Which ultraproducts preserve the validity of formulas of higher order logics? To answer this question, we will introduce natural topologies on ultraproducts. We will show, that ultraproducts preserving certain higher order formulas can be characterized in terms of these topologies. As an application of the above results, we provide a constructive, purely model theoretic characterization for classes definable by second order existential formulas.

We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher-order arithmetic. Let [Formula: see text] be the statement that a non-principal ultrafilter on ℕ exists and let [Formula: see text] be the higher-order extension of ACA0. We show that [Formula: see text] is [Formula: see text]-conservative over [Formula: see text] and thus that [Formula: see text] is conservative over PA. Moreover, we provide a program extraction (...) method and show that from a proof of a strictly [Formula: see text] statement ∀ f ∃ g A qf in [Formula: see text] a realizing term in Gödel's system T can be extracted. This means that one can extract a term t ∈ T, such that ∀ f A qf). (shrink)

In this paper we describe the Curry-Howard-De Bruijn isomorphism between Higher Order Many Sorted Intuitionistic Predicate Logic PREDω and the type system λPREDω, which can be considered a subsystem of the Calculus of Constructions. The type system is presented using the concept of a Pure Type System, which is a very elegant framework for describing type systems. We show in great detail how formulae and proof trees of the logic relate to types and terms of the type system, (...) respectively. Finally, we discuss some consequences of the isomorphism with respect to the relation between the systems discussed in this paper. (shrink)

It is and has been widely assumed, e.g., in Hintikka and Hintikka, that the logical theory available from Wittgenstein’s Tractatus Logico-Philosophicus affords a foundation for the conventional logic represented in standard formulations of classical propositional, first-order predicate, and perhaps higher-order formal systems. The present article is a detailed attempt at a mathematical demonstration, or as much demonstration as the sources will allow, that this assumption is false by contemporary lights and according to a preferred account of argument (...) validity. When Wittgenstein’s description of the forms of propositions or Sätze in the 5-numbered remarks and Remark 6 is given a close reconstruction, one sees that no Tractarian proposition is logically equivalent to a simple universally or existentially quantified formula of first-order predicate logic. Therefore, although Wittgenstein employs the sign ∀—or, in his notation—occasionally in explanations and illustrations, e.g., 4.0411 and 5.1311, when it comes to logic, the sign ∀ should receive in Tractatus a semantical treatment that is nonstandard. En route to that result, we show that the hierarchy of variables–and, hence, of propositions–defined at 5.501 incorporates the expressive power of finitary classical propositional logic. Also, when constructed over a first-order language for arithmetic, formulae corresponding to the specification of 5.501 pick out all and only arithmetic sets of numbers. Consequently, Wittgenstein’s hierarchy of iterated N-propositions–as described in vide Remark 6–does not collapse: at any level k, one finds propositions at k + 1 or above that are not logically equivalent to any proposition formed at k or below. (shrink)

On at least one of its uses, ‘higher-order evidence’ refers to evidence about what opinions are rationalized by your evidence. This chapter surveys the foundational epistemological questions raised by such evidence, the methods that have proven useful for answering them, and the potential consequences and applications of such answers.

RESUMEN Se ha destacado que la Fórmula de Barcan -FB- y la Conversa de la Fórmula de Barcan -CFB- para lógica modal cuantificacional de orden superior parecen válidas. Si se interpreta que los cuantificadores tienen como rango propiedades, la validez de FB y CFB parece implicar la existencia de universales trascendentes, que no requieren estar instanciados para existir en un mundo posible. Se discute esta argumentación, porque la semántica, en la que los resultados de validez se siguen, no requiere que (...) las ‘intensiones' asignadas a las variables de orden superior estén instanciadas en un mundo posible para que la intensión exista ahí. En una semántica modificada, más neutral, FB y CFB de orden superior ya no son válidas. Además se sostiene que, incluso si FB y CFB de orden superior fuesen válidas, no se obtendrían resultados metafísicos sustantivos, pues diferentes formas de nominalismo y teorías de tropos las aceptarían. ABSTRACT It has been pointed out that the Barcan Formula -BF- and the Converse Barcan Formula -CBF- seem to be valid for higher-order modal quantificational logic. If quantifiers are construed as ranging over properties, the validity of BF and CBF seems to entail the existence of transcendent universals that do not require instantiation in order to exist in a possible world. The paper discusses this argument given that semantics, in which validity results follow from one another, do not require that the "intensions" assigned to higher- order variables be instantiated in a possible world in order for the intension to exist in such a world. In a modified, more neutral semantics, higher-order BF and CBF are no longer valid. The paper also argues that even if higher-order BF and CBF were valid, no substantive metaphysical results would be obtained, since different forms of nominalism and theories of tropes would accept them. (shrink)

This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between (...) objects and functions. Russell understood propositional functions as what is obtained when constituents of propositions are replaced by variables, but eventually denied that they were entities in their own right. Both encountered contradictions when supposing there to exist as many objects as functions, and both adopted views about the meaningfulness of higher-order discourse that were difficult to state from within their own strictures. (shrink)

The thesis that agents should calibrate their beliefs in the face of higher-order evidence—i.e., should adjust their first-order beliefs in response to evidence suggesting that the reasoning underlying those beliefs is faulty—is sometimes thought to be in tension with Bayesian approaches to belief update: in order to obey Bayesian norms, it’s claimed, agents must remain steadfast in the face of higher-order evidence. But I argue that this claim is incorrect. In particular, I motivate a (...) minimal constraint on a reasonable treatment of the evolution of self-locating beliefs over time and show that calibrationism is compatible with any generalized Bayesian approach that respects this constraint. I then use this result to argue that remaining steadfast isn’t the response to higher-order evidence that maximizes expected accuracy. (shrink)

Recent authors have drawn attention to a new kind of defeating evidence commonly referred to as higher-order evidence. Such evidence works by inducing doubts that one’s doxastic state is the result of a flawed process – for instance, a process brought about by a reason-distorting drug. I argue that accommodating defeat by higher-order evidence requires a two-tiered theory of justification, and that the phenomenon gives rise to a puzzle. The puzzle is that at least in some (...) situations involving higher-order defeaters the correct epistemic rules issue conflicting recommendations. For instance, a subject ought to believe p, but she ought also to suspend judgment in p. I discuss three responses. The first resists the puzzle by arguing that there is only one correct epistemic rule, an Über-rule. The second accepts that there are genuine epistemic dilemmas. The third appeals to a hierarchy or ordering of correct epistemic rules. I spell out problems for all of these responses. I conclude that the right lesson to draw from the puzzle is that a state can be epistemically rational or justified even if one has what looks to be strong evidence to think that it is not. As such, the considerations put forth constitute a non question-begging argument for a kind of externalism. (shrink)

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics (...) used in metaphysics, and indicate a number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the (...) foundations of the epistemology of disagreement. Third, the answer is not obvious. The Enkratic Intuition---that your first-order opinions must “line up” with your higher-order opinions---is incorrect; epistemic akrasia can be rational. If all this is right, then it leaves us without answers---but with a clear picture of the question, and a fruitful strategy for pursuing it. (shrink)

An overview of higher-order representational theories of consciousness. Representational theories of consciousness attempt to reduce consciousness to “mental representations” rather than directly to neural or other physical states. This approach has been fairly popular over the past few decades. Examples include first-order representationalism (FOR) which attempts to explain conscious experience primarily in terms of world-directed (or first-order) intentional states (Tye 2005) as well as several versions of higher-order representationalism (HOR) which holds that what makes (...) a mental state M conscious is that it is the object of some kind of higher-order mental state directed at M. The primary focus of this entry is on HOR and especially higher-order thought (HOT) theory. The key question that should be answered by any theory of consciousness is: What makes a mental state a conscious mental state? Section 1 introduces the overall representationalist approach to consciousness and briefly discuss Tye’s FOR. Section 2 presents three major versions of HOR: higher-order thought theory, dispositional higher-order thought theory, and higher-order perception theory. In section 3, a number of common and important objections and replies are presented. Section 4 briefly outlines a close connection between HOT theory and conceptualism, that is, the claim that the representational content of a perceptual experience is entirely determined by the conceptual capacities the perceiver brings to bear in her experience. Section 5 examines several hybrid higher-order and “self-representational” theories of consciousness which all hold that conscious states are self-directed in some way. Section 6 addresses the potentially damaging claim that HOT theory requires neural activity in the prefrontal cortex (PFC) in order for one to have conscious states. (shrink)

This paper investigates the metaphysics in higher-order counterfactual logic. I establish the necessity of identity and distinctness and show that the logic is committed to vacuism, which entails that all counteridenticals are true. I prove the Barcan, Converse Barcan, Being Constraint and Necessitism. I then show how to derive the Identity of Indiscernibles in counterfactual logic. I study a form of maximalist ontology which has been claimed to be so expansive as to be inconsistent. I show that it (...) is equivalent to the collapse of the counterfactual into the material conditional---which is itself equivalent to the modal logic TRIV. TRIV is consistent, from which it follows that maximalism is, surprisingly, consistent. I close by arguing that stating the limit assumption requires a higher-order logic. (shrink)

Higher-order defeat occurs when one loses justification for one's beliefs as a result of receiving evidence that those beliefs resulted from a cognitive malfunction. Several philosophers have identified features of higher-order defeat that distinguish it from familiar types of defeat. If higher-order defeat has these features, they are data an account of rational belief must capture. In this article, I identify a new distinguishing feature of higher-order defeat, and I argue that on (...) its own, and in conjunction with the other distinguishing features, it favors an account of higher-order defeat grounded in non-evidential, ‘state-given reasons’ for belief. (shrink)

In the contemporary epistemological literature, peer disagreement is often taken to be an instance of a more general phenomenon of “higher-order evidence.” Correspondingly, its epistemic significance is often thought to turn on the epistemic significance of higher-order evidence in general. This chapter attempts to evaluate this claim, and in doing so to clarify some points of unclarity in the current literature – both about what it is for evidence to be “higher-order,” and about the (...) relationship between disagreement and higher-order evidence. We will begin by considering some candidate definitions of “higher-order evidence,” and offering our own definition that attempts to capture the phenomenon of interest. We will then consider, in light of this definition, whether disagreement and its epistemic significance are best-understood as a kind of higher-order evidence. We’ll argue that although peer disagreement can be epistemically significant qua higher-order evidence, this role doesn’t exhaust its significance, and that it can also serve as straightforward first-order evidence. Finally, we’ll suggest that inattention to this latter point has made broadly conciliatory views about peer disagreement seem somewhat easier to resist than they in fact are. (shrink)

Higher-order realists about properties express their view that there are properties with the help of higher-order rather than first-order quantifiers. They claim two types of advantages for this way of formulating property realism. First, certain gridlocked debates about the nature of properties, such as the immanentism versus transcendentalism dispute, are taken to be dissolved. Second, a further such debate, the tropes versus universals dispute, is taken to be resolved. In this paper I first argue that (...) higher-order realism does not in fact resolve the tropes versus universals dispute. In a constructive spirit, I then develop higher-order realism in a way that leads to a dissolution, rather than a resolution, of this dispute too. (shrink)

Evidentialism is the thesis that a person is justified in believing a proposition iff the person's evidence on balance supports that proposition. In discussing epistemological issues associated with disagreements among epistemic peers, some philosophers have endorsed principles that seem to run contrary to evidentialism, specifying how one should revise one's beliefs in light of disagreement. In this paper, I examine the connection between evidentialism and these principles. I argue that the puzzles about disagreement provide no reason to abandon evidentialism and (...) that there are no true general principles about justified responses to disagreement other than the general evidentialist principle. I then argue that the puzzles about disagreement are primarily puzzles about the evidential impact of higher - order evidence – evidence about the significance or existence of ordinary, or first- order, evidence. I conclude by arguing that such higher - order evidence can often have a profound effect on the justification of first- order beliefs. (shrink)

A critical survey of recent work in epistemology on higher-order evidence. It discusses the nature of higher-order evidence, some puzzles it raises, responses to those puzzles, and problems facing them. It concludes by indicating connections between debates concerning higher-order evidence in epistemology and parallel debates in ethics and aesthetics.

Subverting a once widely held Quinean paradigm, there is a growing consensus among philosophers of logic that higher-order quantifiers (which bind variables in the syntactic position of predicates and sentences) are a perfectly legitimate and useful instrument in the logico-philosophical toolbox, while neither being reducible to nor fully explicable in terms of first-order quantifiers (which bind variables in singular term position). This article discusses the impact of this quantificational paradigm shift on metaphysics, focussing on theories of properties, (...) propositions, and identity, as well as on the metaphysics of modality. (shrink)

This chapter examines the ways in which the debates about the epistemic significance of disagreement are debates about the nature and impact of higher-order evidence.

This paper concerns would-be necessary connections between doxastic attitudes about the epistemic statuses of your doxastic attitudes, or ‘higher-order epistemic attitudes’, and the epistemic statuses of those doxastic attitudes. I will argue that, in some situations, it can be reasonable for a person to believe p and to suspend judgment about whether believing p is reasonable for her. This will set the stage for an account of the virtue of intellectual humility, on which humility is a matter of (...) your higher-order epistemic attitudes. Recent discussions in the epistemology of disagreement have assumed that the question of the proper response to disagreement about p concerns whether you ought to change your doxastic attitude towards p. My conclusion here suggests an alternative approach, on which the question of the proper response to disagreement about p concerns the proper doxastic attitude to adopt concerning the epistemic status of your doxastic attitude towards p.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.HIGHER-ORDER EPISTEMIC ATTITUDES AND INTELLECTUAL HUMILITYVolume 9, Issue 3Allan HazlettDOI: https://doi.org/10.1017/epi.2012.11Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. HIGHER-ORDER EPISTEMIC ATTITUDES AND INTELLECTUAL HUMILITYVolume 9, Issue 3Allan HazlettDOI: https://doi.org/10.1017/epi.2012.11Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. HIGHER-ORDER EPISTEMIC ATTITUDES AND INTELLECTUAL HUMILITYVolume 9, Issue 3Allan HazlettDOI: https://doi.org/10.1017/epi.2012.11Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, (...) according to the view itself, do not exist to be drawn. The paper begins with a non-technical exposition of the main ideas and technical results, which can be read on its own. This exposition is followed by a formal investigation of higher-order contingentism, in which the tools of variable-domain intensional model theory are used to articulate various versions of the view, understood as theories formulated in a higher-order modal language. Our overall assessment is mixed: higher-order contingentism can be fleshed out into an elegant systematic theory, but perhaps only at the cost of abandoning some of its original motivations. (shrink)

According to the Fragmentation Analysis, epistemic akrasia is a state of conflict between beliefs formed by the linguistic and non-linguistic belief-formation systems, and epistemic akrasia is irrational because it is a state of conflict between beliefs so formed. I argue that there are cases of higher-order epistemic akrasia, where both beliefs are formed by the linguistic belief-formation system. Because the Fragmentation Analysis cannot accommodate this possibility, the Fragmentation Analysis is incorrect. I consider three objections to the possibility of (...) higher-order epistemic akrasia. Along the way, I offer a revision of the Fragmentation Analysis that can allow for the possibility of higher-order akrasia while avoiding the problems I point out for the original view. (shrink)

Higher‐order theories purport to account for the conscious character of such states in terms of higher‐order representations. This chapter focuses on three classes of higher‐order theory of phenomenal consciousness, including inner‐sense theory, actualist higher‐order thought theory, and dispositionalist higher‐order thought theory. All three of these higher‐order theories purport to offer reductive explanations of phenomenal consciousness. Inner‐sense theory has important positive virtues, but faces problems; whereas actualist higher‐order (...) thought theory avoids those problems, but at the cost of losing the positive virtues. Actualist higher‐order thought theory has the advantage that no special organs or mechanisms need to be postulated. Dispositionalist higher‐order thought theory claims to split the difference, providing an account that has all of the advantages of inner‐sense theory with none of the flaws. The success of dispositionalist higher‐order thought theory is premised upon the existence of dual analog contents. (shrink)

Ambitious higher-order theories of consciousness aim to account for conscious states when these are understood in terms of what-it-is-like-ness. This paper considers two arguments concerning this aim, and concludes that ambitious theories fail. The misrepresentation argument against HO theories aims to show that the possibility of radical misrepresentation—there being a HO state about a state the subject is not in—leads to a contradiction. In contrast, the awareness argument aims to bolster HO theories by showing that subjects are aware (...) of all their conscious states. Both arguments hinge on how we understand two related notions which are ubiquitous in discussions of consciousness: those of what-it-is-like-ness and there being something it is like for a subject to be in a mental state. This paper examines how HO theorists must understand the two crucial notions if they are to reject the misrepresentation argument but assert the awareness argument. It shows that HO theorists can and do adopt an understanding—the HO reading—which seems to give them what they want. But adopting the HO reading changes the two arguments. On this reading, the awareness argument tells us nothing about those states there is something it is like to be in, and so offers no support to ambitious HO theories. And to respond to the misrepresentation understood according to the HO reading is to simply ignore the argument presented, and so to give no response at all. As things stand, we should deny that HO theories can account for what-it-is-like-ness. (shrink)

Emotional states of consciousness, or what are typically called emotional feelings, are traditionally viewed as being innately programed in subcortical areas of the brain, and are often treated as different from cognitive states of consciousness, such as those related to the perception of external stimuli. We argue that conscious experiences, regardless of their content, arise from one system in the brain. On this view, what differs in emotional and non-emotional states is the kind of inputs that are processed by a (...) general cortical network of cognition, a network essential for conscious experiences. Although subcortical circuits are not directly responsible for conscious feelings, they provide non-conscious inputs that coalesce with other kinds of neural signals in the cognitive assembly of conscious emotional experiences. In building the case for this proposal, we defend a modified version of what is known as the higher-order theory of consciousness. (shrink)

The higher order approach to consciousness attempts to build a theory of consciousness from the insight that a conscious state is one that the subject is conscious of. There is a well-known objection1 to the higher order approach, a version of which is fatal. Proponents of the higher order approach have realized that the objection is significant. They have dealt with it via what David Rosenthal calls a “retreat” (2005b, p. 179) but that retreat (...) fails to solve the problem. (shrink)

There has been considerable puzzlement over how to respond to higher-order evidence. The existing dilemmas can be defused by adopting a ‘two-dimensional’ representation of doxastic attitudes which incorporates not only substantive uncertainty about which first-order state of affairs obtains but also the degree of conviction with which we hold the attitude. This makes it possible that in cases of higher-order evidence the evidence sometimes impacts primarily on our conviction, rather than our substantive uncertainty. I argue (...) that such a two-dimensional representation is naturally developed by making use of imprecise probabilities. (shrink)

Euclid’s definition of a point as “that which has no part” has been a major source of controversy in relation to the epistemological and ontological presuppositions of classical geometry, from the medieval and modern disputes on indivisibilism to the full development of point-free geometries in the 20th century. Such theories stem from the general idea that all talk of points as putative lower-dimensional entities must and can be recovered in terms of suitable higher-order constructs involving only extended regions (...) (or bodies). Here I focus on what is arguably the first thorough proposal of this sort, Whitehead’s theory of “extensive abstraction”, offering a critical reconstruction of the theory through its successive installments: from the purely mereological version of ‘La théorie relationniste de l’espace’ (1916) to the refined versions presented in An Enquiry Concerning the Principles of Natural Knowledge (1919) and in The Concept of Nature (1920) to the last, mereotopological version of Process and Reality (1929). (shrink)

According to what Birch (2022) calls the theory-heavy approach to investigating nonhuman-animal consciousness, we select one of the well-developed theories of consciousness currently debated within contemporary cognitive science and investigate whether animals exhibit the neural structures or cognitive abilities posited by that theory as sufficient for consciousness. Birch argues, however, that this approach is in general problematic because it faces what he dubs the dilemma of demandingness—roughly, that we cannot use theories that are based on the human case to assess (...) consciousness in nonhuman animals and vice versa. We argue here that, though this dilemma may problematize the application of many current accounts of consciousness to nonhuman animals, it does not challenge the use of standard versions of the higher-order thought theory (“HOTT”) of consciousness, according to which a creature is in a conscious mental state just in case it is aware of being in that state via a suitable higher-order thought (“HOT”). We show this in two ways. First, we argue that, unlike many extant theories of consciousness, HOTT is typically motivated by a commonsense, and more importantly, neutral condition on consciousness that applies to humans and animals alike. Second, we offer new empirical and theoretical reasons to think that many nonhuman animals possess the relevant HOTs necessary for consciousness. Considering these issues not only reveals the explanatory power of HOTT and some of its advantages over rival accounts, but also enables us to further extend and clarify the theory. (shrink)

The paper proposes an account of the rational response to higher-order evidence whose key claim is that whenever we acquire such evidence we ought to engage in the inquiring activity of double-checking. Combined with a principle that establishes a connection between rational inquiry and rational belief retention, the account offers a novel explanation of the alleged impermissibility of retaining one’s belief in the face of higher-order evidence. It is argued that this explanation is superior to the (...) main competitor view which appeals to the notion of defeat. (shrink)

Sometimes we get evidence of our own epistemic malfunction. This can come from finding out we’re fatigued, or have been drugged, or that other competent and well-informed thinkers disagree with our beliefs. This sort of evidence seems to seems to behave differently from ordinary evidence about the world. In particular, getting such evidence can put agents in a position where the most rational response involves violating some epistemic ideal.

The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher- (...) class='Hi'>order logic. Our assessment of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value. (shrink)

Evidentialism is the thesis, roughly, that one’s beliefs should fit one’s evidence. The enkratic principle is the thesis, roughly, that one’s beliefs should "line up" with one’s beliefs about which beliefs one ought to have. While both theses have seemed attractive to many, they jointly entail the controversial thesis that self-misleading evidence is impossible. That is to say, if evidentialism and the enkratic principle are both true, one’s evidence cannot support certain false beliefs about which beliefs one’s evidence supports. Recently, (...) a number of epistemologists have challenged the thesis that self-misleading evidence is impossible on the grounds that misleading higher-order evidence does not have the kind of strong and systematic defeating force that would be needed to rule out the possibility of such self-misleading evidence. Here I respond to this challenge by proposing an account of higher-order defeat that does, indeed, render self-misleading evidence impossible. Central to the proposal is the idea that higher-order evidence acquires its normative force by influencing which conditional beliefs it is rational to have. What emerges, I argue, is an independently plausible view of higher-order evidence, which has the additional benefit of allowing us to reconcile evidentialism with the enkratic principle. (shrink)

It seems obvious that when higher-order evidence makes it rational for one to doubt that one’s own belief on some matter is rational, this can undermine the rationality of that belief. This is known as higher-order defeat. However, despite its intuitive plausibility, it has proved puzzling how higher-order defeat works, exactly. To highlight two prominent sources of puzzlement, higher-order defeat seems to defy being understood in terms of conditionalization; and higher-order (...) defeat can sometimes place agents in what seem like epistemic dilemmas. This chapter draws attention to an overlooked aspect of higher-order defeat, namely that it can undermine the resilience of one’s beliefs. The notion of resilience was originally devised to understand how one should reflect the ‘weight’ of one’s evidence. But it can also be applied to understand how one should reflect one’s higher-order evidence. The idea is particularly useful for understanding cases where one’s higher-order evidence indicates that one has failed in correctly assessing the evidence, without indicating whether one has over- or underestimated the degree of evidential support for a proposition. But it is exactly in such cases that the puzzles of higher-order defeat seem most compelling. (shrink)

The problem of higher-order misrepresentation poses a dilemma for the higher-order theory of consciousness. The two ways of conceiving of the theory each run into a different difficulty raised by the problem of misrepresentation. If the theory is conceived relationally, i.e., conceived so as the higher-order state causes or makes a first-order state conscious, then the theory faces a problem raised by Block concerning the implausibility of non-existent conscious states. If conceived non-relationally, i.e., (...) conceived in such a way as it is the higher-order state itself which is the conscious state, then consideration of Neander’s original misrepresentation problem, that this seems to make the first-order state a spinning wheel in the explanation of consciousness, raises the conceptual problem that this version of the higher-order theory seems not to offer a philosophical theory of consciousness that is distinct from the first-order theory. (shrink)

Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain modalized cardinality claims, which shows that in such a (...) language, higher-order contingentists cannot express what is communicated using various instances of talk of ‘possible things’, such as ‘there are uncountably many possible stars’. (shrink)

Thinking about misleading higher-order evidence naturally leads to a puzzle about epistemic rationality: If one’s total evidence can be radically misleading regarding itself, then two widely-accepted requirements of rationality come into conflict, suggesting that there are rational dilemmas. This paper focuses on an often misunderstood and underexplored response to this (and similar) puzzles, the so-called conflicting-ideals view. Drawing on work from defeasible logic, I propose understanding this view as a move away from the default metaepistemological position according to (...) which rationality requirements are strict and governed by a strong, but never explicitly stated logic, toward the more unconventional view, according to which requirements are defeasible and governed by a comparatively weak logic. When understood this way, the response is not committed to dilemmas. (shrink)

ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.

Many theories of rational belief give a special place to logic. They say that an ideally rational agent would never be uncertain about logical facts. In short: they say that ideal rationality requires "logical omniscience." Here I argue against the view that ideal rationality requires logical omniscience on the grounds that the requirement of logical omniscience can come into conflict with the requirement to proportion one’s beliefs to the evidence. I proceed in two steps. First, I rehearse an influential line (...) of argument from the "higher-order evidence" debate, which purports to show that it would be dogmatic, even for a cognitively infallible agent, to refuse to revise her beliefs about logical matters in response to evidence indicating that those beliefs are irrational. Second, I defend this "anti-dogmatism" argument against two responses put forth by Declan Smithies and David Christensen. Against Smithies’ response, I argue that it leads to irrational self-ascriptions of epistemic luck, and that it obscures the distinction between propositional and doxastic justification. Against Christensen’s response, I argue that it clashes with one of two attractive deontic principles, and that it is extensionally inadequate. Taken together, these criticisms will suggest that the connection between logic and rationality cannot be what it is standardly taken to be—ideal rationality does not require logical omniscience. (shrink)

It has been argued that nonreductive physicalism’s problems with mental causation disappear if we abandon the intuitive but naïve production-based conception of causation in favor of one based on counterfactual dependence and difference-making. In recent years, this response has been thoroughly developed and defended by James Woodward, who contends that Kim’s causal exclusion argument, widely thought to be the most serious threat to nonreductive mental causation, cannot even be given a coherent formulation within Woodward’s preferred interventionist framework. But Woodward has, (...) even more recently, defended a pair of necessary conditions on mental causation and higher-order causation more generally, and it is here that the interventionist framework proves less friendly to nonreductive mental causation. Functionalism is arguably the most important species of nonreductive physicalism concerning specifically mental properties, but, as I argue, functional properties fail both of Woodward’s tests of causal relevance, one of them in two different ways. The problem, moreover, seems unique to functionalism, for other types of higher-order properties appear to pass Woodward’s tests. If functionalism faces defeat even in such friendly territory, its problems with mental causation are not an artifact of naïve metaphysics. They run deep. (shrink)

First-order evidence is evidence which bears on whether a proposition is true. Higher-order evidence is evidence which bears on whether a person is able to assess her evidence for or against a proposition. A widespread view is that higher-order evidence makes a difference to whether it is rational for a person to believe a proposition. In this paper, I consider in what way higher-order evidence might do this. More specifically, I consider whether and (...) how higher-order evidence plays a role in determining what it is rational to believe distinct from that which first-order evidence plays. To do this, I turn to the theory of reasons, and try to situate higher-order evidence within it. The only place I find for it there, distinct from that which first-order evidence already occupies, is as a practical reason, that is, as a reason for desire or action. One might take this to show either that the theory of reasons is inadequate as it stands or that higher-order evidence makes no distinctive difference to what it is rational to believe. I tentatively endorse the second option. (shrink)

It has recently been argued that a sensitivity theory of knowledge cannot account for intuitively appealing instances of higher-order knowledge. In this paper, we argue that it can once careful attention is paid to the methods or processes by which we typically form higher-order beliefs. We base our argument on what we take to be a well-motivated and commonsensical view on how higher-order knowledge is typically acquired, and we show how higher-order knowledge (...) is possible in a sensitivity theory once this view is adopted. (shrink)

This paper uses the resources of higher-order logic to articulate a Fregean conception of predicate reference, and of word-world relations more generally, that is immune to the concept horse problem. The paper then addresses a prominent style of expressibility problem for views of broadly this kind, versions of which are due to Linnebo, Hale, and Wright.

Aesthetic subjectivism takes the truth of aesthetic judgments to be relative to the individual making that judgment. Despite widespread suspicion, however, this does not mean that one cannot be wrong about such judgments. Accordingly, this does not mean that one cannot gain higher-order evidence of error and fallibility that bears on the rationality of the aesthetic judgment in question. In this paper, we explain and explore these issues in some detail.