The argument is simple: We've observed a huge quantity of an extremely wide variety of concrete objects, and all of the concrete objects we've observed are contingent; so, probably, all concrete objects whatsoever are contingent. But no Anselmian being is contingent. So, probably, there are no Anselmian beings.
An abductive version of the argument can be constructed as well: our extensive experience of an extremely wide variety of concrete objects is such that we find them all to be contingent. What explains this? The simplest, most conservative explanation of the data with the widest explanatory scope is the hypothesis that all concrete objects are contingent beings. It is thus the best explanation of the data. But no Anselmian being is a contingent being. Therefore, probably, there are no Anselmian beings.
If needed, an abductive (or inductive) argument could be run for a weaker, defeasible, yet burden-shifting principle that normally, concrete objects are contingent. It would take a bit more work to show it, but I think that even apart from the sorts of considerations above, such a principle, when combined with several other considerations, suffices to serve as an undercutting defeater for the key modal premise of the modal ontological argument, as well as the key principle of cosmological arguments, which links the existence of contingent beings to the requirement of their explanatory ground in a necessary being.
One might of course reply that such a hypothesis (viz., that all concrete objects are contingent) has narrower scope than the hypothesis that there is a necessary being as well, on the grounds that the latter, but not the former, can account for the fact that there are contingent beings at all, rather than just nothing. However, the reasons we have for thinking that such an account is needed rely upon the principle of sufficient reason, which is itself in need of inductive or abductive support from our uniform experience. If so, then even if such evidence is likewise universal, we have a mutual canceling-out of the epistemic force of both my hypothesis and the principle of sufficient reason, in which case the PSR doesn't favor the proposed competing hypothesis over mine. But even if this weren't true, we've seen on another occasion that the most defensible versions of PSR may well be satisfied even on the assumption that there are only contingent beings.
If needed, an abductive (or inductive) argument could be run for a weaker, defeasible, yet burden-shifting principle that normally, concrete objects are contingent. It would take a bit more work to show it, but I think that even apart from the sorts of considerations above, such a principle, when combined with several other considerations, suffices to serve as an undercutting defeater for the key modal premise of the modal ontological argument, as well as the key principle of cosmological arguments, which links the existence of contingent beings to the requirement of their explanatory ground in a necessary being.
One might of course reply that such a hypothesis (viz., that all concrete objects are contingent) has narrower scope than the hypothesis that there is a necessary being as well, on the grounds that the latter, but not the former, can account for the fact that there are contingent beings at all, rather than just nothing. However, the reasons we have for thinking that such an account is needed rely upon the principle of sufficient reason, which is itself in need of inductive or abductive support from our uniform experience. If so, then even if such evidence is likewise universal, we have a mutual canceling-out of the epistemic force of both my hypothesis and the principle of sufficient reason, in which case the PSR doesn't favor the proposed competing hypothesis over mine. But even if this weren't true, we've seen on another occasion that the most defensible versions of PSR may well be satisfied even on the assumption that there are only contingent beings.