 Though the core-periphery distinction appears to have been tacitly made throughout the history of philosophy as well as in the practice of contemporary semanticists, the task of making it precise faces considerable challenges. One challenge is to elaborate the distinction content-wise, say in terms of cognitive relations on the part of agents, distinguishing, in some way, between intuition or implicit acceptance and inferential or reflective acceptance (of part of the ontology). A second challenge is to investigate whether the distinction is grounded in the grammar of language. A plausible hypothesis to pursue is that it goes along with the divide between the functional part of language (which includes syncategorematic expressions, syntactic categories and features, and auxiliary verbs) and the lexicon. The example of the contrast between existence and exist suggests, though, that this may be too simplified: the noun existence should belong to the periphery (since it is able to convey just any notion of existence a particular metaphysician has in mind), whereas the verb exist belongs to the core, not permitting a non-ordinary use.