"No experimental result can ever kill a theory: any theory can be saved from counterinstances either by some auxiliary hypothesis or by a suitable reinterpretation of its terms." (Imre Lakatos, "Falsification and the Methodology of Scientific Research Programmes", 1965)
"Blind commitment to a theory is not an intellectual virtue: it is an intellectual crime." (Imre Lakatos, [radio Lecture] 1973)
"Mathematics does not grow through a monotonous increase of the number of indubitably established theorems, but through the incessant improvement of guesses by speculation and criticism." (Imre Lakatos, "Proofs and Refutations", 1976)
"There is an infinite regress in proofs; therefore proofs do not prove. You should realize that proving is a game, to be played while you enjoy it and stopped when you get tired of it." (Imre Lakatos, "Proofs and Refutations", 1976)
"Under the present dominance of formalism, one is tempted to paraphrase Kant: the history of mathematics, lacking the guidance of philosophy, has become blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the of mathematics, has become empty." (Imre Lakatos, "Proofs and Refutations: The Logic of Mathematical Discovery", 1976)
"On the face of it there should be no disagreement about mathematical proof. Everybody looks enviously at the alleged unanimity of mathematicians; but in fact there is a considerable amount of controversy in mathematics. Pure mathematicians disown the proofs of applied mathematicians, while logicians in turn disavow those of pure mathematicians. Logicists disdain the proofs of formalists and some intuitionists dismiss with contempt the proofs of logicists and formalists." (Imre Lakatos,"Mathematics, Science and Epistemology" Vol. 2, 1978)
"Mathematics has been trivialized, derived from indubitable, trivial axioms in which only absolutely clear trivial terms figure, and from which truth pours down in clear channels." (Imre Lakatos, "Mathematics, Science and Epistemology", 1980)
"Philosophy of science without history of science is empty;
history of science without philosophy of science is blind."
"There is no falsification before the emergence of a better theory." (Imre Lakatos, "The Methodology of Scientific Research Programmes" Vol. 1, 1980)
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