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On the Nature of Propositions As Sets of Possible Worlds ON THE NATURE OF PROPOSITIONS AS SETS OF POSSIBLE WORLDS An Examination of Propositions in Modal Realism by Kaleb Moten A thesis submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Honors Bachelor of Arts in Philosophy with Distinction Spring 2019 © 2019 Kaleb Moten All Rights Reserved ON THE NATURE OF PROPOSITIONS AS SETS OF POSSIBLE WORLDS An Examination of Propositions in Modal Realism by Kaleb Moten Approved: __________________________________________________________ Richard Hanley, Ph.D. Professor in charge of thesis on behalf of the Advisory Committee Approved: __________________________________________________________ Noel Swanson, Ph.D. Committee member from the Department of Philosophy Approved: __________________________________________________________ Laura Eisenman, Ph.D. Committee member from the Board of Senior Thesis Readers Approved: __________________________________________________________ Earl Lee II, Ph.D. Deputy Faculty Director, University Honors Program ACKNOWLEDGMENTS I would like to thank Dr. Hanley for taking me under his wing through the entirety of my time here at the university. Though I had a particularly horrible case of the “incredulous stare” when I first heard about modal realism, this project has given me a hearty appreciation for Lewis’ brilliance, which I’m sure makes Hanley happy. I would also like to give a hearty thank you to Dr. Swanson, who is far more humble than he needs to be, considering how much of a genius he is. He also went above and beyond the call of duty as far as the responsibilities of a second reader are concerned, and for that I am extremely grateful. A thank you as well to Dr. Eisenman, whose encouragement helped me push through some of those moments when I felt like I had taken on an impossible task. Of course, my parents also deserve a mention for pushing me to excel academically. I would also like to thank my AP US History teacher Mr. Mailand for peaking my interest in philosophy in the first place. I am tremendously proud of what I have been able to accomplish in this thesis, and I could not have done it without these people. iii TABLE OF CONTENTS LIST OF FIGURES ........................................................................................................ v ABSTRACT .................................................................................................................. vi 1 INTRODUCTION .............................................................................................. 1 1.1 What are Propositions? ............................................................................. 1 1.2 Modality and Possible Worlds .................................................................. 4 1.3 Modal Realism .......................................................................................... 6 2 THE PROBLEM OF EPISTEMIC ACCESS .................................................. 10 2.1 Modal Realism and Causal Theories of Knowledge ............................... 10 2.2 Ersatz Realism and the Utility Argument ............................................... 16 2.3 Modality without Possible Worlds Semantics ........................................ 22 2.4 Lewisian Propositions and Epistemic Access ......................................... 24 3 UNSTRUCTURED VS. STRUCTURED PROPOSITIONS .......................... 28 3.1 Problems with Sets of Possible Worlds as Propositions ......................... 28 3.2 King’s Structured Propositions ............................................................... 31 REFERENCES ............................................................................................................. 39 iv LIST OF FIGURES Figure 3.1 32 Figure 3.2 33 v ABSTRACT While there is broad consensus on the roles propositions can play (they are the bearers of truth values, meanings of sentences, and/or objects of beliefs and attitudes), there is far less consensus on their metaphysical nature. Some philosophers claims that propositions are sets of possible worlds. This thesis examines this claim with a particular focus on modal realism, the idea that these possible worlds are concrete entities of the same sort as the actual world. I examine two problems: first I determine whether sets of Lewisian worlds are the kind of objects we have epistemic access to, and if this alters their ability to take the propositional role. I then compare Lewisian propositions to their structured counterparts to determine if any other theories are more accurate at modeling content. I conclude that the structured propositional view of Jeffrey King solves many of the issue Lewisian propositions encounter while being conservative enough for a modal realist to adopt it with minimal sacrifices. vi Chapter 1 INTRODUCTION 1.1 What are Propositions? Take the sentence, “The stop sign is red.” You may have heard or read such a sentence before. As with most of the sentences you will encounter throughout your life time, this collection of words means something. The words are meant to pick out a particular object with a particular property. Thus, when you read the sentence, you think of said object. However, though this sentence is in English, the same meaning could be conveyed in Spanish, German, or any other language on earth. This common meaning is what many philosophers would call a proposition. To give a more thorough explanation, propositions can function as the bearers of truth values. They are the objects of beliefs and attitudes. They are the meaning of sentences. When we judge a sentence to be either true or false, the thing that has the property of being either true or false is a proposition. Similarly, when the same meaning is expressed in two different languages, the meaning that the two sentences share is a proposition. However, while there seems to be a consensus regarding the structural role of propositions1, there is much less agreement regarding their 1 Although there is broad consensus on the structural role propositions play, there is disagreement about whether propositions play every role listed above. For example, on one view, propositions may be the objects of belief and the meaning of sentences, but the bearing of truth values falls elsewhere (e.g. sentences). 1 metaphysical nature. What sort of objects are they, and how do we know anything about them? The metaphysics of propositions is important for understanding how propositions are able to bear truth values and be the meaning of sentences. The answer to this question varies. Gottlob Frege, one of the first philosophers to begin discussing propositions in the way that we do today, theorized that sentences are combinations of senses and references. A sense is shareable content, somehow accessed through thought. This is what we would call a proposition; the meaning of a sentence is its sense Furthermore, senses are abstract, mind independent objects. A sentence’s referent is its truth value (Beaney, 1997, p. 156-157). An alternative to this theory is that of Bertrand Russell, which suggests that propositions are actually made up of the objects they pick out, rather than being constituents of abstract objects which are somehow related to these objects. Thus, the aforementioned propositions, “the stop sign is red”, is made up of the object, the stop sign, the property of redness, and the relation between the two, denoted by the word “is”. In short, Frege’s propositions are complexes of abstract objects (sense), while Russell’s propositions are complexes of concrete objects (the referents of the words in the sentence). These two theories have sparked two major camps in our contemporary understanding of propositions. Frege’s view is lacking in giving a detailed account of what exactly senses are, and how they can take the propositional role. While it is no longer in favor to describe propositions as senses, this sort of thinking led to viewing propositions as collections of similar abstract objects. One particularly prevalent example of this is thinking of propositions in terms of possible worlds, which will be the focus of the rest of the thesis. 2 Russell’s view, on the other hand, is lacking in terms of its ability to explain how exactly the relation between objects works. Take for example, the two sentences “John shot Will” and “Will shot John.” These should clearly represent two separate propositions, as they have two very different meanings. Thus, Russell suggests that propositions are objects standing in certain relations to one another. The proposition “John shot Will” consists of John standing in the relation of shooting to Will, which differs from Will standing in the relation of shooting to John. However, in solving this problem, Russell creates another; it is impossible for any proposition to be false on this view. If John is not standing in the relation of shooting to Will, this would be an entirely different proposition, rather than the same proposition with a truth value of false (King, 2017). Thus, much of the work in the Russellian camp is geared towards creating an account where propositions can be true and false while incorporating the way in which objects relate to one another. This thesis is divided into two main problems. The first is the debate between whether or not propositions are concrete or abstract (or in the case of modal realism, abstract-like in terms of relation to the actual world). If propositions are abstract (or abstract-like), it becomes unclear how we can know anything about them. We will refer
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