How To Use Axiom In A Sentence

Once tawhid is accepted as the first axiom of thought, the goal of life becomes bridging the gap between the asserter and the asserted. William C. Chittick, Ph.D.: Islam and the Goal of Love
Shakespeare with practical axioms and domestick wisdom. Preface to Shakespeare
Educators have also applied paper folding to such diverse mathematical objects as logical structures, axiomatic systems, and tessellations with geometrical figures.
And Archimedes proved from his axioms on the lever that two unequal weights balance at distances from the fulcrum that are inversely proportional to their weights.
It has become axiomatic in this country that children from deprived areas are destined to fail educationally.

The related axiomatic study of epistemic notions has benefited from application of techniques used for proving incompleteness and indefinability results since the early sixties. Paradoxes and Contemporary Logic
According to Huntington (1933), the term “Boolean algebra” was introduced by Sheffer (1913) in the paper where he showed that one could give a five-equation axiomatization of Boolean algebra using the single fundamental operation of joint exclusion, now known as the Sheffer stroke. The Algebra of Logic Tradition
Ordinary politics adds to these familiar ideals a further one that has no distinct place in utopian axiomatic theory.
A’ B.there exists some form of connection between the antecedent A and the succedent B. Axiom A4, for example, is bad in this respect. Connexive Logic
From a sector perspective, this means that the government's running a deficit on goods and services axiomatically translates into the rest of the economy's running a surplus. SeekingAlpha.com: Home Page
It'll be all-natural and organic, of course; still, he's entering a market in which it is axiomatic that you either grow or die.
Therefore in speculative matters the same truth holds among all men both as to principles and as to conclusions, even though all men do not discern this truth in the conclusions but only in those principles which are called axiomatic notions. The Political Ideas of St. Thomas Aquinas
Plato had made the bold suggestion that there might be a single axiom system to embrace all knowledge.
Every good mathematician knows that is the real job of axioms: once stated, they exist to be satisfied.
But it is ordinary reciprocity that good psychoanalytic practice must, axiomatically, bar from the relationship of analyst and patient.
There is axiomatically no such thing as a light scarf for men in Britain.
There is one context in which the language of possible worlds is undoubtedly useful and even illuminating, namely, in the study of formal axiomatic systems of modal logic.
On his abrupt and unexpected apparition, Diana paled and Ruth flushed slightly, whereupon Sir Rowland might have bethought him, had he been book-learned, of the axiom, "Amour qui rougit, fleurette; amour qui plit, drame du coeur. Mistress Wilding
In the early 1900s it became clear that one has to state precisely what basic assumptions are made in Set Theory; in other words, the need has arisen to axiomatize Set Theory. Set Theory
To verify the properties of the concurrent and reactive systems based on the theorem proving approach, an axiomatization is formulized for the first order projection temporal logic (FPTL).
Scott established the completeness and decidability of various axiomatic tense logics. The Sun Is Not
However he also showed that linear sentence systems do have independent axiom systems.
That Bruno himself, in "the enthusiasm of the idea," drew from his axiom of the "indifference of contraries" the practical consequence which is in very deed latent there, that he was ready to sacrifice to the antinomianism, which is certainly a part of its rigid logic, the austerities, the purity of his own youth, for instance, there is no proof. Gaston de Latour; an unfinished romance
Went to Oxbridge, is treated as an axiomatic 'bad thing'. The Ming Dynasty
Although he lacks the historical context to articulate Kant's Categorical Moral Imperative, he describes a Supreme Being for whom something akin to this axiom is the ultimate measure of a man, a God who believes that one's ethical duty is to acquire and exercise wisdom, to evaluate and constantly re-evaluate one's beliefs -- including what one's ethical duty is -- by applying the utmost objectivity to one's own preconceptions and prejudices. THE HALLS OF PENTHEUS -- PART TWO
The idea is that whenever one is forced to bet on the pignistic level, the degrees of belief from the credal level are used to calculate (fair) betting ratios that satisfy the probability axioms. Formal Representations of Belief
He also examined the consistency of certain propositions in Gödel's system of axiomatic set theory.
Mulla Sadra inherited a variety of theories ranging from Platonic recollection (anamnesis) and division to Peripatetic syllogistics, definitions and axiomatic science. Mulla Sadra
Use of the term axiom reinforces that our computational model is a mathematical, formal system and that analogue execution is a form of deduction from the axioms or assumptions explicitly programmed into the model. PLoS ONE Alerts: New Articles
I start from the simple axiom that I own myself, that my life belongs to me and not to someone else.
Relations needed are, among others, those which assert of a natural number that it codes a sequence, or a formula, or an axiom, or that it is the code, denoted by Sb (ru1 ¦ unZ (x1) ¦ Z (xn)), of a formula obtained from a formula with code r by substituting for its free variable ui the xi th numeral for i = 1, Kurt GÃ¶del
axiomatic wisdom
That axiom is also true in fantasy baseball, where managing a pitching staff down the stretch is often the key to winning a championship because major league teams often don't have the same agendas for their pitchers as fantasy owners do. Keep eye on starters' workloads heading down the stretch
It is axiomatic that traditional agricultural management of the uplands has maintained and conserved these landscapes and their wildlife.
axiomatic physics
In retrospect we can see LeÅniewski's obsession with the fine detail of axiomatics and his rejection of semantics as conditioned by his own idiosyncratic development and the predominant research interests of the 1910s and 1920s. StanisÅaw LeÅniewski
Economic theories have been axiomatized, and articles and books of economics are full of theorems.
For our current purposes, it is convenient to axiomatize this logic as a natural deduction system, taking all tautologies as axioms and the familiar natural deduction rules governing the singular quantifiers and the identity sign as rules of inference. Plural Quantification
Buchanan, however, reworked the entire argument in a classical idiom to define an elective form of monarchy and make it axiomatic that kings were accountable to those who elected them.
The mathematical ballistics of 1918 was neither as refined as axiomatic geometry nor as theoretical as algebraic topology.
The positing of axioms has a direct parallel with Acts of ethical commitment: once made, both result in strict logical entailments, but neither are grounded in anything.
The axiom that ‘simplicity is elegance’ applies to the science of mineralogy as well.
Nevertheless, to rehash a time-worn axiom, there's an exception to every rule and that holds true for baseball records even when comparing those for rookies to ones established by veterans.
But since he's a conservative, that kind of activism is okay with the right because it's their kind of activism, proving again the axiom, IOKIYAR (It's Okay If You're A Republican). November 2005
It has long been an axiom that history is re-written by each generation in terms that make sense to it.
It is an axiom that every research establishment is strong to the extent of an unbreakable link existing between different generations.
These progressives, in the very act of founding their organization, ratified the keystone of conservative reasoning and thus let people think that here was a kind of axiom, an inviolable norm, a kind of prolegomenon for any political reasoning, present or future. Road Trip: Part II
Euclid and Archimedes utilized two important techniques to prove theorems from their axioms: reductio ad absurdum arguments, and a method of exhaustion.
Boethius's theological opuscule known as De Hebdomadibus and Alan of Lille's Regulae Caelestis Iuris are presented as axiomatic but also esoteric, with the express statement of the author that their principles are not accessible to the many. Literary Forms of Medieval Philosophy
I think Reg is onto something with is axiom … it positively invites some elaboration. A Clarification For A Pathological Liar « Unambiguously Ambidextrous
If I would axiomatize science I would try to establish the process and its objects. More incredible chutzpah from John Mark Reynolds - The Panda's Thumb
As Benacerraf and Putnam (1964) have observed, the acknowledgement that supertasks are possible has a profound influence on the philosophy of mathematics: the notion of truth (in arithmetic, say) would no longer be doubtful, in the sense of dependent on the particular axiomatisation used. Supertasks
The adjunction of the negation of such a sentence to the axioms of the system yields a consistent extension of formalized classical mathematics in which an actually false proposition [ein inhaltlich falscher Satz] is derivable.
It is a widely held axiom that they should not negotiate with terrorists.
It cannot be denied that our "think so's," "feel so's," impressions, prejudices and inherited or preconceived ideas may seem as infallible to us as any so-called axiomatic or intuitive truths. To Infidelity and Back
Boulliau: “The axiom that the celestial motions are circular or composed of circles must stand, and therefore I reject and repudiate his ellipses unless he should suppose them to be described by means of a Copernican or Tychonic epicycle.” (letter to Gassendi 1633) Bukiet on Brooklyn Books
Overhere a vote of non confidence is a last resort, but still an axioma with great importance. Balkinization
And when you start caring about sports in Philadelphia, it's pretty much axiomatic that you're going to get your heart broken.
This axiom is problematic in some systems, and some people, finitists such as Hilbert, wanted a consistent way to talk about infinity that stemmed from proofs using finitary means.
up-country axiom: `If it ain't broke, don't fix it "might well apply here. SOMETHING IN THE WATER
The authors seem to accept it as axiomatic that the masses who suffer under tyranny are necessarily pro-American.
Gödel showed, in 1940, that the Axiom of Choice cannot be disproved using the other axioms of set theory.
This is a mathematically fruitful concern (keyword “predicativity”) and it will reappear later in the study of NF (and in ZF too, of course) but it is not this first form that gives rise to the axiomatisation of NF. Quine's New Foundations
All this follows, of course, from the very nature of axiomatics, as explained in the passage quoted from Pasch. Nineteenth Century Geometry
That people are different and should be allowed to make different choices is axiomatic to libertarians but they normally take that as given rather than arguing for it.
There's an old axiom that ‘Duty is heavier than a mountain, death is lighter than a feather.’
The bridge principles must be explicitly added to the union of the original axiomatics in order to ensure completeness. Combining Logics
I would prefer to see them described as axiomatic, and that they are not consistent with any medical concept of which I am aware. Citizendium, the Citizens' Compendium - Recent changes [en]
The second chapter presents a development of absolute and Euclidean geometry based on Hilbert's axioms.
It is this approach that gives rise to an axiomatics, where the axioms were to be numbered among those things identified as the self-evident truths. Hermann Lotze
The resulting system, with ten axioms, is now the most commonly used one for axiomatic set theory.
What animated this article is my sense that we have witnessed, and continue to witness, a largely tacit degradation in the vital axiom of international humanitarian law (IHL) that insists on the analytic independence of jus ad bellum and jus in bello, which, following Michael Walzer, I call the dualistic axiom. Opinio Juris
I abandoned reason: whatever Bronwen did was right; that was axiomatic. TESTIMONIES
It is axiomatic that the effective operation of our system of justice is contingent upon the existence of sufficient public confidence in its ability to perform its functions.
It is axiomatic that traditional agricultural management of the uplands has maintained and conserved these landscapes and their wildlife.
Moreover, whilst Peano arithmetic is axiomatizable, there is a particular model of Peano arithmetic, whose theory is typically referred to as Number theory, which Godel demonstrated to be undecidable and non-axiomatizable. Archive 2009-06-01
I regard it as axiomatic that if you are unwilling to advocate for your interests and in consequence get walked all over by people who do, then you have no-one to blame but yourself.
Euclid's axioms form the foundation of his system of geometry.
If we understand by the term cause the axiom that every change has an occasion, hence that every event is bound up with a number of conditions which when lacking in whole or in part would prevent the appearance of the event, while their presence would compel its appearance, then the whole business of the criminalist is the study of causes. Criminal Psychology: a manual for judges, practitioners, and students
We have therefore the case contemplated in the second axiom, namely, of one term agreeing and the other disagreeing with the same third term; and we know that this can only give ground for a judgement of disagreement between the two terms themselves -- in other words, to a negative conclusion. Deductive Logic
Cardinal Newman's axiom, "It is never worth while to call whity-brown white, for the sake of avoiding scandal"; and Father Faber's own felicitous comment on religious "hedgers," "A moderation which consists in taking immoderate liberties with God is hardly what the Americans and Others
Sensibile forte destruit sensum, a strong object overcometh the sight, according to that axiom in philosophy: fulgorem solis ferre non potes, multo magis creatoris; if thou canst not endure the sunbeams, how canst thou endure that fulgor and brightness of him that made the sun? Anatomy of Melancholy
No, the axiom is concerned with the morality of genocide. Carry-Over Thread
Zermelo introduces axioms of set theory, explicitly formulates AC and uses it to prove the well-ordering theorem, thereby raising a storm of controversy. The Axiom of Choice
These five rules therefore completely axiomatize equational logic in the sense that every consequence of a set A of equations can be produced from A via finitely many applications of these five rules. Algebra
Starting from the axiom that every event has a cause, we have here the _causa finalis_ manifested in the last set of phenomena, the _causa materialis_ and _formalis_ in the first, while the existence of a _causa efficiens_ within the seed or egg and its product, is a corollary from the phenomena of growth and metamorphosis, which proceed in unbroken succession and make up the life of the animal or plant. Collected Essays, Volume V Science and Christian Tradition: Essays
That a conjectural critick should often be mistaken, cannot be wonderful, either to others or himself, if it be considered, that in his art there is no system, no principal and axiomatical truth that regulates subordinate positions. The Works of Samuel Johnson, Volume 05 Miscellaneous Pieces
Maybe you and I use the word "axiomatic" differently, but Field got his 3-act structure from reading 2,000 screenplays and seeing what separated the ones that got made from the ones that didn't. WoW-nnui
The axiom is that golf was never meant to be a fair game, so then the natural response is when does it become an unfair game?
Since Euclid's axiomatic formulation of geometry mathematicians had been trying to prove his fifth postulate as a theorem deduced from the other four axioms.
In few other areas of the law is there greater truth to the axiom that ‘justice delayed is justice denied.’
The items in boldface indicate that the students were handed sets of axioms and theorems.
Since the following biconditional is also a straightforward consequence of the axioms: Wild Dreams Of Reality, 3
It is axiomatic that hard cases make bad law, but this is not a hard case.
It might be set down as an axiomatic statement that no large publishing house in this country could possibly live exclusively from what are known as miscellaneous books, by which is meant current fiction and other ephemeral publications. The Building of a Book A Series of Practical Articles Written by Experts in the Various Departments of Book Making and Distributing
Let the letter ‘M’ represent this operator, and add to the axioms of classical propositional logic the modal axiom M (p v q) iff Mp v Mq.
It is a well-accepted axiom that the software ‘industry’ grew largely because of government indifference, not its help.
This law has been axiomatic in the evolution of the sciences.
Now Frege axiomatized arithmetic with an intuitive collection of axioms, and proofs of number theory results which he had only sketched earlier he now gave formally.
The formalized axiomlogy construct the new foundation for research an existential conditions of the possible worlds.
Powers: first axiomatization of logic; knowledge of eternal, immaterial entities July 5th, 2007
That a conjectural critick should often be mistaken, cannot be wonderful, either to others or himself, if it be considered that in his art there is no system, no principal and axiomatical truth that regulates subordinate positions. Preface to Shakespeare
Boulliau: “The axiom that the celestial motions are circular or composed of circles must stand, and therefore I reject and repudiate his ellipses unless he should suppose them to be described by means of a Copernican or Tychonic epicycle.” (letter to Gassendi 1633) Bukiet on Brooklyn Books
Chomsky is committed to an axiom of biological determinism.
We shall have," said the judge, "these crude and subversionary books from time to time until it is recognized as an axiom of morality that luck is the only fit object of human veneration. Erewhon; or, Over the range
To those, yes, American democrats who quibble, cavil, and lose themselves in conjecture over the risks to which the judge who allows a criminal to live subjects honest people, we countered with Maïmonides's axiom: "It is more satisfying to acquit thousands of the guilty than to execute one sole innocent man. Bernard-Henri Lévy: And to Think That We Still Have to Argue Against the Death Penalty
parroting some timeworn axiom
You may disagree with them on the merits, but this disagreement turns on differences in moral axioms, not the other side's lack of logic.
Nevertheless, to rehash a time-worn axiom, there's an exception to every rule and that holds true for baseball records even when comparing those for rookies to ones established by veterans.
It is an axiomatic fact that governments rise and fall on the state of the economy.
The taller the man, the bigger the hands is an axiom that doesn't necessarily hold true for wide receivers.
Each subject has its own painful application of this misdirected axiom.
Not only did he anticipate Heisenberg's Uncertainty Principle, and set out a finite axiomatization of arithmetic before Peano did, and the basis axiomatic set theory before Zermelo did, but also his notation and terminology were readable and suggestive, giving future logicians a better language to work in than the clunky terms of the Germans. Pragmatic inquiry
Like the photographer who shows his or her aptitude in the selective framing, it is axiomatic that the decisive representation of a single scene in pictorial representation is a key to its beauty.
Although in this book Newton affects a kind of axiomatic presentation beginning with definitions and axioms, and enunciating a series of propositions, the procedures are really analytic in his sense, as he tells us they are: the propositions are not abstract mathematical statements, but affirmations of physical or experimental fact, and they are justified, not by mathematical deduction, but by what he calls Dictionary of the History of Ideas
Taking this as axiom of the syllogism materially treated, we see that herbivorousness, being constantly related to ruminants, is constantly related to camels; mortality to man and, therefore, to Socrates; rusting to the immersion of iron in water generally and, therefore, to this piece of iron. Logic Deductive and Inductive
Upon these axioms the whole structure of microeconomics is based, and the rest of economics generally follows.
It is axiomatic that the differences among the Chiefs of Staff are resolved by the military professionals themselves, with one of them acting as the arbitrator.
Thus, axiomatics can be seen as a formal microcosm of the human mind set -- a mind set which is our "living our life from place". Do we think about what we think about before we think about it?
It is an axiomatic fact that governments rise and fall on the state of the economy.
Even if those terms are "axiomatic," they should be explained or described, and the authors must refrain from constantly introducing new terms that may be ambiguous; rather they should repeat words that were already used and explained. Citizendium, the Citizens' Compendium - Recent changes [en]
It seems axiomatic that everyone would benefit from a better scientific education.
The choice of axioms in a logical system can represent content specific information.
Dedekind regards this principle as being essentially indemonstrable; he ascribes to it, rather, the status of an axiom ‘by which we attribute to the line its continuity, by which we think continuity into the line.’
At the present time, with the considerable experience gained and with additional personnel available, this initial effort should be axiomatic.
And first to begin of politicians, it hath ever been a principal axiom with them to maintain religion or superstition, which they determine of, alter and vary upon all occasions, as to them seems best, they make religion mere policy, a cloak, a human invention, nihil aeque valet ad regendos vulgi animos ac superstitio, as [6386] Tacitus and [6387] Tully hold. Anatomy of Melancholy
You seem to think this is a sophisticated philosophy, but to the Elders of Sodom it appears risibly simplistic -- practically crude and ignorant in its systematisation of potential human behaviour into a set of axioms bearing little relation to reality, and all of these articulated in a one note modality of "must" and "must not," judging this action a virtue to be proud of, that one a vice to be ashamed of. An Open Letter to John C. Wright
Many thought geometry's spare base of axioms and its clean, inexorable logic was scientific knowledge at its best.
Thus, as long the basic set theoretic notions are characterized simply by looking at the model theory of first-order axiomatizations of set theory, then many of these notions ” and, in particular, the notions of countability and uncountability ” will turn out to be unavoidably relative. [ Skolem's Paradox
Since Euclid's axiomatic formulation of geometry mathematicians had been trying to prove his fifth postulate as a theorem deduced from the other four axioms.
It is a tone which implies that certain thing in life are so axiomatic that no discussion of them is necessary or even possible.
(Åukasiewicz's axiomatisation of the syllogistic incorporates his own three-axiom formalisation of propositional logic The Sun Is Not
The Axioms of Religion, who insisted truly born-again believers are "impelled" to be part of the church. Biblical Recorder
He collaborated with the legendary David Hilbert, champion of axiomatics in science and mathematics. The Great Escape
By 1918, the use of military camouflage was axiomatic, and in 1939 war artists were again mobilized to advise on concealment.
The work of Bolyai and Lobachevsky are comparable in that sense, that they both challenge axiomatic assumptions, but their postulates are of Euclidean geometry.
During the long and taxing journey up into the high mountain fastness where the Huntress’s people dwell, I came to view this less as an epigram and more as an axiom. Duet « A Fly in Amber
The entire argument of the Anti-Adiaphorists was by him reduced to the following principle or axiom: "_Nihil est adiaphoron in casu confessionis et scandali. Historical Introductions to the Symbolical Books of the Evangelical Lutheran Church
For although I do not deny that when all the experiments of all the arts shall have been collected and digested, and brought within one man's knowledge and judgment, the mere transferring of the experiments of one art to others may lead, by means of that experience which I term literate, to the discovery of many new things of service to the life and state of man, yet it is no great matter that can be hoped from that; but from the new light of axioms, which having been educed from those particulars by a certain method and rule, shall in their turn point out the way again to new particulars, greater things may be looked for. The New Organon
So the real, indemonstrable axioms are identical propositions.
“We shall have,” said the judge, “these crude and subversionary books from time to time until it is recognised as an axiom of morality that luck is the only fit object of human veneration. Erewhon
It is almost an axiom that no man may make a career in politics in the Republic without stooping to such ignobility: it is as necessary as a loud voice.
It would build on the early work in axiomatizing branches of mathematics, as well as the monumental efforts of logicists like Frege in developing rigorous logical systems.
non-Euclidean geometries discard or replace one or more of the Euclidean axioms
In the same sense that a Cartesian geometry specifies certain axioms, definitions, and postulates as the basis for a formal geometry, an ivory-tower geometry.
However the axiom that the quality and cost of the food in a revolving restaurant is in inverse proportion to the height of the tower doesn't apply here.
In the context of the pervasive nineteenth century idealism of Hegel, Kant and their epigones, this axiomatic statement was anything but banal.
To summarize, then, the upshot of this discussion is this: if we take a purely algebraic approach to the axioms of set theory, then many basic set-theoretic notions ” including the notions of countability and uncountability ” will turn out to be relative. Skolem's Paradox
Given this algebraic conception of axiomatization, then, Skolem appeals to the LÃ¶wenheim-Skolem theorems to argue that the axioms of set theory lack the resources to pin down the notion of uncountability. Skolem's Paradox
That protest is of the essence of true democratic activity is axiomatic.
Indeed, on this basis it is possible to reject the implicit axiom of the lepidomorial theory, that all change occurs through ontogenetic concrescence, as well as the principle that ontogenetic concrescence is possible.
It is axiomatic that all monopoly groups, emerging from time to time, will remain the continuous target of the people so as to keep India free of despotism.
There's nothing axiomatically pejorative about it, and some passages of history have made it a term of honor.
Studying the properties off these observations one sees that they satisfy the necessary axioms to be linear operators, and, in fact, self-adjoint operators. Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask
The pedant might note that the Internet, axiomatically, is all social media, but for the purposes of this discussion, let’s say that social media includes any digital environment built on the contributions of and interactions among people — or in the case of dogster. com, their dogs. The Web 2.0 Bubble
Grammar formalisms - special-purpose systems for the description of linguistic systems and subsystems - can be thought of as logics designed to axiomatize the association of linguistic structures with strings of symbols.
She waits for another useless barrage of platitudes and axioms, but all she catches is the harsh rasp of his breathing.
The Nagel-Schaffner approach to theory reduction assumes a syntactic account of theory structure such that they are axiomatized systems formalizable in first order predicate calculus. Reductionism in Biology
So if the math relates to a physics matter the "axiom" is tested. Critical Thinking
To be both liberal and democratic is to be axiomatically part of a club that examines itself. Torture: crimes with impunity | Editorial
In this paper, we investigate quality control chart construction under random fuzzy environment on the foundation of the axiomatic credibility measure theory.
To them, it was axiomatic that prices and interest rates should be kept down to further their objective of cheap electricity.
Nabokov is their favorite writer, the convenient novelistic illustration of their theoretical axioms.
The construction of the reals from the integers proceeds in several stages: first axiomatize the positive integers, then construct negative from positive integers, then rationals from integers, and finally reals from rationals.
I used to live by the axiom that it's easier to warm up in the cold than cool off in the heat.
In a Hilbert system, for example, we have a number of axioms and rules of inference.
It is a widely held axiom that they should not negotiate with terrorists.
Granted that today women cannot afford to exclude themselves axiomatically from the military complex, where is the line to be drawn? Arms and the Woman: Just Warriors and Greek Feminist Identity
This is proved to be the marginal law of diminishing utility in mathematics, which has an economic law of an axiom, affecting all aspects of social and economic life.
I haven't tied this "axiomatically" - it's a result of years of observing players, and it emerges from my earlier studies on player types. WoW-nnui
Moreover, whilst Peano arithmetic is axiomatizable, there is a particular model of Peano arithmetic, whose theory is typically referred to as Number theory, which Godel demonstrated to be undecidable and non-axiomatizable. Archive 2009-06-01
Establishment the axiom of seize suppresses or the necessity of arrestment axiom.
One of the oft-repeated axioms in baseball is that when the season starts, pitchers generally have the upper hand against hitters. Key fantasy cogs off to slow start? Don't panic yet
A standard axiomatisation for Euclidean plane geometry Finitism in Geometry
The Cartesian philosophy posited two fundamental axioms—the supremacy of reason and the invariability of the laws of nature. Sands of Empire
Therefore every one of these is of some use in speech; but nothing is a part or element of speech (as has been said) except a noun and a verb, which make the first juncture allowing of truth or falsehood, which some call a proposition or protasis, others an axiom, and which Plato called speech. Essays and Miscellanies
. It's not a bad strategy, except that a strategy that relies on inaction is axiomatically vulnerable.
It is axiomatic that all the sites that are infected should be treated if there is to be any hope of cure.
But at some point, you must reach what one might call a moral axiom that you can't logically demonstrate.
In retrospect this appears so, but we have to remember that he abstracted his axioms from observation of the real world.
At the present time, with the considerable experience gained and with additional personnel available, this initial effort should be axiomatic.
We shall have," said the judge, "these crude and subversionary books from time to time until it is recognised as an axiom of morality that luck is the only fit object of human veneration. Erewhon
The threat of global annihilation has so colored the debate that for many people it is considered an axiomatic truth that the use of such weaponry can never be justified.
The Axiom of Choice is closely allied to a group of mathematical propositions collectively known as maximal principles. The Axiom of Choice
He also claimed that when classicists applied deductive logic to these inadequate axioms they inevitably got inadequate results.
Freudenthal studied the relation between axiomatic mathematics and reality, and this study led him to contribute to intuitionism, as well as to the application of mathematics to linguistics.
The search for a spell to ward off the evils attendant upon self-reference has fed into the axiomatisation of set theory in two ways, corresponding to the two ways in which self-reference has been (mis) - understood. Quine's New Foundations
The student who is tempted to skip it and trust to luck should be mindful of Francis Bacon's axiom.
Despite only having three axiom schemata and a single inference rule, it is possible to prove any tautology in the simple Propositional Calculus, PC.
I abandoned reason: whatever Bronwen did was right; that was axiomatic. TESTIMONIES
It appeareth likewise that I have assigned to summary philosophy the common principles and axioms which are promiscuous and indifferent to several sciences; I have assigned unto it likewise the inquiry touching the operation or the relative and adventive characters of essences, as quantity, similitude, diversity, possibility, and the rest, with this distinction and provision; that they be handled as they have efficacy in nature, and not logically. The Advancement of Learning
As to axiomatization, LeÅniewski knew that the pure theory of equivalence could be based on two axioms stating skew-transitivity and associativity: StanisÅaw LeÅniewski
For these and other reasons, it can not be taken as axiomatic that the most extreme threats are the most effective.
Finally, it is worth recalling that the assumption of atomism generally allows for significant simplifications in the axiomatics of mereology. Wild Dreams Of Reality, 3
A mathematical proof is a formal and logical line of reasoning that begins with a set of axioms and moves through logical steps to a conclusion.
They came to accept as axiomatic that the strong and wealthy state is built on the energies of liberated individuals.
Daily, the truth of this proposition - axiomatic to our ancestors, crassly ignored by progressive theorists today - becomes more evident.
The sciences - at any rate the theoretical sciences - are to be axiomatised.
an axiomatic truth
Is it that at first the ancients called that [Greek omitted], or speech, which once was called protasis and now is called axiom or proposition, — which as soon as a man speaks, he speaks either true or false? Essays and Miscellanies

How To Use Axiom In A Sentence

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