Quantum Mechanics
The materialistic determinism has obviously been put to a severe test by the discoveries of the quantum mechanics. To illustrate the difficulties and issues, which it has to face now, let's take a quantum superposition with two different states (A and B). The quantum physics declares (and it was also shown experimentally over and over again) that, before actually carrying out the observation, we cannot predict, which state will be the final one after the resolution of the superposition (as the wave function has "collapsed"), and from a materialistic point of view this unpredictable final state seems to come literally "out of the blue". Although we can give statistical assertions to some extent, like e.g. in 50% of the experimentations the A state will be the result after the collapse and in the other half the B one, but for a certain observation we simply do not possess any method to make a prediction about the final state. Moreover, Bell's theorem seems to indicate that there is even theoretically no chance to find a hidden physical variable sometime in the future (which could possibly explain the behavior of these quantum effects and make predictions about them, purely on a materialistic basis), because this would contradict the well-proved rules of the quantum mechanics. Consequently (at least that is the conclusion of the physicists, the former advocates of the materialistic determinism), now, after the success of the quantum physics, we should accept the world being chaotic and unpredictable, and settle for having only a statistical approach to handle these uncertainties.
But, should we acknowledge this interpretation and the chaotic nature of the physical processes, then of what type is the cause and where are its origins, which does determine that we get e.g. the B state at the end of a particular experiment? And why are there no chaotic quantum effects observable in the macro-world, why do we never encounter cats half living and half dead? "Something" has to determine these phenomena, something must have decided that the final state will be B and not A in that specific experimentation. And if the physics reached its boundaries, while searching for this source of determinism, then why should we sacrifice rather the rationalism (which we certainly do by accepting the world being chaotic), than the purely materialistic perception, which latter clearly does not (and apparently also cannot) supply the complete explanation for the various observations in our world anymore? And why would a theory like e.g. the many-worlds interpretation provide a higher degree of scientific predictability and accuracy (which it obviously does not), than the assumption of the existence of non-physically natured rules and laws behind these observations, which non-material regularities themselves could determine the occurrences potentially in a perfectly predictable, rational and, through the methods of the (social) sciences, completely comprehendible and describable way? For instance, regarding our example above, we could deduce, that that particular experimentation had finally the B state as an outcome, because the mental principles behind the physical world intended to reach this final state (which intention could be entirely understood and flawlessly described with the help of the social sciences), and thus they had determined the physical process (through the medium of the quantum uncertainty) in that exact manner.
Someone could object, that this interpretation would possibly let some kind of spirits or gods slip into the scientific theories, and we would give up the rationalism for a mystical New Age world view. Of course, having a pure physical explanation is much better from a scientific point of view, than referring to "mental principles"; but if we are unable to provide such an explanation (and this seems to be the case with the advent of the quantum mechanics), then we should definitely open our view and take new possible causes into account, instead of accepting the world being chaotic, just because we cannot explain its phenomena in an exclusively physical way. Rationalism is a much more important concept from a scientific aspect, than materialism; actually, rationalism is the science, and a real scientist should have a much greater fear of chaos and unpredictability, than of intellectual principles or even spiritual beings and gods behind the physical realm. The gods' behavior can be entirely comprehended and predicted, as long as we have understood their intentions, whereas the nature of the objective randomness is almost absolutely inconceivable and indescribable by the methods of the science (only a statistical approach can be used, and also this only to a very limited degree).
But then, why do not the scientists of today follow these simple considerations, and why do not they at least try to explain the quantum uncertainties with the help of non-physical rules and principles (which themselves could be understood and described by the social sciences)? It certainly would be the most easy and natural way to overcome the difficulties introduced by the quantum mechanics and its metaphysical consequences: why do not they even attempt to construct such an explanation then? Apparently, for the scientists of today it is much more important to be regarded as a materialist than as a rationalist; they seem literally frightened of possibly being referred to as some religious romanticist, and to avoid this suspicion they feel compelled to choose the mainstream materialistic "explanation" and to settle for a chaotic world view. However, these scientists should consider that the randomness (or rather The Randomness) is in reality much more tyrannic, unpredictable, despotic and unreliable than any gods could ever be, and so they are in fact more religious and devotional than those (mostly dilettante) physicists and philosophers, who actually try to save the deterministic and scientific world view with the help of the supposed intellectual principles behind the physical domain, and who passionately seek an egress out of the perplexity caused by the stunning discoveries of the quantum mechanics, instead of accepting the world being irrational, chaotic and objectively random in its roots.