Arguments Against Laplace's Demon
Due to its canonical assumption of determinism, Laplace's demon is incompatible with interpretations of quantum mechanics that stipulate indeterminacy. The Heisenberg Uncertainty Principle states that exact measurements of positions and momentum cannot be known, together, with more than a given precision.
Chaos theory describes how a deterministic system can nonetheless exhibit behavior that is impossible to predict: as in the butterfly effect, minor variations between the starting conditions of two systems can result in major differences. However, in so far as one is willing to entertain Laplace's premise, no such variation, however minor, has been admitted.
According to chemical engineer Robert Ulanowicz, in his 1986 book Growth and Development, Laplace's demon met its end with early 19th century developments of the concepts of irreversibility, entropy, and the second law of thermodynamics. In other words, Laplace's demon was based on the premise of reversibility and classical mechanics; however, under current theory, thermodynamics (i.e. real processes) are thought to be irreversible in practical terms (compared to the age of the universe, for instance).
In 2008, David Wolpert used Cantor diagonalization to disprove Laplace's demon. He did this by assuming that the demon is a computational device and showing that no two such devices can completely predict each other. If the demon were not contained within and computed by the universe, any accurate simulation of the universe would be indistinguishable from the universe to an internal observer, and the argument remains distinct from what is observable.
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—Zeno Of Elea (c. 490–430 B.C.)
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