Principia Mathematica, the Multiple-Relation Theory of Judgment and Molecular Facts

Abstract

In recent years, Gregory Landini and following him Kevin Klement and Graham Stevens have developed interpretations of Principia Mathematica (PM), according to which, despite their talk of ‘the hierarchy of types’ and of ‘the division of objects into types’ (see, for example, PM I: 168/1611), Whitehead and Russell do not there assume any type—theoretic metaphysics. On their interpretations, far from admitting a metaphysics of entities of different logical types, Russell in PM devises a system which enables him to preserve a central tenet of his 1903 book The Principles of Mathematics (POM) - namely, that every entity can function as a logical subject (in a univocal sense of ‘logical subject’) so that any variable occurring in a subject-position is unrestricted in that it may take absolutely any entity whatsoever as its value.KeywordsActual WorldLogical ConstantMolecular FactCorrespondence ProblemPropositional FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.