An observer-based approach to the sorites paradox and the logic derived from that

TL;DR

This paper introduces fluxing-object semantics (FOS), a three-valued logic derived from an observer-based, time-dependent approach to the sorites paradox, emphasizing the role of partial functions and perceptual gaps in resolving the paradox.

Contribution

It develops a novel semantics called fluxing-object semantics (FOS) that models vague assertions with time-dependent, fluxing entities, connecting the paradox resolution to three-valued logic and perceptual gaps.

Findings

FOS is equivalent to strong Kleene three-valued logic.

Partial functions and observer interruptions explain the sorites paradox resolution.

Watching gaps correspond to physiological and perceptual phenomena.

Abstract

We approach the sorites paradox (SP) through an observer-based and time-dependent approach to truth of vague assertions. Formally the approach gives rise to a semantics, called fluxing-object semantics (FOS), because it involves models that contain ``fluxing objects'', that is, entities changing with time and observer. The models are equipped with agents (observers) and a linear and discrete time axis for time. The changing entities are represented by partial functions of time and agent, and this partiality causes truth-value gaps. If we interpret a truth-value gap as a third truth value, then FOS becomes a three-valued logic, which, quite interestingly, is proved identical to strong Kleene three-valued logic. The sorites phenomena can be represented in a structure of FOS as special objects that change imperceptibly with respect to an observer and with respect to a particular attribute. In this account the key point that eliminates the paradoxical character of sorites is the partiality of functions. When the observer is fixed the partiality corresponds to interrupted watching on his part. The interruption creates watching gaps during which the attributed property of the object as understood by the observer may change, without violating the imperceptibility condition. Interrupted watching has, according to experts on visual attention and focusing capabilities of humans, a firm physiological justification. The relationship of watching gaps with horizon crossing is also discussed.