This paper proposes a new foundational framework for the field of Structural Health Monitoring (SHM). Towards that end, the axioms of SHM presented by Worden et al. (2007) are critically examined. Through logical analysis and targeted counter-examples, several of the original axioms are shown to be ambiguous, redundant, or logically derivable from others. A particularly contested assumption in Worden et al. (2007) is the necessity of a baseline (undamaged) state for damage diagnosis, with that work concluding that such a baseline is required. This paper demonstrates that damage can be inferred directly from the damaged state, without requiring a baseline state. Accordingly, this paper formalizes the alternative viewpoint, enabling the SHM community to make a more informed judgment. Based on the analysis presented here, it is proposed to replace the seven axioms of Worden et al. (2007) with a set of three new axioms. The revised axioms are characterized by conceptual clarity, parsimony, logical independence, and generative capacity, and are therefore framed to expand, rather than constrain, the scope of SHM.