Using Aristotle's philosophy of mathematics to understand the scope of hypothetical and simple necessity in his philosophy of biology

Commentators on Aristotle's philosophy of biology construe teleological explanations in one of two ways. Call these two ways T1: the natural world contains both teleological and nonteleological properties, and T2: the natural world contains only teleological properties, there are no nonteleological properties. The problem of attributing either T1 or T2 to Aristotle arises because the relationship between what he calls "hypothetical ( 3 ,x` upoq3&d12; s3wv ) necessity" and "simple ( a ,plw&d4; v ) necessity" is not clearly understood. Properties that are hypothetically necessitated are teleological (e.g., being rigid for the end of locomotion). Properties that are simply necessitated are nonteleological (e.g., a rigid leg is susceptible to fracture). If we accept T1 it is unclear how hypothetical and simple necessity are related; the former becomes superfluous if we can explain everything via the latter. But, if we accept T2 then this threatens to collapse the distinction Aristotle clearly makes between hypothetical and simple necessity. Commentators argue for either T1 or T2.;The intent of this dissertation is to argue for a version of T that preserves the distinction between hypothetical and simple necessity, yet offers an account of how these two sorts of necessity are related. My approach has two distinct aspects. First, I develop a "map" of Aristotle's metaphysical picture of the universe that classifies the ontology of the objects of biological study and distinguishes them from those of other sciences. Second, I show how Aristotle defines the key terms "hypothetical," "simple," and "necessity" in the context of his philosophy of mathematics and show that these definitions are to be applied in biological contexts. I support this argument by discussing a number of central texts in Aristotle's biology where he forges direct links between mathematical necessity and biological necessity by using former to illustrate his understanding of the latter.;I conclude that the terms "hypothetical" and "simple" do not denote separate kinds of necessity, but two distinct modes by which objects are necessitated; this is how hypothetical and simple necessity are related. However, hypothetical and simple necessity are not synonymous since they apply to different kinds of objects. This is how hypothetical and simple necessity are distinct.