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Information to Users INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. Bell & Howell Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with with permission permission of the of copyright the copyright owner. owner.Further reproductionFurther reproduction prohibited without prohibited permission. without permission. FREGE’S ONTOLOGY AND THE PROBLEMS OF THE THIRD REALM by Sylvia Alexis Rolloff submitted to the Faculty of the College of Arts and Sciences of The American University in Partial Fulfillment of the Requirements for the Degree of Master of Arts in Philosophy Chair: RymHarre_________________ frp^'ini ---- David F. T. Rodier Dean of the College of Arts and Sciences mmi__________ date 1998 The American University Washington, D.C. 20016 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 1395942 UMI Microform 1395942 Copyright 1999, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. FREGFS ONTOLOGY AND THE PROBLEMS OF THE THIRD REALM BY Sylvia Alexis Rolloff ABSTRACT In this thesis, I investigate Gottlob Frege's philosophy, particularly his conception of thoughts as existing in a "third realm" separate from the physical world and independent of human minds. I begin with an exegisis of Frege's philosophy, examine the interpretations of Michael Dummett and Joan Weiner, and finally adjudicate between their differing conceptions of Frege's thought. In conclusion, I find that Frege's third realm is a metaphysical entity, yet one which serves a useful purpose of providing an ontological grounding for the expression of assertoric sentences. ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS Page INTRODUCTION................................................................. 1 CHAPTER 1 Exegesis Historical Background............................................4 Concept-script........................................................ 6 Foundations of Arithmetic...................................... 11 Function, Concept and Object................................20 Sense and Reference..............................................35 Thoughts.................................................................37 CHAPTER 2 Dummett's Interpretation of Frege..............46 CHAPTER 3 Weiner's Interpretation of Frege................73 CONCLUSION.....................................................................90 BIBLIOGRAPHY..................................................................94 iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INTRODUCTION Gottlob Frege started his philosophical work with a simple aim: to establish a secure ontological grounding for the concept of number. This seemingly innocent endeavor has wrought much controversy, not only about the content of his thought, but also over the interpretation of that content. Frege's inquiry into the status of numbers led him on a progressive philosophical path in which the nature of his ontological grounding became more refined and mature as his thought progressed. He begins with a rather unsophisticated realist position and evolves towards a position which cannot accurately be called nominalism, but rather a sparse realism. Frege's original presuppositions involve a rather ontologically naive background of mathematical number and set theory. As his work continues through the years, Frege develops an increasingly metaphysical conception of functions which strongly influences his views of thoughts. Of particular concern to me is Frege's views of thoughts. His conception of thoughts existing in an objective yet non-material "third realm" is where we can see most strongly his progressive embrace of a pared-down ontology. As his thought progresses, the ontological categories in Frege's world become fewer and fewer, until there are only two: concepts and objects. There has been a great deal of debate over whether or not 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 thoughts are concepts or objects within Frege's thought -- or if his formulation of the third realm is merely philosophical myth-making. It is important to remember that the mature Frege is concerned withsharpening the ontological boundaries within his thought, rather than performing a metaphysical investigation. The first chapter of this thesis is an exegesis of Frege's views. I explain his works in the order in which they were written. I intend to emphasize the historical progression of his work, and how his evolving philosophy ties together certain conceptions (e.g., sense and reference, concept and object, truth and falsity) into a progressively more coherent whole. The second chapter deals with Frege's most influential interpreter: Michael Dummett. Dummett views Frege primarily as a philosopher of language, and considers his context principle to be the most important element within Frege's philosophy. Although Dummett's interpretation can be very compelling, it overlooks Frege's original (and maintained) distinction between generalized and instantiated functions. In the third chapter, I explore Joan Weiner's interpretation of Frege. Specifically, she is concerned with Frege's intentions and how they influenced his philosophy, rather than with categorizing Frege as a particular type of philosopher. Weiner maintains (convincingly) that Frege was concerned to produce (through his Begriffsscrift) a logical tool to be used for the advancement of science. "Science" is here broadly conceived as the 19th-century classification which included mathematics, chemistry, history, etc. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 Both Weiner and Dummett bring to the foreground interesting (and sometimes conflicting) interpretations of Frege. My attempt is to adjudicate between the views of these two thinkers as well as to explore a particularly obscure aspect of Frege's thought. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 1 EXEGESIS Historical Background Gottlob Frege attempted to establish an ontological grounding for the concept of number. This ontology springs from logicism, the doctrine that logical concepts can exhaustively explain arithmetical ones. This ultimately unsuccessful attempt led him to a wide-ranging philosophical investigation of logic, numbers, ordinary language and geometry. Although relatively unknown during his lifetime, Frege's stature has grown over the years, and the scholarship on him still examines and contends with his thought. Frege's university studies consisted of mathematics, philosophy and physics. He went on to teach mathematics and mathematical logic. Although the field of mathematics at that time was in the midst of exciting new discoveries, Frege felt that the primitive basis of mathematical entities -- the natural numbers — had not been sufficiently examined or explained. He was determined to supply the foundations of natural numbers and arithmetic as a remedy to this situation. 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 Historical Progression An essential aspect of Frege's work is that it is progressive. His original distinction, in theBegriffsscrift, between generalized and instantiated functions leads his later work through a sharpening of the ontological boundaries between concept and object. Functions (in particular, functions that possess truth-values when instantiated) become subsumed under the category of concept. In conjunction with his progressively more metaphysical conception of functions, Frege's ontological category of "object" grows larger as his thought progresses. Frege's increasing distinction
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