  This chapter is offered as a contribution to the logic of down below. We
attempt to demonstrate that the nature of human agency necessitates that there
actually be such a logic. The ensuing sections develop the suggestion that
cognition down below has a structure strikingly similar to the physical
structure of quantum states. In its general form, this is not an idea that
originates with the present authors. It is known that there exist mathematical
models from the cognitive science of cognition down below that have certain
formal similarities to quantum mechanics. We want to take this idea seriously.
We will propose that the subspaces of von Neumann-Birkhoff lattices are too
crisp for modelling requisite cognitive aspects in relation to subsymbolic
logic. Instead, we adopt an approach which relies on projections into
nonorthogonal density states. The projection operator is motivated from cues
which probe human memory.
