#3798. Qualitative versus quantitative representation: a non-standard analysis of the sorites paradox

October 2026publication date
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Linguistics and Language;
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Abstract:
This paper presents an analysis of the sorites paradox for collective nouns and gradable adjectives within the framework of classical logic. The paradox is explained by distinguishing between qualitative and quantitative representations. By using a non-standard model of R called the hyper real numbers, which contains infinite and infinitesimal numbers, the two paradoxes are shown to have distinct structures. Each paradox can be traced to a different source of vagueness.
Keywords:
Collective nouns; Gradable adjectives; Hyperreals; Infinite numbers; Infinitesimals; Non-Archimedean models; Non-standard models; Sorites paradox; Vagueness

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