This paper is a part of a larger attempt to show that Aristotle held a consistent, fairly elaborate view as to what the different kinds of assumptions are that are needed in a science, how they are related to each other and to the idea of definition, and how they are obtained. I want to argue that Aristotle's different pronouncements on these subjects in the two Analytics hang together quite well, apart from some fluctuation of emphasis and of terminology. The main lines of my argument for this thesis are four. First, I want to point out that Aristotle's syllogistic theory, together with his belief that syllogisms are the universal tool of any sytematic science, naturally led him to a specific view of the ingredients of a science. One is almost tempted to say that Aristotle's views on the first principles of a science are predictable on the basis of his syllogistic theory, including his ideas of the role of existential presuppositions in syllogistic premisses. Secondly, it seems to me that the same result is reached by taking Aristotle up on his statement that "all sciences are based upon definitions" (Post. An. II, 17, 99a22-23). (In quoting Aristotle,