Peter,
I am always astonished about what researchers call fundamental. They usually take a rather complicated subject that bases its structure and behavior on other much deeper concepts. A fundament must be very simple and easily comprehensible. In mathematics, a set is a very fundamental concept but mathematics contains a complete theory about this simple concept. In physics, anything that must be expressed or measured in numbers is already a high-level concept. Thus time and space are certainly no fundamental concepts. Anything that is observable is necessarily a high-level concept. In contrast, a relation can be fundamental and a relational structure can be a well-defined construct. Again mathematics defines a complete theory around lattices, which are relational structures. Classical logic is a special kind of lattice. About 25 axioms define classical logic and make it a self-consistent theory. This might be the argument that caused Birkhoff and von Neumann to name their discovery that the set of closed subspaces of a separable Hilbert space is a particular lattice, to call that lattice quantum logic. They hoped to have discovered a self-consistent theory. And that it IS. Mathematicians call it an orthomodular lattice. At that time nobody interpreted the discovery as a seed from which much more can be derived, such as a plant evolves from a seed. However, the orthomodular lattice is a true fundament of a huge and very powerful theory.
The orthomodular lattice contains no numbers and no fields. It only contains relations and it defines precisely, which relations are tolerated. That is also what classical logic does.
So, the orthomodular lattice is not ridiculous simple. It is just simple enough to be able to figure as a foundation of physical reality.
Hans