“It is difficult even to attach a precise meaning to the term "scientific truth." So different is the meaning of the word "truth" according to whether we are dealing with a fact of experience, a mathematical proposition or a scientific theory. "Religious truth" conveys nothing clear to me at all.” DifferentFactsScienceDifficultTermReligiousClearTheoryMathematicalPrecisePropositionsScientific TheoryScientific TruthReligious Truth Book:Essays in Science Source: Essays in Science
“Chaos has come to be associated with the study of anything complex, but, in fact, the mathematical techniques are directly applicable only to simple systems that appear to be complex.” FactsSimpleStudyComplexesChaosTechniqueMathematical Author:Neil Gershenfeld
“As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be mathematical facts which are true but unknowable.” KnowsMayIdeasFactsViewsAcceptingMathematicalMinoritiesMathematician Author:Abraham Robinson
“The mathematical thermology created by Fourier may tempt us to hope that, as he has estimated the temperature of the space in which we move, me may in time ascertain the mean temperature of the heavenly bodies: but I regard this order of facts as for ever excluded from our recognition. We can never learn their internal constitution, nor, in regard to some of them, how heat is absorbed by their atmosphere. We may therefore define Astronomy as the science by which we discover the laws of the geometrical and mechanical phenomena presented by the heavenly bodies.” MayMeanFactsBodyMovingLawOrderSpaceConstitutionRegardAstronomyRecognitionMathematicalAtmosphereHeatInternalsHeavenlyTemperatureExcludedHeavenly BodiesFourier Book:The Positive Philosophy of Auguste Comte Source: The Positive Philosophy of Auguste Comte
“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