Constraints on Spacetimes

The model is “top down” in its mathematical development, also.  That is, each mathematical postulate has consequences. Each consequence generates a new feature corresponding to physical phenomena.  Thus, the postulate that points are distinguishable one from the other is a consequence of the physical phenomena of fields.  The characteristics of the fields are consequences of constraints by which the points are distinguishable from a primordial set of indistinguishable points.  The constraints segregate different spacetimes.  The characteristic fields of a given spacetime are consequences of the number of dimensions, the metric signature, and the resultant symmetries.

Indeterminism

The element of free will is considered to be justified on empirical grounds.  Specifically, no deterministic model adequately accounts for all physical phenomena.  Even if a sufficiently developed mathematical model of, say, a human being in an environment, were tractable, exact prediction of the complete temporal evolution of the human state would, in this view, not be possible.  The element of free will is that which denies the completeness of any deterministic model of experience.  It is precisely the indeterminant aspect that is free will.

The above is not meant to imply that free will is an attribute only of a complex system, such as a human being in an environment. Rather, this serves as an obvious example of a system with an unpredictable complete temporal evolution. In practice, any system is, in its essence, of a quantum nature. Its dynamical states (the complete set of wavefunctions) are known, perhaps, but the a priori particular state in not known – only the probability that collapse of the wavefunction will result in any given particular state. If “will” is considered to be that attribute of a system that renders it to be persistent, then the notion of “free will” is the notion that the evolution of the system in this persistence is a priori known only with probabilities.

Free Will

The philosophical model unpinning a physical model is a “top down” model. The observable spacetime of the physical model emerges from the philosophical reduction of phenomena from a primordial whole.  The philosophical model, in its steps of reduction, includes a crucial step. This is collapse of a quantum mechanical wavefunction.  This collapse is posited to be an act of free will.  As such, it is characterized by indeterminism which cannot be modeled mathematically.  The deterministic physical model follows as that which can be modeled mathematically.  Thus, the model yields a physical model in the traditional sense, but explicitly includes free will that cannot be modeled mathematically.