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The Davis-Putnam Algorithm Theory was developed by Martin Davis and Hilary Putnam, this was a propositional formula utilized to check the accuracy of first order logic. Dechter, R., & Rish, I. (1994). Directional resolution : the Davis-Putnam procedure, revisited. UC Irvine: Donald Bren School of Information and Computer Sciences. Retrieved from https://escholarship.org/uc/item/3fv0g5hg
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This was the first piece released by Putnam, where he believed and argued that Mathematics is not entirely based on logic. This argument was called the Quine–Putnam indispensability argument. Putnam, H. (1964). Benacerraf, Paul (ed.). Philosophy of Mathematics: Selected Readings. Englewood Cliffs, N.J.: Prentice-Hall. OCLC 1277244158. 2nd ed., Cambridge: Cambridge University Press, 1983. ISBN 0-521-29648-X
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Philosophy of Logic was published at this time, this publishing was entitling the presence of mathematics and logic existing in Philosophy. Putnam, H. (1971). Philosophy of Logic. New York: Harper & Row. ISBN 0-04-160009-6.
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During this time "The Many Faces of Realism" was published, This was Putnam's introduction to realism as it makes a connection to his ideas of cultural relativity. Putnam, H. (1987). The Many Faces of Realism. La Salle, Ill.: Open Court. ISBN 0-8126-9043-5.
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Hilary Putnam released book "Philosophy in an Age of Science", where he bridges together why Philosophy helps to contribute to the understandings of the world. Putnam, H. (2012). De Caro, M.; Macarthur, D. (eds.). Philosophy in an Age of Science. Cambridge, Massachusetts: Harvard University Press. ISBN 978-0-674-05013-6. OCLC 913024858.