Quantification Theory in *8 ofPrincipia Mathematicaand the Empty Domain

History and Philosophy of Logic 26 (1):47-59 (2005)
The second printing of Principia Mathematica in 1925 offered Russell an occasion to assess some criticisms of the Principia and make some suggestions for possible improvements. In Appendix A, Russell offered *8 as a new quantification theory to replace *9 of the original text. As Russell explained in the new introduction to the second edition, the system of *8 sets out quantification theory without free variables. Unfortunately, the system has not been well understood. This paper shows that Russell successfully antedates Quine's system of quantification theory without free variables. It is shown as well, that as with Quine's system, a slight modification yields a quantification theory inclusive of the empty domain.
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DOI 10.1080/0144534042000271148
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W. V. Quine (1951). Mathematical Logic. Cambridge, Harvard University Press.

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