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what does Lakatos mean when he writes "Philosophy of Science without History of Science is empty, History of Science without Philosophy of Science is blind"?

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First, it might be worth to point out that the dictum was first coined by Norwood Russell Hanson (see his 1962, e.g. p. 580). The maxim is cast after a famous passage in Kant's Critique of Pure Reason:

Thoughts without content are empty, intuitions without concepts are blind. (A51/B75)

Lakatos then used it in his 1971 paper.

Though both Hanson and Lakatos appeal to a necessary interplay between history and philosophy of science, they mean to express the idea from opposite perspectives:

  • Hanson argued that philosophers should use historical evidence as foundation for their analysis, for both heuristic and pragmatic reasons. (That is a basic idea of what we call the 'historical turn' in philosophy of science in the early 1960s.)
  • Lakatos - to answer your question - argued instead that historians cannot write history of science without the aid of a theory of science, i.e. history of science cannot replace philosophy of science, but requires it.

These are the primary papers you can read:

  • Hanson, Norwood Russell. 1962. "The Irrelevance of History of Science to Philosophy of Science." The Journal of Philosophy 59: 574–86.

  • Lakatos, Imre. 1971. "History of Science and Its Rational Reconstructions." In PSA 1970. Boston Studies in the Philosophy of Science, vol. viii, edited by Roger C. Buck and Robert S. Cohen, 91–108. Dordrecht: D. Reidel.

Additionally, I can wholeheartedly recommend this recent volume:

  • Mauskopf, Seymour & Schmaltz, Tad (Eds.). 2012. Integrating History and Philosophy of Science: Problems and Prospects. Boston Studies in the Philosophy and History of Science. Springer.
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Note also that Lakatos had written earlier

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 it back on the most intriguing phenomena in the history of mathematics has become empty. ('Proofs and Refutations (I)', The British Journal for the Philosophy of Science, Vol. 14, No. 53 (May, 1963), pp. 1-25)

He was keen to find a common justificatory pattern between science and mathematics, hence the use of 'quasi-empiricism' for the latter. Philosophy, for him, had made the dual mistake of being inductivist about scientific inference and deductivist about mathematical inference.

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