Is anything worth doing?

"Is anything worth doing?" (in a broad sense of "doing") is a question which, if it is worth thinking about, needs to be answered in the positive. But it is clear that the question is worth thinking about. Hence, the answer to it is positive.

I am confident that it can be established that if something is worth doing (or even if the words "is worth doing" express a concept), then naturalism is false. Thus, naturalism is not worth believing in. For if it is false, it is not worth believing in, and if it is true, nothing is worth doing and hence in particular nothing is worth believing in. (I love these sorts of arguments!)

How to establish that if something is worth doing, then naturalism is false? One approach is this. If something is worth doing, then "is worth doing" expresses a property. The only plausible fully naturalistic accounts of the expressiveness of our language are going to have a heavy dollop of causation (or at least explanation) in them. But if naturalism is true, then something's being worth doing (perhaps as opposed to that something is believed to be worth doing) does not enter into causal relations, and is explanatorily inert (unlike perhaps the truthmakers of mathematical truths, which do not enter into causal relations on naturalistic views, but may be explanatorily potent). Of course, this argument sketch has giant holes. But my intuition is that the holes can be filled in.