Depending on the particulars, an argument from silence may be logically correct or incorrect. I’ve argued that the most charitable interpretation of arguments from silence is as explanatory arguments. In order to succeed, arguments from silence must successfully show that the non-existence or non-occurrence of the thing in question is a better explanation than rival theories, such as that the person or people who are silent never heard the claim in question.
Barry Arrington, writing at the Uncommon Descent blog, makes an incomplete (and thus logically incorrect) argument from silence by failing to discredit just this alternative explanation (that his opponents were not aware of the original claim). In a recent post, he says that he wrote a post “over three months ago” stating a major objection to metaphysical naturalism: if metaphysical naturalism is true, then empathy is just another feeling that can be suppressed on the basis of a cost/benefit analysis. But, he says, he hasn’t gotten a serious response to this argument. Therefore, he concludes, his post must be correct because there is no good objection available.
While Arrington succeeds in providing an example of a weak argument from silence — I, for one, hadn’t heard of his argument before now and I suspect many other prominent naturalists were equally unaware of his post–I am not sure Arrington succeeds in providing a good objection to naturalism. But since I’m feeling lazy, I’ll leave the critique as an exercise for the reader.