QGD / MPDT and Poincaré–Weyl Predicativism: Independent Convergence, and Why Physical Grounding Reaches Further

Abstract

Physical constructivism — the position that a mathematical object exists only when a physical process has completed its construction, that notation for a never-terminating process is a prescription rather than a name, and that the set of existing numbers is bounded by the physical resources available to construct them (P12; P16) — was derived from Quantum-Geometry Dynamics' two axioms, independently of the philosophical literature on constructive mathematics. This paper identifies a specific, previously uncited convergence between that position and two historical figures in the philosophy of mathematics: Henri Poincaré, who argued that “there is no actual infinity” and restricted legitimate mathematical definitions to predicative ones on pain of paradox, and Hermann Weyl, whose 1918 Das Kontinuum built the real numbers from predicatively definable sequences rather than presupposing them as elements of an already-completed continuum. The convergence is real and specific: both traditions reject completed infinite totalities, and both treat notation for an infinite object as describing a generative process rather than naming a pre-existing one. The convergence is also independently arrived at — physical constructivism was developed from Quantum-Geometry Dynamics' own axioms between 2010 and 2016, without knowledge of Poincaré's, Weyl's, or any other mathematician's work on this question; Mathematics as a Subset of Physics (P12), the portfolio paper that first states the position formally, addresses it to Eugene Wigner's 1960 puzzle about the effectiveness of mathematics as an expository frame, not as the position's source. This paper argues that the convergence, precisely because it is independent, is evidence for the position rather than a debt to it, and that the two traditions diverge in a way that matters: Poincaré and Weyl's predicativism is an epistemological constraint on legitimate definitions, motivated by the avoidance of paradox, with no physical content and no upper bound on how far a permitted construction may run. QGD's physical constructivism is a physical constraint, grounded in a determinate finite bound (P40's N̂, the total preon(−) count) derived from Axioms 1–2, and it is this physical grounding — not the shared rejection of completed infinities — that lets it dissolve problems predicativism was never positioned to address: ultraviolet divergences, the cosmological constant problem, and the singularities of general relativity (P12 §4; P28 §4; P36 §6; P42).