This talk discusses the nature and importance of core-periphery distinctions in syntax (and phonology) as well as semantics and natural language ontology. Distinctions between a core and a periphery of language are best known from generative syntax. The Chomskyan distinction between the syntactic core and periphery is controversial, though, and does not generally guide the practice of syntactic analysis. I will argue that a core-periphery distinction is indispensable for natural language ontology as well as conceptual meaning, and has in fact been implicitly made by semanticists as well as philosophers (and that throughout the history of philosophy whenever philosophers appealed to natural language to motivate a philosophical notion or view). The talk will try to elucidate the distinction with a range of cases and discuss what it means for the subject matter of linguistic disciplines and natural language ontology in particular.