If the ontology of naturalists implies that there is only a natural world and science is the best way to find out about it, the philosopher should want to question what this “natural world” is. If it is merely made up by bosons and fermions, then we would only need physics to find out about it. But that reasoning seems too simple, since the naturalist argue the importance of all hard sciences, including chemistry and biology. We might then have to define the natural world as what scientific method discovers. However such an argument seems empty and the idea of naturalism being based on a robust foundation appears to wobble.
But if we reason that the anti-naturalists won’t have a clearer answer for such an onerous question, maybe we shouldn’t hold it against them and instead look at naturalistic epistemology. Is a unification of science really as simple as the naturalists make it out to be? The argument is that the only way of certifying knowledge is by using a single general method: formulating theoretical hypotheses and testing their predictions by systematic observation and controlled behaviour. It seems an accomplishment to be able to apply one single method to all the world’s possible objects, creatures, humans and the societies made up by them. Unfortunately sociology, psychology, nor history would have a place, something the naturalists might not have a problem with since they could still value them, just not see them as knowledge. Perhaps there is a way of understanding how physics might better explain the Israeli-Palestinian conflict than history, and chemistry could perhaps more accurately explain the latest financial crisis than economics and sociologists, but what about the heart of natural sciences –mathematics?
Is mathematical proof as a route to science then also false, not scientific as well as the social domain? Even the naturalists should agree that it would be a flat natural science without math. But say we let the naturalists off the hook, perhaps they can one day show what numbers are and how we can have the certainty about them that math reveals. Let us instead turn our focus on the domain of social science.