It is well known that a degree-of-belief function P is coherent if and only if it satisfies the probability calculus. In this paper, we show that the notion of coherence can be extended to higher order probabilities such as P(P(h)=p)=q, and that a higher order degree-of-belief function P is coherent if and only if it satisfies the probability calculus plus the following axiom: P(h)=p iff P(P(h)=p)=1. Also, a number of lemmata which extend an incomplete probability (...) function to a complete one are established. (shrink)

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...) have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

Is it coherent to speak of the probability of a probability, and the probability of a probability of a probability, and so on? We show that it is, in the sense that a regress of higher-order probabilities can lead to convergent sequences that determine all these probabilities. By constructing an implementable model which is based on coin-making machines, we demonstrate the consistency of our regress.

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.

Cognitive Science, Volume 46, Issue 4, April 2022.

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)

It is usually taken as given that consciousness involves superior or more elaborate forms of information processing. Contemporary models equate consciousness with global processing, system complexity, or depth or stability of computation. This is in stark contrast with the powerful philosophical intuition that being conscious is more than just having the ability to compute. I argue that it is also incompatible with current empirical findings. I present a model that is free from the strong assumption that consciousness predicts superior performance. (...) The model is based on Bayesian decision theory, of which signal detection theory is a special case. It reflects the fact that the capacity for perceptual decisions is fundamentally limited by the presence and amount of noise in the system. To optimize performance, one therefore needs to set decision criteria that are based on the behaviour, i.e. the probability distributions, of the internal signals. One important realization is that the knowledge of how our internal signals behave statistically has to be learned over time. Essentially, we are doing statistics on our own brain. This ‘higherorder’ learning, however, may err, and this impairs our ability to set and maintain optimal criteria for perceptual decisions, which I argue is central to perception consciousness. I outline three possibilities of how conscious perception might be affected by failures of ‘higher-order’ representation. These all imply that one can have a dissociation between consciousness and performance. This model readily explains blindsight and hallucinations in formal terms, and is beginning to receive direct empirical support. I end by discussing some philosophical implications of the model. (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)

We present a propositional and a first-order logic for reasoning about higher-order upper and lower probabilities. We provide sound and complete axiomatizations for the logics and we prove decidability in the propositional case. Furthermore, we show that the introduced logics generalize some existing probability logics.

We present a propositional and a first-order logic for reasoning about higher-order upper and lower probabilities. We provide sound and complete axiomatizations for the logics and we prove decidability in the propositional case. Furthermore, we show that the introduced logics generalize some existing probability logics.

Most epistemologists maintain that we are rationally required to believe what our evidence supports. Generally speaking, any factor that makes it more probable that a given state of affairs obtains (or does not obtain) is evidence (for that state of affairs). In line with this view, many metaethicists believe that we are rationally required to believe what’s morally right and wrong based on what our moral evidence (e.g. our moral intuitions, along with descriptive information about the world) supports. However, sometimes (...) we get information about our evidence, such as a theory that explains that all moral intuitions are ultimately caused by evolutionary forces. Such genealogical claims like this take form as a puzzle about how to rationally respond to higher-order evidence in moral epistemology. How should we change our moral views in response to genealogical claims about the evolutionary origin of our moral beliefs or about widespread moral disagreement? This introductory chapter first explains the issue about how to change our moral views based on an easily accessible example. Then it shows how recent debates about the puzzle of higher-order evidence bears on recent debates in moral epistemology, notably the debates about evolutionary debunking arguments in metaethics, the epistemic significance of moral peer disagreement, moral testimony, and collective moral knowledge before it introduces the chapters of this book. (shrink)

Second or higher order probabilities have commonly been viewed with scepticism by those working within the realm of probability and decision theory. The aim of the present note is to show how the notion of second order probabilities can add to our understanding of judgmental and decision processes and how the traditional framework of Bayesian decision theory can be extended in a fruitful way by taking such entities into account. Section one consists of a brief (...) account of arguments put forth against higher order probabilities as well as of counterarguments. In order to provide an example of the applicability of second order probabilities a decision theory encompassing such probabilities will be presented in section two. In section three I will try to emphasize the value of second order probabilities for a deeper and more complete understanding of the notion of risk. (shrink)

For nearly a decade, David Rosenthal has proposed that a mental state M of a creature C is conscious just in case C has a suitable higher-order thought directed toward M. While this theory has had its share of criticism in recent years, I believe that the real difficulties have been ignored. In this essay, I show that the presence of a higher order is insufficient for conscious experience, even if we suppose that the thought satisfies (...) the constraints that Rosenthal lists . The only way Rosenthal's view could possibly yield sufficient conditions is by requiring that the higher-order thought be suitably causally related to its object. Yet, as I also show, the only causal constraint strong enough to do the job is not only ill-motivated but probably false. (shrink)

A knowledge-based decision theory faces what has been called the prodigality problem : given that many propositions are assigned probability 1, agents will be inclined to risk everything when betting on propositions which are known. In order to undo probability 1 assignments in high risk situations, the paper develops a theory which systematically connects higher level goods with higher-order knowledge.

Suppose you hold the following opinions in the philosophy of logic. First-order predicate logic is expressively inadequate to regiment concepts of mathematic and natural language; logicism is plausible and attractive; set theory as an adjunct to logic is unnatural and ontologically extravagant; humanly usable languages are finite in lexicon and syntax; it is worth striving for a Tarskian semantics for mathematics; there are no Platonic abstract objects. Then you are probably already in cognitive distress. One way to decease your (...) unhappiness, short for embracing Platonism, is to accept higher-order logic and look, as did Arthur Prior, for a plausible way to neutralize the ontological commitment to abstract entities that this acceptance appears to entail. (shrink)

Suppose you hold the following opinions in the philosophy of logic. First-order predicate logic is expressively inadequate to regiment concepts of mathematic and natural language; logicism is plausible and attractive; set theory as an adjunct to logic is unnatural and ontologically extravagant; humanly usable languages are finite in lexicon and syntax; it is worth striving for a Tarskian semantics for mathematics; there are no Platonic abstract objects. Then you are probably already in cognitive distress. One way to decease your (...) unhappiness, short for embracing Platonism, is to accept higher-order logic and look, as did Arthur Prior, for a plausible way to neutralize the ontological commitment to abstract entities that this acceptance appears to entail. (shrink)

Some philosophers have claimed that it is meaningless or paradoxical to consider the probability of a probability. Others have however argued that second-order probabilities do not pose any particular problem. We side with the latter group. On condition that the relevant distinctions are taken into account, second-order probabilities can be shown to be perfectly consistent. May the same be said of an infinite hierarchy of higher-order probabilities? Is it consistent to speak of a (...) probability of a probability, and of a probability of a probability of a probability, and so on, {\em ad infinitum}? We argue that it is, for it can be shown that there exists an infinite system of probabilities that has a model. In particular, we define a regress of higher-order probabilities that leads to a convergent series which determines an infinite-order probability value. We demonstrate the consistency of the regress by constructing a model based on coin-making machines. (shrink)

The author uses a series of examples to illustrate two versions of a new, nonprobabilist principle of epistemic rationality, the special and general versions of the metacognitive, expected relative frequency principle. These are used to explain the rationality of revisions to an agent’s degrees of confidence in propositions based on evidence of the reliability or unreliability of the cognitive processes responsible for them—especially reductions in confidence assignments to propositions antecedently regarded as certain—including certainty-reductions to instances of the law of excluded (...) middle or the law of noncontradiction in logic or certainty-reductions to the certainties of probabilist epistemology. The author proposes special and general versions of the MERF principle and uses them to explain the examples, including the reasoning that would lead to thoroughgoing fallibilism—that is, to a state of being certain of nothing. The author responds to the main defenses of probabilism: Dutch Book arguments, Joyce’s potential accuracy defense, and the potential calibration defenses of Shimony and van Fraassen by showing that, even though they do not satisfy the probability axioms, degrees of belief that satisfy the MERF principle minimize expected inaccuracy in Joyce’s sense; they can be externally calibrated in Shimony and van Fraassen’s sense; and they can serve as a basis for rational betting, unlike probabilist degrees of belief, which, in many cases, human beings have no rational way of ascertaining. The author also uses the MERF principle to subsume the various epistemic akrasia principles in the literature. Finally, the author responds to Titelbaum’s argument that epistemic akrasia principles require that we be certain of some epistemological beliefs, if we are rational. (shrink)

Problems are raised with the global workspace hypothesis of consciousness, for example about exactly how global the workspace needs to be for consciousness to suddenly be present. Problems are also raised with Carruthers's version that excludes conceptual representations, and in which phenomenal consciousness can be reduced to physical processes, with instead a different levels of explanation approach to the relation between the brain and the mind advocated. A different theory of phenomenal consciousness is described, in which there is a particular (...) computational system involved in which Higher Order Syntactic Thoughts are used to perform credit assignment on first order thoughts of multiple step plans to correct them by manipulating symbols in a syntactic type of working memory. This provides a good evolutionary reason for the evolution of this kind of computational module, with which, it is proposed, phenomenal consciousness is associated. Some advantages of this HOST approach to phenomenal consciousness are then described with reference not only to the global workspace approach, but also to Higher Order Thought theories. It is hypothesized that the HOST system which requires the ability to manipulate first order symbols in working memory might utilize parts of the prefrontal cortex implicated in working memory, and especially the left inferior frontal gyrus, which is involved in language and probably syntactical processing. Overall, the approach advocated is to identify the computations that are linked to consciousness, and to analyze the neural bases of those computations. [copyright: Copyright © 2020 Rolls.]. (shrink)

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some (...) probability of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic. (shrink)

‘Probability dynamics’ (PD) is a second-order probabilistic theory in which probability distribution d X = (P(X 1), . . . , P(X m )) on partition U m X of sample space Ω is weighted by ‘credence’ (c) ranging from −∞ to +∞. c is the relative degree of certainty of d X in ‘α-evidence’ α X =[c; d X ] on U m X . It is shown that higher-order probabilities cannot provide a theory of (...) PD. PD applies to both subjectivist and frequentist theories. ‘Straight PD’ (SPD) produces associative and commutative mergers of evidence, in which evidences of positive credence are mutually reinforcing. ‘Offsetting PD’ (OPD) sets off conflicting evidences against each other. Subjectivist PD is a quantified second-order logic of action. Frequentist PD relates to descriptions of physical states of affairs. Acceptance of evidence α 1 X = [c 1; d 1 X ] at t 1 updates α 0 X = [c 0; d 0 X ] at t 0 into SPD-merger or OPD-merger . Given ‘co-evidence’ at t 0 < t 1, ‘indirect’ PD accepts evidence at t 1 and produces support for update α 10 X = [c10;d 10 X α 0 X such that in SPD and in OPD. For binary X and Y, with α 0 X = [c 0; P 0(X)] at t 0 (short-hand for ) and the accepted evidence, the support is ; ; where ρ0(X, Y) is the correlation coefficient of X and Y, and update α 10 X of α 0 X is with ‘accord’ λ = 1 in SPD and in OPD. As , tends toward update P 1(Y) of P 0(Y), but P 10(X) does not converge toward ‘ ’ of ‘probability kinematics’. Therefore PD is not compatible with probability kinematics. A process of ‘normalization’ interprets ‘β-evidence’ [[c 1; q 1]& . . . &[c m ; q m ]; U m X ]] with [c j ; q j ] on and m ≥ 3, as an α-evidence on {X 1, . . . , X m }. It is shown that SPD- and OPD-updates can be derived from updated cumulative functions. Time-biased updates are discussed. A PD-based theory of confirmation (PDCT) is presented. (shrink)

This book examines the dominant discourses in higher education. From the moment academics enter higher education, they are met with binaries such as teaching vs. research, quantitative vs. qualitative research, and constructivists vs. positivists. When embarking upon a teaching career in a university there are further binaries that immediately present themselves, with deep vs. surface learning probably being the most pervasive. Kinchin and Gravett contend that this presents a distorted view and contributes to the disconnect between the aims (...) and observable practice of higher education. Rather than celebrating difference, dominant discourses tend to seek similarities in an attempt to simplify and manage the environment, in what the authors perceive as a less than scholarly mode. In order to break down the barriers between 'structuralist' or 'traditional' academics and those who are more familiar with poststructuralist, critical perspectives, the authors explore the overlaps between these perspectives to offer a richer and more inclusive interrogation of the dominant discourses that pervade higher education. Offering methodological approaches to explore these perspectives, the authors bring together academics working in different parts of the university and examine the concept of a 'rich cartography', exploring how this can offer meaning within higher education research and practice. (shrink)

Bayesianism is the position that scientific reasoning is probabilistic and that probabilities are adequately interpreted as an agent's actual subjective degrees of belief, measured by her betting behaviour. Confirmation is one important aspect of scientific reasoning. The thesis of this paper is the following: if scientific reasoning is at all probabilistic, the subjective interpretation has to be given up in order to get right confirmation—and thus scientific reasoning in general. The Bayesian approach to scientific reasoning Bayesian confirmation theory (...) The example The less reliable the source of information, the higher the degree of Bayesian confirmation Measure sensitivity A more general version of the problem of old evidence Conditioning on the entailment relation The counterfactual strategy Generalizing the counterfactual strategy The desired result, and a necessary and sufficient condition for it Actual degrees of belief The common knock-down feature, or ‘anything goes’ The problem of prior probabilities. (shrink)

Most legal evidence scholars agree that proof of guilt beyond a reasonable doubt requires the belief that the defendant probably committed the alleged acts. However, they also agree that this is not a sufficient condition, as this belief may be unreasonable. I focus on two popular proposals for additional conditions: (i) that the degree of belief should be robust and (ii) that it should be reasonable given the available evidence (should be an evidential probability). Both criteria face difficulties regarding their (...) meaning and utility. I propose an interpretation which overcomes these difficulties and which combines the two conditions into a single criterion on which both conditions are about the possibility of overlooked, exculpatory information. Proof of guilt beyond a reasonable doubt requires that we are sufficiently certain that we did not miss such information for the sake of achieving accurate beliefs and a just error distribution. How certain we can be that we did not miss anything relevant depends on our higher-order evidence. One important type of higher-order evidence is whether the hypotheses under consideration are sufficiently detailed. This point leads to a novel way of combining the Bayesian and explanation-based accounts of rational legal proof. (shrink)

Epistemic transparency tells us that, if an agent S knows a given proposition p , then S knows that she knows that p . This idea is usually encoded in the so-called KK principle of epistemic logic. The paper develops an argument in favor of a moderate version of KK , which I dub quasi-transparency , as a normative rather than a descriptive principle. In the second Section I put forward the suggestion that epistemic transparency is not a demand of (...) ideal rationality, but of ideal epistemic responsibility, and hence that ideally responsible agents verify transparency principles of some sort; I also contend that their satisfaction should not be tied to an internalist epistemology. The central argument in favor of transparency is then addressed in Sections 3 to 8, through the development of a formal system. I show that, in a well-behaved formal setting, a moderate version of transparency is imposed upon us as a result of a number of independent decisions on the structure of higher-order probabilities, as long as we request that our probability and knowledge attributions cohere with each other. Thus I give a rationale to build a model for a hierarchy of languages with different levels of knowledge and probability operators; we obtain an analogous to KK for successive knowledge operators without actually demanding transitivity. The formal argument reinforces the philosophical intuition that epistemic transparency is an important desideratum we should not be too ready to dismiss. (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)

The technique of minimizing information (infomin) has been commonly employed as a general method for both choosing and updating a subjective probability function. We argue that, in a wide class of cases, the use of infomin methods fails to cohere with our standard conception of rational degrees of belief. We introduce the notion of a deceptive updating method and argue that non-deceptiveness is a necessary condition for rational coherence. Infomin has been criticized on the grounds that there are no (...) class='Hi'>higher order probabilities that ‘support’ it, but the appeal to higher order probabilities is a substantial assumption that some might reject. Our elementary arguments from deceptiveness do not rely on this assumption. While deceptiveness implies lack of higher order support, the converse does not, in general, hold, which indicates that deceptiveness is a more objectionable property. We offer a new proof of the claim that infomin updating of any strictly-positive prior with respect to conditional-probability constraints is deceptive. In the case of expected-value constraints, infomin updating of the uniform prior is deceptive for some random variables but not for others. We establish both a necessary condition and a sufficient condition (which extends the scope of the phenomenon beyond cases previously considered) for deceptiveness in this setting. Along the way, we clarify the relation which obtains between the strong notion of higher order support, in which the higher order probability is defined over the full space of first order probabilities, and the apparently weaker notion, in which it is defined over some smaller parameter space. We show that under certain natural assumptions, the two are equivalent. Finally, we offer an interpretation of Jaynes, according to which his own appeal to infomin methods avoids the incoherencies discussed in this paper. (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)

Richard Swinburne, in his The Existence of God (2004), presents a cosmological argument in defence of theism (Swinburne 1991: 119, 135). God, Swinburne argues, is more likely to bring about an ordered universe than other states (ibid.: 144, 299). To defend this view, Swinburne presents the following arguments: (1) That this ordered universe is a priori improbable (2004: 49, 150, 1991: 304 et seq.), given the stringent requirements for life (cf. also Leslie 2000: 12), and the Second Law of Thermodynamics (...) (Giancoli 1990: 396); (2) That it seems as if this ordered universe can be explained by theism; (3) A theistic explanation for the universe is more probable because it is a simple explanation. To this end, Swinburne makes use of Bayes’ Theorem. Symbolically, this claim can be represented as (e) for the evidence of the existence of a complex universe, and (h) for a hypothesis. Swinburne’s argument is that theism has a higher prior probability, P(htheism) > P(hmaterialism), since theism is simpler than materialism. He concludes that P(e|htheism) > P(e|hmaterialism). In this paper I will address only this argument (3) above, and defend the view that it is false: theism is not simpler than materialism, nor it is more probably true. I conclude that theism is less probable than materialism, expressed by P(htheism) < P(hmaterialism) : 2/N(2n+1) < 1/n, where N is the number of possible universes and n the number of entities in existence. (shrink)

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.

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)

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)

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)

My aim in this paper is to develop and defend a novel answer to a question that has recently generated a considerable amount of controversy. The question concerns the normative significance of peer disagreement. Suppose that you and I have been exposed to the same evidence and arguments that bear on some proposition: there is no relevant consideration which is available to you but not to me, or vice versa. For the sake of concreteness, we might picture.

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 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)

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)

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.

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)