Wang Xinhua

In what sense can a body of knowledge continue after its language, tools, and even its proof environment have changed? I previously answered this question by distinguishing a theory’s core from its periphery and treating theoretical continuity as the preservation of core commitments amid peripheral revision. This article revises that account. Structural centrality can show how much of a present system depends on a given element, while methodological protection can explain why researchers are reluctant to revise certain assumptions. Neither, however, can by itself establish a historical relation between two stages of inquiry. Yet the alternative notion of epistemic uptake is too broad: researchers can cite, translate, and use the results of another tradition without becoming its successors. Rather than offer a single identity criterion for every knowledge tradition, I examine a narrower relation: migration-based epistemic succession. Here an earlier body of work is explicitly made the object of migration, and what is migrated includes results that already possess epistemic standing, not merely files, interfaces, or behavioral outputs. Those results must acquire standing as usable knowledge under a new proof environment and new standards of acceptance. The earlier stage’s role as a completion benchmark is strong evidence for this relation, but it is neither necessary for every kind of epistemic succession nor sufficient to turn an ordinary software compatibility project into one. The migration of mathlib from Lean 3 to Lean 4 makes this relation unusually visible. Lean 4 reimplemented much of the prover’s infrastructure, so old source code, tactics, and metaprograms could not simply be carried over. At the same time, mathport, declaration alignments, porting notes, and status records continued to take mathlib3 as their point of reference. Old theorems could be reproved or absorbed into more general results; interfaces and tactics could be replaced; but mathematical claims still had to regain acceptable proof status in the new environment. On this basis, I distinguish engineering migration, epistemic succession, and epistemic appraisal. Argumentative responsibility is not part of the definition of succession: a live counterexample must be addressed because it still bears on present reasoning, not because historical inheritance creates a new basic epistemic duty.

Set against the backdrop of rapid knowledge iteration and the technological transformation wrought by artificial intelligence, and responding to the epistemological anxiety of contemporary society, this paper explores the dialectical relationship between “change” and “invariance” in the evolution of knowledge systems. It integrates analytic philosophy’s critique of exceptionalism about logic, the sociology of science’s reflection on the Mertonian norms, and the conception of truth in Marxist historical materialism, and it draws on the hard-core/protective-belt structure of Lakatos’s “scientific research programmes” in an attempt to dispel the static, absolutely a priori conception of truth while avoiding the trap of relativism. The study argues that the “invariance” of a theoretical system does not consist in frozen, specific propositions but is manifested as an underlying cognitive disposition, an objective material foundation, and a core value anchor; its auxiliary secondary rules and peripheral norms, by contrast, must absorb empirical shocks and the anomalies of the age through an adaptive “change.” Taking the repair mechanism of Russell’s paradox and the reconstruction of the Mertonian norms in the post-academic era as representative cases, this paper attempts to construct an evolutionary model of “revising secondary rules so as to maintain core identity,” and offers a preliminary response to the theoretical difficulty of “how to distinguish the core from the periphery.” The model helps to establish, in a world of uncertainty, a theoretical identity that is at once flexible and stable.