Determinism as a philosophical position is summarized in the "consequence argument":
Consequence Argument: "If determinism is true, then our acts are the consequences of the laws of nature and events in the past. But it is not up to us what went on before we were born, and neither is it up to us what the laws of nature are. Therefore the consequences of these things (including our present acts) are not up to us." —Peter van Inwagen An Essay on Free Will, p. 16
From a scientific standpoint, determinism takes the form of physical determinism. A law of nature is deterministic if its theoretical formulation connects certain physical states ineluctably to others. Human language is subject to ambiguity and is thus non-deterministic, whereas formal or mathematical languages are required to be deterministic, which means that given a known state and a known input, the next state is entirely predictable and can be counted on. Mathematical processes which are non-deterministic are said to be stochastic. Physical determinism 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
The idea of 'cause-and-effect' is replaced with that of 'logical implication' according to one or another theory that connects events. There is no implication here of 'cause' and 'effect', but merely the theoretical implication that certain 'states' are connected to other 'states', which may be earlier or later in time. These physical states may be described in various ways, for example, using wavefunctions that determine the probabilities of observable events involving individual 'elementary' particles, or using the specification of gross variables, like temperature and pressure, that have meaning only for numbers of particles large enough to allow a statistical interpretation. Such logical implication connecting probabilities is a far cry from the rigid determinism envisioned by Pierre-Simon Laplace, who had classical physics in mind.
"We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow. Given for one instant an intelligence which could comprehend all the forces by which nature is animated...for it, nothing would be uncertain and the future, as the past, would be present to its eyes. The human mind offers...a feeble idea of this intelligence. —Pierre Simon Laplace, A Philosophical Essay on Probabilities, p. 4
The philosophical position of determinism can be interpreted so as to be independent of the precise form of the 'laws of nature', although any supposed implication of 'causation' is to be replaced by something closer to 'association' via an empirically grounded theoretical apparatus, for example, a model-dependent reality.
- Peter van Inwangen (1986). “The problems and how we shall approach them”, An Essay on Free Will. Oxford University Press, p. 16. ISBN 0198249241.
- Ernest Nagel (1999). “§V: Alternative descriptions of physical state”, The Structure of Science: Problems in the Logic of Scientific Explanation, 2nd. Hackett, pp. 285-292. ISBN 0915144719.
- The notion of cause introduces unnecessary complications best avoided as done here. For example, see Bertrand Russell (1912-1913). "On the notion of cause". Proceedings of the Aristotelian Society (New Series) 13: pp. 1-26.
- Apparently, Laplace's view was enunciated earlier by Marie-Jean-Antoine-Nicolas Caritat, the Marquis de Condorcet in correspondence with Jean d'Alembert: Roger Hahn (2005). Pierre Simon Laplace, 1749-1827: A Determined Scientist. Harvard University Press, p. 52. ISBN 0674018923.
- Pierre Simon Laplace (1951). FW Truscott and FL Emory, translators: A Philosophical Essay on Probabilities, translated into English from the original French 6th ed. Dover Publications, p. 4. ISBN 0486288757.