This volume explores the use of higher-order logics in metaphysics. Seventeen original essays trace the development of higher-order metaphysics, discuss different ways in which higher-order languages and logics may be used, and consider their application to various central topics of metaphysics.

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- (...) class='Hi'>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)

According to relationism, for Alice to believe that some rabbits can speak is for Alice to stand in a relation to a further entity, some rabbits can speak. But what could this further entity possibly be? Higher-order metaphysics seems to offer a simple, natural answer. On this view (roughly put), expressions in different syntactic categories (for instance: names, predicates, sentences) in general denote entities in correspondingly different ontological categories. Alice's belief can thus be understood to relate her (...) to a sui generis entity denoted by "some rabbits can speak", belonging to a different ontological category than Alice herself. This straightforward account of the attitudes has historically been deemed so attractive that it was seen as providing an important motivation for higher-order metaphysics itself (Prior [1971]). But I argue that it is not as straightforward as it might seem, and in fact that propositional attitudes present a foundational challenge for higher-order metaphysics. (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)

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)

Although higher-order metaphysics seems prima facie to be a promising new approach to metaphysics, it is nonetheless based on a mistake. This mistake is tied to a misuse of formal languages in metaphysics in general, not just to the use of higher-order rather than lower-order languages. I hope to highlight the mistake by discussing a popular recent example of higher- order metaphysics: the argument that reality is not structured using (...) reasoning inspired by the Russell-Myhill paradox. A key issue will be the relationship between higher-order quantification in formal languages and quantification in English, in particular the questions whether such quantifiers are already to be found in English, and whether they could simply be added to English if not in order to gain expressive strength. I will conclude that little of metaphysical significance follows from this Russell-Myhill inspired argument against structure. The reason why the results of higher-order logic show little of metaphysical significance generalizes to other uses of higher-order logic in metaphysical theorizing, and with it supports that higher-order metaphysics is a flawed research program. I end with some reflections on what positive role formal tools like higher-order logic can have in metaphysics, and what the fundamental mistake is on which higher-order metaphysics is based. (shrink)

Higher-order logic augments first-order logic with devices that let us generalize into grammatical positions other than that of a singular term. Some recent metaphysicians have advocated for using these devices to raise and answer questions that bear on many traditional issues in philosophy. In contrast to these 'higher-order metaphysicians', traditional metaphysics has often focused on parallel, but importantly different, questions concerning special sorts of abstract objects: propositions, properties and relations. The answers to the (...) class='Hi'>higher-order and the property-theoretic questions may coincide sometimes but will often come apart. I argue that when they do, the higher-order questions are closer to the metaphysical action and so it would be better for these debates to proceed in higher-order terms. (shrink)

I review the volume ``Higher-Order Metaphysics'' edited by Peter Fritz and Nicholas K. Jones.

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (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 higher-order thought (HOT) theory of consciousness is a reductive representational theory of consciousness which says that what makes a mental state conscious is that there is a suitable HOT directed at that mental state. Although it seems that any neural realization of the theory must be somewhat widely distributed in the brain, it remains unclear just how widely distributed it needs to be. In section I, I provide some background and define some key terms. In section II, (...) I argue against the view that HOT theory should treat first-order (i.e. world-directed) conscious states as requiring prefrontal cortical activity though it is reasonable to suppose that conscious states are realized in the brain. In section III, I then explore some of the key background metaphysical issues involved in understanding the nature of consciousness, such as the debate between realism and idealism as well as the prospects for solving the so-called “hard problem” of consciousness. Some of the differences in question often mirror the traditional differences between Western and Eastern perspectives on the nature of consciousness. Overall, I argue that some form of realism and physicalism is more plausible than the opposing views. I also argue that materialists (and especially HOT theorists) can offer plausible replies to the hard problem. (shrink)

Conspicuously missing some planks, a latter-day Ship of Theseus catches the eye when one picks up this Book of Three Authors. Teasingly, differentiated pre.

This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it (...) is then shown how we can use pure higher-order logic to ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)

We discuss the one–many problem as it appears in the Philebus and find that it is not restricted to the usually understood problem about the identity of universals across particulars that instantiate them (the Hylomorphic Dispersal Problem). In fact some of the most interesting aspects of the problem occur purely with respect to the relationship between Forms. We argue that contemporary metaphysicians may draw from the Philebus at least three different one–many relationships between universals themselves: instantiation, subkind and part, and (...) thereby construct three new ‘problems of the one and the many’ (an Eidetic Dispersal Problem, a Genus–Species Problem, and an Eidetic Combination Problem), which are as problematic as the version generally discussed. We then argue that this taxonomy sheds new and interesting light on certain discussions of higher-order universals in recent Australian analytic philosophy. (shrink)

One of the distinctive properties of conscious states is the peculiar self- awareness implicit in them. Two rival accounts of this self-awareness are discussed. According to a Neo-Brentanian account, a mental state M is conscious iff M represents its very own occurrence. According to the Higher-Order Monitoring account, M is merely accompanied by a numerically distinct representation of its occurrence. According to both, then, M is conscious in virtue of figuring in a higher-order content. The disagreement (...) is over the question whether the higher-order content is carried by M itself or by a differ- ent state. While the Neo-Brentanian theory is phenomenologically more attractive, it is often felt to be somewhat mysterious. It is argued that the difference between the Neo- Brentanian and Higher-Order Monitoring theories is smaller and more empirical than may initially seem, and that the Neo-Brentanian theory can be readily demystified. These considerations make it prima facie preferable to the Higher-Order Monitoring theory. (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)

Higher-order vagueness is widely thought to be a feature of vague predicates that any adequate theory of vagueness must accommodate. It takes a variety of forms. Perhaps the most familiar is the supposed existence, or at least possibility, of higher-order borderline cases—borderline borderline cases, borderline borderline borderline cases, and so forth. A second form of higherorder vagueness, what I will call ‘prescriptive’ higher-order vagueness, is thought to characterize complex predicates constructed from vague predicates by (...) attaching operators having to do with the predicates’ proper application. For example, the predicates ‘mandates application of “old”’ and ‘can competently be called “old”’ are prescriptively higher-order vague. Higher-order vagueness appears in other guises as well,1 but these two have been of particular interest to philosophers and will be my target here. I want to expose some misconceptions about them. If I am right, higher-order vagueness is less prevalent, and less important theoretically, than is usually supposed.2 In what follows I am going to assume that vagueness is a semantic feature of natural language. For the most part I won’t discuss epistemic or pragmatic views, and I will say nothing about so-called metaphysical vagueness. (shrink)

In this paper I take second order-quantification to be a sui generis form of quantification, irreducible to first-order quantification, and I examine the implications of doing so for the debate over the existence of properties. Nicholas K. Jones has argued that adding sui generis second-order quantification to our ideology is enough to establish that properties exist. I argue that Jones does not settle the question of whether there are properties because—like other ontological questions—it is first-order. Then (...) I examine three of the main arguments for the existence of properties. I conclude that sui generis second-order quantification defeats the “one over many” argument and that, coupled with second-order predication, it also defeats the reference and quantification arguments. (shrink)

Higher‐order metaphysicians take facts to be higher‐order beings, i.e., entities in the range of irreducibly higher‐order quantifiers. In this paper, I investigate the impact of this conception of facts on the debate about the reality of tense. I identify two major repercussions. The first concerns the logical space of tense realism: on a higher‐order conception of facts, a prominent version of tense realism, dynamic absolutism, turns out to conflict with the laws of (...) (higher‐order tense) logic. The second concerns our understanding of the positions occupying this logical space: on a higher‐order conception of facts, an attractive interpretation of the central tense realist notion of ‘facts constituting reality’ becomes unavailable. I discuss these results in the context of the more general project of higher‐order metaphysics and the (meta)metaphysics of time, drawing out their implications for the nature of the disputes both between realists and anti‐realists about tense and between different tense realist factions. (shrink)

On an optimistic version of realist moral epistemology, a significant range of ordinary moral beliefs, construed in realist terms, constitute knowledge—or at least some weaker positive epistemic status, such as epistemic justification. The “debunking challenge” to this view grants prima facie justification but claims that it is “debunked” (i.e., defeated), yielding the final verdict that moral beliefs are ultima facie unjustified. Notable candidate “debunkers” (i.e., defeaters) include the so-called “evolutionary debunking arguments,” the “Benacerraf-Field Challenge,” and persistent moral disagreement among epistemic (...) peers. Such defeaters are best treated as higher-order evidence—viz., evidence contesting the merits of the first-order evidence on which moral beliefs are based. This chapter first develops a theory of higher-order defeat in general, which it then applies to debunking in particular. The result: the challenge fails entirely on epistemic grounds—regardless of whether or not its empirical and metaphysical presuppositions are correct. An advantage of this purely epistemic defense over alternative strategies is that the former extends even to laypersons who themselves lack the expertise necessary to formulate an adequate response. However, this leaves open the prospects for non-epistemological interpretations of debunking (e.g., moral or ontological). The chapter therefore concludes with brief suggestions in that direction. (shrink)

Theories of what it is for a mental state to be conscious must answer two questions. We must say how we're conscious of our conscious mental states. And we must explain why we seem to be conscious of them in a way that's immediate. Thomas Natsoulas distinguishes three strategies for explaining what it is for mental states to be conscious. I show that the differences among those strategies are due to the divergent answers they give to the foregoing questions. Natsoulas (...) finds most promising the strategy that amounts to the higher-order-thought hypothesis that I've defended elsewhere. But he raises a difficulty for it, which he thinks probably can be met only by modifying that strategy. I argue that this is unnecessary. The difficulty is a special case of a general question, the answer to which is independent of any issues about consciousness. So it's no part of a theory of consciousness to address the problem, much less solve it. Moreover, the difficulty seems to have intuitive force only given the picture that underlies the other two explanatory strategies, which both Natsoulas and I reject. (shrink)

Recent work in the ontology of music suggests that we will avoid confusion if we distinguish between two kinds of question that are typically posed in music ontology. Thus, a distinction has been made between fundamental ontology and higher-order ontology. The former addresses questions about the basic metaphysical options from which ontologists choose. For instance, are musical works types, indicated types, classes of particulars, or some other kind of entity? Higher-order ontology addresses the question of what (...) lies ‘at the centre’ of a specific form of music, such as rock or jazz—or perhaps classical music. The argument of this essay is, first, that a close examination of the best efforts in two of these territories shows that they have the effect of pressing the music in each sphere into implausible Procrustean beds. Second, it is argued that the general question that higher-order ontologies pose, that is, ‘What work-kind is it that lies at the centre of a given kind of music, F?’ is a question based on a mistaken but seductive assumption, namely that the concept of the work of F has actual application. In fact, these concepts—upon which higher-order ontology depends—are mere artefacts of philosophy. The question is also addressed why the assumption is so seductive. Finally, the question finally is posed about what, if anything, is implied from the foregoing about the traditional ontology of classical music. (shrink)

Experts are sharply divided concerning the prevalence and influence of misinformation. Some have emphasized the severe epistemic and political threats posed by misinformation and have argued that some such threats have been realized in the real world. Others have argued that such concerns overstate the prevalence of misinformation and the gullibility of ordinary persons. Rather than taking a stand on this issue, I consider what would follow from the supposition that this latter perspective is correct. I argue that, if the (...) prevalence and influence of misinformation are indeed overstated, then many reports as to the prevalence and influence of misinformation constitute a kind of higher-order misinformation. I argue that higher-order misinformation presents its own challenges. In particular, higher-order misinformation, ironically, would lend credibility to the very misinformation whose influence it exaggerates. Additionally, higher-order misinformation would lead to underestimations of the reasons favoring opposing views. In short, higher-order misinformation constitutes misleading higher-order evidence concerning the quality of the evidence on which individuals form their beliefs. (shrink)

This paper makes a comparison between naturalist and non-naturalist theories of consciousness with respect to their explanatory merits. It focuses on David Rosenthal's higher-order thought theory, arguing that the motives for higher-order theories are based on a confusion of three distinct meanings of the term 'intrinsic'. The explanatory power of HOT theories is compared with that of an alternative nonrepresentational theory, offered as an example of a naturalistic account. The latter is found overall to have more (...) virtues and less shortcomings that the higher-order theory. (shrink)

This book articulates and defends Fregean realism, a theory of properties based on Frege's insight that properties are not objects, but rather the satisfaction conditions of predicates. Robert Trueman argues that this approach is the key not only to dissolving a host of longstanding metaphysical puzzles, such as Bradley's Regress and the Problem of Universals, but also to understanding the relationship between states of affairs, propositions, and the truth conditions of sentences. Fregean realism, Trueman suggests, ultimately leads to a version (...) of the identity theory of truth, the theory that true propositions are identical to obtaining states of affairs. In other words, the identity theory collapses the gap between mind and world. This book will be of interest to anyone working in logic, metaphysics, the philosophy of language or the philosophy of mind. (shrink)

Supervenience theses promise ontological economy without reducibility. The problem is that they face a dilemma: either the relation of supervenience entails reducibility or it is mysterious. Recently higher-order universals have been invoked to avoid the dilemma. This article develops a higher-order framework in which this claim can be assessed. It is shown that reducibility can be avoided, but only at the cost of a rather radical metaphysical proposal.

Special quantifiers are quantifiers like 'something', 'everything', and 'several things'. They are special both semantically and syntactically and play quite an important role in philosophy, in discussions of ontological commitment to abstract objects, of higher-order metaphysics, and of the apparent need for propositions. This paper will review and discuss in detail the syntactic and semantic peculiarities of special quantifiers and show that they are incompatible with substitutional and higher-order analyses that have recently been proposed. It (...) instead defends and develops in formal detail a semantic analysis of special quantifiers as nominalizing quantifiers. On this analysis, special quantifiers involve both singular objectual quantification and implicit on non-singular (higher-order, plural, or mass) quantification. The analysis rests on a range of recent insights and proposals in generative syntactic theory, in particular the recognition of '–thing' as a light noun and a potential classifier as well as recent views of the decomposition of attitudinal and locutionary verbs in syntax. (shrink)

Serious actualism is the prima facie plausible thesis that things couldn’t have been related while being nothing. The thesis plays an important role in a number of arguments in metaphysics, e.g., in Plantinga’s argument for the claim that propositions do not ontologically depend on the things that they are about and in Williamson’s argument for the claim that he, Williamson, is necessarily something. Salmon has put forward that which is, arguably, the most pressing challenge to serious actualists. Salmon’s objection (...) is based on a scenario intended to elicit the judgment that merely possible entities may nonetheless be actually referred to, and so may actually have properties. It is shown that predicativism, the thesis that names are true of their bearers, provides the resources for replying to Salmon’s objection. In addition, an argument for serious actualism based on Stephanou, 219–250 2007) is offered. Finally, it is shown that once serious actualism is conjoined with some minimal assumptions, it implies property necessitism, the thesis that necessarily all properties are necessarily something, as well as a strong comprehension principle for higher-order modal logic according to which for every condition there necessarily is the property of being a thing satisfying that condition. (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)

The aim of this paper is, firstly, to identify the areas of conceptual confusion about the notion of auditory object that could benefit from a cooperation between philosophy and psychology of perception. Secondly, I try to clarify in what sense there may be individual entities that exist only in time focusing on auditory objects, and to establish what kind of relationship links the existence of such purely temporal entities with the existence of spatiotemporal entities such as bodies or physical objects. (...) Finally, a new definition of auditory object, conceived as a partially mind-dependent object, or Meinongian higher-order object based on inferiora, is discussed. (shrink)

In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that the (...) search for the true axioms of set theory is. We show that the obvious responses to this argument fail. However, a new response has emerged that purports to prove, from higher-order logical principles, that metaphysical possibility is the broadest kind of possibility applying to propositions, and is to that extent special. We distill two lines of reasoning from the literature, and argue that their import depends on premises that any ‘modal pluralist’ should deny. Both presuppose that there is a unique typed hierarchy, which is what the modal pluralist, in the context of higher-order logic, should disavow. In other words, both presupposes that there is a unique candidate for what higher-order claims could mean. We consider the worry that, in a higher-order setting, modal pluralism faces an insuperable problem of articulation, collapses into modal monism, is vulnerable to the Russell-Myhill paradox, or even contravenes the truism that there is a unique actual world, and argue that these worries are misplaced. We also sketch the bearing of the resulting ‘Higher-Order Pluralism’ on the theory of content. One theme of the discussion is that, if Higher-Order Pluralism is correct, then there is no fixed metatheory from which to characterize higher-order reality. (shrink)

Recently, some philosophers have argued that we should take quantification of any (finite) order to be a legitimate and irreducible, sui generis kind of quantification. In particular, they hold that a semantic theory for higher-order quantification must itself be couched in higher-order terms. Øystein Linnebo has criticized such views on the grounds that they are committed to general claims about the semantic values of expressions that are by their own lights inexpressible. I show that Linnebo’s (...) objection rests on the assumption of a notion of semantic value or contribution which both applies to expressions of any order, and picks out, for each expression, an extra-linguistic correlate of that expression. I go on to argue that higher-orderists can plausibly reject this assumption, by means of a hierarchy of notions they can use to describe the extra-lingustic correlates of expressions of different orders. (shrink)

Higher-order evidence appears to have the ability to defeat rational belief. It is not obvious, however, why exactly the defeat happens. In this paper, I consider two competing explanations of higher-order defeat: the “Objective Higher-Order Defeat Explanation” and the “Subjective Higher-Order Defat Explanation.” According to the former explanation, possessing sufficiently strong higher-order evidence to indicate that one’s belief about p fails to be rational is necessary and sufficient for defeating one’s (...) belief about p. I argue that this type of explanation is defective or at best collapses into the other type of explanation. According to the latter explanation, Believing that one’s belief about p fails to be rational (in response to higher-order evidence about p) is necessary and sufficient for defeating one’s belief about p. I argue that this type of explanation is better suited to explain higher-order defeat given that what one is rational to believe partly depends on the relations among one’s doxastic attitudes. Finally, I address an peculiar feature of the Subjective Higher-Order Defeat Explanation: higher-order defeat becomes contingent on one’s response to the higher-order evidence. (shrink)

This paper argues that higher‐order thought (HOT) models of consciousness face serious logical problems. The precise form these problems take varies depending on whether HOT models are understood as attempts to explicate the concept of (intransitive state) consciousness or as attempts to identify the property in virtue of which mental states are (intransitively) conscious. Understood in the former way, HOT models face a problem of circularity. Understood in the latter way, such models face a problem of regress.

This is the first comprehensive textbook on higher order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages -- their model theory and proof theory, the theory of λ-abstraction and its generalizations -- and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more (...) appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics. A Philosophical Introduction to Higher Order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study. Author Andrew Bacon organizes the book's 18 chapters around four main parts: I. Typed Language II. Higher Order Languages III. General Higher-Order Languages IV. Higher-Order Model Theory In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources. Key Features Is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics Introduces the basic formal tools that are needed to theorize in, and model, higher order languages Offers an abundance of: - Simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions - More difficult exercises designed to facilitate long-term learning Contains annotated sections on further reading, pointing the reader to related literature, learning resources, and historical context. (shrink)

Nonnaturalist realism is the view that normative properties are unique kind of stance-independent properties. It has been argued that such views fail to explain why two actions that are exactly alike otherwise must also have the same normative properties. Mark Schroeder and Knut Olav Skarsaune have recently suggested that nonnaturalist realists can respond to this supervenience challenge by taking the primary bearers of normative properties to be action kinds. This paper develops their response in two ways. First, it provides additional (...) motivation for the previous claim about the bearers of normative properties by drawing from the work of H. A. Prichard. Second, and more importantly, it formulates a plausible metaphysical framework based on the contemporary trope theory to explain why action kinds would have their second-order properties, including their normative properties, necessarily. (shrink)

Peter Carruthers's essays on consciousness and related issues have had a substantial impact on the field, and many of his best are now collected here in revised form. The first half of the volume is devoted to developing, elaborating, and defending against competitors one particular sort of reductive explanation of phenomenal consciousness, which Carruthers now refers to as 'dual-content theory'. Phenomenal consciousness - the feel of experience - is supposed to constitute the 'hard problem' for a scientific world view, and (...) many have claimed that it is an irredeemable mystery. But Carruthers here claims to have explained it. He argues that phenomenally conscious states are ones that possess both an 'analog' intentional content and a corresponding higher-order analog content, representing the first-order content of the experience. It is the higher-order analog content that enables our phenomenally conscious experiences to present themselves to us, and that constitutes their distinctive subjective aspect, or feel.The next two chapters explore some of the differences between conscious experience and conscious thought, and argue for the plausibility of some kind of eliminativism about conscious thinking. Then the final four chapters focus on the minds of non-human animals. Carruthers argues that even if the experiences of animals aren't phenomenally conscious, this needn't prevent the frustrations and sufferings of animals from being appropriate objects of sympathy and concern. Nor need it mean that there is any sort of radical 'Cartesian divide' between our minds and theirs of deep significance for comparative psychology. In the final chapter, he argues provocatively that even insects have minds that include a belief/desire/perception psychology much like our own. So mindedness and phenomenal consciousness couldn't be further apart.Carruthers's writing throughout is distinctively clear and direct. The collection will be of great interest to anyone working in philosophy of mind or cognitive science. (shrink)

If an agent prefers one kind of agents to the other agents, then the agent has first-order preferences. If the agent prefers agents with one kind of preferences to the other agents, then the agent has second-order preferences. The article proposes a sound, complete, and decidable logical system capable of expressing higher-order preferences.

Relying on a range of now-familiar thought-experiments, it has seemed to many philosophers that phenomenal consciousness is beyond the scope of reductive explanation. (Phenomenal consciousness is a form of state-consciousness, which contrasts with creature-consciousness, or perceptual-consciousness. The different forms of state-consciousness include various kinds of access-consciousness, both first-order and higher-order--see Rosenthal, 1986; Block, 1995; Lycan, 1996; Carruthers, 2000. Phenomenal consciousness is the property that mental states have when it is like something to possess them, or when they (...) have subjectively-accessible feels; or as some would say, when they have qualia (see fn.1 below).) Others have thought that we can undermine the credibility of those thought-experiments by allowing that we possess purely recognitional concepts for the properties of our conscious mental states. This paper is concerned to explain, and then to meet, the challenge of showing how purely recognitional concepts are possible if there are no such things as qualia--in the strong sense of intrinsic (non-relational, non-intentional) properties of experience. It argues that an appeal to higher-order experiences is necessary to meet this challenge, and then deploys a novel form of higher-order thought theory to explain how such experiences are generated. (shrink)

I discuss whether Michael Tye, in Ten Problems of Consciousness. Cambridge, Massachusetts: MIT Press, 1966, holds that phenomenal properties are neurological properties, but that what gives them their phenomenal property names are their highly complex interconnections with other neurological properties and, most especially, subjects' surroundings. Or, alternatively, whether he holds that they are higher-level, wide functional properties in the sense of being properties of having properties that fill some specified wide or distal roles.

This is a review of "Properties and Propositions: The Metaphysics of Higher-Order Logic" by Robert Trueman. Following an overview of the main themes of the book, I discuss the metaphysical presuppositions of Trueman's Fregean notation for predicate abstraction and evaluate his argument for strict typing.

An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the `width' of the set theoretic universe, such as Cantor's continuum hypothesis. Within a higher-order framework I (...) show that contingency about the width of the set-theoretic universe refutes two orthodoxies concerning the structure of modal reality: the view that the broadest necessity has a logic of S5, and the "Leibniz biconditionals" stating that what is possible, in the broadest sense of possible, is what is true in some possible world. Nonetheless, I suggest that the underlying picture of modal set-theory is coherent and has attractions. (shrink)

According to the rationality thesis , the possession of propositional attitudes is inextricably tied to rationality. How in this context should we conceive of rationality? In one sense, being rational is contrasted with being non-rational, as when human beings are described as rational animals. In another sense, being rational is contrasted with being irrational. I shall call rationality in this latter sense evaluative rationality . Whatever else it might involve, evaluative rationality surely has to do with satisfying requirements of rationality (...) such as, presumably, the following: That one avoid inconsistency in beliefs. That one not adopt new beliefs unless what one knows entails or is evidence for the truth of those beliefs. That one not have φing as a goal yet do nothing necessary for one to φ. (shrink)