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Multiple Realizability
Putnam is known best for his work concerning the philosophy of mind. His most recognized original contributions in that field came with several key papers published in the late 1960s that set the hypothesis of multiple realizability. https://en.wikipedia.org/wiki/Multiple_realizability -
Mathematics
Hilary Putnam made significant contributions to the philosophy of mathematics with the Quine-Putnam "indispensability argument" for mathematical realism. This argument has been considered to be one of the most challenging arguments in the acceptance of the existence of abstract mathematics. He contributed to Hilbert's tenth problem in mathematics when it was solved with proof that relied heavily on research by Putnam. https://en.wikipedia.org/wiki/Hilary_Putnam#Philosophy_of_mind -
Philosophy of Language
Putnam's biggest contribution to the philosophy of language is that meaning isn't something that is just in your head. His meaning is that even though a word means something to you doesn't mean it has the same meaning to someone else. This is explained in his famous "Twin Earth" thought experiment. He also specifies that there is a finate sequence of elements for the description of meaning of every term in the language. https://en.wikipedia.org/wiki/Hilary_Putnam#Philosophy_of_mind -
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Metaphilosophy and Ontology
In the late 70s and into the 80s Putnam abandoned his defence of metaphysical realism and adopted another view called "internal realism." This change in view is due to mathematical logic and some ideas from Quine. Internal realism is the view that the structure of the world is a function of the human mind. https://en.wikipedia.org/wiki/Hilary_Putnam#Philosophy_of_mind