Abstract

Instantial reasoning uses facts about an arbitrary or undetermined instance as a basis for drawing general conclusions. For example, a typical procedure for proving a general fact is to prove the fact for an `arbitrary' instance and then generalize from that instance. This method dates back at least to Euclid's Elements and continues to be a common and essential method of reasoning today. ;Instantial reasoning employs terms that, though syntactically singular, display both singular and general semantic characteristics. Consequently, standard semantic accounts of singular and general terms are not easily extendible to instantial terms. ;Debates about the proper interpretation of instantial terms extend back at least to Locke and Berkeley's dispute about abstract triangles. But thus far no theory has provided an account that is both formally adequate and philosophically plausible. The central goal of this dissertation is to remedy that lack by providing a semantic interpretation of instantial terms which makes sense of their use in a variety of reasoning patterns. ;This dissertation introduces the problem of instantial reasoning and reviews the traditional disputes surrounding it. It then examines the two leading theories of instantial reasoning in detail. The strengths and weaknesses of each theory are noted, and each theory is shown to provide an implausible account of some central characteristic of instantial terms. ;The final chapter argues that instantial terms are semantically distinct from both singular and general terms. A new type of semantic entity, the holey proposition, is introduced and it is argued that instantial terms are best understood as indicating holes in holey propositions. The theory of holey propositions is developed and is shown to provide a formally adequate and philosophically plausible account of instantial reasoning