Early Russell on Types and Plurals
AbstractIn 1903, in The Principles of Mathematics (PoM), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was shortlived— rejected before PoM even appeared in print. However, aside from mentions of a few misgivings, there is little evidence about why he abandoned this view. In this paper, I attempt to clarify Russell’s early views about plurality, arguing that they did not involve countenancing special kinds of plural things distinct from individuals. I also clarify what his misgivings about these views were, making it clear that while the plural understanding of classes helped solve certain forms of Russell’s paradox, certain other Cantorian paradoxes remained. Finally, I aim to show that Russell’s abandonment of something like plural logic is understandable given his own conception of logic and philosophical aims when compared to the views and approaches taken by contemporary advocates of plural logic.
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