Most of us in Western society have heard of the term ‘naturalism’. Metaphysical naturalism is the position that the only entities that exist are natural entities, and anything that is mental depends on the physical. Supernaturalism, however, gives priority to the mental, and anything that is physical is dependent on the mental.
Non-supernaturalism is the rejection of supernaturalism (I suppose we could also call this position asupernaturalism). One can also go further and disbelieve in the existence of the supernatural. Non-supernaturalism is a disjunction of positions and naturalism is just one position Thus while naturalism entails the former, the former does not entail the latter. The other world views are what Paul Draper labels ‘otherism’, which includes things like pansychism, etc.
Therefore in order to show that supernaturalism is probably true, it isn’t enough to show that naturalism is false or probably false. Not to mention, most of the people who argue against naturalism don’t even argue that naturalism is probably false, at least not in their various arguments. For example, arguing that consciousness is unlikely to exist on naturalism is not the same thing as arguing that naturalism is probably false. And of course, there could be further-more specific- facts about consciousness that support naturalism over supernaturalism (e.g. the dependency of mind on brain, etc.)
Another related argument is the argument from reason. Of course, again, that alone wouldn’t show that naturalism is probably false (at least non-deductive arguments). And even if it did, that wouldn’t show that supernaturalism is probably true. In addition, the argument from reason is offset by arguments from reason for naturalism, particularly the argument from cognitive biases.
None of this is to say that there aren’t disagreements about how to define naturalism. Some people want to say that naturalism is just about concrete reality, which means that one can be a naturalist and also think that numbers exist in the platonic sense (because numbers are abstract). If naturalism is just about concrete reality, then (if naturalism is true) that rules out God, angels, demons, ghosts, etc. It’s important to note that the philosophical definition of ‘concrete’ might not be what ordinary people would expect. When people say the number two exists, they are saying that it has no causal powers; not having causal powers is a popular view about what makes something abstract. They also mean that the number two exists outside of space and time. Therefore, if the number two exists, then it would be timeless, spaceless, immaterial, uncaused, necessary, eternal, and causally powerless.
Speaking of disagreement, naturalists often disagree about the nature of the mind. To be sure they agree that the mind is ultimately reducible and/or dependent on the brain. However, they can disagree on the specifics. For instance, is the mind identical to the brain? Is the mind actually a thing or just a process? Is the mind-body problem just a problem of language?* And the disagreements don’t end there.
Notes
*Wittgenstein would say the mind-body problem is just a linguistic issue. Firstly, we can’t describe physical reality without mentioning first-person and third-person states. Secondly, looking for consciousness inside the brain is like opening up a computer and wondering where the internet is. It’s not even so much that we are saying it’s false that ‘the internet is in the computer’. Rather, to suppose that the internet is in the computer is either meaningless and/or a category mistake.
Philosophy of Religion blog 
If ‘Natural’ means ‘having an identity’ or ‘the proper subject of causal explanation’, then it is hard to see what would make something super-natural.
Epiphenomena would qualify, and abstractions, like the noble #2, are merely manners of speech.
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