Through an exploration of theoretical physics, this paper suggests the need for regrounding natural science in phenomenological philosophy. To begin, the philosophical roots of the prevailing scientific paradigm are traced to the thinking of Plato, Descartes, and Newton. The crisis in modern science is then investigated, tracking developments in physics, science's premier discipline. Einsteinian special relativity is interpreted as a response to the threat of discontinuity implied by the Michelson-Morley experiment, a challenge to classical objectivism that Einstein sought to counteract. (...) We see that Einstein's efforts to banish discontinuity ultimately fall into the “black hole” predicted in his general theory of relativity. The unavoidable discontinuity that haunts Einstein's theory is also central to quantum mechanics. Here too the attempt has been made to manage discontinuity, only to have this strategy thwarted in the end by the intractable problem of quantum gravity. The irrepressible discontinuity manifested in the phenomena of modern physics proves to be linked to a merging of subject and object that flies in the face of Cartesian philosophy. To accommodate these radically non-classical phenomena, a new philosophical foundation is called for: phenomenology. Phenomenological philosophy is elaborated through Merleau-Ponty's concept of depth and is then brought into focus for use in theoretical physics via qualitative work with topology and hypercomplex numbers. In the final part of this paper, a detailed summary is offered of the specific application of topological phenomenology to quantum gravity that was systematically articulated in The Self-Evolving Cosmos (Rosen 2008a). (shrink)