Where Fundamental Physics Ends: Distinguishability, Necessity, and the Boundary of Explanation

How far must a fundamental physical theory explain its own foundations before it can reasonably be regarded as complete? The demand for deeper explanation appears initially straightforward: if a theory contains an unexplained equation, primitive, law, or constant, ask why it has that form. Yet the procedure has no obvious terminating point. Even a theory reduced to a single relation such as (x = a^2) permits the question: why (x = a^2) rather than another relation? A deeper principle explaining the equation itself immediately permits the corresponding question about that principle. This paper argues that immunity to further "why" questions is therefore an inappropriate completion criterion for fundamental physics. Any describable structure possesses enough distinction to support additional questions concerning why it has that description. The Central Proposal We propose instead that the scientific boundary should be defined through physical distinguishability. A deeper explanatory layer belongs to physics when alternatives at that layer produce distinguishable physical consequences. When hypothesized alternatives become observationally and dynamically indistinguishable from within the physical system, further discrimination is no longer demanded by the physical theory, even though metaphysical questions may remain meaningful. A black-box analogy formalizes the distinction. An observer confined to a box may infer properties of passing vehicles from acoustic signals. If vehicle velocity changes the signal, velocity is in principle identifiable. If vehicle color produces no difference whatsoever in the available signal, color cannot be recovered by improving the acoustic theory. The limitation is informational rather than computational. The Stopping Principle This leads to a proposed stopping principle: Fundamental physics ends not when further questions become impossible, but when further answers cease to make a physically distinguishable difference. Distinction as an Ontological Floor We further argue that physical description itself presupposes distinction. A completely non-distinguished "thing" possesses no property, relation, state, boundary, number, or change through which it could enter a physical description. This motivates distinguishability as a possible ontological floor without claiming a solution to the metaphysical question of why existence exists. Application to the Canvas Model Applied to the Canvas Model, this perspective suggests that the Eight Primitives need not explain why anything exists. Their appropriate scientific role is instead to constitute, if successful and irreducible, a minimal set of physically meaningful distinctions sufficient to generate observable physics. What This Paper Provides · A rigorous argument that the infinite regress of explanation cannot be terminated by finding a proposition about which no further "why" question can be asked· A formal distinction between physical necessity and metaphysical necessity· A proposed stopping principle based on physical distinguishability· The concept of identifiability: does the observable universe uniquely determine its generating basis?· A hierarchy of theoretical depth: Description → Unification → Generation → Necessity → Identifiability· A black-box observer thought experiment that illustrates why some questions are physically inaccessible· Application to the Canvas Model's Eight Primitives, suggesting they need not explain existence itself Keywords: distinguishability, identifiability, physical necessity, metaphysical necessity, Canvas Model, primitives, black-box observer, infinite regress, boundary of explanation, theory of everything