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Lesniewski and Ontological Commitment

In Denis Miéville & D. Vernant (eds.), Stanislaw Lesniewski Aujourd'hui. Université De Grenoble. pp. 103-119 (1995)

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  1. Plural Quantifiers: A Modal Interpretation.Rafal Urbaniak - 2014 - Synthese 191 (7):1-22.
    One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that (...)
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  • Lesniewski and Russell's Paradox: Some Problems.Rafal Urbaniak - 2008 - History and Philosophy of Logic 29 (2):115-146.
    Sobocinski in his paper on Leśniewski's solution to Russell's paradox (1949b) argued that Leśniewski has succeeded in explaining it away. The general strategy of this alleged explanation is presented. The key element of this attempt is the distinction between the collective (mereological) and the distributive (set-theoretic) understanding of the set. The mereological part of the solution, although correct, is likely to fall short of providing foundations of mathematics. I argue that the remaining part of the solution which suggests a specific (...)
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