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)

Bayesian models of legal arguments generally aim to produce a single integrated model, combining each of the legal arguments under consideration. This combined approach implicitly assumes that variables and their relationships can be represented without any contradiction or misalignment, and in a way that makes sense with respect to the competing argument narratives. This paper describes a novel approach to compare and ‘average’ Bayesian models of legal arguments that have been built independently and with no attempt to make them consistent (...) in terms of variables, causal assumptions or parameterization. The approach involves assessing whether competing models of legal arguments are explained or predict facts uncovered before or during the trial process. Those models that are more heavily disconfirmed by the facts are given lower weight, as model plausibility measures, in the Bayesian model comparison and averaging framework adopted. In this way a plurality of arguments is allowed yet a single judgement based on all arguments is possible and rational. (shrink)

We explore the ethics of deliberately exposing consenting adults to SARS-CoV-2 to induce immunity to the virus (“DEI” for short). We explain what a responsible DEI program might look like. We explore a consequentialist argument for DEI according to which DEI is a viable harm-reduction strategy. Then we consider a non-consequentialist argument for DEI that draws on the moral significance of consent. Additionally, we consider arguments for the view that DEI is unethical on the grounds that, given that large-scale DEI (...) would be highly likely to result in some severe illnesses and deaths, DEI amounts to a form of killing. Our thesis is that incorporating a DEI program alongside the status-quo “calibrate-the-curve” responses could have significant advantages at the early stages of pandemics. These potential advantages mean that, at a minimum, research into DEI would have been justified early in the COVID-19 pandemic, and that DEI programs should be explored as potential additions to our overall approach to emerging pandemics in the future. (shrink)

The financial turmoil of the past several years has caused many to question the integrity, stability, and very purpose of financial systems which, in today’s world, represent a unique blend of primarily capitalism but also aspects of socialism and collectivism as well. A key factor contributing to this sustained period of economic upheaval has been the uncertainty surrounding capital markets – the fuel that powers all modern economies. Capital markets have, in the minds of many, come to represent the embodiment (...) of greed, unrestrained egoism, and exploitation of the vulnerable – conceptions at complete odds with the central values of social justice as set forth in both Christian and Jewish primary sources: caring for the poor, protecting the weak, and the promotion of justice. -/- In this paper I argue that capital markets, rather than being a means for the powerful to exploit the weak, have in fact become a force for social good in the aggregate. Indeed capital markets are, in fact, a social contract and as such must be governed by a set of normative ethical principles – both self imposed, and imposed by government regulation. I explore the ethical difficulties that have led to the systemic problems and market failures that lead to not only this current financial crisis, but literally all financial crises over the past eight hundred years. Capital markets, left to their own devices and without both self and governmental oversight, quickly become hotbeds of manipulation and exploitation. In order for markets to function properly, principles of basic fairness must become normative. It is when capital markets become unfair and unjust, that they fail. Thus, these markets must be structured in such a way as to 1) promote Rawl’s “Justice as Fairness” principle and 2) align the interests of market participants to produce universally beneficial market efficiency and stability. -/- Finally, I propose concrete ways in which the power of capital markets may be harnessed to promote the central moral values of Christian tradition and be used by people of faith to promote the ideals of social justice. (shrink)

This paper clarifies the usage of Albert Hirschman’s categories of market behaviour as of exit and voice in debates about workplace democracy by taking seriously his critique of the neoclassical analysis of competition. Pro-market liberals are generally hostile to the idea of workplace democracy and tend to favour top-down hierarchies as a way of organising labour. This hostility is generally inspired by the neoclassical analysis of exploitation and efficiency, which leads them to defend distributions achieved through exit-based competitive equilibria. Following (...) Hirschman, I propose to consider a hypothetical alternative: a democratic equilibrium, reached through the use of voice. I show that it would present the same appealing characteristics than its competitive counterpart while also accounting for the non-ideal conditions in which markets operate. Support for free markets should entail support for workplace democracy minimally understood as a strengthening of voice. (shrink)

This report by the WHO Consultative Group on Equity and Universal Health Coverage addresses how countries can make fair progress towards the goal of universal coverage. It explains the relevant tradeoffs between different desirable ends and offers guidance on how to make these tradeoffs.

Efforts by governments, firms, and patients to deliver pioneering drugs for critical health needs face a challenge of diminishing efficiency in developing those medicines. While multi-sectoral collaborations involving firms, researchers, patients, and policymakers are widely recognized as crucial for countering this decline, existing incentives to engage in drug development predominantly target drug manufacturers and thereby do little to stimulate collaborative innovation. In this mini review, we consider the unexplored potential within pharmaceutical regulations to create novel incentives to encourage a diverse (...) set of actors from the public and private spheres to engage in the kind of collaborative knowledge exchange requisite for fostering enhanced innovation in early drug development. (shrink)

All disciplines must define their basic units and core processes. In evolutionary biology, the core process is natural selection and the basic unit of selection and adaptation is the individual. To operationalize the theory of natural selection we must count individuals, as they are the bearers of fitness. While canonical individuals have often been taken to be multicellular organisms, the hierarchy of life shows that new kinds of individuals have evolved. A variety of criteria have been used to define biological (...) individuality. Some criteria rely on the presence/absence of a particular property while others advocate an approach that reflects the process of natural selection. The plethora of approaches to classifying individuality has resulted in confusion regarding how to study individuality in a given taxon. (shrink)

A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the (...) number of truth values, and it is shown that this bound is tight. (shrink)

Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. I (...) prove soundness and completeness theorems with respect to Hodes’ semantics, as well as semantics with fewer restrictions on the accessibility relation. (shrink)

During much of the past century, it was widely believed that phonemes--the human speech sounds that constitute words--have no inherent semantic meaning, and that the relationship between a combination of phonemes (a word) and its referent is simply arbitrary. Although recent work has challenged this picture by revealing psychological associations between certain phonemes and particular semantic contents, the precise mechanisms underlying these associations have not been fully elucidated. Here we provide novel evidence that certain phonemes have an inherent, non-arbitrary emotional (...) quality. Moreover, we show that the perceived emotional valence of certain phoneme combinations depends on a specific acoustic feature--namely, the dynamic shift within the phonemes' first two frequency components. These data suggest a phoneme-relevant acoustic property influencing the communication of emotion in humans, and provide further evidence against previously held assumptions regarding the structure of human language. This finding has potential applications for a variety of social, educational, clinical, and marketing contexts. (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)

The COVID-19 pandemic prompted immense work on the investigation of the SARS-CoV-2 virus. Rapid, accurate, and consistent interpretation of generated data is thereby of fundamental concern. Ontologies––structured, controlled, vocabularies––are designed to support consistency of interpretation, and thereby to prevent the development of data silos. This paper describes how ontologies are serving this purpose in the COVID-19 research domain, by following principles of the Open Biological and Biomedical Ontology (OBO) Foundry and by reusing existing ontologies such as the Infectious Disease Ontology (...) (IDO) Core, which provides terminological content common to investigations of all infectious diseases. We report here on the development of an IDO extension, the Virus Infectious Disease Ontology (VIDO), a reference ontology covering viral infectious diseases. We motivate term and definition choices, showcase reuse of terms from existing OBO ontologies, illustrate how ontological decisions were motivated by relevant life science research, and connect VIDO to the Coronavirus Infectious Disease Ontology (CIDO). We next use terms from these ontologies to annotate selections from life science research on SARS-CoV-2, highlighting how ontologies employing a common upper-level vocabulary may be seamlessly interwoven. Finally, we outline future work, including bacteria and fungus infectious disease reference ontologies currently under development, then cite uses of VIDO and CIDO in host-pathogen data analytics, electronic health record annotation, and ontology conflict-resolution projects. (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.

Investigation of neural and cognitive processes underlying individual variation in moral preferences is underway, with notable similarities emerging between moral- and risk-based decision-making. Here we specifically assessed moral distributive justice preferences and non-moral financial gambling preferences in the same individuals, and report an association between these seemingly disparate forms of decision-making. Moreover, we find this association between distributive justice and risky decision-making exists primarily when the latter is assessed with the Iowa Gambling Task. These findings are consistent with neuroimaging studies (...) of brain function during moral and risky decision-making. This research also constitutes the first replication of a novel experimental measure of distributive justice decision-making, for which individual variation in performance was found. Further examination of decision-making processes across different contexts may lead to an improved understanding of the factors affecting moral behaviour. (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)

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)

The UK has been ‘following the science’ in response to the COVID-19 pandemic in line with the national framework for the use of scientific advice in assessment of risk. We argue that the way in which it does so is unsatisfactory in two important respects. Firstly, pandemic policy making is not based on a comprehensive assessment of policy impacts. And secondly, the focus on reasonable worst-case scenarios as a way of managing uncertainty results in a loss of decision-relevant information and (...) does not provide a coherent basis for policy making. (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)

What are the possible varieties of cognition-artifact relations, and which dimensions are relevant for exploring these varieties? This question is answered in two steps. First, three levels of functional and informational integration between human agent and cognitive artifact are distinguished. These levels are based on the degree of interactivity and direction of information flow, and range from monocausal and bicausal relations to continuous reciprocal causation. In these levels there is a hierarchy of integrative processes in which there is an increasing (...) degree of hybridization. Therefore, from a functional and informational level of abstraction, it becomes increasingly difficult to distinguish between agent and artifact in this hierarchy. Second, a multidimensional matrix for exploring cognition-artifact relations is sketched. The dimensions in the matrix include reliability, durability, trust, procedural and representational transparency, individualization, bandwidth, speed of information flow, distribution of computation, and cognitive and artifactual transformation. Together, these dimensions constitute a multidimensional space in which particular cognition-artifact relations can be located. The higher a particular cognition-artifact relation scores on these dimensions, the more integration and hybridization occurs, and the more tightly coupled the overall system is. It is then better, for explanatory reasons, to see agent and artifact as one cognitive system with a distributed informational architecture. (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.

Many existing biomedical vocabulary standards rest on incomplete, inconsistent or confused accounts of basic terms pertaining to diseases, diagnoses, and clinical phenotypes. Here we outline what we believe to be a logically and biologically coherent framework for the representation of such entities and of the relations between them. We defend a view of disease as involving in every case some physical basis within the organism that bears a disposition toward the execution of pathological processes. We present our view in the (...) form of a list of terms and definitions designed to provide a consistent starting point for the representation of both disease and diagnosis in information systems in the future. (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)

Vaccine research, as well as the development, testing, clinical trials, and commercial uses of vaccines involve complex processes with various biological data that include gene and protein expression, analysis of molecular and cellular interactions, study of tissue and whole body responses, and extensive epidemiological modeling. Although many data resources are available to meet different aspects of vaccine needs, it remains a challenge how we are to standardize vaccine annotation, integrate data about varied vaccine types and resources, and support advanced vaccine (...) data analysis and inference. To address these problems, the community-based Vaccine Ontology (VO) has been developed through collaboration with vaccine researchers and many national and international centers and programs, including the National Center for Biomedical Ontology (NCBO), the Infectious Disease Ontology (IDO) Initiative, and the Ontology for Biomedical Investigations (OBI). VO utilizes the Basic Formal Ontology (BFO) as the top ontology and the Relation Ontology (RO) for definition of term relationships. VO is represented in the Web Ontology Language (OWL) and edited using the Protégé-OWL. Currently VO contains more than 2000 terms and relationships. VO emphasizes on classification of vaccines and vaccine components, vaccine quality and phenotypes, and host immune response to vaccines. These reflect different aspects of vaccine composition and biology and can thus be used to model individual vaccines. More than 200 licensed vaccines and many vaccine candidates in research or clinical trials have been modeled in VO. VO is being used for vaccine literature mining through collaboration with the National Center for Integrative Biomedical Informatics (NCIBI). Multiple VO applications will be presented. (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.

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)

La cobertura universal de salud está en el centro de la acción actual para fortalecer los sistemas de salud y mejorar el nivel y la distribución de la salud y los servicios de salud. Este documento es el informe fi nal del Grupo Consultivo de la OMS sobre la Equidad y Cobertura Universal de Salud. Aquí se abordan los temas clave de la justicia (fairness) y la equidad que surgen en el camino hacia la cobertura universal de salud. Por lo (...) tanto, el informe es pertinente para cada agente que infl uye en ese camino y en particular para los gobiernos, ya que se encargan de supervisar y guiar el progreso hacia la cobertura universal de salud. (shrink)

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal (...) logic of linear discrete time with gaps follows. (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)

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.

In this brief dialogue I consider the humanity and morality of the doctrine of eternal punishment.

Theology Without Walls - or 'trans-religious theology' - is a theological approach dedicated to reflecting upon the nature of divine reality as it may be revealed in any of the world’s religious traditions, without confining itself to any one in particular. In this paper I discuss some of the basic assumptions and implications of the Theology Without Walls project and suggest that this approach to theology, and to religion in general, promises to help resolve antagonisms and divisions that have long (...) plagued human religiosity. (shrink)

Neo-Fregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of non-reflexive abstraction relations to restricted abstraction principles.

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)

Orang-utans played a communication game in two studies testing their ability to produce and comprehend requestive pointing. While the ‘communicator’ could see but not obtain hidden food, the ‘donor’ could release the food to the communicator, but could not see its location for herself. They could coordinate successfully if the communicator pointed to the food, and if the donor comprehended his communicative goal and responded pro-socially. In Study 1, one orang-utan pointed regularly and accurately for peers. However, they responded only (...) rarely. In Study 2, a human experimenter played the communicator’s role in three conditions, testing the apes’ comprehension of points of different heights and different degrees of ostension. There was no effect of condition. However, across conditions one donor performed well individually, and as a group orang-utans’ comprehension performance tended towards significance. We explain this on the grounds that comprehension required inferences that they found difficult – but not impossible. The finding has valuable implications for our thinking about the development of pointing in phylogeny. (shrink)

This report from the WHO Consultative Group on Equity and Universal Health Coverage offers advice on how to make progress fairly towards universal health coverage.

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.

The effort of Fichte’s Foundations of the Entire Science of Knowledge is to ground the whole of the science in so called principles. This aim is a specific expression of the project of self-assurance of human being characterizing the important movement of modern metaphysics. The movement towards self-assurance even culminates here: it gets a form of showing human being as an entity founding itself and in totality with itself the whole of actuality. The foundation of science is therefore in this (...) Fichte’s work completely subordinated to the project of explicit self-constitution of human being based in practical-theoretical mastering of consciousness of its own ontological-ontical priority. (shrink)

Critics have often misunderstood the higher-order theory (HOT) of consciousness. Here we clarify its position on several issues, and distinguish it from other views such as the global The higher-order theory (HOT) of consciousness has often been misunderstood by critics. Here we clarify its position on several issues, and distinguish it from other views such as the global workspace theory (GWT) and early sensory models (e.g. first-order local recurrency theories). For example, HOT has been criticized for over-intellectualizing consciousness. We show (...) that while higher-order states are cognitively assembled, the requirements are actually considerably less than often presumed. In this sense HOT may be viewed as an intermediate position between GWT and early sensory views. Also, we clarify that most proponents of HOT do not stipulate consciousness as equivalent to metacognition or confidence. Further, compared to other existing theories, HOT can arguably account better for complex everyday experiences, such as of emotions and episodic memories. This makes HOT particularly useful as a framework for conceptualizing pathological mental states. (shrink)

This chapter describes Kurt Gödel's paper on the incompleteness theorems. Gödel's incompleteness results are two of the most fundamental and important contributions to logic and the foundations of mathematics. It had been assumed that first-order number theory is complete in the sense that any sentence in the language of number theory would be either provable from the axioms or refutable. Gödel's first incompleteness theorem showed that this assumption was false: it states that there are sentences of number theory that are (...) neither provable nor refutable. The first theorem is general in the sense that it applies to any axiomatic theory, which is ω-consistent, has an effective proof procedure, and is strong enough to represent basic arithmetic. Their importance lies in their generality: although proved specifically for extensions of system, the method Gödel used is applicable in a wide variety of circumstances. Gödel's results had a profound influence on the further development of the foundations of mathematics. It pointed the way to a reconceptualization of the view of axiomatic foundations. (shrink)

It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, (...) Delta-3-1 comprehension axioms are not logical truths. What I am going to suggest, however, is that there is a special case to be made on behalf of Pi-1-1 comprehension. Making the case involves investigating extensions of first-order logic that do not rely upon the presence of second-order quantifiers. A formal system for so-called "ancestral logic" is developed, and it is then extended to yield what I call "Arché logic". (shrink)

Although Kurt Gödel does not figure prominently in the history of computabilty theory, he exerted a significant influence on some of the founders of the field, both through his published work and through personal interaction. In particular, Gödel’s 1931 paper on incompleteness and the methods developed therein were important for the early development of recursive function theory and the lambda calculus at the hands of Church, Kleene, and Rosser. Church and his students studied Gödel 1931, and Gödel taught a seminar (...) at Princeton in 1934. Seen in the historical context, Gödel was an important catalyst for the emergence of computability theory in the mid 1930s. (shrink)

An investigation of what Frege means by his doctrine that functions (and so concepts) are 'unsaturated'. We argue that this doctrine is far less peculiar than it is usually taken to be. What makes it hard to understand, oddly enough, is the fact that it is so deeply embedded in our contemporary understanding of logic and language. To see this, we look at how it emerges out of Frege's confrontation with the Booleans and how it expresses a fundamental difference between (...) Frege's approach to logic and theirs. (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 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 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)

History of science and philosophy of science are not perfectly complementary disciplines. Several important asymmetries govern their relationship. These asymmetries, concerning levels of analysis, evidence, theories, writing, and training show that to be a decent philosopher of science is more difficult than being a decent historian. But to be a good historian-well, the degree of difficulty is reversed.