  I introduce a new approach to semantic information based upon the influence
of erasure operations (interventions) upon distributions of a system's future
trajectories through its phase space. Semantic (meaningful) information is
distinguished from syntactic information by the property of having some
intrinsic causal power on the future of a given system. As Shannon famously
stated, syntactic information is a simple property of probability distributions
(the elementary Shannon expression), or correlations between two subsystems and
thus does not tell us anything about the meaning of a given message. Kolchinsky
& Wolpert (2018) introduced a powerful framework for computing semantic
information, which employs interventions upon the state of a system (either
initial or dynamic) to erase syntactic information that might influence the
viability of a subsystem (such as an organism in an environment). In this work
I adapt this framework such that rather than using the viability of a
subsystem, we simply observe the changes in future trajectories through a
system's phase space as a result of informational interventions (erasures or
scrambling). This allows for a more general formalisation of semantic
information that does not assume a primary role for the viability of a
subsystem (to use examples from Kolchinsky & Wolpert (2018), a rock, a
hurricane, or a cell). Many systems of interest have a semantic component, such
as a neural network, but may not have such an intrinsic connection to viability
as living organisms or dissipative structures. Hence this simple approach to
semantic information could be applied to any living, non-living or
technological system in order to quantify whether a given quantity of syntactic
information within it also has semantic or causal power.
