Quantification Theory in *9 of Principia Mathematica

History and Philosophy of Logic 21 (1):57-77 (2000)
Abstract
This paper examines the quantification theory of *9 of Principia Mathematica. The focus of the discussion is not the philosophical role that section *9 plays in Principia's full ramified type-theory. Rather, the paper assesses the system of *9 as a quantificational theory for the ordinary predicate calculus. The quantifier-free part of the system of *9 is examined and some misunderstandings of it are corrected. A flaw in the system of *9 is discovered, but it is shown that with a minor repair the system is semantically complete. Finally, the system is contrasted with the system of *8 of Principia's second edition
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References found in this work BETA
W. V. Quine (1951). Mathematical Logic. Cambridge, Harvard University Press.
W. V. Quine (1954). Quantification and the Empty Domain. Journal of Symbolic Logic 19 (3):177-179.
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