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By Michael Atiyah

Professor Atiyah is among the maximum dwelling mathematicians and is celebrated during the mathematical global. he's a recipient of the Fields Medal, the mathematical similar of the Nobel Prize, and continues to be on the height of his profession. His large variety of released papers, concentrating on the components of algebraic geometry and topology, have the following been gathered into six volumes, divided thematically for simple reference via contributors drawn to a selected topic. Volumes III and IV disguise papers written in 1963-84 and are the results of an extended collaboration with I. M. Singer at the Index idea of elliptic operators

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I am grateful to all three for financial support and to collaborators on them for intellectual support. I am also grateful to Eileen Munro for help with the child welfare example and to Adam Spray and Ravit Alfandari for help in editing. Evidence, External Validity, and Explanatory Relevance 27 REFERENCES Achinstein, P. 2004. A Challenge to Positive Relevance Theorists: Reply to Roush. Philosophy of Science 71 (4): 521–24. ——— . 2001. The Book of Evidence. New York: Oxford University Press. ——— .

1999. Development as Freedom. New York: Knopf. ——— . 1985. Commodities and Capabilities. Oxford: Oxford University Press. White, H. 2009. Theory-Based Impact Evaluation: Principles and Practice. New Delhi: The International Initiative for Impact Evaluation. NOTES 1. The ideas of Peter Achinstein I draw on here are primarily from Achinstein 2001; 1983. But of course I also draw from his long series of works over three decades from Achinstein 1978 onwards. 2. For Achinstein’s views on why purely probabilistic characterizations of evidence do not work, see, inter alia, Achinstein 2004, 1996, 1981a.

At the methodological and meta-methodological level, scientific realism requires an adequate empirical basis, or pool of instances of scientific practice. Here is where the historical record plays the key role in Achinstein’s approach. I call this position methodological historicism. It requires a philosophical understanding of scientific concepts, restricted to the application of abstract definitions to actual historical scientific 29 30 Philosophy of Science Matters cases. This application is constrained by the scientists’ explicit beliefs and conceptions.

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