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Abstract
The sorites paradox (interpreted as the paradox of small natural numbers) is analyzed using mathematical fuzzy logic. In the first part, we present an extension of BL-fuzzy logic by a new unary connective At of almost true and the crisp Peano arithmetic extended by a fuzzy predicate of feasibility. Then we give examples of possible semantics of At and examples of semantics of feasible numbers. In the second part, we present an analysis of the sorites paradox within fuzzy logic with evaluated syntax and show that under a very natural assumption we obtain a consistent fuzzy theory. Thus, sorites is not paradoxical at all.
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