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Proof Quotes

“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
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“As far as France is concerned, we are ready to envisage everything that can be done under UNSCR 1441. [...] But I repeat that every possibility offered by the present resolution must be explored, that there are a lot of them and they still leave us with a lot of leeway when it comes to ways of achieving the objective of eliminating any weapons of mass destruction which may exist in Iraq. I'd like nevertheless to note that, as things stand at the moment, I have, to my knowledge, no indisputable proof in this sphere.”

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Author:Jacques Chirac
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“I learned early that business is business and politics is politics. The proof is how few important businessmen have made good politicians. They may think that they are very smart about everything because they made millions of dollars by digging a hole in the ground and finding oil, but the talent and luck needed to become rich are not the same talent and luck needed to succeed on Parliament Hill.”

ThinkingMayMadeImportantMillionsRichTalentNeededPoliticianSucceedFindingsSmartLuckDollarsOilProofHolesHillsBusinessmanParliamentDiggingVery SmartBecome RichGood PoliticiansDigging A Hole
Author:Jean Chretien
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“The ultimate proof of total forgiveness takes place when we sincerely petition the Father to let those who have hurt us off the hook—even if they have hurt not only us, but also those close to us.”

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Book:Total Forgiveness: When Everything in You Wants to Hold a Grudge, Point a Finger, and Remember the Pain—God Wants You to Lay it All Aside
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“I am afraid that those comments go back to the late 80's. At that time I was a skeptic - the argument based on Koch's postulates to try to distinguish between cause and association. Today I would regard the success of the many antiviral agents which lower the virus titers (to be expected) and also resolve the failure of the immune system (only expected if the virus is the cause of the failure) as a reasonable proof of the causation argument .”

IfsTryingTodayCausesLateArgumentRegardExpectedProofAgentsReasonableResolveCommentAssociationVirusesImmuneSkepticImmune SystemCausation
Author:Walter Gilbert
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“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.”

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Author:David Hilbert
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“I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.”

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Author:G. H. Hardy
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“[A]t the beginning of November 2001, there was a series of meetings between White House advisers and senior Hollywood executives with the aim of co-ordinating the war effort and establishing how Hollywood could help in the "war against terrorism" by getting the right ideological message across not only to Americans, but also to the Hollywood public around the globe the ultimate empirical proof that Hollywood does in fact function as an "ideological state apparatus.”

DoeWarStatesFactsHelpingHouseWhiteEffortMessagesHollywoodUltimateFunctionAimMeetingsSeriesTerrorismProofExecutivesWhite HouseGlobesSeniorIdeologicalNovemberAdviser
Book:Welcome to the Desert of the Real!: Five Essays on September 11 and Related Dates
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“By a kind of happy pre-established harmony, such as a later age discovered between the needs of society and the self-interest of the individual, success in business is in itself almost a sign of spiritual grace, for it is a proof that a man has laboured faithfully in his vocation.”

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Book:Religion And The Rise Of Capitalism
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“I HAVE no patience with the hypothesis occasionally expressed, and often implied, especially in tales written to teach children to be good, that babies are born pretty much alike, and that the sole agencies in creating differences between boy and boy, and man and man, are steady application and moral effort. It is in the most unqualified manner that I object to pretensions of natural equality. The experiences of the nursery, the school, the University, and of professional careers, are a chain of proofs to the contrary.”

MenChildrenSchoolBornNaturalDifferencesEffortMoralBoysCareersTeachWrittenObjectsBabyCreatingUniversityBe GoodProofContraryTalesChainsAgencyApplicationSteadySoleHypothesisPretensionNurseryImpliedUnqualifiedNo PatienceProfessional CareerI Have No Patience
Book:Hereditary Genius: An Inquiry Into Its Laws and Consequences
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“The Soul is a fact, but it is not physical. ... Survivors of near-death experiences attest that some part of them apparently detaches from their physical bodies following the death of the body, but while that is proof of the soul for them, it does not prove it to us. The Soul is like divine music that only God can hear; it is the force of endless resurrection; the soul is like a fire that never goes out.”

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Author:Caroline Myss
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“The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. ... Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.”

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Author:George Polya
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“All mass movements strive, therefore, to interpose a fact-proof screen between the faithful and the realities of the world. They do this by claiming that the ultimate and absolute truth is already embodied in their doctrine and that there is no truth nor certitude outside it. The facts on which the true believer bases his conclusions must not be derived from his experience or observation but from holy writ.”

WorldFactsRealityMovementHolyTruth IsMassUltimateBasesAbsolutesStriveProofScreensBelieverDoctrineConclusionObservationFaithfulAbsolute TruthTrue BelieverCertitude
Book:Between the Devil and the Dragon: The Best Essays and Aphorisms of Eric Hoffer
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“The prevailing tendency to regard all the marked distinctions of human character as innate, and in the main indelible, and to ignore the irresistible proofs that by far the greater part of those differences, whether between individuals, races, or sexes are such as not only might but naturally would be produced by differences in circumstances, is one of the chief hinderances to the rational treatment of great social questions, and one of the greatest stumbling blocks to human improvement.”

HumansCharacterMightWould BeIndividualSocialSexDifferencesRaceGreaterCircumstancesEthicsRegardProofImprovementRationalTendenciesBlockChiefsDistinctionTreatmentInnateIrresistiblePrevailingStumblingIndelibleStumbling Blocks
Book:Autobiography of John Stuart Mill
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“Margaret Miles offers a stunning treatment of human experience, coaxing humans to leave dualisms behind and embrace our intelligent bodies. In a foundational text, she draws on the arts, philosophy and theology, and her experience as a hospice volunteer to explore concrete alternatives to privileging the rational mind. Her erudition, wisdom, and graceful writing are compelling proof of the intelligent body.”

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Author:Mary E. Hunt
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“As far as I know, Clifford Pickover is the first mathematician to write a book about areas where math and theology overlap. Are there mathematical proofs of God? Who are the great mathematicians who believed in a deity? Does numerology lead anywhere when applied to sacred literature? Pickover covers these and many other off-trail topics with his usual verve, humor, and clarity. And along the way the reader will learn a great deal of serious mathematics.”

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Author:Martin Gardner
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“Many causes may vitiate a writer's judgement of his own works. On that which has cost him much labour he sets a high value, because he is unwilling to think that he has been diligent in vain: what has been produced without toilsome efforts is considered with delight as a proof of vigorous faculties and fertile invention; and the last work, whatever it be, has necessarily most of the grace of novelty.”

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Book:The works of Samuel Johnson, LL.D.: Together with his life, and notes on his Lives of the poets, by Sir John Hawkins, Knt. In eleven volumes ...
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“In virtually every Continental state at this time, aristocracies had to live with the risk that their property might be pillaged or confiscated. Only in Great Britain did it prove possible to float the idea that aristocratic property was in some magical and strictly intangible way the people's property also. The fact that hundreds of thousands of men and women today are willing to accept that privately owned country houses and their contents are part of Britain's national heritage is one more proof of how successfully the British elite reconstructed its cultural image in an age of revolution.”

PeopleMenWayIdeasCountryStatesFactsMightAgeTodayHouseAcceptingRiskWillingRevolutionProveMen And WomenPropertyBritishProofBritainHeritageElitesFloatsAristocracyGreat BritainIntangibleBritish HistoryContinentalAristocraticCountry Houses
Book:Britons: Forging the Nation, 1707-1837
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“David Irving has consistenly applied an evidential double standard, demanding absolute documentary proof to convict the Germans (as when he sought to show that Hitler was not responsible for the Holocaust), while relying on circumstantial evidence to condemn the British (as in his account of the Allied bombing of Dresden).”

ShowsStandardsEvidenceAccountsAbsolutesResponsibleBritishProofHolocaustDocumentariesBombingDouble StandardBritish HistoryDresdenConvictsCircumstantial Evidence
Book:History in Our Time
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“If a large number of people who are convinced alien abductions are real are hypnotising even larger numbers of others who suspect they might be, then it is likely there will be many alien abduction narratives flying around, as, indeed, there are. Of course, this is not proof they are not true, but it does provide a persuasive context for a simple psychosocial explanation. Hypnotism is a technique that triggers a mass storytelling project in which all the stories are linked.”

PeopleIfsDoeRealStoriesMightCoursesSimpleNumbersProjectsMassConvincedProofTechniqueAstronomyFlyingStorytellingAliensNarrativeExplanationSuspectsLinkedTriggersLarge NumbersPersuasiveAbductionAlien Abduction
Author:Bryan Appleyard
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“The commotions that have taken place in America, as far as they are yet known to me, offer nothing threatening. They are a proof that the people have liberty enough, and I could not wish them less than they have. If the happiness of the mass of the people can be secured at the expense of a little tempest now and then, or even of a little blood, it will be a precious purchase. 'Malo libertatem periculosam quam quietem servitutem.' Let common sense and common honesty have fair play, and they will soon set things to rights.”

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Book:Correspondence
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“If my interlocutor desires to convince me that Jupiter has inhabitants, and that his description of them is accurate, it is for him to bring forward evidence in support of his contention. The burden of proof evidently lies on him; it is not for me to prove that no such beings exist before my non-belief is justified, but for him to prove that they do exist before my belief can be fairly claimed. Similarly, it is for the affirmer of God's existence to bring evidence in support of his affirmation; the burden of proof lies on him.”

IfsLyingDesireBeliefExistenceSupportAtheismProveEvidenceBurdenPositive AtheismProofConvinceDescriptionAccurateAffirmationJustifiedContentionJupiterBurden Of Proof
Book:The Origins of Theosophy (Routledge Revivals): Annie Besant - The Atheist Years
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“Religious liberty in a nation is as real as the liberty of its least popular religious minority. Look not to the size of cathedrals or even to the words on the statute books for proof of the reality of religious freedom. Ask what is the fate of the Protestant in Spain, the Jew in Saudi Arabia, the Arab in Israel, the Catholic in Poland or the atheist in the United States.”

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Author:Paul Blanshard
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“If it is to be established that there is a God, then we have to have good grounds for believing that this is indeed so. Until and unless some such grounds are produced we have literally no reason at all for believing; and in that situation the only reasonable posture must be that of either the negative atheist or the agnostic. So the onus of proof has to rest on the proposition of theism.”

IfsBelieveReasonSituationAtheismNegativeAtheistPositive AtheismProofReasonableNo ReasonAgnosticPropositionsFlewPostureTheism
Book:Philosophical Essays
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“It is naïve to suppose that the acceptance of evolution theory depends upon the evidence of a number of so-called "proofs"; it depends rather upon the fact that the evolutionary theory permeates and supports every branch of biological science, much as the notion of the roundness of the earth underlies all geodesy and all cosmological theories on which the shape of the earth has a bearing. Thus antievolutionism is of the same stature as flat-earthism.”

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Author:Peter Medawar
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