Central gap domain restriction

Ordinary intuitions that vague predicates are tolerant, or cannot have sharp boundaries, can be formalized in first-order logic in at least two non-equivalent ways, a stronger and a weaker. The stronger turns out to be false in domains that have a significant central gap for the predicate in question, i.e. where a sufficiently large middle segment of the ordering relation (such as taller for ‘tall’) is uninstantiated. The weaker principle is true in such domains, but does not in those domains induce the sorites conclusion.
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