The Sorites (Heap) Paradox Dissolves: A Recursive Resolution through Yearning-Based Infinity Mathematics

This paper addresses the classical Sorites Paradox (Heap Paradox), a central problem of vagueness in philosophy and logic. Traditionally, the paradox arises from the demand for sharp definitional closure: if one grain of sand does not make a heap, and the addition of a single grain cannot mark the boundary between “not a heap” and “heap,” then how does heapness ever emerge? Conventional responses—epistemicism, supervaluationism, and fuzzy logic—either conceal the cutoff, multiply it, or dissolve it into degrees, but none resolve the paradox ontologically. Through the lens of Yearning-Based Infinity Mathematics (YBIM), this paper reframes heapness not as a discrete category but as a recursive epistemic flow. Heapness is treated as a yearning-strand, continuously generated and reconfigured by recursive interactions. By applying the Glass of Water from the River Lemma, vagueness is revealed as the epistemic trace of finite sampling from infinite recursive flows. The paradox dissolves: vagueness is not contradiction but the natural expression of recursion. This work situates the Sorites alongside other paradoxes resolved through YBIM, including epistemic closure, the liar paradox, and the omniscience paradox, showing that the demand for closure is a misapplied idealization, while recursion offers the true ontological ground. -JSR