Let’s define Naturalism as the view that everything is either physical or causally dependent on the physical. On this definition, Naturalism encompasses both “hard naturalism” (strict reductive physicalism) and “soft naturalism” (which allows for some non-physical things such as minds, provided those non-physical things are causally dependent on physical things).
For completeness, let’s also define physical as a catch-all term for those entities and properties recognized by modern physics (subatomic particles, forces, etc.) or any reasonable refinement thereof (i.e., any refinement that doesn’t introduce radically different ontological categories). On this view, whatever is physical must be spatiotemporal.
I now offer a reductio ad absurdum of Naturalism, as defined above, which deduces the non-truth of Naturalism from its truth.
- Naturalism is true. [assumption for reductio]
- If Naturalism is true, then Naturalism is possibly true.
- If Naturalism is possibly true, then, necessarily, Naturalism is possibly true.
- Necessarily, Naturalism is possibly true. [from 1, 2, 3]
- There is at least one necessary truth. [from 4]
- There is at least one necessarily true proposition. [from 5]
- Necessarily, if some proposition P is true, then P exists.
- If some proposition P is necessarily true, then P necessarily exists. [from 7]
- There is at least one necessarily existent proposition. [from 6, 8]
- There is something that does not exist contingently. [from 9]
- If Naturalism is true, then everything that exists, exists contingently.
- Not everything that exists, exists contingently. [from 10]
- Naturalism is not true. [from 11, 12]