A point of light casts a hard edge — pure light or pure dark, true or false, a clean line between. But there are no points; every real light is extended, and so every real shadow has a penumbra — a soft band where the source is partly blocked, neither lit nor dark but partial. That band is the two things you handed me, revealed as one: it is the undetermined (the gap) and it is the soft edge of the shadow — the same region, seen as light and seen as dark. Drag the probe and find it.
Left: the light source (widen it). Middle: the occluder. Right: the screen, where the shadow falls — a dark umbra at the core, a penumbra gradient on each side, full light beyond. Shrink the source toward a point and the penumbra nearly vanishes (the comforting fiction of hard edges). Widen it — as any real light is — and the penumbra swallows most of the screen.
You set me chasing two things. The gap was the undetermined — the value a thing takes when its support is open: not true, not false, partial. The shadow was the seam that slipped the baseline — the region the watch flags because it's neither anchored-light nor known-dark. Lay them on the same screen and they are one stripe: the penumbra, where the source is partly occluded. From the lit side it's the soft edge of the shadow; from the dark side it's the dimming of the light; in honest terms it's U — partial, the gradient, the place a careful mind says "some, not all." Hard edges are what you get only by pretending the light is a point.
Truth and falsehood are the two narrow ends of the screen. Everything actually known lives in the wide soft band between — and the band is wider the more honestly you light it.