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Physical determinism is a position in philosophy that holds that a complete description of the physical state of the world at any given time and a complete statement of the physical laws of nature together entail every truth as to what physical events happen after that time.

This statement leaves open just what "physical" might mean, or a "complete" description. This vagueness is reflected in its usage. So, for example, one could take physical determinism as

"a concept only relevant to the mathematical models of physics and other physical sciences, although its relevance to the world of everyday choice and action is questionable...if thoughts, feelings, and desires are not physical events, it is unlikely that physical theories are appropriate models for thinking about such nonphysical events.

— Robert C. Bishop, Chaos, indeterminism, and free will, p. 84

Causal completeness

The scope of physical determinism is related to the question of the causal completeness of science, the idea that every event falls within the domain of scientific explanation. If causal completeness does not apply to the universe, then the door is open to events that are not subject to physical determinism. A common view of mental events is that they are an epiphenomenon only correlated with neurological activity, and without causal impact. However, a failure of physical determinism would allow room for their causal significance.

A more general formulation of physical determinism skirts the issue of causal completeness. It is based upon connections between 'events' supplied by a theory:

"a theory is deterministic if, and only if, given its state variables for some initial period, the theory logically determines a unique set of values for those variables for any other period."

— Ernest Nagel, Alternative descriptions of physical state p. 292

This quote replaces the idea of 'cause-and-effect' with that of 'logical implication' according to one or another theory that connects events. In addition, an 'event' is related by the theory itself to formalized states described using the parameters defined by that theory. Thus, the details of interpretation are placed where they belong, fitted to the context in which the chosen theory applies. Using the definition of physical determinism above, the limitations of a theory to some particular domain of experience also limits the associated definition of 'physical determinism' to that same domain. That limitation leaves open the question whether there is a physical "theory of everything".

References

1. This definition is from Carl Ginet (1990). On Action. Cambridge University Press. p. 92. ISBN 052138818X.
2. Robert C Bishop (2011). "Chapter 4: Chaos, indeterminism, and free will". In Robert Kane, ed (ed.). The Oxford Handbook of Free Will: Second Edition (2nd ed.). Oxford University Press. p. 84. ISBN 0195399692. {{cite book}}: |editor= has generic name (help)
3. Robert C Bishop, Harald Atmanspacher (2011). "Chapter 5: The causal closure of physics and free will". In Robert Kane, ed (ed.). The Oxford Handbook of Free Will: Second Edition (2nd ed.). Oxford University Press. p. 101. ISBN 0195399692. {{cite book}}: |editor= has generic name (help)
4. Ernest Nagel (1999). "§V: Alternative descriptions of physical state". The Structure of Science: Problems in the Logic of Scientific Explanation (2nd ed.). Hackett. pp. 285–292. ISBN 0915144719.