Here is an argument schema.
If X is reducible to the natural, then likely the vast improvement of natural science over the last three hundred years would have led to a much better knowledge of X.
If X is not reducible to the natural, then it is not likely that the vast improvement of natural science over the last three hundred years would have led to a much better knowledge of X.
The vast improvement of natural science over the last three hundred years has not led to a much better knowledge of X.
So, probably, X is not reducible to the natural.
Some options for X:
ethics
aesthetics
value in general.
I think the best response would be to dispute (1), by saying that (1) is only plausible if we know how to do the reduction. The mere existence of a reduction, when we do not know how to run it, is not enough.
Maybe. But I still think we get some evidence against reductionistic theories in ethics, aesthetics and value in general from fact that great progress in science hasn’t led to great progress in these areas.
I agree we get some evidence for that. But I also think we get some evidence for the proposition that the vast improvement of natural science over the last three hundred years has come at the cost of systematically distorting our understanding of nature.
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We should add ‘composition’ and ‘purposiveness’ to the list of candidates for X.
I agree about purposiveness. But with the development of formal mereology, I think we have made progress on composition, and one might try (I don't know with what success) make a case that there is some connection between formal mereology and atomistic science.
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