  There are many views as to what Aristotle's hypotheses are: (i) existence claims, (ii) any true assumption within a science, and (iii) the stipulation of objects at the beginning of a typical proof in Greek mathematics. Examples might be, ‘Let A be a unit,’ (where the object is stipulated to be a unit) or, more characteristically of Greek mathematics, ‘Let there be a line AB’ (where a line is stipulated to exist, namely AB). In fact, all these interpretations may have a modicum of what Aristotle means. In that case, Aristotle implies that any assumption within a science that asserts or denies something is a hypothesis. However, he singles out existence claims. How do existence claims work in Aristotle's conceptions of science? From Physics iv, we have claims such as ‘There is place,’ and ‘There is no void.’ However, the examples that Aristotle uses in the Posterior Analytics are claims such as that the genus exists, or specifically that there are units, or that there are points and lines. Aristotle also points out that sometimes the hypothesis of the genus is omitted as too obvious. Only by comparing these general claims with their use in Aristotelian mathematics can we get a sense of what Aristotle means. Aristotle intends us to understand that prior to the demonstrations in a scientific treatise, the treatise should state starting propositions. These include general claims broader than the science, definitions which are stated as stipulations and not as assertions, and a claim that the basic entities ‘exist’. What counts as an acceptable existence claim is relative to the actual science. The opening of a proof, ‘Let there be a line AB,’ is an application of the basic hypothesis of the science. Since Aristotle regards such proofs through particular lines as general proofs, the opening claim is actually to be understood as standing for the general claim that there are lines. This is how the hypothesis is used as a premise. The stipulation, ‘Let there be a triangle ABC,’ would not be a hypothesis on this interpretation, since he holds that the existence of triangles is to be proved, so that this instantiates a derived proposition.