This paper tackles the task of uncalibrated photometric stereo for 3D object reconstruction, where both the object shape, object reflectance, and lighting directions are unknown. This is an extremely difficult task, and the challenge is further compounded with the existence of the well-known generalized bas-relief (GBR) ambiguity in photometric stereo. Previous methods to resolve this ambiguity either rely on an overly simplified reflectance model, or assume special light distribution. We propose a new method that jointly optimizes object shape, light directions, and light intensities, all under general surfaces and lights assumptions. The specularities are used explicitly to solve uncalibrated photometric stereo via a neural inverse rendering process. We gradually fit specularities from shiny to rough using novel progressive specular bases. Our method leverages a physically based rendering equation by minimizing the reconstruction error on a per-object-basis. Our method demonstrates state-of-the-art accuracy in light estimation and shape recovery on real-world datasets.