may be an agnostic; an atheist may not be an agnostic. An atheist may deny that there is God, and in this case his atheism is dogmatic and not agnostic. Or he may refuse to acknowledge that there is a God simply on the ground that he perceives no evidence for his existence and finds the arguments which have been advanced in proof of it invalid. In this case his atheism is critical, not agnostic. The atheist may be, and not infrequently is, an agnostic. — Robert Flint

It is good to keep in mind ... that nobody has ever succeeded in producing even one new species by the accumulation of micromutations. Darwin's theory of natural selection has never had any proof, yet it has been universally accepted. — Richard Goldschmidt