base, basis, bedrock, bottom, cornerstone, footing, foundation, ground, keystone, root, underpinning, warp, warp and woof

anchorage, bed, brace, bulwark, buttress, framework, infrastructure, mount, prop, shore, stay, substratum, substructure, supportassumption, justification, premise(also premiss), presumption, presupposition, rationale, supposition, theory, thesis, warrantbackbone, center, core, eye, focus, heart, hub, kernel, nucleus, seatessence, quintessence, soul, touchstone