Quotessence
Home / Topics / Axioms Quotes

Axioms Quotes

Browse 245 quotes about Axioms.

Related topics

MayMathematicsPoliticalThinkingMenNumbersWayExistencePrinciplesScienceTheoremsTheoryWorldFactsFundamentalsIfsKnowsMathematicalPeopleReasonTwoUnderstanding

Axioms Quotes

“Talk can neither be verified nor falsified in any rigorous sense. This is an open secret which hermeneutics and aesthetics, from Aristotle to Croce, have laboured to exorcise or to conceal from themselves and their clients. This ontological, which is to say both primordial and essential axiom (or platitude) of ineradicable undecidability needs, none the less, to be closely argued.”

NeedsSecretEssentialsClientsAestheticsAxiomsPlatitudesHermeneutics
Author:George Steiner
Create image

“The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry.”

WorldLinesWork OutDiscoveringRemedyUnfortunateParallelsGeometryAxiomsStraight LinesCollisionTheoristsRebuke
Book:General Theory Of Employment , Interest And Money
Create image

“Man is naturally self-centered and he is inclined to regard expediency as the supreme standard for what is right and wrong. However, we must not convert an inclination into an axiom that just as man's perceptions cannot operate outside time and space, so his motivations cannot operate outside expediency; that man can never transcend his own self. The most fatal trap into which thinking may fall is the equation of existence and expediency.”

ThinkingMenMaySelfMotivationFallSpaceExistencePerceptionStandardsRegardSupremeTrapsEquationsTime And SpaceInclinationSelf CenteredAxiomsExpediency
Author:Abraham Joshua Heschel
Create image

“It was an axiom of "containment" that no part of the known world could be considered neutral. "Neutralism" was among the Cold Warriors' gravest curse words, applied with caustic hostility to India and even France. Those who were not with were against, subjected to intense economic and ideological and sometimes military pressure to fall into line.”

WorldSometimesFallLinesKnownEconomicMilitaryColdIndiaPressureIntenseWarriorFranceCurseCold WarHostilityIdeologicalAxiomsContainmentCausticCurse Words
Book:For the Sake of Argument: Essays and Minority Reports
Create image

“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.”

FirstsHas BeensPhilosophyUseAgeTermNaturalPartyPrinciplesIssuesMathematicsLaysReasoningBranchesMathematicianGroundedDisputesSectsAxiomsExcludedSophistryNatural Philosophy
Author:Thomas Reid
Create image

“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.”

MenMayImportantEndsLastsUsedTakenExampleDegreesBenefitsIncreaseInstanceMealsEnjoymentPortionsQuantityCommodityUtilityDecreaseAxioms
Book:Papers and correspondence of William Stanley Jevons
Create image

“The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.”

MayWholeHandsRealityUsedNumbersCasesConceptsConsequenceBasesProofDistinctionNeglectQuantityEntityPropositionsAxioms
Author:Georg Cantor
Create image

“Mathematics is a presuppositionless science. To found it I do not need God, as does Kronecker, or the assumption of a special faculty of our understanding attuned to the principle of mathematical induction, as does Poincaré, or the primal intuition of Brouwer, or, finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot be compensated for by consistency proofs.”

NeedsDoeFactsFoundUnderstandingPrinciplesSpecialMathematicsIntuitionProofMathematicalAssumptionFacultyInfinityConsistencyPrimalAxiomsCompletenessNeed God
Author:David Hilbert
Create image

“The opinions that the price of commodities depends solely on the proportion of supply and demand, or demand to supply, has become almost an axiom in political economy, and has been the source of much error in that science.”

Has BeensPoliticalOpinionEconomySourceDependsDemandErrorsProportionCommodityAxiomsPolitical EconomySupply And Demand
Book:The Works of David Ricardo. With a notice of the life and writings of the author: by J. R. McCulloch
Create image

“A crucial difference between lite libertarians and the right kind is that to the former, the idea of liberty is propositional - a deracinated principle, unmoored from the realities of history, hierarchy, biology, tradition, culture, values. Conversely, the paleolibertarian grasps that ordered liberty has a civilizational dimension, stripped of which the libertarian non-aggression axiom, by which we all must live, cannot endure.”

KindIdeasRealityValuesCultureDifferencesLibertyPrinciplesTraditionEndureLibertarianFormerDimensionsBiologyCrucialAggressionHierarchyAxioms
Author:Ilana Mercer
Create image

“For Stirner, the social axiom of conservative, liberal, and socialist schools of political thought alike is in itself repressive: it disguises as potentially redemptive an order whose central function is inhibitory of the individual's interests.”

SchoolPoliticalOrderIndividualSocialInterestFunctionConservativeDisguiseSocialistAxioms
Book:Break-Out from the Crystal Palace: The Anarcho-Psychological Critique: Stirner, Nietzsche, Dostoevsky
Create image

“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.”

FeelsMindHelpingFeelingsCertainIndividualCommunityImaginationEffortBearsBirthPleaseMathematicsFellowsStructureHistoricalNotionMathAccidentsMathematicalAffectedMathematicianConstructsStampsAxiomsCombined Effort
Book:Gesammelte Abhandlungen
Create image

“It is accepted as an axiom by all Americans that the civil power ought to be not only neutral and impartial as between different forms of faith, but ought to leave these matters entirely on one side, regarding them no more than it regards the artistic or literary pursuits of the citizens.”

DifferentMatterFormSidesAtheismOughtCitizensRegardPositive AtheismAcceptedPursuitArtisticAxioms
Book:The American Commonwealth: Vol. 4: Illustrations and Reflections & Social Institutions
Create image

“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.”

IfsMindTwoCountryFactsGamesSeriousGoes OnCapableAffairInternationalScreensNewspapersSurrenderSmokeNecksBottlesSurroundRelevantSovereigntyAxiomsBeing PlayedInternational Affairs
Book:The Collected Essays, Journalism and Letters of George Orwell: In front of your nose, 1945-1950
Create image

“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.”

MayFormIndividualLanguageTermRaceExperienceInstrumentsUnityIntuitionAbstractOrganizedMultipleAxioms
Book:Problems of Life and Mind: v.1-2 . The foundations of a creed
Create image

“What government supports, government controls. This is an ancient axiom repeatedly ratified by experience. . . . Indeed, as is well known, acceptance of tax aid has led to the secularization of many church-related colleges and universities.”

WellsStatesGovernmentChurchKnownSupportAcceptanceCollegeTaxesUniversityAncientAidsRelatedWell KnownAxiomsColleges And Universities
Book:Church schools & public money: the politics of parochiaid
Create image

“To be sure an European woman would blush to her fingers' ends at the very idea of appearing publicly stark naked; but education and prejudice are everything, since it is an axiom, that where there is no feeling of self-reproach, there can assuredly be no shame.”

IdeasEndsSelfFeelingsPrejudiceShameFingersNakedAppearingStarksAxiomsReproachNudity
Book:Narrative of a Five Years' Expedition Against the Revolted Negroes of Surinam: In Guiana ... from the Year 1772 to 1777 ; Elucidating the History of that Country and Describing Its Productions, Viz. Quadrupeds, Birds, [etc.] Trees, Shrubs, [etc.] with an Account of the Indians and Negroes of Guinea
Create image

“..why 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?”

BelieveSchoolAsksSocialSituationKnownSonDrinkingWorkersSavedReformRemedyResortsPsychiatristAxiomsSocial WorkerActualityCounselor
Author:James Lee Burke
Create image

“The two basic maxims of the so-called historical criticism are the postulate of the common and the axiom of the ordinary. Postulate of the common: everything really great, good, and beautiful, is improbable, since it is extraordinary and therefore at least suspect. Axiom of the ordinary: our conditions and environment must have existed everywhere, for they are really so natural.”

TwoBeautifulNaturalCommonHistoryEnvironmentConditionsOrdinaryCriticismHistoricalExtraordinarySuspectsReally GreatMaximsAxiomsImprobable
Author:Karl Wilhelm Friedrich Schlegel
Create image

“I am asked if I would not be gratified if my friends would procure me promotion to a brigadier-generalship. My feeling is that I would rather be one of the good colonels than one of the poor generals. The colonel of a regiment has one of the most agreeable positions in the service, and one of the most useful. "A good colonel makes a good regiment," is an axiom.”

IfsWarFeelingsPoorPositionMy FriendsCivil WarPromotionAxiomsColonels
Book:Conspicuous Gallantry: Civil War Diary and Letters of Rutherford B. Hayes (Abridged)
Create image

“What exactly is mathematics? Many have tried but nobody has really succeeded in defining mathematics; it is always something else. Roughly speaking, people know that it deals with numbers, figures, with relations, operations, and that its formal procedures involving axioms, proofs, lemmas, theorems have not changed since the time of Archimedes.”

PeopleKnowsDealsNumbersFiguresChangedRelationMathematicsProofOperationsFormalDefiningProceduresInvolvingAxiomsTheoremsExactly Is
Author:Stanislaw Ulam
Create image