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What were C.S Peirce's contributions to theory of relations?

In my study of Peirce I came across a number statements that he extended De Morgan's relation algebra. What exactly are his contributions to relation algebra?
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Was C.S Peirce in his abductive reasoning influenced by the generalization from special cases that is used by mathematicians?

I am reading some random bits from Peirce's collected works and they give me the impression that Peirce tried to integrate every(or nearly every) major scientific and mathematical concept which he was ...
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What did Hans Bethe think of von Neumann's quantum logic?

Nobel laureate Hans Bethe was a friend of mathematician-physicist John von Neumann, and he once said: "I have sometimes wondered whether a brain like von Neumann's does not indicate a species ...
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