This book is about one of the most baffling of all paradoxes – the famous Liar paradox. Suppose we say: 'We are lying now'. Then if we are lying, we are telling the truth; and if we are telling the truth we are lying. This paradox is more than an intriguing puzzle, since it involves the concept of truth. Thus any coherent theory of truth must deal with the Liar. Keith Simmons discusses the solutions proposed by medieval philosophers (...) and offers his own solutions and in the process assesses other attempts to solve the paradox. Unlike such attempts, Simmons' 'singularity' solution does not abandon classical semantics and does not appeal to the kind of hierarchical view found in Barwise's and Etchemendy's The Liar. Moreover, Simmons' solution resolves the vexing problem of semantic universality – the problem of whether there are semantic concepts beyond the expressive reach of a natural language such as English. (shrink)

This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by our concepts of denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions 'denotes', 'extension' and 'true' are context-sensitive. The second, inspired by a brief, tantalizing remark of Godel's, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities (...) is presented and applied to a wide variety of versions of the definability paradoxes, Russell's paradox, and the Liar paradox. Keith Simmons argues that the singularity theory satisfies the following desiderata: it recognizes that the proper setting of the semantic paradoxes is natural language, not regimented formal languages; it minimizes any revision to our semantic concepts; it respects as far as possible Tarski's intuition that natural languages are universal; it responds adequately to the threat of revenge paradoxes; and it preserves classical logic and semantics. Simmons draws out the consequences of the singularity theory for deflationary views of our semantic concepts, and concludes that if we accept the singularity theory, we must reject deflationism. (shrink)

University of North Carolina at Chapel Hill.

I argue for an account of semantic paradox that requires minimal logical revision. I first consider a phenomenon that is common to the paradoxes of definability, Russell’s paradox and the Liar. The phenomenon—which I call Repetition—is this: given a paradoxical expression, we can go on to produce a semantically unproblematic expression composed of the very same words. I argue that Kripke’s and Field’s theories of truth make heavy weather of Repetition, and suggest a simpler contextual account. I go on to (...) outline a ‘singularity’ theory of semantical predicates in the spirit of remarks of Gödel. According to this theory, ‘denotes’, ‘extension’ and ‘true’ are context-sensitive expression that apply almost everywhere on a given occasion of use, except for certain singular points. I then turn to revenge paradoxes, and argue that even the dialetheist is subject to revenge. I then examine how the singularity theory responds to revenge. (shrink)

Consider the following argument written on the board in room 227: 1 = 1. So, the argument on the board in room 227 is not valid. This argument generates a paradox. The aim of this paper is to present a resolution of this paradox and related paradoxes of validity, including a version of the Curry paradox. The proposal stresses the close connections between these validity paradoxes and paradoxes of truth and paradoxes of denotation. So a more general aim is to (...) provide a unified response to semantic paradox. The positive proposal is in part inspired by a brief, tantalizing suggestion of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concept of validity, for example, is everywhere applicable except for certain singular points or singularities. A second central claim is that ‘valid’ is a context-sensitive predicate. The key notions of this contextual-singularity theory are presented and applied to a variety of cases. Any purported solution to paradox must deal with the phenomenon of revenge, and a response to revenge is outlined. The paper closes with remarks about the accommodation of Tarski’s claim that natural languages are universal. (shrink)

In this paper, I examine a solution to the Liar paradox found in the work of Ockham, Burley, and Pseudo-Sherwood. I reject the accounts of this solution offered by modern commentators. I argue that this medieval line suggests a non-hierarchical solution to the Liar, according to which ?true? is analysed as an indexical term, and paradox is avoided by minimal restrictions on tokens of ?true?. In certain respects, this solution resembles the recent approaches of Charles Parsons and Tyler Burge; in (...) other respects, it is related to a suggestion of Gödel. But, as a whole, it suggests an original solution to the Liar paradox, quite unlike any current proposals. (shrink)

In 1905, Richard discovered his paradox of definability, and in a letter written that year he presented both the paradox and a solution to it.Soon afterwards, Poincaré endorsed a variant of Richard?s solution.In this paper, I critically examine Richard?s and Poincaré?s ways out.I draw on an objection of Peano?s, and argue that their stated solutions do not work.But I also claim that their writings suggest another way out, different from their stated solutions, and different from the orthodox Tarskian approach.I argue (...) that this second solution does not prevent the return of the paradox. (shrink)

In this paper, I raise some interconnected concerns for Paul Horwich’s minimal theory of truth, framed by these three questions: How should the minimal theory be formulated? How does the minimal theory address the liar paradox? What is the explanatory role of the concept of truth? I conclude that we cannot be linguistic or conceptual deflationists about truth.

A Curry paradox about truth is generated by the following sentence, written on the board in room 101:If the sentence on the board in room 101 is true then 1 ≠ 1.A Curry paradox about validity is generated by the following argument, written on the board in room 102:The argument on the board in room 102 is valid. Therefore, 1 ≠ 1.Though the sentence and the argument generate Curry paradoxes, they also generate more basic paradoxes, in a sense to be (...) made clear. I argue that if we solve these more basic paradoxes, we have solutions to both kinds of Curry paradox. The positive proposal is in part inspired by a brief remark of Gödel’s, that the paradoxes might appear “as something analogous to dividing by zero”—so that the concepts of truth and validity, for example, are everywhere applicable except for certain singular points or singularities. A second central claim is that 'true' and 'valid' are context-sensitive predicates. This contextual-singularity approach to the Curry paradoxes applies also to other paradoxes of truth, validity, denotation, and predicate-extension. So a more general aim of the paper is to provide a unified response to semantic paradox. (shrink)

This volume is designed to set out some of the central issues in the theory of truth. It draws together, for the first time, the debates between philosophers who favor 'robust' or 'substantive' theories of truth, and those other, 'deflationist' or minimalists, who deny that such theories can be given. The editors provide a substantial introduction, in which they look at how the debates relate to further issues, such as the Liar paradox and formal truth theories.

In this paper I present two new paradoxes, a definability paradox (related to the paradoxes of Berry, Richard and König), and a paradox about extensions (related to Russell’s paradox). However, unlike the familiar definability paradoxes and Russell’s paradox, these new paradoxes involve no self-reference or circularity.

This chapter contains sections titled: Introduction Semantic Paradoxes: Some Proposals Sets and Extensions Three Paradoxes A Contextual Approach A Singularity Proposal Universality.

This dissertation is a critical examination of dialetheism, the view that there are true contradictions. Dialetheism's proponents argue that adopting the view will allow us to solve hitherto unsolved problems, including the well-known logical paradoxes. ;Dialetheism faces three kinds of challenge. Challenges of the first kind put in doubt the intrinsic coherence of dialetheism. It can be claimed, for example, that it is incoherent for a claim to be both true and false; that claims known to be false cannot be (...) accepted; that claims known to be false cannot be rationally accepted; and that dialetheism entails the falsity of some of its own theoretical claims. The second kind of challenge concerns the use of paraconsistent logics, which dialetheists must adopt on pain of accepting the truth of every proposition. I examine a number of paraconsistent logics, and conclude that either they come at an unacceptably high price or they do not support the dialetheist project. ;I devote most attention to the third kind of challenge, according to which dialetheism fails to provide the promised solutions to the paradoxes and other previously intractable problems, and so we lose the major motivation for the theory. Proponents claim that dialetheism allows for the solution of numerous problems, particularly in metaphysics, law, and logic. In the case of metaphysics, it is claimed that dialetheism allows us to deal with puzzles involving change, vagueness, and motion. However, I argue that the proposed solution does not eliminate the old metaphysical problems, and in fact gives rise to new ones. In the case of law, it is claimed that dialetheism can allow us to deal with legal contradiction. I argue there are more plausible means of solving such conflicts. The strongest case for dialetheism is that it allows us to solve logical and semantic paradoxes of self-reference, some of which have endured for well over two thousand years. I construct a paradox that the dialetheist cannot accommodate, and which shows that dialetheism never provided a solution to the paradoxes at all, even in their more familiar forms. (shrink)

This dissertation is a critical examination of dialetheism, the view that there are true contradictions. Dialetheism's proponents argue that adopting the view will allow us to solve hitherto unsolved problems, including the well-known logical paradoxes. ;Dialetheism faces three kinds of challenge. Challenges of the first kind put in doubt the intrinsic coherence of dialetheism. It can be claimed, for example, that it is incoherent for a claim to be both true and false; that claims known to be false cannot be (...) accepted; that claims known to be false cannot be rationally accepted; and that dialetheism entails the falsity of some of its own theoretical claims. The second kind of challenge concerns the use of paraconsistent logics, which dialetheists must adopt on pain of accepting the truth of every proposition. I examine a number of paraconsistent logics, and conclude that either they come at an unacceptably high price or they do not support the dialetheist project. ;I devote most attention to the third kind of challenge, according to which dialetheism fails to provide the promised solutions to the paradoxes and other previously intractable problems, and so we lose the major motivation for the theory. Proponents claim that dialetheism allows for the solution of numerous problems, particularly in metaphysics, law, and logic. In the case of metaphysics, it is claimed that dialetheism allows us to deal with puzzles involving change, vagueness, and motion. However, I argue that the proposed solution does not eliminate the old metaphysical problems, and in fact gives rise to new ones. In the case of law, it is claimed that dialetheism can allow us to deal with legal contradiction. I argue there are more plausible means of solving such conflicts. The strongest case for dialetheism is that it allows us to solve logical and semantic paradoxes of self-reference, some of which have endured for well over two thousand years. I construct a paradox that the dialetheist cannot accommodate, and which shows that dialetheism never provided a solution to the paradoxes at all, even in their more familiar forms. (shrink)

University of North Carolina at Chapel Hill.

There is a core metaphysical claim shared by all deflationists: truth is not a genuine, substantive property. But anyone who denies that truth is a genuine property must still make sense of our pervasive truth talk. In addressing questions about the meaning and function of ‘true’, deflationists engage in a linguistic or semantic project, a project that typically goes hand-in-hand with a deflationary account of the concept of truth. A thoroughgoing deflationary account of truth will go beyond the negative metaphysical (...) claim about truth and the positive linguistic account of the word ‘true’: it will also maintain that the concept of truth is a ‘thin’ concept that bears no substantive conceptual connections to other concepts to which it is traditionally tied. (shrink)

_ Semantic Singularities: Paradoxes of Reference, Predication and Truth _ By SimmonsKeithOxford University Press, 2018. x + 250 pp.

Philosophical work on truth covers two streams of inquiry, one concerning the nature (if any) of truth, the other concerning truth-related paradox, especially the Liar. For the most part these streams have proceeded fairly independently of each other. In his "Deflationary Truth and the Liar" (JPL 28:455-488, 1999) Keith Simmons argues that the two streams bear on one another in an important way; specifically, the Liar poses a greater problem for deflationary conceptions of truth than it does for (...) inflationist conceptions. We agree with Simmons on this point; however, we disagree with his main conclusion. In a nutshell, Simmons' main conclusion is that deflationists can solve the Liar only by compromising deflationism. If Simmons is right, then deflationists cannot solve the Liar paradox. In this paper we argue that, pace Simmons, there is an approach to the Liar that is available to deflationists, namely dialetheism. (shrink)

Methodological pluralism is advocated in this book, which takes students on an investigative tour of uncertainty in the social sciences, with particular emphasis on the scientific response to uncertainty. Much of the material is drawn from the disciplines of international relations and politics.

Addressing Merleau-Ponty's work Phenomenology of Perception, in dialogue with The Visible and the Invisible, his lectures at the Collège de France, and his reading of Proust, this book argues that at play in his thought is a philosophy of “ontological lateness”. This describes the manner in which philosophical reflection is fated to lag behind its objects; therefore an absolute grasp on being remains beyond its reach. Merleau-Ponty articulates this philosophy against the backdrop of what he calls “cruel thought”, a style (...) of reflecting that seeks resolution by limiting, circumscribing, and arresting its object. By contrast, the philosophy of ontological lateness seeks no such finality-no apocalypsis or unveiling-but is characterized by its ability to accept the veiling of being and its own constitutive lack of punctuality. To this extent, his thinking inaugurates a new relation to the becoming of sense that overcomes cruel thought. Merleau-Ponty's work gives voice to a wisdom of dispossession that allows for the withdrawal of being. Never before has anyone engaged with the theme of Merleau-Ponty's own understanding of philosophy in such a sustained way as Whitmoyer does in this volume. (shrink)

In the mathematics education research literature, there is a growing body of scholarship on how mathematicians practice their craft. The purpose of this chapter is to survey some of this literature and explain how it can contribute to the philosophy of mathematical practice. We first describe how mathematics educators use empirical methodologies to investigate the behaviors of mathematicians and argue that findings from these studies can inform the philosophy of mathematical practice. We then illustrate this by summarizing research on mathematicians’ (...) understandings and mathematicians’ proof reading. (shrink)

Ontological pluralism is the view that there are different fundamental ways of being. Trenton Merricks has recently raised three objections to combining pluralism with a generic way of being enjoyed by absolutely everything there is: first, that the resulting view contradicts the pluralist’s core intuition; second, that it is especially vulnerable to the charge—due to Peter van Inwagen—that it posits a difference in being where there is simply a difference in kind; and, third, that it is in tension with various (...) historically influential motivations for pluralism. I reply to each of these objections in turn. My replies will help to bring out the true nature of the pluralist’s basic commitments. (shrink)

Interpretation is the process whereby a hearer reasons to an interpretation of a speaker's discourse. The hearer normally adopts a credulous attitude to the discourse, at least for the purposes of interpreting it. That is to say the hearer tries to accommodate the truth of all the speaker's utterances in deriving an intended model. We present a nonmonotonic logical model of this process which defines unique minimal preferred models and efficiently simulates a kind of closed-world reasoning of particular interest for (...) human cognition. Byrne's “suppression” data (Byrne, 1989) are used to illustrate how variants on this logic can capture and motivate subtly different interpretative stances which different subjects adopt, thus indicating where more fine-grained empirical data are required to understand what subjects are doing in this task. We then show that this logical competence model can be implemented in spreading activation network models. A one pass process interprets the textual input by constructing a network which then computes minimal preferred models for (3-valued) valuations of the set of propositions of the text. The neural implementation distinguishes easy forward reasoning from more complex backward reasoning in a way that may be useful in explaining directionality in human reasoning. (shrink)

By carefully considering Galileo’s letters to Castelli and Christina, we argue that his position regarding the relationship between Scripture and science is not only of historical importance, but continues to stand as a perspective worth taking seriously in the context of contemporary philosophical debates. In particular, we contend that there are at least five areas of contemporary concern where Galileo’s arguments are especially relevant: (1) the supposed conflict between science and religion, (2) the status and stakes of evidence, (3) the (...) question of biblical infallibility in light of scientific progress, (4) metaphorical approaches to biblical hermeneutics, and (5) possible dialogical constraints on public discourse. (shrink)

Jerrold J. Katz often explained his semantic theory by way of an analogy with physical atomism and an attendant analogy with chemistry. In this chapter, I track the origin and uses of these analogies by Katz, both in explaining and defending his decompositional semantic theory, through the various phases of his work throughout his career.

David Hume’s arguments against believing reports of miracles are shown to be very weak. Laws of nature, I suggest, are best seen not as exceptionless rules but as context-dependent realizations of natural powers. In that context miracles transcend the natural order not as "violations" but as intelligible realizations of a divine supernatural purpose. Miracles are not parts of scientific theory but can be parts of a web of rational belief fully consistent with science. (edited).

Pessimism is, roughly, the view that life is not worth living. In chapter 46 of the second volume of The World as Will and Representation, Arthur Schopenhauer provides an oft-neglected argument for this view. The argument is that a life is worth living only if it does not contain any uncompensated evils; but since all our lives happen to contain such evils, none of them are worth living. The now standard interpretation of this argument (endorsed by Kuno Fischer and Christopher (...) Janaway) proceeds from the claim that the value—or rather valuelessness—of life’s goods makes compensation impossible. But this interpretation is neither philosophically attractive nor faithful to the text. In this paper, I develop and defend an alternative interpretation (suggested by Wilhelm Windelband and Mark Migotti) according to which it is instead the actual temporal arrangement of life’s goods and evils that makes compensation impossible. (shrink)

Counterfactual thinking involves the imagination of non-factual alternatives to reality. We investigated the spontaneous generation of both upward counterfactuals, which improve on reality, and downward counterfactuals, which worsen reality. All subjects gained $5 playing a computer-simulated blackjack game. However, this outcome was framed to be perceived as either a win, a neutral event, or a loss. "Loss" frames produced more upward and fewer downward counterfactuals than did either "win" or "neutral" frames, but the overall prevalence of counterfactual thinking did not (...) vary with outcome valence. In addition, subjects who expected to play the game again made more upward counterfactuals and were less satisfied with the outcome than were subjects who did not expect to play again. However, once subjects saw the cards from which they could have selected had they "hit" again (two winning cards and two losing cards), all subjects generated primarily upward counterfactuals and showed a corresponding decrease in satisfaction. These results implicate both cognitive and motivational factors in the generation of counterfactuals and tell us something about the functional value of counterfactual thinking: downward counterfactuals provide comfort; upward counterfactuals prepare one for the future. (shrink)

Indigenous peoples are disproportionally vulnerable to climate change. At the same time, they possess valuable knowledge for fair and sustainable climate adaptation planning and policymaking. Yet Indigenous peoples and knowledges are often excluded from or underrepresented within adaptation plans and policies. In this paper we ask whether the concept of epistemic injustice can be applied to the context of climate adaptation and the underrepresentation of Indigenous knowledges within adaptation policies and strategies. In recent years, the concept of epistemic injustice has (...) gained prominence, indicating that someone has been unfairly discriminated against in their capacity as a knower. We argue that many climate adaptation policies are epistemically unjust towards Indigenous peoples because of the underrepresentation of Indigenous knowledges by showing how the case of Indigenous knowledges in climate adaptation planning and policy satisfies five conditions of epistemic injustice. We further consider what challenges there are to integrating local and Indigenous knowledges within development in general, and climate adaptation strategies in particular and how these can be addressed. Whether the lack of Indigenous knowledges in climate adaptation policies constitutes an epistemic injustice matters because an injustice denotes an unfair advantage to one group – whether by design or default – that ought to be remedied and redressed. (shrink)