The Reflexive Collapse of Subjective Proof: Formalising the Infinite Recursive Paradox of Subjective Proof Systems

This sequel paper extends and deepens the results of Volume I, “The Mathematics of Why Proof Is Subjective, and Therefore Means Nothing.” Volume I established that proof is not an objective detector of truth, but a conditional performance inside subjective axiomatic, semantic, and interpretive frameworks. Volume II formalises the recursive consequences of that claim. If proof is subjective, then the proof used to demonstrate subjectivity is itself subjective. This destabilises the original argument, which in turn re‑validates it, which destabilises it again, and so on. The result is an infinite regress structure in which the truth‑value of the original proof oscillates indefinitely. This paper introduces several new Carlo‑class constructs:- The Recursive Subjectivity Operator - The Infinite Regress Engine - The Truth‑Limbo State (TLS) - The Carlo Collapse Ladder - The Epistemic Suspension Limit (ESL) These tools allow us to formalise the reflexive collapse generated when a proof attempts to prove its own subjectivity. The sequel demonstrates that Volume I cannot escape the consequences of its own argument: its proof is subjective; therefore its conclusion is subjective; therefore its validity oscillates indefinitely. The collapse is not a flaw. It is the only stable structure available to systems that attempt to prove their own subjectivity. Together, Volume I and Volume II form a complete Carlo‑class reflexive system. FEATURED EQUATIONS: Recursive Subjectivity Operator: \[R(P) = “The proof of P is subjective.”\] Iterated recursion: \[Rⁿ(P) = R(Rⁿ⁻¹(P))\] Truth‑value oscillation model: \[Tₙ(P) ={cases}True, & n even \, & n odd{cases}\] Epistemic Suspension Limit: \[ESL = limn → ∞ Tₙ(P)\] This limit does not exist, demonstrating that the truth‑value of Volume I is suspended in an infinite recursive loop. This work concerns subjective proof, recursive paradoxes, infinite regress structures, truth‑limbo states, epistemic suspension, reflexive instability, axiomatic subjectivity, semantic drift, interpretation entropy, model divergence, Gödel echo propagation, meta‑proof collapse, cultural variability in mathematical reasoning, the Carlo collapse ladder, foundations of logic, mathematical epistemology, and the philosophy of formal systems. Contact: For enquiries or research questions related to this work, email matthewcarlo.research@gmail.com