I would actually suggest that Hobbes' fundamental claim (the root assumption from which his larger thought extends) is that human nature is, at its core, materialistic. Indeed, when reading Leviathan, note that it does not begin with political theory or discussions on the State of Nature, rather it begins with an explanation for how individual human beings think and operate. Note, for example, the following passage, taken from the book's first chapter:
"4. The cause of sense, is the external body, or object, which preseth the organ proper to each sense, either immediately, as in the taste and touch; or mediately, as in seeing, hearing and smelling: which pressure, by the mediation of the nerves, and other strings, and membranes of the body, continued inwards to the brain and heart, causeth there a resistance, or counter-pressure, or endeavour of the heart, to deliver itself." (Hobbes, Leviathan, ed. J. C. A. Glaskin, Oxford University Press: New York, 1996, p. 1)
When taken as a whole, Hobbes emerges as a materialist, who envisions human beings in terms of being a kind of biological machine, in stark contrast to traditional Christian views on the soul, or to Cartesian dualism. This is one of the aspects of Hobbes' thought which made him so controversial in his own time (even among the Absolutists, who tended to adhere to Divine Right Theory), and it serves as the foundation on which so much of his thought tends to rest.