Abstract
Fuzzy membership and the standard Zadeh truth-value operations are usually introduced as mathematical primitives. This paper derives their full truth-value algebra from native physical contents supplied independently by five theories: Newtonian mechanics, Schrödinger quantum mechanics, perturbative string theory, the M2/M5 brane sectors of M-theory, and general relativity. The corresponding contents are Liouville volume, Born density, perturbative S-matrix channel content |Mα|2dΦα obtained from unitarity and Cutkosky cuts, the positive geometric/tension density derived from the M2/M5 worldvolume actions, and relativistic proper volume. Normalization gives values in [0,1] and physical complementation gives 1−μ. An exact characterization proves that the Zadeh minimum and maximum identities hold for a pair of physical properties if and only if the pair is comparable modulo a content-null set; strict positivity reduces this to ordinary nesting. The physical integral contents are nonatomic and divisible, so a nested physical chain can be constructed whose normalized contents realize every u ∈ [0,1]. Hence min, max, and 1−u close on the physically realized truth values, giving the full Zadeh algebra ([0,1],min,max,1−·) at the truth-value level. A common localization theorem, with the common carrier and Boolean domain made explicit, recovers Boolean indicators under concentration away from the property boundary.