Quotes & Sayings About Axioms

Freedom can be manifested only in the void of beliefs, in the absence of axioms, and only where the laws have no more authority than a hypothesis. — Emile M. Cioran

I am not a mathematician, but I was aware that for centuries, mathematics was considered the queen of the sciences because it claimed certainty. It was grounded on some fundamental certainties - axioms - that led to others. — Tom Stoppard

The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth. — Hermann Weyl

The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms. — Albert Einstein

Not only the individual experience slowly acquired, but the accumulated experience of the race, organized in language, condensed in instruments and axioms, and in what may be called the inherited intuitions
these form the multiple unity which is expressed in the abstract term experience. — George Henry Lewes

A dozen more questions occurred to me. Not to mention twenty-two possible solutions to each one, sixteen resulting hypotheses and counter-theorems, eight abstract speculations, a quadrilateral equation, two axioms, and a limerick. That's raw intelligence for you. — Jonathan Stroud

The once-surprising existence of non-Euclidean models of Euclid's first four axioms can be seen as a sort of mathematical joke. — John Allen Paulos

Reflect on the "I" which can grasp all this. If the "I' can grasp the idea of the universe and its laws, then that "I" stands above all other things, stands aside from all other things, judges them, fathoms them. In that case, the "I" is not only liberated from earthly axioms, the earthly laws, but has its own law, which transcends the earthly. Now, whence comes that law? Certainly not from earth, where all reaches its issue, and vanishes beyond recall. Is that no indication of immortality? If there were no personal immortality, would you be worrying yourself about it, be searching for an answer? ... — Fyodor Dostoyevsky

It is from this wide extension of design that so much instruction is derived. It is this which fills the plays of Shakespeare with practical axioms and domestick wisdom. It was said of Euripides, that every verse was a precept and it may be said of Shakespeare, that from his works may be collected a system of civil and oeconomical prudence. Yet his real power is not shown in the splendour of particular passages, but by the progress of his fable, and the tenour of his dialogue; and he that tries to recommend him by select quotations, will succeed like the pedant in Hierocles, who, when he offered his house to sale, carried a brick in his pocket as a specimen. — Samuel Johnson

In brief, the teaching process, as commonly observed, has nothing to do with the investigation and establishment of facts, assuming that actual facts may ever be determined. Its sole purpose is to cram the pupils, as rapidly and as painlessly as possible, with the largest conceivable outfit of current axioms, in all departments of human thought - to make the pupil a good citizen, which is to say, a citizen differing as little as possible, in positive knowledge and habits of mind, from all other citizens. In other words, it is the mission of the pedagogue, not to make his pupils think, but to make them think right, and the more nearly his own mind pulsates with the great ebbs and flows of popular delusion and emotion, the more admirably he performs his function. He may be an ass, but this is surely no demerit in a man paid to make asses of his customers. — H.L. Mencken

Philosophy begins when one learns to doubt - particularly to doubt one's cherished beliefs, one's dogmas and one's axioms. — Will Durant

Jean Valjean disconcerted him. All the axioms which had served him as points of support all his life long, had crumbled away in the presence of this man. Jean Valjean's generosity towards him, Javert, crushed him. — Victor Hugo

It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it. — Bernhard Riemann

He's been spoiled 'til salt won't save him. — Frances Hodgson Burnett

That is, for a mathematical Platonist, what the C.H. proofs really show is that set theory needs to find a better set of core axioms than classical ZFS, or at least it will need to add some further postulates that are-like the Axiom of Choice-both "self-evident" and Consistent with classical axioms. If you're interested, Godel's own personal view was that the Continuum Hypothesis is false, that there are actually a whole (Infinity Symbol) of Zeno-type (Infinity Symbol)s nested between (Aleph0) and c, and that sooner or later a principle would be found that proved this. As of now no such principle's ever been found. Godel and Cantor both died in confinement, bequeathing a world with no finite circumference. One that spins, now, in a new kind of all-formal Void. Mathematics continues to get out of bed. — David Foster Wallace

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. — George Polya

For axioms in philosophy are not axioms until they are proved upon our pulses. — John Keats

One of the central axioms of libertarianism is the idea that the same morality applies to every person, whether acting on behalf of a public apparatus or in his individual capacity. Society and individuals must be judged as a whole: if something is morally unacceptable, it should be so for everybody. In Human Action, Mises affirms that the most weighty — Anonymous

If nature leads us to mathematical forms of great simplicity and beauty - by forms, I am referring to coherent systems of hypotheses, axioms, etc. - to forms that no one has previously encountered, we cannot help thinking that they are "true," that they reveal a genuine feature of nature ... . You must have felt this too: the almost frightening simplicity and wholeness of the relationships which nature suddenly spreads out before us and for which none of us was in the least prepared. — Werner Heisenberg

Based on the considerations of history, ancient history, and international axioms, the logic of following up a citizen with his shadow for the purpose of the demarcation of political frontiers of any state has been discounted for international conventions. For example the Arabs cannot ask Spain just because they were there some time in the past nor can they ask for any other area outside the frontiers of the Arab homeland — Saddam Hussein

Things happen when they should, not when they can. — Raheel Farooq

There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immovable, proceeds to judgment and to the discovery of middle axioms. And this way is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried. — Francis Bacon

In the Principia Mathematica, Bertrand Russell and Alfred Whitehead attempted to give a rigorous foundation to mathematics using formal logic as their basis. They began with what they considered to be axioms, and used those to derive theorems of increasing complexity. By page 362, they had established enough to prove 1 + 1 = 2. — Ted Chiang

Pointed axioms and acute replies fly loose about the world, and are assigned successively to those whom it may be the fashion to celebrate. — Samuel Johnson

Those reliable axioms about the taste and expectations of the mass movie audience are not so much laws of nature as artifacts of corporate strategy. And the lessons derived from them conveniently serve to strengthen a status quo that increasingly marginalizes risk, originality and intelligence. — A.O. Scott

Truth can be stated simply, but cannot be understood as such. — Raheel Farooq

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. — Kurt Godel

We find sects and parties in most branches of science; and disputes which are carried on from age to age, without being brought to an issue. Sophistry has been more effectually excluded from mathematics and natural philosophy than from other sciences. In mathematics it had no place from the beginning; mathematicians having had the wisdom to define accurately the terms they use, and to lay down, as axioms, the first principles on which their reasoning is grounded. Accordingly, we find no parties among mathematicians, and hardly any disputes. — Thomas Reid

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought. — Eric Temple Bell

It cannot be that axioms established by argumentation should avail for the discovery of new works, since the subtlety of nature is greater many times over than the subtlety of argument. But axioms duly and orderly formed from particulars easily discover the way to new particulars, and thus render sciences active. — Francis Bacon

We do everything by custom, even believe by it; our very axioms, let us boast of free-thinking as we may, are oftenest simply such beliefs as we have never heard questioned. — Thomas Carlyle

The eye of understanding is like the eye of the sense; for as you may see great objects through small crannies or levels, so you may see great axioms of nature through small and contemptible instances. — Francis Bacon

We must start with scientific fundamentals, and that means with the data of experiments and not with assumed axioms predicated only upon the misleading nature of that which only superficially seems to be obvious. It is the consensus of great scientists that science is the attempt to set in order the facts of experience. — R. Buckminster Fuller

AXIOM. - Property is the Right of Increase claimed by the Proprietor over any thing which he has stamped as his own. — Pierre-Joseph Proudhon

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. — Isaac Newton

We should never forget the two axioms: 'Jesus is with me' and whatever happens, happens by the will of God. — Charles De Foucauld

I tell you the solemn truth, that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics. — Henry Adams

I collect axioms, paradoxes, maxims, teaching stories, proverbs, and aphorisms of all sorts, because I love to see complex ideas distilled into a few words. — Gretchen Rubin

The principles of Jefferson are the definitions and axioms of free society. — Abraham Lincoln

One of the axioms that most religions, Judaism included, accept about God is that God is good. But those are just words. What does it actually mean to be good? One of the things it means, Luzzatto says, is that one acts to benefit others. If there is no world, though, then there are no others that God can benefit; He exists alone in numinous solitude. God acted to create a world so that there would be other beings existing besides Himself, beings upon whom He could bestow goodness. In short, God created the world because goodness demanded it. — David Fohrman

A science is something which is constructed from truth on workable axioms. There are 55 axioms in scientology which are very demonstrably true, and on these can be constructed a great deal. — L. Ron Hubbard

Do you remember, Meir, that epigram quoted in the name of Rabbi Johanan ben Zaccai: 'There is no truth unless there be a faith on which it may rest'? Ironically enough the only sure principle I have achieved is this which I have known almost all my life. And it is so. For all truths rest ultimately on some act of faith, geometry on axioms, the sciences on the assumptions of the objective existence and orderliness of the world of nature. In every realm one must lay down postulates or he shall have nothing at all. So with morality and religion. Faith and reason are not antagonists. On the contrary, salvation is through the commingling of the two, the former to establish first premises, the latter to purify them of confusion and to draw the fullness of their implications. It is not certainty which one acquires so, only plausibility, but that is the best we can hope for. — Milton Steinberg

Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they? — Alfred Renyi

The axioms of physics translate the laws of ethics. Thus, "the whole is greater than its part;" "reaction is equal to action;" "the smallest weight may be made to lift the greatest, the difference of weight being compensated by time;" and many the like propositions, which have an ethical as well as physical sense. These propositions have a much more extensive and universal sense when applied to human life, than when confined to technical use. — Ralph Waldo Emerson

Though moral axioms to guide the conduct of the practitioner have existed since the beginnings of the profession of healing, Western doctors are most likely to view the Hippocratic Oath of approximately two-and-a-half millennia ago as the first codified set of statements to which they can look for guidance. — Sherwin B. Nuland

A priori one should expect a chaotic world which cannot be grasped by the mind in any way ... The kind of order created by Newton's theory of gravitation ... is wholly different. Even if the axioms of the theory are proposed by man, the success of such a project presupposes a high degree of ordering of the objective world ... That is the "miracle" which is being constantly reinforced as our knowledge expands. — Albert Einstein

One of the fundamental axioms of masculine self-regard is that the tools and appurtenances of a man's life must be containable within the pockets of his jacket and pants. Wallet, keys, gum, show or ball game tickets, Kleenex, condoms, cell phone, maybe a lighter and a pack of cigarettes: Just cram it all in there, motherfucker. — Michael Chabon

Life cannot be captured in a few axioms. And that is just what I keep trying to do. But it won't work, for life is full of endless nuances and cannot be captured in just a few formulae. — Etty Hillesum

Geometry, like arithmetic, requires for its logical development only a small number of simple, fundamental principles. These fundamental principles are called the axioms of geometry. — David Hilbert

Boarding-House Geometry DEFINITIONS AND AXIOMS All boarding-houses are the same boarding-house. Boarders in the same boarding-house and on the same flat are equal to one another. A single room is that which has no parts and no magnitude. The landlady of a boarding-house is a — Stephen Leacock

Camilla he tormented simply because she was a girl. In some ways she was his more vulnerable target - through no fault of her own, but simply because in Greekdom, generally speaking, women are lesser creatures, better seen than heard. This prevailing sentiment among the Argives is so pervasive that it lingers in the bones of the language itself; I can think of no better illustration of this than the fact that in Greek grammar, one of the very first axioms I learned is that men have friends, women have relatives, and animals have their own kind. — Donna Tartt

Yet Gotama's Dhamma is more than just a series of axioms. It is to be lived rather than simply adopted and believed in. It entails that one embrace this world in all its contingency and specificity, with all its ambiguity and flaws. — Stephen Batchelor

You know, in formal logic, an inconsistent set of axioms can be used to prove anything at all. Once you have a single contradiction, A and not A, there's nothing you can't derive from it. — Greg Egan

An axiomatic system establishes a reverberating relationship between what a mathematician assumes (the axioms) and what he or she can derive (the theorems). In the best of circumstances, the relationship is clear enough so that the mathematician can submit his or her reasoning to an informal checklist, passing from step to step with the easy confidence the steps are small enough so that he cannot be embarrassed nor she tripped up. — David Berlinski

Too often, contemporary continental philosophers take the "other" of philosophy to mean literature, but not religion, which is for them just a little too wholly other, a little beyond their much heralded tolerance of alterity. They retain an antagonism to religious texts inherited straight from the Enlightenment, even though they pride themselves on having made the axioms and dogmas of the Enlightenment questionable. But the truth is that contemporary continental philosophy is marked by the language of the call and the response, of the gift, of hospitality to the other, of the widow, the orphan and the stranger, and by the very idea of the "wholly other," a discourse that any with the ears to hear knows has a Scriptural provenance and a Scriptural resonance. ("A Prologue", Journal of Philosophy and Scripture 1.1, Fall 2003, p. 1). — John D. Caputo

If there are such things as political axioms, the propriety of the judicial power of a government being co-extensive with its legislative, may be ranked among the number. — Alexander Hamilton

It is not true that the dead cannot be folded. Square becomes kite becomes swan; history becomes rumor becomes song. Even the act of remembrance creases the truth. What the paper-folding diagrams fail to mention is that each fold enacts itself upon the secret marrow of your ethics, the axioms of your thoughts. Whether this is the most important thing the diagrams fail to mention is a matter of opinion. — Yoon Ha Lee

In addition, the teaching of theories from axioms, or some close imitation of them such as the basic laws of an algebra, is usually an educational disaster. — Ivor Grattan-Guinness

Science in its everyday practice is much closer to art than to philosophy. When I look at Godel's proof of his undecidability theorem, I do not see a philosophical argument. The proof is a soaring piece of architecture, as unique and as lovely as Chartres Cathedral. Godel took Hilbert's formalized axioms of mathematics as his building blocks and built out of them a lofty structure of ideas into which he could finally insert his undecidable arithmetical statement as the keystone of the arch. The proof is a great work of art. It is a construction, not a reduction. It destroyed Hilbert's dream of reducing all mathematics to a few equations, and replaced it with a greater dream of mathematics as an endlessly growing realm of ideas. Godel proved that in mathematics the whole is always greater than the sum of the parts. Every formalization of mathematics raises questions that reach beyond the limits of the formalism into unexplored territory. — Freeman Dyson

By refraining from reducing multiplication to addition we are enabled through these axioms to banish continuity, which is so difficult to fix precisely, from the logical structure of geometry. — Hermann Weyl

This means that, where appropriate, we will dive into mathematical equations, mathematical intuition, mathematical axioms, and cartoon versions of big mathematical ideas. — Joel Grus

Paradoxes are less paradoxical in their reference to truth than most of the most plausible axioms. — Raheel Farooq

The productions of the mind and hand seem very numerous in books and manufactures. But all this variety lies in an exquisite subtlety and derivations from a few things already known, not in the number of axioms. VIII — Francis Bacon

You don't know how much I need such a friend," she said. "My aunt is full of copy-book axioms, but they were all meant to apply to conduct in the early fifties. I always feel that to live up to them would include wearing book-muslin with gigot sleeves. And the other women - my best friends - well, they use me or abuse me; but they don't care a straw what happens to me. I've been about too long - people are getting tired of me; they are beginning to say I ought to marry. — Edith Wharton

I'm not against the concept of Creators/God, I'm against the antiquated beliefs that there are evil things, which are merely axioms we concocted out of our inadequacy as mortal beings, primitive brain, and underdeveloped technology. — Andreas Laurencius

I guess that's supposed to be deconstruction's original program, right? People have been under some sort of metaphysical anesthesia, so you dismantle the metaphysics' axioms and prejudices, show it in cross section and reveal the advantages of its abandonment. It's literally aggravating: you awaken them to the fact that they've been unconsciously imbibing some narcotic pharmakon since they were old enough to say "Momma."
-Interview with Larry McCaffery (1993) — David Foster Wallace

As soon as science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a system of thought a theory. The theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the 'truth' of the theory lies. — Albert Einstein

Are the axioms of logic adequate to reality or are they a means and measure for us to create reality, the concept "reality", for ourselves? — Friedrich Nietzsche

What's more, I believe in argument and I even love it. Argument is our most steadfast pathway toward truth, for it is the only proven arbalest against superstitious thinking, or lackadaisical axioms. — Elizabeth Gilbert

Blaise Pascal used to mark with charcoal the walls of his playroom, seeking a means of making a circle perfectly round and a triangle whose sides and angle were all equal. He discovered these things for himself and then began to seek the relationship which existed between them. He did not know any mathematical terms and so he made up his own. Using these names he made axioms and finally developed perfect demonstrations, until he had come to the thirty-second proposition of Euclid. — Catharine Cox Miles

While the game of deadlocks and bottle-necks goes on, another more serious game is also being played. It is governed by two axioms. One is that there can be no peace without a general surrender of sovereignty: the other is that no country capable of defending its sovereignty ever surrenders it. If one keeps these axioms in mind one can generally see the relevant facts in international affairs through the smoke-screen with which the newspapers surround them. — George Orwell

Since these words went into William's fermenting little brain not as word memories, but as circuitry for storing word memories, bricks used to build the kiln for firing bricks, he has no recollection of the rhyme, yet the ideas in it are axioms of his mental geometry. — Dennis Vickers

When Keats says: 'Axioms in philosophy are not axioms until they are proved upon our pulses', what he means is that we don't necessarily believe what a poem is saying if it comes out and tells us in an absolutely head-on, in-your-face way; we only believe it to be true if we feel it to be true. — Andrew Motion

It's an old axiom of mine: marry your enemies and behead your friends. — Robert N. Lee

Underlying the preaching of the Puritans are three basic axioms: 1. The unique place of preaching is to convert, feed and sustain, 2. The life of the preacher must radiate the reality of what he preaches, 3. Prayer and solid Bible study are basic to effective preaching. — J.I. Packer

And what if they took over? What if they relieved us of power? We tend to assume that sentient machines would be inevitably demonic. But what if they were responsible leaders? Could they do much worse than we've done? They would immediately institute a system of laws. The constitution would be algorithmic. They would govern the world according to functions and the axioms their programmers gave them. — Louisa Hall

Finally there are simple ideas of which no definition can be given; there are also axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof. — Gottfried Leibniz

What are your Axioms, and Categories, and Systems, and Aphorisms? Words, words ... Be not the slave of Words ... — Thomas Carlyle

Hy is it that in problematic situations almost everyone resorts to axioms and societal remedies that in actuality almost nobody believes in? ... ask yourself, have you ever known anyone whose marriage was saved by a marriage counselor, whose drinking was cured by a psychiatrist, whose son was kept out of reform school by a social worker? — James Lee Burke

I do not want to presuppose anything as known. I see in my explanation in section 1 the definition of the concepts point, straight line and plane, if one adds to these all the axioms of groups i-v as characteristics. If one is looking for other definitions of point, perhaps by means of paraphrase in terms of extensionless, etc., then, of course, I would most decidedly have to oppose such an enterprise. One is then looking for something that can never be found, for there is nothing there, and everything gets lost, becomes confused and vague, and degenerates into a game of hide and seek. — David Hilbert

It is not enough merely to memorize and spout vocal axioms good singing is infinitely more than much talk and head-knowledge. — Jerome Hines

You might ask why we cannot teach physics by just giving the basic laws on page one and then showing how they work in all possible circumstances, as we do in Euclidean geometry, where we state the axioms and then make all sorts of deductions. (So, — Richard Feynman

Those authors are to be read at schools that supply most axioms of prudence. — Samuel Johnson

We can ... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics. — Hans Reichenbach

An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical. — David Berlinski

Axioms are delightful in theory, but impossible in practice. — Antoine Rivarol

A few rules include all that is necessary for the perfection of the definitions, the axioms, and the demonstrations, and consequently of the entire method of the geometrical proofs of the
art of persuading. — Blaise Pascal

It's one of the old show business axioms. No matter how successful you've been, there's always a younger and sexier seal coming along. — George Burns

You can go through your whole life telling yourself that life is logical, life is prosaic, life is sane. Above all sane. And I think it is. I've had a lot of time to think about that. And what I keep coming back to is [her] dying declaration: 'So you understand that when we increase the number of variables, the axioms themselves never change.' — Stephen King

My grandmother has hundreds of axioms. One of them was 'If you think you want something, wait a month.' One of three things will happen if you follow this sage advice. One: You will forget. Two: You will no longer need it. Or three: You will need it more. Most often numbers one and two will happen. — Matthew Sleeth

Applying the axioms of physical science to human life has something reprehensible to it. — Albert Einstein

No very good sense can be given to the idea that the elements of Euclidean geometry may be found in nature because either everything is found in nature or nothing is. Euclidean geometry is a theory, and the elements of a theory may be interpreted only in terms demanded by the theory itself. Euclid's axioms are satisfied in the Euclidean plane. Nature has nothing to do with it. — David Berlinski

The novel is... the anti-form proper to modernity itself (which is to say, of capitalism and its cultural and epistemological categories, its daily life). This means... that the novel is also a vehicle of creative destruction. Its function, in some properly capitalist 'cultural revolution', is the perpetual undoing of traditional narrative paradigms and their replacement, not by new paradigms, but by something radically different. To use Deleuzian language for a moment, modernity, capitalist modernity, is the moment of passage from codes to axioms, from meaningful sequences, or indeed, if you prefer, from meaning itself, to operational categories, to functions and rules; or, in yet another language, this time more historical and philosophical, it is the transition from metaphysics to epistemologies and pragmatisms, we might even say from content to form. — Fredric Jameson

You can "prove" anything on the verbal level, just be accepting the necessary axioms at the beginning. — Robert Anton Wilson

One of the most important axioms is, that as the quantity of any commodity, for instance, plain food, which a man has to consume, increases, so the utility or benefit derived from the last portion used decreases in degree. The decrease in enjoyment between the beginning and the end of a meal may be taken as an example. — William Stanley Jevons

For hundreds of pages the closely-reasoned arguments unroll, axioms and theorems interlock. And what remains with us in the end? A general sense that the world can be expressed in closely-reasoned arguments, in interlocking axioms and theorems. — Michael Frayn

We know that there is no absolute knowledge, that there are only theories; but we forget this. The better educated we are, the harder we believe in axioms. — Lincoln Steffens

How odd that Americans, and not just their presidents, have come to think of their Constitution as something separable from the government it's supposed to constitute. In theory, it should be as binding on rulers as the laws of physics are on engineers who design bridges; in practice, its axioms have become mere options. Of course engineers don't have to take oaths to respect the law of gravity; reality gives them no choice. Politics, as we see, makes all human laws optional for politicians. — Joseph Sobran

There are two principles on which all men of intellectual integrity and good will can agree, as a 'basic minimum,' as a precondition of any discussion, co-operation or movement toward an intellectual Renaissance ... They are not axioms, but until a man has proved them to himself and has accepted them, he is not fit for an intellectual discussion. These two principles are: a. that emotions are not tools of cognition; b. that no man has the right to initiate the use of physical force against others. — Ayn Rand

His work seems to confirm my old axiom: it is useless to try to keep the whole body alive. — Adolfo Bioy Casares