Kripke-Wittgenstein meaning scepticism appears as a serious threat to the idea that there could be meaning-constituting facts. Some people argue that the only viable response is to adopt semantic primitivism (SP). SP is the doctrine that meaning-facts are sui generis and irreducibly semantic. The idea is that by allowing such primitive semantic facts into our ontology Kripke's sceptical paradox cannot arise. I argue that SP is untenable in spite of its apparent resourcefulness. No version of SP can account for the normative and practical aspects of meaning while remaining non-reductive. A sparse, basic SP does not adequately deal with the sceptical paradox. A richer SP, with an added intuitive epistemology, can only explain the practical aspect of meaning by aligning itself with reductive use-based accounts of meaning. SP with essential relations between meanings and meaning-bearers could possibly avoid these problems, but we have no reason to think such a version of SP is really non-reductive. I conclude that Kripke-Wittgenstein meaning scepticism should not lead us to adopt SP, instead we should re-examine use-based, dispositionalist accounts of meaning.