Quantification Theory in *9 of Principia Mathematica

History and Philosophy of Logic 21 (1):57-77 (2000)
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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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Gregory Landini
University of Iowa

Citations of this work

Russell: Logic.Gregory Landini - 2018 - Internet Encyclopedia of Philosophy.

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References found in this work

Introduction to mathematical philosophy.Bertrand Russell - 1919 - New York: Dover Publications.
Mathematical logic.Willard Van Orman Quine - 1951 - Cambridge,: Harvard University Press.
Introduction to Mathematical Philosophy.Bertrand Russell - 1919 - Revue Philosophique de la France Et de l'Etranger 89:465-466.
Principia mathematica.A. N. Whitehead - 1926 - Mind 35 (137):130.
Principia mathematica.Alfred North Whitehead & Bertrand Russell - 1910 - Cambridge,: University Press. Edited by Bertrand Russell.

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