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Logic in Whitehead’s universal algebra. (English) Zbl 1261.03008

Summary: In his [A treatise on universal algebra. Cambridge: The University Press; New York: The Macmillan (1898; JFM 29.0066.03); Reprint of the 1898 original. Cambridge: Cambridge University Press (2009; Zbl 1205.15005)], A. N. Whitehead intended to investigate all systems of symbolic reasoning related to ordinary algebra on the basis of the algebras of Grassmann and Hamilton, and on the basis of Boole’s symbolic logic. We consider Whitehead’s version of the algebra of symbolic logic presented there. Later on, in his last contribution to logic, he came back to questions and problems related to Principia Mathematica. This was the occasion for restating some of his positions on logic.

MSC:

03-03 History of mathematical logic and foundations
03G05 Logical aspects of Boolean algebras
03G25 Other algebras related to logic
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