31.4 Associative spaces
What I find interesting concerning causal sets is that they may be used to model
the general operation of dispositions even in the non-physical spaces. It is not
now necessary that sprinklings be generated over a uniform space-time, so causal
sets could be used to model the networks of causal processes within the spaces for
higher-level operations, spaces which do not have uniform metrics. It could be feasible
to define the partially-ordered sets of events for the operations of mental dispositions
where the space, we have presumed, has some kind of associative metric associated
with types of mental meanings or relations.
To extend causal set theory for this purpose, we will have to generalize the
theory in order that new events can be indeterministically generated since
the existing theory assumes we are already given a full network of events extending
through all space and time. It is in the process of generating new events that the
details of the metric become important. The likelihood of interaction depends on
proximity. Proximity depends on the metric.
More specific investigation of the possible nature of mental spaces is needed.
There has been some work on this by Smythies (1956)
and Smythies (2003), but we should not
assume (as he did) that the mental spaces are in a higher-dimensional manifold that
also includes physical space. To begin with, we have to develop the formulation
of causal sets to allow for non-deterministic causation to produce links, so that
we are able to distinguish the links connecting actual events from those which have
only some propensity of occurring.