Conclusion-Invariant Argumentation and Perceived Redundancy: A Comparative Model of Inferential Progress in Philosophy, Mathematics, and the Sciences

Source abstract

Why can philosophical argumentation appear unusually repetitive even when its literature becomes increasingly sophisticated? One underexamined feature is the recurrence of distinct argumentative routes that preserve a central conclusion while changing premises, conceptualizations, standards of evidence, or inferential strategies. This paper calls the pattern conclusion-invariant branching (CIB). It distinguishes CIB from genuine redundancy: different arguments can support the same conclusion while increasing robustness, revealing independent grounds, answering new objections, or improving understanding. The paper argues that a stronger explanation of perceived redundancy must combine three dimensions: conclusion invariance, epistemic or constraint gain, and downstream inferential uptake. The last concerns whether results become stable inputs to later inquiry, rather than remaining local contributions to a recurring dispute. The resulting model distinguishes productive convergence, boundary-refining invariance, compensatory argumentation, and low-gain argumentative recycling. It is compared across philosophy, mathematics, and empirical science without assuming that mathematics and science develop linearly or that philosophy makes no progress. Philosophicalprogress scholarship has extensively examined disagreement, convergence, and competing progress criteria; mathematical-philosophical literature has examined multiple proofs of the same theorem. A targeted literature review did not establish that the specific three-part model proposed here is already a standard theory, but neither does it warrant a claim that the underlying phenomenon has never been discussed. The proposed contribution is therefore a provisional analytic synthesis: to explain why some argumentation feels redundant, track not merely the number or diversity of arguments, but whether conclusion-preserving variation creates new constraints, improves explanatory understanding, and feeds into reusable inferential structures. The paper derives testable hypotheses and outlines a comparative research design.