Abstract: The topic for this paper is the phenomenon of apparent value incommensurability—two goods are apparently incommensurable when it appears that neither is better than the other nor are they equally good. I shall consider three theories of this phenomenon. Indeterminists like Broome (1997) hold that the phenomenon is due to vagueness: when two goods appear to be incommensurable, this owes to the fact that “better than” is vague. Incommensurabilists like Chang (2002) hold that some goods appear to be incommensurable (...) because they genuinely are, because it is determinately the case than neither is better than the other, nor are they equally good. I defend epistemicism, the view that the appearance of value incommensurability is due only to our ignorance of how goods compare. In reality, all goods are commensurable. I offer two arguments for epistemicism and against other views. First, epistemicists are committed to less unexplained axiological structure than are non-epistemicists, who must explain the extra structure that they posit. Second, only epistemicists have an adequate explanation of some facts about the scope of apparent incommensurability. Finally, I identify a class of putative counterexamples to the epistemicist’s analysis, and argue that these counterexamples do not succeed. If my arguments are sound, then, we have very good reason to think that for any two things that are good, either one is (determinately) better than the other, or they are (determinately) equally good. (shrink)

Artificial Intelligence (AI) pervades humanity in 2022, and it is notoriously difficult to understand how certain aspects of it work. There is a movement—_Explainable_ Artificial Intelligence (XAI)—to develop new methods for explaining the behaviours of AI systems. We aim to highlight one important philosophical significance of XAI—it has a role to play in the elimination of vagueness. To show this, consider that the use of AI in what has been labeled _surveillance capitalism_ has resulted in humans quickly gaining the capability (...) to identify and classify most of the occasions in which languages are used. We show that the knowability of this information is incompatible with what a certain theory of vagueness—_epistemicism_—says about vagueness. We argue that one way the epistemicist could respond to this threat is to claim that this process brought about the end of vagueness. However, we suggest an alternative interpretation, namely that epistemicism is false, but there is a weaker doctrine we dub _technological epistemicism_, which is the view that vagueness is due to ignorance of linguistic usage, but the ignorance can be overcome. The idea is that knowing more of the relevant data and how to process it enables us to know the semantic values of our words and sentences with higher confidence and precision. Finally, we argue that humans are probably not going to believe what future AI algorithms tell us about the sharp boundaries of our vague words unless the AI involved can be explained in terms understandable by humans. That is, if people are going to accept that AI can tell them about the sharp boundaries of the meanings of their words, then it is going to have to be XAI. (shrink)

Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics, which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supply a classical concept of truth and to fully (...) support the rules and metarules of classical logic, and it is applied to vague terms as well as to theoretical or open-ended terms from mathematics and science. The theory also demonstrates how diachronic or synchronic interpretational continuity across languages is compatible with semantic indeterminacy. (shrink)

The extensions of vague predicates like ‘is bald’, ‘is tall’, and ‘is a heap’ apparently lack sharp boundaries, and this makes such predicates susceptible to soritical reasoning, i.e. reasoning that leads to some version of the notorious sorites paradox. This essay is concerned with a certain kind of theory of vagueness, according to which the symptoms and puzzles of vagueness should be accounted for in terms of a particular species of context sensitivity exhibited by vague expressions. The basic idea is (...) that the extensions of vague predicates vary with certain contextual factors, and that this fact can explain why they appear to lack sharp boundaries. This kind of view is referred to as contextualism about vagueness. A detailed characterisation of contextualism about vagueness is given in chapter two and three. In chapter two, a generic version of contextualism about vagueness is developed, and some alternative forms of context sensitivity are introduced. In chapter three, the specific contextual factors appealed to by different contextualists are discussed. In chapter four, different contextualist diagnoses of the sorites paradox are considered, and found to be problematic in various ways. It is argued that contrary to what some of its proponents have claimed, contextualism about vagueness is not superior to other comparable theories of vagueness when it comes to explaining the appeal of soritical reasoning. In chapter five, a certain version of the sorites paradox, known as the forced march sorites, is discussed. It is argued that “data” about how speakers would behave in the forced march cannot lend any firm support to contextualism about vagueness. In chapter six, some problems concerning the instability of the contextual factors are considered. One problem is that contextualist diagnoses of the sorites which locate a fallacy of equivocation in the reasoning seem to render non-soritical reasoning fallacious as well. A model for treating this problem is suggested, but on closer consideration, it turns out to be problematic. Moreover, this model is of no help in solving the more general problem that even if classical logic remains valid for vague language on some contextualist views, the instability of the extensions of vague predicates makes it difficult to know when a certain piece of reasoning instantiates a valid argument form. Other difficulties arise with respect to speech reports and belief contents. Chapter seven concludes with a summary and some methodological remarks. (shrink)

What is the relation of logic to thinking? My dissertation offers a new argument for the claim that logic is constitutive of thinking in the following sense: representational activity counts as thinking only if it manifests sensitivity to logical rules. In short, thinking has to be minimally logical. An account of thinking has to allow for our freedom to question or revise our commitments – even seemingly obvious conceptual connections – without loss of understanding. This freedom, I argue, requires that (...) thinkers have general abilities to respond to support and tension among their thoughts. And these abilities are constituted by following logical rules. So thinkers have to follow logical rules. But there isn’t just one correct logic for thinking. I show that my view is consistent with logical pluralism: there are a range of correct logics, any one of which a thinker might follow. A logic for thinking does, however, have to contain certain minimal principles: Modus Ponens and Non-Contradiction, and perhaps others. We follow logical rules by exercising logical capacities, which display a distinctive first-person/third-person asymmetry: a subject can find the instances of a rule compelling without seeing them as instances of a rule. As a result, there are two limits on illogical thinking. First, thinkers have to tend to find instances of logical rules compelling. Second, thinkers can’t think in obviously illogical ways. So thinking has to be logical – but not perfectly so. When we try to think, but fail, we produce nonsense. But our failures to think are often subjectively indistinguishable from thinking. To explain how this occurs, I offer an account of nonsense. To be under the illusion that some nonsense makes sense is to enter a pretence that the nonsense is meaningful. Our use of nonsense within the pretence relies on the role of logical form in understanding. Finally, while the normativity of logic doesn’t fall directly out of logical constitutivism, it’s possible to build an attractive account of logical normativity which has logical constitutivism as an integral part. I argue that thinking is necessary for human flourishing, and that this is the source of logical normativity. (shrink)

One of the few points of agreement between most theists and non-theists working on the problem of evil is that the existence of a perfect God is incompatible with the existence of pointless evil. In a series of influential papers, however, Peter van Inwagen has argued that careful attention to the reasoning behind this claim reveals fatal difficulties related to the Sorites Paradox. In this paper, I explain van Inwagen’s appeal to sorites reasoning, distinguish between two different arguments in his (...) work, and argue that they both commit the same so-far-unnoticed mistake. (shrink)

This paper aims to support the claim that analytic metaphysics should be more cautious regarding the constraints that truthmaking considerations impose on metaphysical theories. To this end, I reply to Briggs and Forbes (2017), whoargue that certain truthmaking commitments are incurred by a Humean metaphysics and by the Growing-Block theory. First, I argue that Humean Supervenience does not need to endorse a standard version of truthmaker maximalism. This undermines Briggs and Forbes’s conclusion that Humean Supervenience and the Growing-Block theory are (...) incompatible. Second, I argue that the Growing-Block theory does not commit us to any weaker version of truthmaker maximalism, which also undermines Briggs and Forbes’s conclusion. Finally, I point out other reasons to think that any version of truthmaker maximalism is disputable, undermining a fortiori Briggs and Forbes’s conclusion and supporting the moral that metaphysical theories—or at least Humean Supervenience, the Growing-Block theory, and presentism—are little constrained by truthmaking commitments. (shrink)

ABSTRACT Our ascriptions of content to past utterances assign to them a level of conceptual continuity and determinacy that extends beyond what could be grounded in the usage up to their time of utterance. If one accepts such ascriptions, one can argue either that future use must be added to the grounding base, or that such cases show that meaning is not, ultimately, grounded in use. The following will defend the first option as the more promising of the two, though (...) this ultimately requires understanding the relation between use and meaning as ‘normative’ in two important ways. The first way is that the function from use to meaning must be of a sort that allows us to maintain a robust distinction between actual and correct use. The second sort of normativity is unique to theories that extend the grounding base into the future. In particular, if meaning is partially a function of future use, we can see our commitment to the ‘determinacy’ of meaning as a practical commitment that structures our linguistic practices rather than a theoretical commitment that merely describes them. (shrink)

In this dissertation, I argue that vagueness is a metaphysical phenomenon---that properties and objects can be vague---and propose a trivalent theory of vagueness meant to account for the vagueness in the world. In the first half, I argue against the theories that preserve classical logic. These theories include epistemicism, contextualism, and semantic nihilism. My objections to these theories are independent of considerations of the possibility that vagueness is a metaphysical phenomenon. However, I also argue that these theories are not capable (...) of accommodating metaphysical vagueness. As I move into my positive theory, I first argue for the possibility of metaphysical vagueness and respond to objections that charge that the world cannot be vague. One of these objections is Gareth Evans' much-disputed argument that vague identities are impossible. I then describe what I call the logic of states of affairs. The logic of states of affairs has as its atomic elements states of affairs that can obtain, unobtain, or be indeterminate. Finally, I argue that the logic of states of affairs is a better choice for a theory of vagueness than other logics that could accommodate metaphysical vagueness such as supervaluationism and degree theories. Preference should be given to the logic of states of affairs because it provides a better explanation of higher-order vagueness and does a better job of matching our ordinary understandings of logical operators than supervaluationism does and because it provides a more general account of indeterminacy than the account given by degree theories. Advisor: Reina Hayaki. (shrink)

Various psychopathologies of self-awareness, such as somatoparaphrenia and thought insertion in schizophrenia, might seem to threaten the viability of the higher-order thought (HOT) theory of consciousness since it requires a HOT about one’s own mental state to accompany every conscious state. The HOT theory of consciousness says that what makes a mental state a conscious mental state is that there is a HOT to the effect that “I am in mental state M.” I have argued in previous work that a (...) HOT theorist can adequately respond to this concern with respect to somatoparaphrenia and thought insertion. There is also Cotard syndrome which is a rare neuropsychiatric disorder in which people hold the delusional belief that they are dead, do not exist, or have lost their blood or internal organs. In this paper, I argue that HOT theory has nothing to fear from it either and can consistently account for what happens in such unusual cases. I analyze Cotard syndrome in light of my previous discussion of somatoparaphrenia and thought insertion, and argue that HOT theory can provide a somewhat analogous account without the worry of inconsistency. It is crucial to recognize that there are multiple “self-concepts” and levels of HOTs which can help to provide a more nuanced explanation. With regard to the connection between consciousness and self-consciousness, it is proposed that Cotard patients are indeed capable of having some “I-thoughts” about their bodies and mental states. (shrink)

In this thesis, I will defend a new kind of compatibilist account of free action, indirect conscious control compatibilism (or indirect compatibilism for short), and argue that some of our actions are free according to it. My argument has three components, and involves the development of a brand new tool for experimental philosophy, and the use of cognitive neuroscience. The first component of the argument shows that compatibilism (of some kind) is a conceptual truth. Contrary to the current orthodoxy in (...) the free will literature, which is that our concept of free will is an incompatibilist concept - a concept according to which we have free will only if determinism is false - I will show that our concept of free will is in fact a compatibilist concept - a concept according to which we can have free will even if determinism is true - and I do so using a new experimental philosophy methodology inspired by two-dimensional semantics. -/- Of course, even if our concept of free will is a compatibilist concept, this does not mean that there are any free actions in the world: the current empirical evidence from the brain sciences appears to show that there might be no, or very few, free actions in the world, even on many compatibilist understandings of what it would take for there to be free will. The second component of the argument addresses this concern by extending our understanding of compatibilism. Agents act freely either when their actions are caused by compatibilistically acceptable psychological processes, or are indirectly caused by those same processes. Hence the name of my account: indirect compatibilism. -/- The final component of the argument defends my new account against some interesting objections and provides evidence from cognitive neuroscience that some of our actions count as free by the lights of indirect compatibilism. (shrink)

Development of decision-support and intelligent agent systems necessitates mathematical descriptions of uncertainty and fuzziness in order to model vagueness. This paper seeks to present an outline of Peirce’s triadic logic as a practical new way to model vagueness in the context of artificial intelligence. Charles Sanders Peirce was an American scientist–philosopher and a great logician whose triadic logic is a culmination of the study of semiotics and the mathematical study of anti-Cantorean model of continuity and infinitesimals. After presenting Peircean semiotics (...) within AI perspective, a mathematical formulation of a Peircean triadic set is given in relationship with classical and fuzzy sets. Using basic logical operators, all possible respective implication operators, bi-equivalence operators, valid rules of inference, and associative, distributive and commutative logical properties are derived and verified through the truth function approach. In order to suggest practical directions, aggregation operators for Peirce’s triadic logic have been formulated. A mathematical formulation of a medical diagnostic problem and ER diagram of a library management system using Peirce’s triadic relation show potential for further applications of the proposed triadic set and triadic logic. Alongside, a classical AI game—The Wumpus World—is implemented to show practical efficacy in comparison with binary implementation. Besides giving some preliminary formulations for trichotomous set theory and definition of finite automaton, development of hybrid architectures for intelligent agents and evolutionary computations are discussed as potential practical avenues for Peirce’s triadic logic. (shrink)

The sentences employed in semantic paradoxes display a wide range of semantic behaviours. However, the main theories of truth currently available either fail to provide a theory of paradox altogether, or can only account for some paradoxical phenomena by resorting to multiple interpretations of the language. In this paper, I explore the wide range of semantic behaviours displayed by paradoxical sentences, and I develop a unified theory of truth and paradox, that is a theory of truth that also provides a (...) unified account of paradoxical sentences. The theory I propose here yields a threefold classification of paradoxical sentences – liar-like sentences, truth-teller-like sentences, and revenge sentences. Unlike existing treatments of semantic paradox, the theory put forward in this paper yields a way of interpreting all three kinds of paradoxical sentences, as well as unparadoxical sentences, within a single model. (shrink)

Is faith that p compatible with disbelief that p? I argue that it is. After surveying some recent literature on the compatibility of propositional and non-propositional forms of faith with the lack of belief, I take the next step and offer several arguments for the thesis that both these forms of faith are also compatible, in certain cases, with outright disbelief. This is contrary to the views of some significant recent commentators on propositional faith, including Robert Audi and Daniel Howard-Snyder. (...) The primary argument revolves around the possibility of maintaining a single faith through drastic changes in cognitive attitude. I argue that once we allow that propositional faith is compatible with weaker cognitive attitudes than belief, such as acceptance or assent, there is prima facie reason to consider propositional faith as sometimes compatible with disbelief. I then consider objections and offer some final reflections on the significance of the thesis. (shrink)

I defend a solution to the puzzle of petitionary prayer based on some ideas of Aquinas, Gregory the Great, and contemporary desert theorists. I then address a series of objections. Along the way broader issues about the nature of desert, what is required for an action to have a point, and what is required for a puzzle to have a solution are discussed.

Most paradoxes of self-reference have a dual or ‘hypodox’. The Liar paradox (Lr = ‘Lr is false’) has the Truth-Teller (Tt = ‘Tt is true’). Russell’s paradox, which involves the set of sets that are not self-membered, has a dual involving the set of sets which are self-membered, etc. It is widely believed that these duals are not paradoxical or at least not as paradoxical as the paradoxes of which they are duals. In this paper, I argue that some paradox’s (...) duals or hypodoxes are as paradoxical as the paradoxes of which they are duals, and that they raise neglected and interestingly different problems. I first focus on Richard’s paradox (arguably the simplest case of a paradoxical dual), showing both that its dual is as paradoxical as Richard’s paradox itself, and that the classical, Richard-Poincaré solution to the latter does not generalize to the former in any obvious way. I then argue that my argument applies mutatis mutandis to other paradoxes of self-reference as well, the dual of the Liar (the Truth-Teller) proving paradoxical. (shrink)

Conceptual Engineering alleges that philosophical problems are best treated via revising or replacing our concepts (or words). The goal here is not to defend Conceptual Engineering but rather show that it can (and should) invoke Neutralism—the broad view that philosophical progress can take place when (and sometimes only when) a thoroughly neutral, non-specific theory, treatment, or methodology is adopted. A neutralist treatment of one form of skepticism is used as a case study and is compared with various non-neutral rivals. Along (...) the way, a new taxonomy for paradox is proposed. (shrink)

We present counterexamples to the widespread assumption that Moorean sentences cannot be rationally asserted. We then explain why Moorean assertions of the sort we discuss do not incur the irrationality charge. Our argument involves an appeal to the dual-process theory of the mind and a contrast between the conditions for ascribing beliefs to oneself and the conditions for making assertions about independently existing states of affairs. We conclude by contrasting beliefs of the sort we discuss with the structurally similar but (...) rationally impermissible beliefs of certain psychiatric patients. (shrink)

This dialogue between Achilles and the Tortoise – in the spirit of those of Carroll and Hofstadter – argues against the idea, identified with the “traditional” interpretation of Aristotle’s “sea battle argument”, that future contingents are an exception to the Principle of Bivalence. It presents examples of correct everyday predictions, without which one would not be able to decide and to act; however, doing this is incompatible with the belief that the content of these predictions lacks a truth-value. The cost (...) of using a non-classical logic to cope with that may be too high for Stagirite’s defenders, and they would still need to explain why our ordinary predictions seem to have a binary truth-value. In the end, the paper suggests that the problem of future contingents – and of free will – is not a logical problem at all, but rather a limit on what an agent can believe before taking a decision. (shrink)

In his seminal paper, ‘Can There Be Vague Objects?’ (1978), Gareth Evans advanced an argument purporting to prove that the idea of indeterminate identity is incoherent. Aware that his argument was incomplete as it stands, Evans added a remark at the end of his paper, in which he explained how the original argument needed to be modified to arrive at an explicit contradiction. This paper aims to develop a modified version of Evans’ original argument, which I argue is more promising (...) than the modification that Evans proposed in his remark. Last, a structurally similar argument against the idea of indeterminate existence is presented. (shrink)

On some accounts of vagueness, predicates like “is a heap” are tolerant. That is, their correct application tolerates sufficiently small changes in the objects to which they are applied. Of course, such views face the sorites paradox, and various solutions have been proposed. One proposed solution involves banning repeated appeals to tolerance, while affirming tolerance in any individual case. In effect, this solution rejects the reasoning of the sorites argument. This paper discusses a thorny problem afflicting this approach to vagueness. (...) In particular, it is shown that, on the foregoing view, whether an object is a heap will sometimes depend on factors extrinsic to that object, such as whether its components came from other heaps. More generally, the paper raises the issue of how to count heaps in a tolerance-friendly framework. (shrink)

Semantic paradoxes like the liar are notorious challenges to truth theories. A paradox can be phrased with minimal resources and minimal assumptions. It is not surprising, then, that the liar is also a challenge to minimalism about truth. Horwich (1990) deals swiftly with the paradox, after discriminating between other strategies for avoiding it without compromising minimalism. He dismisses the denial of classical logic, the denial that the concept of truth can coherently be applied to propositions, and the denial that the (...) liar sentence expresses a proposition, but he endorses the denial that the liar is an acceptable instance of the equivalence schema (E). This paper has two main parts. It first shows that Horwich’s preferred denial is also problematic. As Simmons (1999), Beall and Armour-Garb (2003), and Asay (2015) argued, the solution is ad hoc, faces a possible loss of expressibility, and is ultimately unstable. Finally, the paper explores a different combination of possibilities for minimalism: treating the truth-predicate as context-dependent, rejecting the notion that the liar expresses a proposition, and reinterpreting negation in some contexts as metalinguistic denial. The paper argues that these are preferable options, but signposts possible dangers ahead. (shrink)

This is a paper about the nature of metaphysical laws and their relation to the phenomenon of vagueness. Metaphysical laws are introduced as analogous to natural laws, and metaphysical indeterminism is modeled on causal indeterminacy. This kind of indeterminacy is then put to work in developing a novel theory of vagueness and a solution to the sorites paradox.

The Ramseyan thesis that the probability of an indicative conditional is equal to the corresponding conditional probability of its consequent given its antecedent is both widely confirmed and subject to attested counterexamples (e.g., McGee 2000, Kaufmann 2004). This raises several puzzling questions. For instance, why are there interpretations of conditionals that violate this Ramseyan thesis in certain contexts, and why are they otherwise very rare? In this paper, I raise some challenges to Stefan Kaufmann's account of why the Ramseyan thesis (...) sometimes fails, and motivate my own theory. On my theory, the proposition expressed by an indicative conditional is partially determined by a background partition, and hence its probability depends on the choice of such a partition. I hold that this background partition is contextually determined, and in certain conditions is set by a salient question under discussion in the context. I show how the resulting theory offers compelling answers to the puzzling questions raised by failures of the Ramseyan thesis. (shrink)

Category mistakes are sentences such as ”The number two is blue’ or ”Green ideas sleep furiously’. Such sentences are highly infelicitous and thus a prominent view claims that they are meaningless. Category mistakes are also highly prevalent in figurative language. That is to say, it is very common for sentences which are used figuratively to be such that, if taken literally, they would constitute category mistakes. In this paper I argue that the view that category mistakes are meaningless is inconsistent (...) with many central and otherwise plausible theories of figurative language. Thus if the meaninglessness view is correct, the theories in question must each be rejected, and conversely, if any of the theories in question is correct, the meaninglessness view must be wrong. The debates concerning the semantics of figurative language and concerning the semantic status of category mistakes are closely connected. (shrink)

There is an interesting logical/semantic issue with some mathematical languages and theories. In the language of (pure) complex analysis, the two square roots of i’ manage to pick out a unique object? This is perhaps the most prominent example of the phenomenon, but there are some others. The issue is related to matters concerning the use of definite descriptions and singular pronouns, such as donkey anaphora and the problem of indistinguishable participants. Taking a cue from some work in linguistics and (...) the philosophy of language, I suggest that i functions like a parameter in natural deduction systems. This may require some rethinking of the role of singular terms, at least in mathematical languages. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, such (...) as the question of how actuality can be understood and formally represented in a branching framework. The present volume is intended to be a 360 degree reflection on the tree model. The contributions is gathers concern the model and its alternatives, both from a semantic and from a metaphysical point of view. ​. (shrink)

One feature of vague predicates is that, as far as appearances go, they lack sharp application boundaries. I argue that we would not be able to locate boundaries even if vague predicates had sharp boundaries. I do so by developing an idealized cognitive model of a categorization faculty which has mobile and dynamic sortals (`classes', `concepts' or `categories') and formally prove that the degree of precision with which boundaries of such sortals can be located is inversely constrained by their flexibility. (...) Given the literature, it is plausible that we are appropriately like the model. Hence, an inability to locate sharp boundaries is not necessarily because there are none; boundaries could be sharp and it is plausible that we would nevertheless be unable to locate them. (shrink)

The No-No Paradox consists of a pair of statements, each of which ?says? the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker: Given the relevant instances of the T-schema, one of the two statements comprising the ?paradox? must be true (and the other false), but symmetry constraints prevent us from determining which, and thus prevent there being a truthmaker grounding the relevant assignment of truth values. Sorensen's view (...) is mistaken: situated within an appropriate background theory of truth, the statements comprising the No-No Paradox are genuinely paradoxical in the same sense as is the Liar (and thus, on Sorensen's view, must fail to have truth values). This result has consequences beyond Sorensen's semantic framework. In particular, the No-No Paradox, properly understood, is not only a new paradox, but also provides us with a new type of paradox, one which depends upon a general background theory of the truth predicate in a way that the Liar Paradox and similar constructions do not. (shrink)

Consider the following sentences: The neighbouring sentence is not true. The neighbouring sentence is not true. Call these the no-no sentences. Symmetry considerations dictate that the no-no sentences must both possess the same truth-value. Suppose they are both true. Given Tarski’s truth-schema—if a sentence S says that p then S is true iff p—and given what they say, they are both not true. Contradiction! Conclude: they are not both true. Suppose they are both false. Given Tarski’s falsity-schema—if a sentence S (...) says that p then S is false iff not-p—and given what they say, they are both true, and so not false. Contradiction! Conclude: they are not both false. Thus, despite their symmetry, the no-no sentences must differ in truth-value. Such is the no-no paradox.[1] Sorensen (2001, 2005a, 2005b) has argued that: (1) The no-no paradox is not a version of the liar but rather a cousin of the truth-teller paradox. (2) Even so, the no-no paradox is more paradoxical than the truth-teller. (3) The no-no and truth-teller sentences have groundless truthvalues—they are bivalent but give rise to “truthmaker gaps”. (4) It is metaphysically impossible to know these truth-values. (5) A truthmaker gap response to the no-no paradox provides reason to accept a version of epistemicism. In this paper it is shown that a truthmaker gap solution to the no-no and truth-teller paradoxes runs afoul of the dunno-dunno paradox, the strengthened no-no paradox, and the strengthened truth-teller paradox. In consequence, the no-no paradox is best seen as a form of the liar paradox. As such, it cannot provide a case for epistemicism. (shrink)

The paper challenges Williamson’s safety based explanation for why we cannot know the cut-off point of vague expressions. We assume throughout (most of) the paper that Williamson is correct in saying that vague expressions have sharp cut-off points, but we argue that Williamson’s explanation for why we do not and cannot know these cut-off points is unsatisfactory. -/- In sect 2 we present Williamson's position in some detail. In particular, we note that Williamson's explanation relies on taking a particular safety (...) principle ('Meta-linguistic belief safety' or 'MBS') as a necessary condition on knowledge. In section 3, we show that even if MBS were a necessary condition on knowledge, that would not be sufficient to show that we cannot know the cut-off points of vague expressions. In section 4, we present our main case against Williamson's explanation: we argue that MBS is not a necessary condition on knowledge, by presenting a series of cases where one's belief violates MBS but nevertheless constitutes knowledge. In section 5, we present and respond to an objection to our view. And in section 6, we briefly discuss the possible directions a theory of vagueness can take, if our objection to Williamson's theory is taken on board. (shrink)

A notion of truth as applicable to events of assertoric use ( utterances ) of a sentence token is arguably presupposed and required by our evaluative practices of the use of language. The truth of an utterance seems clearly to depend on what the utterance says . This fundamental dependence seems in turn to be captured by the schema that, if an utterance u says that P , then u is true iff P . Such a schema may thus be (...) thought to constitute a suitable basis for an adequate theory of utterance truth, so much so that it seems straightforwardly to avoid the problems arising from context dependence and the semantic paradoxes which notoriously beset theories of utterance truth based on a simple disquotational schema. The paper argues that appearances are deceptive in both cases. On the one hand, the schema cannot allow for plausible if not uncontroversial non-indexical forms of context dependence, arising from the possibility that what an utterance says can be the case or not relative to different situations and that the truth of an utterance u of a sentence φ arguably depends on the truth of φ at the situation "associated" with u . On the other hand, a quantified utterance-truth variation on the liar paradox shows that the schema entails some consequence φ and at the same time the untruth of any utterance of φ; moreover, a resilient quantified propositional variation on the contingent liar paradox is offered, which only relies on resources usually employed by theories of utterance truth based on the schema. (shrink)

Authors have a lot of leeway with regard to what they can make true in their story. In general, if the author says that p is true in the fiction we’re reading, we believe that p is true in that fiction. And if we’re playing along with the fictional game, we imagine that, along with everything else in the story, p is true. But there are exceptions to these general principles. Many authors, most notably Kendall Walton and Tamar Szabó Gendler, (...) have discussed apparent counterexamples when p is “morally deviant”. Many other statements that are conceptually impossible also seem to be counterexamples. In this paper I do four things. I survey the range of counterexamples, or at least putative counterexamples, to the principles. Then I look to explanations of the counterexamples. I argue, following Gendler, that the explanation cannot simply be that morally deviant claims are impossible. I argue that the distinctive attitudes we have towards moral propositions cannot explain the counterexamples, since some of the examples don’t involve moral concepts. And I put forward a proposed explanation that turns on the role of ‘higher-level concepts’, concepts that if they are satisfied are satisfied in virtue of more fundamental facts about the world, in fiction, and in imagination. (shrink)

Philosophy Compass 2: 896-909. (Link to Philosophy Compass.).

It is sometimes said that there are two, competing versions of W. V. O. Quine’s unrelenting empiricism, perhaps divided according to temporal periods of his career. According to one, logic is exempt from, or lies outside the scope of, the attack on the analytic-synthetic distinction. This logic-friendly Quine holds that logical truths and, presumably, logical inferences are analytic in the traditional sense. Logical truths are knowable a priori, and, importantly, they are incorrigible, and so immune from revision. The other, radical (...) reading of Quine does not exempt logic from the attack on analyticity and a priority. Logical truths and inferences are themselves part of the web of belief, and the same global methodology applies to logic as to any other part of the web, such as theoretical chemistry or ordinary beliefs about ordinary objects. Everything, including logic, is up for grabs in our struggle for holistic confirmation. The purpose of this paper is to examine the law of non-contradiction, and the concomitant principle of ex falso quodlibet, from the perspective of the principles advocated by the radical Quine. I show that he has no compelling reason to accept either of these. To put it bluntly, neither the law of non-contradiction nor the rule of ex falso quodlibet is empirically confirmed, and these principles fare poorly on the various criteria for theory acceptance on the methodology of the radical Quine. So the radical Quine is led rather quickly and rather directly into something in the neighborhood of Graham Priest’s dialetheism. (shrink)

In §2-4, I survey three extant ways of making sense of indeterminate truth and find each of them wanting. All the later sections of the paper are concerned with showing that the most promising way of making sense of indeterminate truth is via either a theory of truthmaker gaps or via a theory of truthmaking gaps. The first intimations of a truthmaker–truthmaking gap theory of indeterminacy are to be found in Quine (1981). In §5, we see how Quine proposes to (...) solve Unger’s problem of the many via positing the possibility of groundless truth. In §6, I elaborate the truthmaker gap model of indeterminacy first sketched by Sorensen (2001, ch.11) and use it to give a reductive analysis of indeterminate truth. In §7, I briefly assess what kind of formal framework can best express the possibility of truthmaker gaps. In §8, I contrast what I dub ‘the ordinary conception of worldly indeterminacy’ with Williamson’s conception of worldly indeterminacy. In §9, I show how one can distinguish linguistic from worldly indeterminacy on a truthmaker gap conception. In §10, I briefly sketch the relationship between truthmaker gaps and ignorance. In §11, I assess whether a truthmaker gap conception of vagueness is really just a form of epistemicism. In §12, I propose that truthmaker gaps can yield a plausible model of (semantic) presupposition failure. In §13, in response to the worry that a truthmaker gap conception of indeterminacy is both parochial and controversial—since it commits us to an implausibly strong theory of truthmaking—I set forth a truthmaking gap conception of indeterminacy. In §14, I answer the worry that groundless truths, of whatever species, are just unacceptably queer. A key part of this answer is that a truthmaker–truthmaking gap model of indeterminacy turns out to be considerably less queer than any model of indeterminacy which gives up on Tarski’s T-schema for truth (and cognate schemas). (shrink)

It is intuitive to suppose that the question of whether I persist through a given period will always have a metaphysically substantive ‘yes’ or ‘no’ answer. Derek Parfit challenges this intuition. Given the truth of Reductionism, he argues, identity can be indeterminate. The main argument Parfit marshals in support of this claim employs his Sorites-style Combined Spectrum thought experiment. Despite its influence, there are conspicuous gaps in his argument. Notably, he claims that identity is indeterminate when questions about persistence are (...) ‘empty’. But indeterminacy in Sorites puzzles is traditionally held to result from vagueness – a topic Parfit avoids. Without an account of the relationships between vagueness, indeterminacy, and question-emptiness, his argument remains incomplete. I begin by outlining Parfit’s argument as it stands. I then propose that we can provide the missing details by supplementing Parfit’s treatment of the Combined Spectrum with Sider’s notion of nonsubstantivity. This gives us a clearer understanding of Parfit’s indeterminacy claim, and affords the room to accommodate vagueness in his argument. Once we spell out what this means, however, it becomes clear that a more radical conclusion is justified by Parfit’s reasoning: it is always an empty question whether a person persists. (shrink)

A finite chain of valid arguments can never lead from truth to falsehood. Call this the concatenation principle, or CP. Some propose to reject CP in response to the sorites paradox. I offer...

Restrictionism is a response to the Liar and other paradoxes concerning truth. Restrictionists—as I will call proponents of the strategy—respond to these paradoxes by giving up instances of the schema -/- <p> is true iff p. -/- My aim is to show that the current unpopularity of restrictionism is undeserved. I will argue that, whilst cautious versions of the strategy may face serious problems, a radical and previously overlooked version of restrictionism provides a strong and defensible response to the paradoxes.

We present a strategy to dissolve semantic paradoxes which proceeds from an explanation of why paradoxical sentences or their definitions are semantically defective. This explanation is compatible with the acceptability of impredicative definitions, self-referential sentences and semantically closed languages and leaves the status of the so-called truth-teller sentence unaffected. It is based on platitudes which encode innocuous constraints on successful definition and successful expression of propositional content. We show that the construction of liar paradoxes and of certain versions of Curry's (...) paradox rests on presuppositions that violate these innocuous constraints. Other versions of Curry's paradox are shown not to be paradoxical at all once their presuppositions are made explicit. Part of what we say rehearses a proposal originally made by Laurence Goldstein in 1985. Like Goldstein we dispose of certain paradoxes by rejecting some of the premises from which they must be taken to proceed. However, we disagree with his more recent view that the premises to be rejected are neither true nor false. (shrink)

In 1907 Borel published a remarkable essay on the paradox of the Heap (“Un paradoxe économique: le sophisme du tas de blé et les vérités statistiques”), in which Borel proposes what is likely the first statistical account of vagueness ever written, and where he discusses the practical implications of the sorites paradox, including in economics. Borel’s paper was integrated in his book Le Hasard, published 1914, but has gone mostly unnoticed since its publication. One of the originalities of Borel’s essay (...) is that it puts forward a model of vagueness as imprecision, making particular use of the Gaussian law of measurement errors to model categorization. The aim of our paper is to give a presentation of the historical context of Borel’s essay, to spell out the mathematical details of his model, and to provide a critical assessment of his theory. Three aspects of Borel’s account are particularly discussed: the first concerns the comparison between Borel’s statistical account and posterior degree-theoretic accounts of vagueness. The second concerns the anti-epistemicist flavor of Borel’s approach, whereby the idea of statistical fluctuation is used to undermine the notion of sharp boundary for vague predicates. The third concerns the problematic link between Borel’s model of vagueness as imprecision and the notion of semantic indeterminacy. An English translation of Borel’s original essay is appended to this paper (Erkenntnis, this issue). (shrink)

This volume analyzes and studies how vagueness occurs and matters as a specific problem in the context of theories that are primarily about something else.

I argue that van Fraassen's Judy Benjamin Problem and Elga's Sleeping Beauty Problem have the same structure.

In ‘Epistemic Modals’ (2007), Seth Yalcin proposes Stalnaker-style semantics for epistemic possibility. He is inspired by John MacFarlane’s ingenious defence of relativism, in which claims of epistemic possibility are made rigidly from the perspective of the assessor’s actual stock of information (rather than from the speaker’s knowledge base or that of his audience or community). The innovations of MacFarlane and Yalcin independently reinforce the modal collapse espoused by Jaakko Hintikka in his 1962 epistemic logic (which relied on the implausible KK (...) principle and heavy idealizations). I respond to this new challenge with fresh objections to the underlying S4 equivalence: p p . I also propose counter-analyses of the intriguing data which Yalcin cites in support of his new semantics. A key collateral motivation for this defence of irredundant iterations is to ward off a threat to higher order vagueness. (shrink)

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems (...) to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox. (shrink)