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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, by the logic of proofs and refutations.

Imre Lakatos

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Imre Lakatos
Age: 51 †
Born: 1922
Born: November 9
Died: 1974
Died: February 2
Mathematician
Philosopher
Physicist
University Teacher
Imre Lipschitz
Lakatos Imre
Imre Lakatos
Criticism
Monotonous
Increase
Incessant
Number
Speculation
Indubitably
Grow
Established
Guesses
Numbers
Improvement
Grows
Proof
Refutation
Doe
Logic
Proofs
Mathematics
Theorems

More quotes by Imre Lakatos

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The classical example of a successful research programme is Newton's gravitational theory: possibly the most successful research programme ever.
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It is not that we propose a theory and Nature may shout NO rather, we propose a maze of theories, and Nature may shout INCONSISTENT.
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The positive heuristic of the programme saves the scientist from becoming confused by the ocean of anomalies.
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It would be wrong to assume that one must stay with a research programme until it has exhausted all its heuristic power, that one must not introduce a rival programme before everybody agrees that the point of degeneration has probably been reached.
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If even in science there is no a way of judging a theory but by assessing the number, faith and vocal energy of its supporters, then this must be even more so in the social sciences: truth lies in power.
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Indeed, this epistemological theory of the relation between theory and experiment differs sharply from the epistemological theory of naive falsificationism.
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In degenerating programmes, however, theories are fabricated only in order to accommodate known facts
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Philosophy of science without history of science is empty history of science without philosophy of science is blind.
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The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.
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The proving power of the intellect or the senses was questioned by the skeptics more than two thousand years ago but they were browbeaten into confusion by the glory of Newtonian physics.
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Belief may be a regrettably unavoidable biological weakness to be kept under the control of criticism: but commitment is for Popper an outright crime.
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There is no falsification before the emergence of a better theory.
Imre Lakatos
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Blind commitment to a theory is not an intellectual virtue: it is an intellectual crime.
Imre Lakatos
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Intellectual honesty consists in stating the precise conditions under which one will give up one's belief.
Imre Lakatos
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The great scientific achievements are research programmes which can be evaluated in terms of progressive and degenerative problemshifts and scientific revolutions consist of one research programme superceding (overtaking in progress) another. This methodology offers a new rational reconstruction of science.
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Man's respect for knowledge is one of his most peculiar characteristics. Knowledge in Latin is scientia, and science came to be the name of the most respectable kind of knowledge.
Imre Lakatos