Emergence as Phase Transition: A Unified Framework from Philosophical Redefinition to Biological Self-Organization

The concept of "emergence" has become pervasive across philosophy, complex systems theory, and biology, yet
suffers from fundamental definitional ambiguity. Chalmers' influential distinction between "weak" and "strong"
emergence fails to provide operational criteria: weak emergence conflates computational intractability with
ontological novelty, while strong emergence lacks empirical instantiation. This paper proposes a radical
redefinition grounded in physics: emergence is the appearance of a non-zero order parameter following
symmetry-breaking phase transition at a critical point. Using the Landau-Ginzburg-Stuart framework as the
canonical form, we demonstrate that this definition provides measurable critical conditions, identifiable order
parameters, and traceable dynamics. Following Anderson's "More is Different" (1972) and Batterman's asymptotic
analysis (2002), we show that genuine novelty arises through symmetry breaking without violating physical
closure. Butterfield's "emergence before the limit" (2011) addresses finite-size concerns. This unified framework
rescues "emergence" from buzzword status and establishes it as a rigorous scientific concept with predictive power.
Biological and social applications are developed in companion papers.