I argue for the possibility of an extremely intimate connection between the emotional content of the music and the emotional state of the person who produces that music. Under certain specified conditions, the music may not just influence, but also partially constitute the musician’s emotional state.

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

This paper examines the causal basis of our ability to attribute emotions to music, developing and synthesizing the existing arousal, resemblance and persona theories of musical expressivity to do so. The principal claim is that music hijacks the simulation mechanism of the brain, a mechanism which has evolved to detect one's own and other people's emotions.

The author proposes a dimensional model of our emotion concepts that is intended to be largely independent of one’s theory of emotions and applicable to the different ways in which emotions are measured. He outlines some conditions for selecting the dimensions based on these motivations and general conceptual grounds. Given these conditions he then advances an 8-dimensional model that is shown to effectively differentiate emotion labels both within and across cultures, as well as more obscure expressive language. The 8 dimensions (...) are: (1) attracted—repulsed, (2) powerful—weak, (3) free—constrained, (4) certain—uncertain, (5) generalized—focused, (6) future directed—past directed, (7) enduring—sudden, (8) socially connected—disconnected. (shrink)

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...) successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

This book defends Aestheticism- the claim that everything is aesthetically valuable and that a life lived in pursuit of aesthetic value can be a particularly good one. Furthermore, in distilling aesthetic qualities, artists have a special role to play in teaching us to recognize values; a critical component of virtue. I ground my account upon an analysis of aesthetic value as ‘objectified final value’, which is underwritten by an original psychological claim that all aesthetic values are distal versions of practical (...) values. This is followed by systematic accounts of beauty, sublimity, comedy, drama, and tragedy, as well as appendix entries on the cute, the cool, the kitsch, the uncanny, the horrific, the erotic, and the furious. (shrink)

Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improvement on previous such appeals by showing how it answers (...) or sidesteps problems that have been raised for previous work in this area. (shrink)

It is an important feature of creatures like us that our various motivations compete for control over our behaviour, including mental behaviour such as imagining and attending. In large part, this competition is adjudicated by the stimulation of affect — the intrinsically pleasant or unpleasant aspects of experience. In this paper I argue that the motivation-affect system controls a sub-type of attention called 'alerting attention' to bring various goals and stimuli to consciousness and thereby prioritize those contents for action. This (...) view allows me to flesh out the global workspace theory of consciousness, as well as some of the phenomenal characteristics of conscious experience. (shrink)

The Intergovernmental Panel on Climate Change has developed a novel framework for assessing and communicating uncertainty in the findings published in their periodic assessment reports. But how should these uncertainty assessments inform decisions? We take a formal decision-making perspective to investigate how scientific input formulated in the IPCC’s novel framework might inform decisions in a principled way through a normative decision model.

The fear of death resists philosophical attempts at reconciliation. Building on theories of emotion, I argue that we can understand our fear as triggered by a de se mode of thinking about death which comes into conflict with our will to live. The discursive mode of philosophy may help us to avoid the de se mode of thinking about death, but it does not satisfactorily address the problem. I focus instead on the voluntary diminishment of one’s will to live. I (...) argue that we can encourage a natural tendency for the will to live to decline as we approach death. I then consider two objections: Is not the will to live too fundamental for us to control? And even if we can control it, would not a declining will to live result in a general despair that it is better to resist? I argue that both of these objections can be overcome. (shrink)

If we were to connect two individuals’ brains together, how would this affect the individuals’ conscious experiences? In particular, it is possible for two people to share any of their conscious experiences; to simultaneously enjoy some token experiences while remaining distinct subjects? The case of the Hogan twins—craniopagus conjoined twins whose brains are connected at the thalamus—seems to show that this can happen. I argue that while practical empirical methods cannot tell us directly whether or not the twins share conscious (...) experiences, considerations about the locality of content processing in the brain entails that they most likely do so. (shrink)

This article defends a persona theory of musical expressivity. After briefly summarising the major arguments for this view, it applies persona theory to the issue of whether music can express complex emotions. The expression of jealousy is then discussed by analysis of two examples from Piazzolla and Janacek.

In this chapter I analyse group flow: a state in which performers report intense interpersonal absorption with the music and each other. I compare group flow to individual flow, and argue that the same essential structure can be discerned. I argue that group flow does not justify an anti-representationalist enactivist interpretation. However, I claim that the cognitive task in which the music is produced is irreducibly collective.

In this article we examine obsessive compulsive disorder (OCD). We examine and reject two existing models of this disorder: the Dysfunctional Belief Model and the Inference‐Based Approach. Instead, we propose that the main distinctive characteristic of OCD is a hyperactive sub‐personal signal of being in error, experienced by the individual as uncertainty about his or her intentional actions (including mental actions). This signalling interacts with the anxiety sensitivities of the individual to trigger conscious checking processes, including speculations about possible harms. (...) We examine the implications of this model for the individual's capacity to control his or her thoughts. (shrink)

The literature on the venerable aesthetic category of the sublime often provides us with lists of sublime phenomena — mountains, storms, deserts, volcanoes, oceans, the starry sky, and so on. But it has long been recognized that what matters is the experience of such objects. We then find that one of the most consistent claims about this experience is that it involves an element of fear. Meanwhile, the recognition of the sublime as a category of aesthetic appreciation implies that attraction, (...) admiration or pleasure is also present.1However, there is also a sense of fear and attraction when we watch car chases or fights. Neither of these is an occasion for the sublime so much as a visceral sort of excitement.2 As .. (shrink)

In this paper I present an account of musical arousal that takes into account key demands of formalist philosophers such as Peter Kivy and Nick Zangwill. Formalists prioritise our understanding and appreciation of the music itself. As a result, they demand that any feelings we have in response to music must be directed at the music alone, without being distracted by non-musical associations. To accommodate these requirements I appeal to a mechanism of contagion which I synthesize with the expectation-based arousal (...) mechanism proposed by Leonard Meyer. This account connects musical expressivity and arousal in a way that formalists have rejected, but I argue that it provides the best explanation of our observations of listener responses while also focusing on the music itself. (shrink)

I argue that while the feeling of bodily responses is not necessary to emotion, these feelings contribute significant meaningful content to everyday emotional experience. Emotional bodily feelings represent a ‘state of self’, analysed as a sense of one's body affording certain patterns of interaction with the environment. Recognising that there are two sources of intentional content in everyday emotional experience allows us to reconcile the diverging intuitions that people have about emotional states, and to understand better the long-standing debate between (...) bodily feeling-based and appraisal-based theories of emotion. (shrink)

This paper contrasts individual and collective listening to music, with particular regard to the expressive qualities of music. In the first half of the paper a general model of joint attention is introduced. According to this model, perceiving together modifies the intrinsic structure of the perceptual task, and encourages a convergence of responses to a greater or lesser degree. The model is then applied to music, looking first at the silent listening situation typical to the classical concert hall, and second (...) the noisy listening situation typical to rock or jazz concerts. (shrink)

In this brief comment on a target article by Koelsch et al., I argue that emotions are more sensitive to context than other affective states.

I claim that the significance of comic works to influence our attitudes is limited by the conditions under which we find things funny. I argue that we can only find something funny if we regard it as norm-violating in a way that doesn’t make certain cognitive or pragmatic demands upon us. It is compatible with these conditions that humour reinforces our attitude that something is norm-violating. However, it is not compatible with these conditions that, on the basis of finding it (...) funny, we come to reject some existing attitude. Such a rejection would require that we recognize our attitude as norm-violating in a way that has pragmatic force. Thus if a humorous work reveals the absurdity of something, we can either find it funny and not have our attitudes significantly influenced, or else be significantly influenced but not find it funny. (shrink)

I examine the role that the musical instrument plays in shaping a performer's expressive activity and emotional state. I argue that the historical development of the musical instrument has fluctuated between two key values: that of sharing with other musicians, and that of creatively exploring new possibilities. I introduce 'the mood organ'- a sensor-based computer instrument that automatically turns signals of the wearer's emotional state into expressive music.

This paper identifies a tension between the commitment to forming rationally justified emotions and the happy life. To illustrate this tension I begin with a critical evaluation of the positive psychology technique known as ‘gratitude training’. I argue that gratitude training is at odds with the kind of critical monitoring that several philosophers have claimed is regulative of emotional rationality. More generally, critical monitoring undermines exuberance, an attitude that plays a central role in contemporary models of the happy life. Thus, (...) prominent notions of what it takes to maintain emotion rationality and what it takes to maintain happiness are in tension. To resolve this tension, I argue that some people have good reason to depreciate critical monitoring—even while maintaining the requirement of emotion rationality that we be sensitive to facts about how our concerns are faring. (shrink)

Effective altruism sounds so innocuous—who could possibly be opposed to doing good more effectively? Yet it has inspired significant backlash in recent years. This paper addresses some common misconceptions and argues that the core “beneficentric” ideas of effective altruism are both excellent and widely neglected. Reasonable people may disagree on details of implementation, but all should share the basic goals or values underlying effective altruism.

This paper develops a mechanistic account of basic mental agency by identifying similarities between two of its major exemplars: endogenous attention and imagination. Five key similarities are identified: i) that both capacities are driven by currently prioritised goals that are either person-level or apt to become person-level. ii) that both deliver their outputs to the working memory iii) that both range across all and only conceptual contents; iv) that both proceed under the guidance of norms and/or habits; and v) that (...) both directly activate rather than inhibit content. These five features are consolidated by proposing that basic mental agency is essentially the power to call for conceptual content and hold it within our working memories. (shrink)

This article reviews some of the ways in which philosophical problems concerning music can be informed by approaches from the cognitive sciences (principally psychology and neuroscience). Focusing on the issues of musical expressiveness and the arousal of emotions by music, the key philosophical problems and their alternative solutions are outlined. There is room for optimism that while current experimental data does not always unambiguously satisfy philosophical scrutiny, it can potentially support one theory over another, and in some cases allow us (...) to synthesize or reject traditional philosophical differences. (shrink)

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...) primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)

Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.

I believe the first thing to say about value is that it is something that we do. We value things. There is no value out there independent of valuing beings. Thi.

There is too much that we do not know about COVID-19. The longer we take to find it out, the more lives will be lost. In this paper, we will defend a principle of risk parity: if it is permissible to expose some members of society (e.g. health workers or the economically vulnerable) to a certain level of ex ante risk in order to minimize overall harm from the virus, then it is permissible to expose fully informed volunteers to a (...) comparable level of risk in the context of promising research into the virus. We apply this principle to three examples of risky research: skipping animal trials for promising treatments, human challenge trials to speed up vaccine development, and low-dose controlled infection or “variolation.” We conclude that if volunteers, fully informed about the risks, are willing to help fight the pandemic by aiding promising research, there are strong moral reasons to gratefully accept their help. To refuse it would implicitly subject others to still graver risks. (shrink)

What we value, like, endorse, want, and prefer changes over the course of our lives. Richard Pettigrew presents a theory of rational decision making for agents who recognise that their values will change over time and whose decisions will affect those future times.

A summary of The Emotional Mind: A Control Theory of Affective States is presented: I claim that a convincing account of the emotions requires a rethink of how the mind as a whole is structured. I provide this reconceptualization by introducing a fundamental type of mental concept called “valent representation" and then systematically elaborating this fundamental type in stages. In this way, accounts are provided of the various sorts of affective states ranging from pains and pleasures to character traits.

In Mind and World, John McDowell argues against the view that perceptual representation is non-conceptual. The central worry is that this view cannot offer any reasonable account of how perception bears rationally upon belief. I argue that this worry, though sensible, can be met, if we are clear that perceptual representation is, though non-conceptual, still in some sense 'assertoric': Perception, like belief, represents things as being thus and so.

I defend the claim that fictional narratives provide cognitive benefits to readers in virtue of helping them to understand character. Fictions allow readers to rehearse the skill of selecting and organizing into narratives those episodes of a life that reflect traits or values. Two further benefits follow: first, fictional narratives provide character models that we can apply to real-life individuals (including ourselves), and second, fictional narratives help readers to reflect on the value priorities that constitute character. I defend the plausibility (...) of these cognitive benefits against certain worries raised by Gregory Currie and Peter Goldie. (shrink)

In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.

This paper analyses the phenomenology and epistemology of chatbots such as ChatGPT and Bard. The computational architecture underpinning these chatbots are large language models (LLMs), which are generative AI (Artificial Intelligence) systems trained on a massive dataset of text extracted from the Web. We conceptualise these LLMs as multifunctional computational cognitive artifacts, used for various cognitive tasks such as translating, summarizing, answering questions, information-seeking, and much more. Phenomenologically, LLMs can be experienced as a “quasi-other”; when that happens, users anthropomorphise them. (...) For most users, current LLMs are black boxes, i.e., for the most part, they lack data transparency and algorithmic transparency. They can, however, be phenomenologically and informationally transparent, in which case there is an interactional flow. Anthropomorphising and interactional flow can, in some users, create an attitude of (unwarranted) trust towards the output LLMs generate. We conclude this paper by drawing on the epistemology of trust and testimony to examine the epistemic implications of these dimensions. Whilst LLMs generally generate accurate responses, we observe two epistemic pitfalls. Ideally, users should be able to match the level of trust that they place in LLMs to the degree that LLMs are trustworthy. However, both their data and algorithmic opacity and their phenomenological and informational transparency can make it difficult for users to calibrate their trust correctly. The effects of these limitations are twofold: users may adopt unwarranted attitudes of trust towards the outputs of LLMs (which is particularly problematic when LLMs hallucinate), and the trustworthiness of LLMs may be undermined. (shrink)

Disagreement is common: even informed, intelligent, and generally reasonable people often come to different conclusions when confronted with what seems to be the same evidence. Can the competing conclusions be reasonable? If not, what can we reasonably think about the situation? This volume examines the epistemology of disagreement. Philosophical questions about disagreement arise in various areas, notably politics, ethics, aesthetics, and the philosophy of religion: but this will be the first book focusing on the general epistemic issues arising from informed (...) disagreement. Ten leading philosophers offer specially written essays which together will offer a starting-point for future work on this topic. (shrink)

Conservative assumptions in medical ethics risk immense harms during a pandemic. Public health institutions and public discourse alike have repeatedly privileged inaction over aggressive medical interventions to address the pandemic, perversely increasing population-wide risks while claiming to be guided by ‘caution’. This puzzling disconnect between rhetoric and reality is suggestive of an underlying philosophical confusion. In this paper, I argue that we have been misled by status quo bias—exaggerating the moral significance of the risks inherent in medical interventions, while systematically (...) neglecting the risks inherent in the status quo prospect of an out-of-control pandemic. By coming to appreciate the possibility and significance of status quo risk, we will be better prepared to respond appropriately when the next pandemic strikes. (shrink)

David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...) little attention, and on a number of philosophical reconstructions of the viewpoint (in particular, by Hand, Kitcher, and Tait). (shrink)

In this paper, we seek a reliabilist account of justified credence. Reliabilism about justified beliefs comes in two varieties: process reliabilism (Goldman, 1979, 2008) and indicator reliabilism (Alston, 1988, 2005). Existing accounts of reliabilism about justified credence comes in the same two varieties: Jeff Dunn (2015) proposes a version of process reliabilism, while Weng Hong Tang (2016) offers a version of indicator reliabilism. As we will see, both face the same objection. If they are right about what justification is, it (...) is mysterious why we care about justification, for neither of the accounts explains how justification is connected to anything of epistemic value. We will call this the Connection Problem. I begin by describing Dunn’s process reliabilism and Tang’s indicator reliabilism. I argue that, understood correctly, they are, in fact, extensionally equivalent. That is, Dunn and Tang reach the top of the same mountain, albeit by different routes. However, I argue that both face the Connection Problem. In response, I offer my own version of reliabilism, which is both process and indicator, and I argue that it solves that problem. Furthermore, I show that it is also extensionally equivalent to Dunn’s reliabilism and Tang’s. Thus, I reach the top of the same mountain as well. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...) on it. As I show, whether this is possible depends on the formulation of the norm under consideration. (shrink)

This paper applies a virtue epistemology approach to using the Internet, as to improve our information-seeking behaviours. Virtue epistemology focusses on the cognitive character of agents and is less concerned with the nature of truth and epistemic justification as compared to traditional analytic epistemology. Due to this focus on cognitive character and agency, it is a fruitful but underexplored approach to using the Internet in an epistemically desirable way. Thus, the central question in this paper is: How to use the (...) Internet in an epistemically virtuous way? Using the work of Jason Baehr, it starts by outlining nine intellectual or epistemic virtues: curiosity, intellectual autonomy, intellectual humility, attentiveness, intellectual carefulness, intellectual thoroughness, open-mindedness, intellectual courage and intellectual tenacity. It then explores how we should deploy these virtues and avoid the corresponding vices when interacting with the Internet, particularly search engines. Whilst an epistemically virtuous use of the Internet will not guarantee that one will acquire true beliefs, understanding or even knowledge, it will strongly improve one’s information-seeking behaviours. The paper ends with arguing that teaching and assessing online intellectual virtues should be part of school and university curricula, perhaps embedded in critical thinking courses, or even better, as individual units. (shrink)

This Element, written for researchers and students in philosophy and the behavioral sciences, reviews and critically assesses extant work on number concepts in developmental psychology and cognitive science. It has four main aims. First, it characterizes the core commitments of mainstream number cognition research, including the commitment to representationalism, the hypothesis that there exist certain number-specific cognitive systems, and the key milestones in the development of number cognition. Second, it provides a taxonomy of influential views within mainstream number cognition research, (...) along with the central challenges these views face. Third, it identifies and critically assesses a series of core philosophical assumptions often adopted by number cognition researchers. Finally, the Element articulates and defends a novel version of pluralism about number concepts. (shrink)

All humans have an equal basic moral status. They possess the same fundamental rights, and the comparable interests of each person should count the same in calculations that determine social policy. Neither supposed racial differences, nor skin color, sex, sexual orientation, ethnicity, intelligence, nor any other differences among humans negate their fundamental equal worth and dignity. These platitudes are virtually universally affirmed. A white supremacist racist or an admirer of Adolf Hitler who denies them is rightly regarded as beyond the (...) pale of civilized dialogue. However, a very simple line of argument developed by Peter Singer challenges our understanding of these platitudes and forces us to rethink the basis and nature of the moral equality of all humans. What I call the “Singer Problem” arises if one accepts that the morally significant cognitive capacities that are relevant to the determination of the fundamental moral status of a being vary from individual to individual by degree. The problem is to specify a moral principle determining fundamental moral status that assigns a superior status to humans compared to other animals on the basis of the superior cognitive capacities of humans but also assigns all human persons an equal fundamental moral status regardless of their differing cognitive capacities. More broadly posed, the problem is to specify moral principles that yield intuitively satisfactory implications for the treatment of human individuals and other individual animals given that cognitive capacities differ across species and individuals. A search for a resolution of the Singer problem leads to disappointing results. (shrink)