First principles (ἀρχάι) are crucial to Aristotle's conception of scientific knowledge (επιστήμη). In the Posterior Analytics, Aristotle teaches us that all scientific knowledge is either knowledge arrived at through demonstration from first principles or knowledge of the first principles themselves. The first principles of a given science are the primary premises (τὰ πρώτα) of that science (Pst. An., 72a7); they express the essential characteristics of the substance about which the given science is concerned; and all other scientific knowledge is derived from the first principles through syllogistic inference.
The first principles of the various sciences are expressed through definition (ὁρισμός). More precisely, the first principle of a science is a definition which provides an indemonstrable account of the essence (λόγος του τί έστιν ἀναπόδεικτος) of the subject matter of the science. Throughout the Posterior Analytics, Aristotle assumes that such definitions (usually termed "real definitions") are not only possible but actual, provides explanations for how we come to possess these definitions, and outlines methods for stating them clearly. Examples of first principles include the definition of "man" as "two-footed animal" and the definition of "arithmetical unit" as "indivisible quantity."
At least two conclusions follow from these considerations concerning first principles. First, unless we are in possession of the first principles of some science, we can have no scientific knowledge. Second, since we possess a first principle only if we possess a definition, any problem which threatens to undermine Aristotle’s theory of definition is a threat to the project of Aristotelian science. In this paper, I investigate a problem for Aristotle's theory of definition of which Aristotle was fully aware, and I argue for an interpretation of Aristotle's solution to that problem which helps, in part, to explain the connections among Books Zeta, Eta, Theta, and Iota of the Metaphysics.
Wheeler, Mark R., "The Parts of Definitions, Unity, and Sameness in Aristotle's Metaphysics" (1994). The Society for Ancient Greek Philosophy Newsletter. 318.