Determinism and Indeterminism
Determinism is a rich and varied concept. At an abstract level of analysis, Jordan Howard Sobel (1998) identifies at least ninety varieties of what determinism could be like. When it comes to thinking about what deterministic laws and theories in physical sciences might be like, the situation is much clearer. There is a criterion by which to judge whether a law—expressed as some form of equation—is deterministic. A theory would then be deterministic just in case all its laws taken as a whole were deterministic. In contrast, if a law fails this criterion, then it is indeterministic and any theory whose laws taken as a whole fail this criterion must also be indeterministic. Although it is widely believed that classical physics is deterministic and quantum mechanics is indeterministic, application of this criterion yields some surprises for these standard judgments.
Framework for Physical Theories
Laws and theories in physics are formulated in terms of dynamical or evolution equations. These equations are taken to describe the change in time of the relevant variables characterizing the system in question. Additionally, a complete specification of the initial state referred to as the initial conditions for the system and/or a characterization of the boundaries for the system known as the boundary conditions must also be given.
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