To borrow a colorful phrase from Kant, this dissertation offers a prolegomenon to any future semantic theory. The dissertation investigates Yablo's omega-liar paradox and draws the following consequence. Any semantic theory that accepts the existence of semantic objects must face Yablo's paradox. The dissertation endeavors to position Yablo's omega-liar in a role analogous to that which Russell's paradox has for the foundations of mathematics. Russell's paradox showed that if we wed mathematics to sets, then because of the many different possible restrictions available for blocking the paradox, mathematics fractionates. There would be different mathematics. This is intolerable. It is similarly intolerable to have restrictions on the `objects' of Intentionality. Hence, in the light of Yablo's omega-liar, Intentionality cannot be wed to any theory of semantic objects. We ought, therefore, to think of Yablo's paradox as a natural language paradox, and as such we must accept its implications for the semantics of natural language, namely that those entities which are `meanings' (natural or otherwise) must not be construed as objects. To establish our result, Yablo's paradox is examined in light of the criticisms of Priest (and his followers). Priest maintains that Yablo's original omega-liar is flawed in its employment of a Tarski-style T-schema for its truth-predicate. Priest argues that the paradox is not formulable unless it employs a "satisfaction" predicate in place of its truth-predicate. Priest is mistaken. However, it will be shown that the omega-liar paradox depends essentially on the assumption of semantic objects. No formulation of the paradox is possible without this assumption. Given this, the dissertation looks at three different sorts of theories of propositions, and argues that two fail to specify a complete syntax for the Yablo sentences. Purely intensional propositions, however, are able to complete the syntax and thus generate the paradox. In the end, however, the restrictions normally associated with purely intensional propositions begin to look surprisingly like the hierarchies that Yablo sought to avoid with his paradox. The result is that while Yablo's paradox is syntactically formable within systems with formal hierarchies, it is not semantically so.

Abstract In this research report, the author defends Peter van Inwagen’s modal skepticism. Van Inwagen accepts that we have much basic, everyday modal knowledge, but denies that we have the capacity to justify philosophically interesting modal claims that are far removed from this basic knowledge. The author also defends the argument by means of which van Inwagen supports his modal skepticism. Van Inwagen argues that Stephen Yablo’s recent and influential account of the relationship between conceivability and possibility supports his skeptical claims. The author’s defence involves a creative interpretation and development of Yablo’s account, which results in a recursive account of modal epistemology, what the author calls the “safe explanation” model of modal epistemology. The defence of van Inwagen’s argument also involves a rebuttal to objections offered to van Inwagen by Geirrson and Sosa.

Ted Sider writes that "many are impressed with the utility of possible worlds in linguistics and philosophy", and this is true, in particular, of those with an interest in modal logic. However, in the midst of the marvelous milieu brought on by the development of possible world semantics, some have stopped to ask just what it is that possible worlds are. They certainly seem useful, and we seem to understand how to use them and talk about them, but what precisely is it that we're talking about when we talk of possible worlds? In this thesis, I will attempt to outline the most significant and well-recognized view in this debate: that of David Lewis. Through my discussion of him, I will find occasion to discuss some alternative views that have arisen. After finishing my presentation of Lewis, I will discuss where people have begun to take this debate and address the question of whether progress can be made towards a substantive answer. In Chapter I, I begin by presenting the motivation of the question of possible worlds found in the study of modal logic. I then present the major approaches taken to answering the questions that were raised, leading into my discussion of David Lewis's famous and robust account. I present key features of Lewis's view and then move into his criticisms of the other major responses. This much should suffice as a relatively thorough treatment of the answers that have come before. In Chapter II, I discuss the current state of the debate. I begin by mentioning several problems that can be spotted in Lewis's views in particular. I then move to Menzel's account, which tries to answer the question of possible worlds from a new angle, jettisoning the direction taken by Lewis and his contemporaries. I explain why Menzel has taken this new approach, and then move into another new approach, this time given by Stephen Yablo. I discuss how these two approaches can help serve each other in helpful ways. But, at last, I present several hurdles these two views would have to overcome in order to play together nicely.

This dissertation is centered around a set of apparently conflicting intuitions that we may have about mathematics. On the one hand, we are inclined to believe that the theorems of mathematics are true. Since many of these theorems are existence assertions, it seems that if we accept them as true, we also commit ourselves to the existence of mathematical objects. On the other hand, mathematical objects are usually thought of as abstract objects that are non-spatiotemporal and causally inert. This makes it difficult to understand how we can have knowledge of them and how they can have any relevance for our mathematical theories. I begin by characterizing a realist position in the philosophy of mathematics and discussing two of the most influential arguments for that kind of view. Next, after highlighting some of the difficulties that realism faces, I look at a few alternative approaches that attempt to account for our mathematical practice without making the assumption that there exist abstract mathematical entities. More specifically, I examine the fictionalist views developed by Hartry Field, Mark Balaguer, and Stephen Yablo, respectively. A common feature of these views is that they accept that mathematics interpreted at face value is committed to the existence of abstract objects. In order to avoid this commitment, they claim that mathematics, when taken at face value, is false. I argue that the fictionalist idea of mathematics as consisting of falsehoods is counter-intuitive and that we should aim for an account that can accommodate both the intuition that mathematics is true and the intuition that the causal inertness of abstract mathematical objects makes them irrelevant to mathematical practice and mathematical knowledge. The solution that I propose is based on Rudolf Carnap's distinction between an internal and an external perspective on existence. I argue that the most reasonable interpretation of the notions of mathematical truth and existence is that they are internal to mathematics and, hence, that mathematical truth cannot be used to draw the conclusion that mathematical objects exist in an external/ontological sense.