Might the world be structured, as Leibniz thought, so that every part of matter is divided ad infinitum? The Physicist David Bohm accepted infinitely decomposable matter, and even Steven Weinberg, a staunch supporter of the idea that science is converging on a final theory, admits the possibility of an endless chain of ever more fundamental theories. However, if there is no fundamental level, physicalism, thought of as the view that everything is determined by fundamental phenomena and that all fundamental phenomena are physical, turns out false, for in such a world, there are no fundamental phenomena, and so fundamental phenomena determine nothing. While some take physicalism necessarily to posit a fundamental level, here I present a thesis of physicalism that allows for its truth even in an infinitely decomposable world.