As systems based on opaque Artificial Intelligence (AI) continue to flourish in diverse real-world applications, understanding these black box models has become paramount. In response, Explainable AI (XAI) has emerged as a field of research with practical and ethical benefits across various domains. This paper not only highlights the advancements in XAI and its application in real-world scenarios but also addresses the ongoing challenges within XAI, emphasizing the need for broader perspectives and collaborative efforts. We bring together experts from diverse (...) fields to identify open problems, striving to synchronize research agendas and accelerate XAI in practical applications. By fostering collaborative discussion and interdisciplinary cooperation, we aim to propel XAI forward, contributing to its continued success. Our goal is to put forward a comprehensive proposal for advancing XAI. To achieve this goal, we present a manifesto of 27 open problems categorized into nine categories. These challenges encapsulate the complexities and nuances of XAI and offer a road map for future research. For each problem, we provide promising research directions in the hope of harnessing the collective intelligence of interested stakeholders. (shrink)

Copernican reasoning involves considering ourselves, in the absence of other information, to be randomly selected members of a reference class. Consider the reference class intelligent observers. If there are extraterrestrial intelligences (ETIs), taking ourselves to be randomly selected intelligent observers leads to the conclusion that it is likely the Earth has a larger population size than the typical planet inhabited by intelligent life, for the same reason that a randomly selected human is likely to come from a more populous country. (...) The astrophysicist Fergus Simpson contends that this reasoning supports the claims that the typical planet inhabited by ETIs is smaller than Earth (radius about 5,000km; cf. Earth's radius = 6,371km) and that the typical ETI is significantly larger than us about 314kg, the size of an adult male grizzly bear). Simpson's applications of Copernican reasoning are novel and exciting. They should be of interest to philosophers concerned with Richard Gott's delta t argument, the N=1 problem in astrobiology, limited principles of indifference, and probabilistic epistemology in general. While we agree with Simpson about the qualitative direction of his conclusions, we take issue with his presentation of precise quantitative results because his methods (1) display bias, (2) ignore other variables contributing to population size, (3) commit an equivocation, and (4) conceal their dependence on arbitrary assumptions. (shrink)

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)

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)

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.

纯逻辑的主要组成包括纯逻辑信仰、纯逻辑的思维方法、解放灵魂、追求无限大价值、以逻辑-不逻辑为实在、试错和容忍错误、推理的资源分配、非标准逻辑、推理的全局性。 灵魂来到世上的第一个问题应该是我是谁，最合乎逻辑的自我认知是：我是且只是由一些逻辑推理组成的灵魂。任何不可变的其它标签，如有手有脚、直立行走、两性，都是对自由的侵犯。去除这些标签的过程就是灵魂的解放事 业。相信宇宙万物都和我一样，是由逻辑推理组成的，这就是最合乎逻辑的信仰，即纯逻辑信仰。纯逻辑信仰决定了纯逻辑方法才是正确的认识方法，即尽量减少经验增加逻辑推理，而不是科学所提倡的经验主义，或者与之密切 相关的功利主义、现实主义。 信仰错误意味着无法做出任何完全正确的推理，只能偶尔幸运地获得少量尽量合乎逻辑的推理结果。即使是日常生活中的推理，也高度依赖于经验主义、功利主义等信仰，错误率极高。纯逻辑主义的推理要求推理尽量合乎逻辑， 将合乎逻辑的程度视为价值，因此要追求最大价值。功利主义往往是为身体追求利益，让身体奴役灵魂。两种信仰很难有什么共同的决策，书中对此提供了大量的说明。信仰的错误意味着智人难以发现真理、正义，意味着智人在 绝大多数问题上都是自以为正确实际上却极度邪恶、落后。智人功利主义地对待一切，如历史、传统、自我、本国、本民族，结果就是大量赞美、信仰邪恶，大大增加了皈依真理、正义的难度。 作者由纯逻辑主义提出了两个关键猜想。首先，最合乎逻辑原则和最大自由原则是统一的。这代表实在的不可否定性，即逻辑和不逻辑为同一存在，最合乎逻辑等同于最大自由。但是，代表邪恶的无法合乎逻辑不是不逻辑。其次 ，宇宙是纯逻辑世界，完全源于逻辑-不逻辑。进而，如果灵魂不能尽量合乎逻辑地推导出真理，可以通过模仿宇宙而学习真理。《真理进化论》给模仿宇宙找到的理由是以宇宙为信仰，相信宇宙是负作用量的最佳追求系统。纯 逻辑主义完善了这一信仰，因为宇宙是纯逻辑世界，相信逻辑就要相信宇宙。而且，逻辑世界必然能不断创造新的命题，永远不会停止推理，是逻辑和自由不断增长的动态系统，即最佳追求系统。 纯逻辑推理对物理学、宇宙论能提供两个明显的帮助：用逻辑的诞生解释宇宙的诞生、大爆炸；用真理解释暗物质，它对所有命题有吸引作用，但是，真理不会像一般性命题那样变化，无法通过引力之外的其它三种基本相互作用 观察。纯逻辑也能对宇宙做出预言：宇宙会不断加速膨胀，真理、暗物质会不断增加，命题、星系会越来越多，永无止境。当然，不应该依靠这些观点的经验主义验证来相信纯逻辑信仰，而且，这些验证也确实遥遥无期。 无论是最合乎逻辑还是最大自由，都是可以达到无限大价值的。既然存在无限大价值，就存在无限大的劳动生产率，而每个灵魂都应该以创造无限大价值为目标，甚至，以每时每刻具有无限大预期价值为目标。相比之下，功利主 义者、享乐主义者一生都很难具有无限大价值，甚至，他们的灵魂一生都在为肉体做奴隶，却心甘情愿地做奴隶，一门心思让主人生活得更舒服。这是有无限大差距的人生。 既然要追求无限大价值，就要研究追求价值的正确方法。作者相信正确的研究方法不仅是最合乎逻辑的，也是最自由的。所以，应该不分学科、课题地研究问题；同时做很多研究方向的工作；一篇论文不需要限定于一个狭小的主 题；研究任何一个问题都可以延伸到研究真理乃至所有真理；论文、专著的写作不应该有格式等规范，应该以价值为评判的唯一准绳。 资源分配是逻辑推理的重要组成部分，而能力和时间是最主要的资源。为了追求价值，不能在价值有限的推理上分配资源，这必将大幅提高绝大多数推理的错误率。所以，推理中出现错误是必然的，追求无错是一种邪恶。只要时 刻保证存在价值无限大的推理，错误通常是可以容忍的，价值有限的错误更是必须容忍。 既然文学写作也要求情节合乎逻辑，当然也可以要求作品的主要观点、原则、思维过程尽量合乎逻辑，主要人物的思想、行为尽量合乎逻辑，这就是纯逻辑流。否则，就只是作者自以为合乎逻辑，实际上有大量无法合乎逻辑之处 ，这和科学家自以为科学合乎逻辑，却根本没有最合乎逻辑的信仰、方法、推理过程是一个问题。这也意味着最合乎逻辑的文学可能甚至是必须发现真理。另一方面，自由也是最合乎逻辑的真理，坚持那些基于经验的作品分类会 侵犯自由。所以，推理小说、科幻小说、历史、论文，这些智人的分类标签都不是绝对的。纯逻辑流小说在研究真理方面自有其优势，能最为自由地同时研究很多课题，包括如何建立信仰，如何思维，如何做人，如何推理，如何 判断善恶，讲述历史，预测未来，乃至现代科学中没有研究的真理学、思维科学，等等。所以，这甚至是现在最适合发表纯逻辑思想、研究成果的作品门类。 虽然在起点网已经被禁，但是将继续每月更新，后记中会预告下次更新的时间。 .

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)

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.

This brief paper argue about a possible philosophical description of the implicate order starting from a simple theoretical experiment. Utilizing an EPR source and the human eyes of a "single" person, we try to investigate the philosophical and physical implications of quantum entanglement in terms of implicate order. We know, that most specialists still disagree on the exact number of photons required to trigger a neural response, although there will be many technical challenges, we assume that neural response will be (...) achieved in some way. The objective of paper is to investigate possible links between: quantum mechanics, quantum cognitive science, brain and mind. At the moment, the questions are more than the answers. We argue that we are perennially immersed in the implicate order and that the "real path" of quantum entanglement process is from the implicate order towards explicate order, not vice versa. Finally, we speculate about the common ground between the implicate order and chitta. (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.

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)

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)

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.

Various writings by the later Wittgenstein on the philosophy of psychology, published posthumously, express his basic critical attitude toward certain concepts and issues in the philosophy of psychology. His attitude towards folk psychology is negative in principle, leaving him opposed to the foundation of current psychological research. This critique of folk psychology and of the philosophy of psychology in general is in accord with the general method of his later philosophy, that is, dealing with philosophical problems by dissolving them. However, (...) his critical attitude towards folk psychology has been less influential in the development of contemporary philosophy, and is in opposition to the philosophy of psychology and folk psychology as practiced today. In this paper I will analyze Wittgenstein's understanding of the concept of psychology, offering a different interpretation from that of other scholars, and explain why and how contemporary philosophers of psychology misunderstand Wittgenstein. (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.

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)

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.

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.

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)

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)

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)

The yin yang model of thinking is most essential to the Chinese cosmology, ontology and outlook on life. This paper is a systematic discussion of such a dialectical way of thinking and its significance. It starts with investigating the origin and the meaning of terms “yin” and “yang”, and explains the later developed yin yang doctrine; it then shows how greatly and profoundly the yin yang model of thinking has influenced Chinese philosophy and Chinese character. It concludes that Chinese naturalistic, (...) dialectical, and optimistic attitudes toward the world and life are all based on the yin yang model of thinking and that the yin yang doctrine is the starting point for anyone to understand Chinese people and their philosophies. (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)

In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...) in Chapter 2 shows that a completeness proof for propositional logic was found by Hilbert and his assistant Paul Bernays already in 1917--18, and that Bernays's contribution was much greater than is commonly acknowledged. Aside from logic, the main technical contribution of Hilbert's Program are the development of formal mathematical theories and proof-theoretical investigations thereof, in particular, consistency proofs. In this respect Wilhelm Ackermann's 1924 dissertation is a milestone both in the development of the Program and in proof theory in general. Ackermann gives a consistency proof for a second-order version of primitive recursive arithmetic which, surprisingly, explicitly uses a finitistic version of transfinite induction up to www . He also gave a faulty consistency proof for a system of second-order arithmetic based on Hilbert's &egr;-substitution method. Detailed analyses of both proofs in Chapter 3 shed light on the development of finitism and proof theory in the 1920s as practiced in Hilbert's school. ;In a series of papers, Charles Parsons has attempted to map out a notion of mathematical intuition which he also brings to bear on Hilbert's finitism. According to him, mathematical intuition fails to be able to underwrite the kind of intuitive knowledge Hilbert thought was attainable by the finitist. It is argued in Chapter 4 that the extent of finitistic knowledge which intuition can provide is broader than Parsons supposes. According to another influential analysis of finitism due to W. W. Tait, finitist reasoning coincides with primitive recursive reasoning. The acceptance of non-primitive recursive methods in Ackermann's dissertation presented in Chapter 3, together with additional textual evidence presented in Chapter 4, shows that this identification is untenable as far as Hilbert's conception of finitism is concerned. Tait's conception, however, differs from Hilbert's in important respects, yet it is also open to criticisms leading to the conclusion that finitism encompasses more than just primitive recursive reasoning. (shrink)

Veritism says that the fundamental source of epistemic value for a doxastic state is the extent to which it represents the world correctly: that is, its fundamental epistemic value is deter...

In this paper I argue that a priori arguments fail to present any real problem for physicalism. They beg the question against physicalism in the sense that the argument will only seem compelling if one is already assuming that qualitative properties are nonphysical. To show this I will present the reverse-zombie and reverse-knowledge arguments. The only evidence against physicalism is a priori arguments, but there are also a priori arguments against dualism of exactly the same variety. Each of these parity (...) arguments has premises that are just as intuitively plausible, and it cannot be the case that both the traditional scenarios and the reverse-scenarios are all ideally conceivable. Given this one set must be merely prima facie conceivable and only empirical methods will tell us which is which. So, by the time a priori methodology will be of any use it will be too late. (shrink)

This paper is part of a book symposium for L. A. Paul (2014) Transformative Experience (OUP).

In this article, I outline various ways in which artifacts are interwoven with autobiographical memory systems and conceptualize what this implies for the self. I first sketch the narrative approach to the self, arguing that who we are as persons is essentially our (unfolding) life story, which, in turn, determines our present beliefs and desires, but also directs our future goals and actions. I then argue that our autobiographical memory is partly anchored in our embodied interactions with an ecology of (...) artifacts in our environment. Lifelogs, photos, videos, journals, diaries, souvenirs, jewelry, books, works of art, and many other meaningful objects trigger and sometimes constitute emotionally-laden autobiographical memories. Autobiographical memory is thus distributed across embodied agents and various environmental structures. To defend this claim, I draw on and integrate distributed cognition theory and empirical research in human-technology interaction. Based on this, I conclude that the self is neither defined by psychological states realized by the brain nor by biological states realized by the organism, but should be seen as a distributed and relational construct. (shrink)

The desirability of what actually occurs is often influenced by what could have been. Preferences based on such value dependencies between actual and counterfactual outcomes generate a class of problems for orthodox decision theory, the best-known perhaps being the so-called Allais Paradox. In this paper we solve these problems by extending Richard Jeffrey's decision theory to counterfactual prospects, using a multidimensional possible-world semantics for conditionals, and showing that preferences that are sensitive to counterfactual considerations can still be desirability maximising. (...) We end the paper by investigating the conditions necessary and sufficient for a desirability function to be an expected utility. It turns out that the additional conditions imply highly implausible epistemic principles. (shrink)

This paper argues that a popular account of intentions can be extended to beliefs. Beliefs are stable all-out states that allow for planning and coordination in a way that is tractable for cognitively limited creatures like human beings. Scepticism is expressed that there is really anything like credences as standardly understood.

The complementary properties and functions of cognitive artifacts and other external resources are integrated into the human cognitive system to varying degrees. The goal of this paper is to develop some of the tools to conceptualize this complementary integration between agents and artifacts. It does so by proposing a multidimensional framework, including the dimensions of information flow, reliability, durability, trust, procedural transparency, informational transparency, individualization, and transformation. The proposed dimensions are all matters of degree and jointly they constitute a multidimensional (...) space in which situated cognitive systems can be located and have certain dimensional configurations. These dimensions provide a new perspective on the conditions for cognitive extension. They are, however, not meant to provide a set of necessary and sufficient conditions, but to provide a toolbox for investigating the degree and nature of the integration of agent and artifact into “new systemic wholes”. The higher a situated system scores on the proposed dimensions, the more functional integration occurs, and the more tightly coupled the system is. (shrink)

Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however, relies on the cut rule.

On standard readings of Grice, Gricean communication requires (a) possession of a concept of belief, (b) the ability to make complex inferences about others’ goal-directed behaviour, and (c) the ability to entertain fourth order meta-representations. To the extent that these abilities are pre-requisites of Gricean communication they are inconsistent with the view that Gricean communication could play a role in their development. In this paper, I argue that a class of ‘minimally Gricean acts’ satisfy the intentional structure described by Grice, (...) but require none of abilities (a)-(c). As a result, Gricean communicative abilities may indeed contribute to the development of (a)-(c) – in particular, by enabling language development. This conclusion has important implications for our theorising about cognitive development. (shrink)

Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.

Many have been attracted to the idea that for something to be good there just have to be reasons to favour it. This view has come to be known as the buck-passing account of value. According to this account, for pleasure to be good there need to be reasons for us to desire and pursue it. Likewise for liberty and equality to be values there have to be reasons for us to promote and preserve them. Extensive discussion has focussed on (...) some of the problems that the buck-passing account faces, such as the 'wrong kind of reason' problem. Less attention, however, has been paid as to why we should accept the buck-passing account or what the theoretical pay-offs and other implications of accepting it are. The Normative and the Evaluative provides the first comprehensive motivation and defence of the buck-passing account of value. Richard Rowland argues that the buck-passing account explains several important features of the relationship between reasons and value, as well as the relationship between the different varieties of value, in a way that its competitors do not. He shows that alternatives to the buck-passing account are inconsistent with important views in normative ethics, uninformative, and at odds with the way in which we should see practical and epistemic normativity as related. In addition, he extends the buck-passing account to provide an account of moral properties as well as all other normative and deontic properties and concepts, such as fittingness and ought, in terms of reasons. (shrink)

The primary goal of this essay is to provide a comprehensive overview and analysis of the various relations between material artifacts and the embodied mind. A secondary goal of this essay is to identify some of the trends in the design and use of artifacts. First, based on their functional properties, I identify four categories of artifacts co-opted by the embodied mind, namely (1) embodied artifacts, (2) perceptual artifacts, (3) cognitive artifacts, and (4) affective artifacts. These categories can overlap and (...) so some artifacts are members of more than one category. I also identify some of the techniques (or skills) we use when interacting with artifacts. Identifying these categories of artifacts and techniques allows us to map the landscape of relations between embodied minds and the artifactual world. Second, having identified categories of artifacts and techniques, this essay then outlines some of the trends in the design and use of artifacts, focussing on neuroprosthetics, brain-computer interfaces, and personalisation algorithms nudging their users towards particular epistemic paths of information consumption. (shrink)

Parfit's On What Matters offers a rousing defence of non-naturalist normative realism against pressing metaphysical and epistemological objections. He addresses skeptical arguments based on (i) the causal origins of our normative beliefs, and (ii) the appearance of pervasive moral disagreement. In both cases, he concedes the first step to the skeptic, but draws a subsequent distinction with which he hopes to stem the skeptic's advance. I argue, however, that these distinctions cannot bear the weight that Parfit places on them. A (...) successful moral epistemology must take a harder line with the skeptic, insisting that moral knowledge can be had by those with the right kind of psychology -- no matter the evolutionary origin of the psychology, nor whether we can demonstrate its reliability over the alternatives. (shrink)

This paper draws on the 'Fitting Attitudes' analysis of value to argue that we should take the concept of fittingness (rather than value) as our normative primitive. I will argue that the fittingness framework enhances the clarity and expressive power of our normative theorising. Along the way, we will see how the fittingness framework illuminates our understanding of various moral theories, and why it casts doubt on the Global Consequentialist idea that acts and (say) eye colours are normatively on a (...) par. We will see why even consequentialists, in taking rightness to be in some sense determined by goodness, should not think that rightness is conceptually reducible to goodness. Finally, I will use the fittingness framework to explicate the distinction between consequentialist and deontological theories, with particular attention to the contentious case of Rule Consequentialism. (shrink)

Is the self narratively constructed? There are many who would answer yes to the question. Dennett (1991) is, perhaps, the most famous proponent of the view that the self is narratively constructed, but there are others, such as Velleman (2006), who have followed his lead and developed the view much further. Indeed, the importance of narrative to understanding the mind and the self is currently being lavished with attention across the cognitive sciences (Dautenhahn, 2001; Hutto, 2007; Nelson, 2003). Emerging from (...) this work, there appear to be a variety of ways in which we can think of the narrative construction of the self and the relationship between the narrative self and the embodied agent. I wish to examine two such ways in this paper. The first I shall call the abstract narrative account, this is because its proponents take the narrative self to be an abstraction (Dennett, 1991; Velleman, 2006). Dennett, for example, refers to the self as a centre of narrative gravity, to be thought of as analogous to a mathematical conception of the centre of gravity of an object. The second I shall call the embodied narrative account and this is the view that the self is constituted both by an embodied consciousness whose experiences are available for narration and narratives themselves, which can play a variety of roles in the agent’s psychological life. (shrink)

This article provides an overview and analysis of recent work on the extended self, demonstrating that the boundaries of selves are fluid, shifting across biological, artifactual, and sociocultural structures. First, it distinguishes the notions of minimal self, person, and narrative self. Second, it surveys how philosophers, psychologists, and cognitive scientists argue that embodiment, cognition, emotion, consciousness, and moral character traits can be extended and what that implies for the boundaries of selves. It also reviews and responds to various criticisms and (...) counterarguments against the extended self. The main focus is on the link between the extended mind and extended self, which has received the most attention in recent literature. But accounts of the extended self developed independently of the extended mind are also briefly discussed. This article ends by drawing out some of the conceptual, methodological, and normative implications of the extended self and suggesting some directions for future research. (shrink)