This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Neutralism is 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. The broad goal here is to articulate a distinct, specific kind of sorites paradox (The Observational Sorites Paradox) and show that it can be effectively treated via Neutralism.

It is tempting to think that one’s perceptual evidence comprises just what issues from perceiving with each of the respective sensory modalities. However, empirical, rational, and phenomenological considerations show that one’s perceptual evidence can outstrip what one possesses due to perceiving with each separate sense. Some novel perceptual evidence stems from the coordinated use of multiple senses. This paper argues that some perceptual evidence in this respect is distinctively multisensory.

According to anti-atomism, we represent color properties (e.g., red) in virtue of representing color relations (e.g., redder than). I motivate anti-atomism with a puzzle involving a series of pairwise indistinguishable chips. I then develop two versions of anti-atomism.

Fallibilists about looks deny that the relation of looking the same as is non-transitive. Regarding familiar examples of coloured patches suggesting that such a relation is non-transitive, they argue that, in fact, indiscriminable adjacent patches may well look different, despite their perceptual indiscriminability: it’s just that we cannot notice the relevant differences in the chromatic appearances of such patches. In this paper, I present an argument that fallibilism about looks requires commitment to an empirically false consequence. To succeed in deflecting (...) putative cases of non-transitivity, fallibilists would have to claim that there can’t be any perceptual limitations of any kind on human chromatic discrimination. But there are good reasons to think such limitations exist. (shrink)

Conceptualists have it that the representational content of perceptual experience is determined by the concepts a subject applies in having such an experience. Conceptualists like Bill Brewer [1999] and John McDowell [1994] have laid particular emphasis on demonstrative concepts in trying to account for the fact that subjects can perceive and discriminate very many specific shades of colour in experience. Against this, it has been objected that such demonstrative concepts have incoherent conditions of extension and/or of individuation, due to the (...) fact that chromatic indiscriminability is non-transitive. In this paper, I consider three different versions of this objection and show why each fails. (shrink)

Can identity itself be vague? Can there be vague objects? Does a positive answer to either question entail a positive answer to the other? In this paper we answer these questions as follows: No, No, and Yes. First, we discuss Evans’s famous 1978 argument and argue that the main lesson that it imparts is that identity itself cannot be vague. We defend the argument from objections and endorse this conclusion. We acknowledge, however, that the argument does not by itself establish (...) either that there cannot be vague objects or that there cannot be identity statements that are indeterminate for ontic reasons. And we further acknowledge that it does not by itself establish that there cannot be identity statements that are indeterminate in virtue of the existence of vague objects. We then go on to argue that, despite this, one who believes in vague objects cannot endorse Evans’s argument. To establish this we offer supplementary arguments that show that if vague objects exist then identity is vague, and that if identity is vague then vague objects exist. Finally we draw attention to an argument parallel to that of Evans’s, but safer, which can be employed against the putative ontic indeterminacy in identity of vague objects which can be differentiated by identity-free properties. (shrink)

The way in which vision represents objects as being the same despite movement and qualitative changes has been extensively investigated in contemporary psychology. However, the formal properties of the visual sameness relation are still unclear, for example, whether it is an identity-like, equivalence relation. The paper concerns one aspect of this problem: the transitivity of visual sameness. Results obtained by using different experimental paradigms are analysed, in particular studies using streaming/bouncing stimuli, multiple object tracking experiments and investigations concerning object-specific preview (...) benefit, and it is argued that the transitive interpretation of visual sameness is the most plausible given the current stage of knowledge. What is more, it is claimed that the way in which visual sameness is represented suggests that in some cases it should be characterized as a “primitive sameness”, similarly as in philosophical theories postulating “thisness”. (shrink)

According to certain views about human ontology, the way we seem is very different from the way we are. The appearances are a threat to such views. Here I take up and defuse the threat to one such view.Pure immaterialism says that each of us is wholly immaterial. The appearances suggest otherwise. I argue that despite the fact that we might sometimes appear to be at least partly material, and that we can be perceptually justified in believing something solely on (...) the basis of having a perceptual experience as of its being the case, none of us is ever perceptually justified in believing that we are even partly material (or that we’re not). Bottom line: we might be able to know whether we’re material, but we can’t know just by looking. (shrink)

According to the standard argument from targetless higher-order representations, the possibility of such representations presents a dilemma for higher-order theorists. In this article I argue that there are two theoretically well-motivated replies to the standard argument. Consequently, the standard argument against higher-order theories fails. I then go on to argue that while certain versions of higher-order theory can adequately respond to the standard argument, they both, nevertheless, fail to explain the fineness-of-grain that phenomenally conscious experience appears to have.

I defend, to a certain extent, the traditional view that perceptual indiscriminability is non-transitive. The argument proceeds by considering important recent work by Benj Hellie: Hellie argues that colour perception represents ‘inexactly’, and that this results in violations of the transitivity of colour indiscriminability. I show that Hellie’s argument remains inconclusive, since he does not demonstrate conclusively that colour perception really does represent inexactly. My own argument for the non-transitivity of perceptual indiscriminability uses inexactness instead as one horn of a (...) dilemma: the key idea is that there is a class of perceptual experiences which might plausibly be supposed either to represent inexactly or to represent exactly—but which demonstrate the non-transitivity of perceptual indiscriminability either way. (shrink)

Is observational indiscriminability non-transitive? This was once an accepted truth, and it was used by philosophers like Armstrong and Dummett to argue against the existence of appearances (sense data, sensory items). It was objected, however, early on by Jackson and Pinkerton, and more recently by vagueness contextualists like Raffman and Fara, that the case for non-transitivity is flawed. The reason is the context dependence of appearance. I argue here that if we take context dependence properly into account, we still have (...) (a modified version of) non-transitivity, and that therefore we still face the problem of appearances. (shrink)

Perceptual content is conceptual. In this paper, some arguments against this thesis are examined and rebutted. The Richness argument, that we could not have concepts for all the colours, is queried: Doesn't the Munsell system give us such concepts? The argument that we can perceive colours and shapes without possessing the relevant concepts is rebutted: we cannot do this, but the kind of concept-possession that is relevant here is not intellectual but perceptual.

Taking a series of colour patches, starting with one that clearly looks red, and making each so similar in colour to the previous one that it looks the same as it, we appear to be able to show that a yellow patch looks red. I ask whether phenomenal sorites paradoxes, such as this, are subject to a unique kind of solution that is unavailable in relation to other sorites paradoxes. I argue that they do not need such a solution, nor (...) do they succumb to one. In particular, I reject the claim made by Fara and Raffman that looks the same is a transitive relation, which would allow us to solve phenomenal sorites paradoxes by denying the possibility of the required kind of sorites series. (shrink)

Vagueness is understood as the problem of associating imprecise application criteria with ordinary predicates such as ‘bald’ or ‘blue’. It is often construed as due to one’s tolerance to a minute difference in forming a verdict on the application of a vague predicate. This paper reports an experiment conducted to test the effect of tolerance, using as paradigm categorisation tasks performed with respect to transitional series, e.g., a series of tomatoes from red to orange. The findings suggest a negative effect (...) of tolerance on categorisation with vague predicates. The implication of the findings for certain commonly-held assumptions about tolerance is discussed. (shrink)

Vagueness is understood as the problem of associating imprecise application criteria with ordinary predicates such as ‘bald’ or ‘blue’. It is often construed as due to one’s tolerance to a minute difference in forming a verdict on the application of a vague predicate. This paper reports an experiment conducted to test the effect of tolerance, using as paradigm categorisation tasks performed with respect to transitional series, e.g., a series of tomatoes from red to orange. The findings suggest a negative effect (...) of tolerance on categorisation with vague predicates. The implication of the findings for certain commonly-held assumptions about tolerance is discussed. (shrink)

Perception represents colours inexactly. This inexactness results from phenomenally manifest noise, and results in apparent violations of the transitivity of perceptual indiscriminability. Whether these violations are genuine depends on what is meant by 'transitivity of perceptual indiscriminability'.

In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system we call Centered semantics. (...) We then propose a semantics of degrees of clarity, inspired from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the unclarity of unclarity. (shrink)

This unique anthology of new, contributed essays offers a range of perspectives on various aspects of ontic vagueness. It seeks to answer core questions pertaining to onticism, the view that vagueness exists in the world itself. The questions to be addressed include whether vague objects must have vague identity, and whether ontic vagueness has a distinctive logic, one that is not shared by semantic or epistemic vagueness. The essays in this volume explain the motivations behind onticism, such as the plausibility (...) of mereological vagueness and indeterminacy in quantum mechanics and they offer various arguments both for and against ontic vagueness; onticism is also compared with other, competing theories of vagueness such as semanticism, the view that vagueness exists only in our linguistic representation of the world. Gareth Evans’s influential paper of 1978, “Can There Be Vague Objects?” gave a simple but cogent argument against the coherence of ontic vagueness. Onticism was subsequently dismissed by many. However, in recent years, researchers have become aware of the logical gaps in Evans’s argument and this has triggered a new wave of interest in onticism. Onticism is now widely regarded as at least a coherent view. Reflecting this growing consensus, the present anthology for the first time puts together essays that are focused on onticism and its various facets and it fills in the lacuna in the literature on vagueness, a much-discussed subject in contemporary philosophy. (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.

Let's be externalists about perceptual consciousness and think the form of veridical perceptual consciousness includes /seeing this or that mind-independent particular and its colors/. Let's also take internalism seriously, granting that spectral inversion and hallucination can be "phenomenally" the same as normal seeing. Then perceptual consciousness and phenomenality are different, and so we need to say how they are related. It's complicated!<br><br>Phenomenal sameness is (against all odds) /reflective indiscriminability/. I build a "displaced perception" account of reflection on which indiscriminability stems (...) from shared "qualia". Qualia are compatible with direct realism: while they generate an explanatory gap (and colors do not), so does /seeing/; qualia are excluded from perceptual consciousness by its "transparency"; instead, qualia are aspects of thought about the perceived environment. <br><br>The asymmetry between my treatments of color and seeing is grounded in the asymmetry between ignorance and error: while inversion shows that normal subjects are ignorant of the natures of the colors, hallucination shows not that perceivers are ignorant of the nature of seeing but that hallucinators are prone to error about their condition. Past literature has treated inversion and hallucination as on a par: externalists see error in both cases, while internalists see mutual ignorance. My account is so complicated because plausible results require mixing it up. (shrink)

Version of March 05, 2007. An extended abstract of the paper appeared in the Proceedings of the 2006 Prague Colloquium on "Reasoning about Vagueness and Uncertainty".

My main aim is to clarify what we mean by ‘look’ sentences such as (1) below – ones that we use to talk about visual experience: -/- (1) The ball looked red to Sue -/- This is to help better understand a part of natural language that has so far resisted treatment, and also to help better understand the nature of visual experience. -/- By appealing to general linguistic principles I argue for the following account. First, we use (1) to (...) talk about an event. Second, we use the verb ‘look’ to specify the kind of event about which we are talking – it is a looking event. Third, we use the subject ‘the ball’ to specify a stimulus of the event – something that looks some way in the event. Fourth, we use the adjunct ‘to Sue’ to specify an experiencer of the event – someone to whom things look some way in the event. Finally, we use the complement ‘red’ to specify a way of the event – a way in which the event occurs (I take ways of occurring to be properties of events). Which way do we use ‘red’ in (1) to specify? I argue: the maximally specific way w such that the following is generically true: looking events whose stimulus is red occur in way w (it is important that this is understood generically: this is what does much of the work in explaining our use of (1) and other ‘look’ sentences). Putting this together, what we mean by (1) is: there was a looking event whose stimulus was the ball, whose experiencer was Sue, and which occurred in the maximally specific way that looking events occur when their stimulus is red. -/- This account of how we use ‘red’ in (1) is one of the most interesting aspects of my thesis. It extends to an account of how we use ‘proud’ in ‘John walks proud’, ‘as if he is American’ in ‘John talks as if he is American’, ‘like a duck’ in ‘John sounds like a duck’, and so on. In each case we use the expression in question to specify a way: the maximally specific way proud people walk, the maximally specific way American people talk, and so on. So the study of ‘look’ sentences has much to tell us about the functioning of many other English language constructions, and suggests that ways have a significant role to play in the semantics of natural language – a fact that has not yet been sufficiently recognised by linguists or philosophers of language. -/- My thesis also has implications for the philosophy of perception. One of the central questions about perception is: What is the nature of visual experience? What is it, for example, for a ball to look red to Sue? My thesis offers an answer: What it is for the ball to look red to Sue is for whatever it is that we mean by ‘The ball looks red to Sue’ to be the case, and what we mean by ‘The ball looks red to Sue’ is that there is a looking event whose stimulus is the ball, whose experiencer is Sue, and which is occurring in a certain way. It thus delivers an adverbial account of visual experience, one that has the resources to better deal with problems that are traditionally thought to be decisive against adverbial accounts. (shrink)

Of the many families of words that are thought to be vague, so-called observational predicates may be both the most fascinating and the most confounding. Roughly, observational predicates are terms that apply to objects on the basis of how those objects appear to us perceptually speaking. ‘Red’, ‘loud’, ‘sweet’, ‘acrid’, and ‘smooth’ are good examples. Delia Graff explains that a “predicate is observational just in case its applicability to an object (given a fixed context of evaluation) depends only on the (...) way that object appears” (2001, 3). By the same token observational predicates are, as Crispin Wright observes, terms “whose senses are taught entirely by ostension” (1976). Like other vague predicates, observational words appear to generate sorites paradoxes. Consider for example a series of 20 colored patches progressing from a clearly red one to a clearly orange one, so ordered that each patch is just noticeably different in hue from the one before. The following argument then seems forced upon us: (1) Patch #1 is red. (2) Any patch that differs only slightly in hue from a red patch is itself red. (3) Therefore patch #20 is red. Premise (2) expresses what Wright has called the tolerance of ‘red’: the application of the predicate tolerates small changes in a decisive parameter (here, hue). Of course, most vague predicates, hence most versions of the sorites, are not observational. For instance, given a series of. (shrink)

Suppose you are presented with three red objects. You are then asked to take a careful look at each possible pair of objects, and to decide whether or not their members look chromatically the same. You carry out the instructions thoroughly, and the following propositions sum up the results of your empirical investigation: <blockquote> i. red object #1 looks the same in colour as red object #2. </blockquote> ii. red object #2 looks the same in colour as red object #3.

Humans have only finite discriminatory capacities. This simple fact seems to be incompatible with the existence of appearances. As many authors have noted, the hypothesis that appearances exist seems to be refuted by reductio: Let A, B, C be three uniformly coloured surfaces presented to a subject in optimal viewing conditions, such that A, B, and C resemble one another perfectly except with respect to their colours. Their colours differ slightly in the following way: the difference between A and B (...) and the difference between B and C are below the discrimination threshold, but the difference between A and C is above this threshold. According to an intuitive construal of what an appearance is, given that A and B appear (to the subject) identical in colour, A and B have the same (colour1) appearance P1; likewise, B and C have the same appearance P2. B's appearance is both P1 and P2. This seems to imply that P1=P2. But then, A and C also have the same appearance, which contradicts the hypothesis that A and C are discriminable. If A and C are discriminable with respect to their colour, they do not have the same appearance with respect to colour. The paradox arising from such a series of judgments of sameness or difference between pairs of coloured surfaces seems to belong to the class of sorites paradoxes. I will show that there is a way to construe colours and their appearances in a way that does not fall prey to the reduction just sketched. (shrink)