In the history of science, Laplace's demon was the first published articulation of causal or scientific determinism by Pierre-Simon Laplace in 1814. According to determinism, if someone knows the precise location and momentum of every atom in the universe, their past and future values for any given time are entailed; they can be calculated from the laws of classical mechanics.
English translation 
We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.—Pierre Simon Laplace, A Philosophical Essay on Probabilities
This intellect is often referred to as Laplace's demon (and sometimes Laplace's Superman, after Hans Reichenbach). Laplace, himself, did not use the word "demon", which was a later embellishment. As translated into English above, he simply referred to: "Une intelligence... Rien ne serait incertain pour elle, et l'avenir comme le passé, seraient présent à ses yeux."
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.
Recent views 
There has recently been proposed a limit on the computational power of the universe, i.e. the ability of Laplace's Demon to process an infinite amount of information. The limit is based on the maximum entropy of the universe, the speed of light, and the minimum amount of time taken to move information across the Planck length, and the figure was shown to be about 10120 bits. Accordingly, anything that requires more than this amount of data cannot be computed in the amount of time that has elapsed so far in the universe.
Another theory suggests that if Laplace's demon were to occupy a parallel universe or alternate dimension from which it could determine the implied data and do the necessary calculations on an alternate and greater time line the aforementioned time limitation would not apply. This position is for instance explained in David Deutsch's The Fabric of Reality, who says that realizing a 300-qubit quantum computer would prove the existence of parallel universes carrying the computation.
It must be admitted that the openness of the future would be hard to defend in the rigidly deterministic universe that Laplace regarded as the inexorable consequence of taking Newtonian ideas seriously. We have seen that in that world, full knowledge of the present, together with unlimited calculating power, implies total knowledge of a rigorously entailed past and future. Nothing really novel ever happened; history was a reiterated tautology. However, the iron grip of Laplace's calculating demon has been relaxed by the twentieth century discovery of widespread intrinsic unpredictabilities present in nature, both at the microscopic level of quantum events and also at the macroscopic level of the behavior of exquisitely sensitive chaotic systems. We have noted already that the question of whether these epistemological deficiencies are to be interpreted as signs of an ontological openness is a metaphysical issue, not to be settled by the natural sciences alone. In the case of chaotic systems, we have seen that it is possible to develop an interpretation that leads to the existence of extra causal principles with the form of the 'active information', and that these might well be capable of accommodating the action of both human and divine agency. Such a programme would then achieve Pannenberg's desired defense of the openness of history, as theology wishes to understand it, not by appeal to field theory but to the ideas of the top-down effects of active information. There is much that is necessarily speculative here, but I believe that these ideas afford a better model than field for the presence and activity of the Spirit.—John Polkinghorne, Faith, Science and Understanding
See also 
- Hawking, Stephen. "Does God Play Dice?". Public Lectures.
- Pierre-Simon Laplace, "A Philosophical Essay on Probabilities" (full text).
- Laplace, Pierre Simon, A Philosophical Essay on Probabilities, translated into English from the original French 6th ed. by Truscott,F.W. and Emory,F.L., Dover Publications (New York, 1951) p.4
- Stanford Encyclopedia of Philosophy, "Causal Determinism"
- David H. Wolpert (2008). "Physical limits of inference". Physica D 237 (9): 1257–1281. arXiv:arXiv:0708.1362. doi:10.1016/j.physd.2008.03.040.
- P.-M. Binder (2008). "Theories of almost everything". Nature 455 (7215): 884–885. doi:10.1038/455884a.
- Physical Review Focus (24 May 2002). "If the Universe Were a Computer". APS.
- Polkinghorne, J.C. (2001). Faith, Science and Understanding. Yale Nota Bene. Yale University Press. p. 166. ISBN 9780300091281.