Cosmology is discussed in a historical and philosophical context from the conceptual framework of Newton vis-A-vis Einstein's approach to cosmology in general relativity. It is argued that there is a contradiction within the Newtonian approach when it is based on all three of his laws of motion, as well as bis law of universal gravitation. For Newton's third law of motion, implying a closed system at the outset, is seen to be an important precursor for Einstein's theory of general relativity in the problem of cosmology. Important conceptual differences are Newton's ''action-at-a-distance '' concept and atomism, as well as the feature that gravitational forces can only be attractive. These are contrasted with Einstein's full use of the continuous field concept and holism, wherein forces propagate at a finite speed between the matter components of a closed system and generally entail both attractive and repulsive forces. The essay concludes with a discussion of the contemporary inflationary universe cosmology in the contexts of these competing cosmological approaches.