There are various well-known paradoxes of modal recombination. This paper offers a solution to a variety of such paradoxes in the form of a new conception of metaphysical modality. On the proposed conception, metaphysical modality exhibits a type of indefinite extensibility. Indeed, for any objective modality there will always be some further, broader objective modality; in other terms, modal space will always be open to expansion. Keywords Metaphysical necessity • Indefinite extensibility •

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... odal logic Call a modality objective when it is non-epistemic, non-deontic, non-linguistic, and non-intentional. The objective modalities are roughly the modalities expressed by circumstantial modal terms. 1 We routinely use such terms in natural language to express various practical modalities, and, on occasion, nomological modality. Yet, although uncommon in natural language, circumstantial modal auxiliary verbs like 'must' can be used unrestrictedly, that is without restriction to any set of circumstances; on this reading, 'it must be that φ' is true when φ is the case whatever the circumstances. When read as such, the objective modality expressed by the modal is metaphysical modality. Metaphysical modality is accordingly the maximal objective modality: possibility according to any objective modality entails possibility according to metaphysical modality. 2 1 The term 'objective modality' was introduced in the relevant sense by Williamson [28], who connects it to Angelika Kratzer's [12, chap. 2] notion of a circumstantial modal expression. A rough test for whether a modal term is circumstantial is whether it is sensitive to the mode under which a proposition in its scope is presented. 2 Some philosophers might be tempted by the idea that metaphysical modality is in some sense a restriction of logical modality. This is compatible with the claim that metaphysical modality is the maximal objective modality, for logical modality is a linguistic modality and thus not objective in the relevant sense.