“Mystery is an inescapable ingredient of mathematics. Mathematics is full of unanswered questions, which far outnumber known theorems and results. It's the nature of mathematics to pose more problems than it can solve. Indeed, mathematics itself may be built on small islands of truth comprising the pieces of mathematics that can be validated by relatively short proofs. All else is speculation.” MayProblemResultsKnownPiecesMysteryBuiltLogicMathematicsSolveProofCertaintyUncertaintyIslandsReasoningIngredientsSpeculationOntologyTheoremsUnanswered QuestionsUnanswered Author:Ivars Peterson
“The deep paradox uncovered by AI research: the only way to deal efficiently with very complex problems is to move away from pure logic.... Most of the time, reaching the right decision requires little reasoning.... Expert systems are, thus, not about reasoning: they are about knowing.... Reasoning takes time, so we try to do it as seldom as possible. Instead we store the results of our reasoning for later reference.” WayTryingLittlesProblemMovingDecisionResultsDealsKnowingPureResearchLogicComplexesStoresExpertsReasoningReachingParadoxArtificial IntelligenceTake TimeRight DecisionComplex Problems Author:Daniel Crevier
“There is another method of obtaining money... It does not presuppose the existence of accumulated results of previous development, and hence may be considered as the only one which is available in strict logic. This method of obtaining money is the creation of purchasing power by banks. The form it takes is immaterial.” MayDoeFormPoliticsResultsExistenceEconomyCreationDevelopmentLogicMethodAvailableLiberalismStrictObtainingPurchasingPurchasing Power Author:Joseph A. Schumpeter
“Logic, too, also rests on assumptions that do not correspond to anything in the real world, e.g., on the assumption that there areequal things, that the same thing is identical at different points in time: but this science arose as a result of the opposite belief (that such things actually exist in the real world). And it is the same with mathematics, which would certainly never have arisen if it had been understood from the beginning that there is no such thing in nature as a perfectly straight line, a true circle, and absolute measure.” IfsWorldDifferentRealBeliefLinesResultsUnderstoodLogicOppositesAbsolutesMathematicsEqualityCirclesAssumptionReal WorldIdenticalStraight Lines Author:Friedrich Nietzsche
“Neither logic nor scientific evidence supports such a belief. Although spinal manipulation can relieve certain types of back pain, neck pain, and other musculoskeletal symptoms, there is no scientific evidence that it can restore or maintain health. As a result of expressing my opinion on this subject, I have been called a chiropractic heretic.” Has BeensPainCertainBeliefResultsOpinionSupportSubjectsTypeEvidenceLogicTherapyNecksInjuryManipulationSymptomsHereticChiropracticBack PainScientific Evidence Book:Inside Chiropractic: A Patient's Guide Source: Inside Chiropractic: A Patient's Guide
“I think logicians hate my work, they detest it! And I'm like pornography, I'm sort of an unmentionable subject in the world of logic, because my results are so disgusting!” ThinkingWorldScienceHateResultsSubjectsLogicMathematicsDisgustingPornographyDetest Author:Gregory Chaitin