  The problem of understanding quantum mechanics is in large measure the
problem of finding appropriate ways of thinking about the spatial and temporal
aspects of the physical world. The standard, substantival, set-theoretic
conception of space is inconsistent with quantum mechanics, and so is the
doctrine of local realism, the principle of local causality, and the
mathematical physicist's golden calf, determinism. The said problem is made
intractable by our obtruding onto the physical world a theoretical framework
that is more detailed than the physical world. This framework portraits space
and time as infinitely and intrinsically differentiated, whereas the physical
world is only finitely differentiated spacewise and timewise, namely to the
extent that spatiotemporal relations and distinctions are warranted by facts.
This has the following consequences: (i) The contingent properties of the
physical world, including the times at which they are possessed, are indefinite
and extrinsic. (ii) We cannot think of reality as being built "from the bottom
up", out of locally instantiated physical properties. Instead we must conceive
of the physical world as being built "from the top down": By entering into a
multitude of spatial relations with itself, "existence itself" takes on both
the aspect of a spatially differentiated world and the aspect of a multiplicity
of formless relata, the fundamental particles. At the root of our
interpretational difficulties is the "cookie cutter paradigm", according to
which the world's synchronic multiplicity is founded on the introduction of
surfaces that carve up space in the manner of three-dimensional cookie cutters.
The neurophysiological underpinnings of this insidious notion are discussed.
