Abstract

This book is in the Studies in Philosophy: Outstanding Dissertations series. Its central theme is that Frege’s concept-notation is inadequate because it does not formalize his semantic theory after the introduction of the sense-reference distinction in 1891. This failing, according to Klement, opens Frege up to a number of philosophical and logical challenges that can be met only by completing the project of showing “how Frege’s mature semantic views would be incorporated into his mature logical system”, a project which, Klement plausibly argues, Frege would have endorsed. This involves: allowing the concept-notation to represent explicitly what is expressed in natural language with indirect constructions such as “said that...” or “believes that... ”; allowing principles to be formulated over this notion which capture inferences involving indirect constructions such as: The Morning Star is a planet, Gottlob believes the Morning Star is a planet, so, Gottlob believes something true; being able to respond to certain objections to Frege’s views, some first bruited by Russell and in later correspondence, others involving the identity conditions on intensional entities and “quantifying in” ; making the concept-notation reflect Frege’s ontology; and evaluating the consistency of Frege’s ontology. The chapters of this book are devoted to fulfilling this project “based upon a careful reading of Frege’s own works”, and their contents are mostly self-explanatory. Chapter 2 sets out the formal apparatus of the Grundgeseze, even the bits Frege left out. Chapter 3 is the most philosophical. Senses are construed as interpersonally accessible information uniquely true of the references they determine—senses are objects and functions in the “third realm.” Singular terms are associated with an impossibly rich hierarchy of senses as objects. Functors, including predicates, are associated with senses as functions. Sentences are associated with thoughts as objects, composed of constituent sense-functions, and in many cases, also sense-objects. Robust compositionality at the level of sense raises the question of the nature of the relation between constituents and the whole—is it functional, or not? Compositionality potentially conflicts with a number of other claims, and Klement’s conclusion is reasonable: “the context principle, the priority thesis, and the possibility of there existing multiple decompositions for the same Gedanke, do not pose any great difficulty for the compositionality principle or the understanding of Gedanke as having determinate inner structures”. Chapter 4 sets out Church’s original system and investigates reformulations suggested by Church himself, Kaplan, and others. Chapter 5 presents Klement’s formalization of an intensional logic of sense and reference, based on the results of chapters 2 and 4, and sufficient for indirect speech and quantifying-in, but containing a contradiction. Chapter 6 takes up arguments of early Russell, Searle, and Bergmann. Chapter 7 addresses strategies for repairing the inconsistencies of chapter 5, but in a Fregean spirit: dropping some realms of entities, restricting their number, or modifying our conception of their nature.