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.