Natural set theory and natural logic
The hypothesis is proposed that humans have a natural way of dealing with plural objects (‘sets’), from which, apart from other features, the null set and the universe of all objects are absent. An elaboration of this theory, together with the assumption that natural ontology is defined in terms of entities, sets of entities, and properties as a separate category, leads to the formulation of a default basic‐natural predicate logic (BNPC), reflecting native logical intuitions without any extra pragmatic (Gricean) assumptions. This logic closely resembles the predicate logic proposed by William Hamilton around 1850. In this logic, no is not equivalent with not some, which explains the apparent lexical gap * nall, and analogously for * nand.
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