Indeterminacy is invoked in several philosophical debates. In the philosophy of language, we say that the application conditions of vague predicates are indeterminate. In the philosophy of mathematics, some argue that statements like the Continuum Hypothesis are indeterminate. In the philosophy of physics, some conceptualize the lack of value-definiteness in quantum mechanics in terms of indeterminacy. In this talk, I will focus on indeterminacy as a feature of our language and/or our theories (semantic or representational indeterminacy), rather than as a characteristic of reality (metaphysical). I have two main aims. First, I will try to understand what constitutes genuine semantic indeterminacy. Secondly, I will analyse a case study from the philosophy of mathematics. Hopefully, this work will apply to additional case studies in both the philosophy of mathematics and the philosophy of the sciences.