The Society for Ancient Greek Philosophy Newsletter

Document Type


Publication Date



Existence Claims in the Posterior Analytics

Richard McKirahan

This paper treats several questions about the place of existence claims in theory of science presented in the Posterior Analytics. On the basis of a close reading of the text it shows that Aristotle identifies existence claims as a distinct kind of scientific principles (alongside definitions and common principles), that what these principles declare to exist are the subjects as opposed to the attributes that the science studies (triangles, as opposed to the property of having angles equal to two right angles), and not all the subjects, but a subset of them, the primitive subjects from whose existence can be demonstrated the existence the remaining (derivative) subjects. The paper goes on to discuss the role that existence claims play in demonstrative science, arguing that they do not occur as premises in demonstrations (which state per se attributes of subjects whose existence the demonstrations presuppose) but that they are required for two reasons: first because for Aristotle there is no science of the non-existent, and second because the per se relations between subjects and attributes, which are the premises and conclusions of demonstrations, are grounded in the essences of their subjects and attributes and only things that exist can have essences. It takes up the question whether scientific existence claims are general (triangles or tigers exist tout court) or restricted to the subject genus of the science in question (triangles exist as subjects of geometry, tigers as subjects of biology) and answers that the latter is in effect the case even though the claims will typically be stated generally. It shows that the primitive existence claims satisfy the criteria for scientific principles stated in APo 1.2, and concludes with a discussion of the difficult question whether Aristotle is committed to the view that the subjects of sciences exist of necessity. It concludes that there is no need for tigers to have existed forever in the past and for them to exist forever in the future in order for to be a subject for scientific knowledge; Aristotle is not committed to holding that triangles must always exist even if no individual triangle always exist. When he says that the universals with which scientific proofs exist are “always” (aei) and “eternal” (aïdion) he means that they exist without reference to time. In the claim “Triangles have angles equal to two right angles” the verb is used in the “timeless present” and the claim means no more than any triangle, whenever it may exist has angles equal to two right angles.


Richard McKirahan presented “Existence Claims in the Posterior Analytics” at the meeting of the Society with the Pacific Division of the American Philosophical Association March 24, 1988 in Portland, Oregon. It was incorporated into his 1992 book, Principles and Proofs: Aristotle’s Theory of Demonstrative Science. Princeton.

For information about the author, see: