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I haven't seen a valid anti materialist argument.

Depends on how you define "material". Are quantum probability waves material or are they something different with the potential to be material?

Stuart Kauffman talks about the "poised realm" that sits in the interface between relativity and quantum mechanics.

"If quantum can convert to classical and classical can convert to quantum via decoherence and recoherence, then there may be an entire new "Poised Realm" between quantum and classical worlds. Why? Well, it takes time for a quantum system to decohere, often on the order of a femtosecond, or 10 to the -15 seconds...Conversely, presumably, but not surely, it takes time for recoherence to happen. No data are available, but lets say a femtosecond. During these intervals, the quantum system is losing coherence in some or all of its "quantum degrees of freedom", or recohering with respect to some or all of its quantum degrees of freedom. Thus, there must be time periods where the system is in my "Poised Realm. https://www.npr.org/sections/13.7/2010/03/is_there_a_poised_...

He then suggests that the poised realm is indeterminate but not random, what he calls nonrandom lawlessness and I call nonrandom indeterminacy.

"Second, the most radical part of this article proposes that the quantum classical interface is not always describable by a law: specifically in a special relativity setting, no function, F, maps the present state of the system mind-brain into its future. In its place is a nonrandom yet lawless process. I seek in this non-random yet lawless process a source for a responsible free will." https://arxiv.org/abs/0907.2494

Obviously speculative but to my limited mind plausible.
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