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Has any well-known philosopher tried to "prove" that determinism is true? This means, has anybody given a metaphysical argument for the necessary truth of determinism?

I searched for examples, but did not find anything. The argument doesn't have to be convincing, it's enough that it is not obviously flawed.

It's important to note that there is a subtle difference between predeterminism ("no alternative possibilities") and determinism. It has to be an argument for determinism, which is:

Given the state of the whole universe, every subsequent event can theoretically be determined.

The "history" of the universe must not be included in the state of the universe.

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Most philosophers didn't feel that determinism needed to be proved per-se. Instead they thought determinism to be a logical corollary of materialist universe governed by the laws of physics. Democritus was arguably the first determinist, with his concepts of physical determinism and logical necessity, both of these positions he saw as consequences of his materialist atomist theory of the universe, where everything was causally determined by the motion of atoms, thus removing any need for supernatural gods and fates. Similar views on causality and materialism were held by the Stoics.

Similarly, most modern philosophers saw determinism as a direct consequence of successful classical physical theories like Newton's laws of motion. Again, they saw the issue as an obvious consequences of these physical theories, and one that didn't require a proof in itself. Laplace's demon is probably the most famous statement of such a position:

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

It should be noted that the type of determinism you mention has been disproved, first by the empirical results of quantum mechanics, and more recently by Wolpert's theorem. Wolpert's result is particularly interesting, since it puts a limit on what an intelligent agent can predict in a universe, regardless of whether the universe is random (by QM) or not, effectively showing that Laplace's demon is impossible.

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    Quantum mechanics doesn't prove determinism wrong. The randomness observed could come from an unknown deterministic source, or it could be explained by the deterministic many worlds interpretation. – Houshalter Mar 8 '16 at 19:34
  • @Houshalter : The OP clearly mentions two different type of determinism, and is asking about the second type "Given the state of the whole universe, every subsequent event can theoretically be determined." -- this type of determinism has been disqualified by QM, even in the MW interpretation, where from the point of view of an observer in one universe, the events still seem random. Also hidden variable theories (your 'unknown deterministic source') have been disproven by Bell's theorem in the 1960s and Aspect experiments confirming it in 198. – Alexander S King Mar 9 '16 at 17:50
  • Very interesting, but sadly not an answer to the question. I found it mentioned somewhere that there were indeed philosophers who tried to give a metaphysical "proof" for determinism (supposedly even Bertrand Russell). It would be interesting to analyze those arguments for errors – wolf-revo-cats Mar 10 '16 at 19:54
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    @AlexanderSKing Bell's theorem just proves there are no local hidden variables. However it's impossible to prove if a source of randomness is truly random or not. – Houshalter Mar 10 '16 at 20:15
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Many, although not all, determinists are also materialists (as Alexander King said above, for them determinism is just the corollary to the laws of physics). Since for these, there isn't really much to meta-physics, one wouldn't expect meta-physical arguments.

Within the theologic philosophy/philosophy of religion, however, there are those who are deterministic but not materialistic, so their attempts seek to explain things on a more metaphysical basis. See for example, Martin Luther's On the Bondage of the Free Will -

For if man has lost his freedom, and is forced to serve sin, and cannot will good, what conclusion can more justly be drawn concerning him, than that he sins and wills evil necessarily?

and

But now that God has taken my salvation out of the control of my own will, and put it under the control of His, and promised to save me, not according to my working or running, but according to His own grace and mercy, I have the comfortable certainty that He is faithful and will not lie to me, and that He is also great and powerful, so that no devils or opposition can break Him or pluck me from Him.

According to Martin Luther then, because of the nature of sin and what it's done to our souls, we are "forced to serve sin," and it is only by God's grace that we are prevented from sinning - in either case, it is not our own doing.

(A list of quotes from the work).

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