 According to a platonic realist, directions exist and have a nature which is independent of anyone’s beliefs, linguistic practices, conceptual schemes, and so on. But doesn’t the availability of (A), (B), and (C) undermine the existence claim at the heart of platonic realism? After all, (A), (B), and (C) allow us to paraphrase any sentence whose truth appears to entail the existence of abstract objects into a sentence whose truth involves only the existence of concrete inscriptions. Doesn’t this show that an analytic reduction can aid someone wishing to question the existence claim involved in a particular form of realism? There is a powerful argument, first developed by William Alston (1958), and convincingly resuscitated by Crispin Wright (1983, Ch.1), that suggests not. The analytic reductionist who wishes to wield the contextual definitions against the existence claim at the heart of platonic realism takes them to show that the apparent reference to abstract objects on the left-hand sides of the definitions is merely apparent: in fact, the truth of the relevant sentences entails only the existence of a range of concrete inscriptions. But the platonic realist can retort: what the contextual definitions show is that the apparent lack of reference to abstract objects on the right-hand sides is merely apparent. In fact, the platonic realist can say, the truth of the sentences figuring on the right-hand sides implicitly involves reference to abstract objects. If there is no way to break this deadlock the existence of the analytic reductive paraphrases will leave the existence claim at the heart of the relevant form of realism untouched. So the issue of this style of reductionism appears to be orthogonal to debates between realists and non-realists.