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.