1) Mathematical formalisms are effective because they specify geometric spaces or matrices of relations that are isomorphic to the relations between phenomena as distinguished by observers in their domain of structural coupling. 2) As structure-determined systems, observers can only operate based on the coherences that arise from their history of structural coupling and living. They do not have access to any independent reality. 3) Natural phenomena are abstractions that observers generate through their linguistic operations in realizing their living, not characterizations of independent features of reality. Mathematical formalisms apply to these observer-generated coherences, not an external reality.