We present the axiomatic foundation of the Second Law of Information, deriving it from first principles without physical analogies. The law states that a classification problem is learnable if and only if there exists a representation ϕ where ρϕ < 1. We establish two fundamental thresholds: the universal mathematical threshold ρ = 1 (where local structure equals random), and the physical death threshold ρdeath ≈ 1.23 (derived from Ising 3D critical exponents).