This paper sets out an inferentialist approach to abstract objects—arguing that it provides a deflationary account of abstracta—and draws attention to some distinctive and attractive features of the account. In brief, a consequence of the kind of semantic inferentialism developed by Brandom is that quantifiers are essentially sortally restricted. As a result, there is a plurality of particular quantifiers, a plurality of senses of ‘exists’, and a plurality of kinds of existence. The inferentialist litmus test for which senses of ‘exists’ are ‘ontologically robust’ or ‘weightless’, I argue, is whether the standards of correctness and incorrectness for existence claims are internal to the linguistic practice itself, or are, in some part, external to the linguistic practice. In the former case, existence claims are responsible only to the internal rules of the linguistic practice and are ontologically weightless. In the latter case, existence claims are responsible to worldly facts and are ontologically robust. On this account, ordinary empirical claims (for example) are ontologically robust, whereas claims about mathematical objects (for example) are ontologically weightless.