Cosmos+Taxis published a special issue with a symposium discussing Robert Vinten's book Wittgenstein and the Social Sciences. The symposium was edited by Richard Eldridge and it contains contributions from Paul Roth (Distinguished Professor, UC Santa Cruz), Daniel Little (Professor, University of Michigan, Dearborn), Rafael Azize (Associate Professor, Federal University of Bahia), Richard Raatzsch (Professor, EBS Universität), and Rupert Read (Associate Professor, UEA) - with a response by Robert Vinten ('Response to Critics'). Within the issue the papers compare (...) Wittgenstein's philosophy to art, compare Wittgenstein to Brecht, and examine the nature of the social sciences. (shrink)

Yago es el mal incondicional\ sus acciones no pueden justificarse y, sin embargo, puede ser defendidas [T1]. Esta es la tesis que defiende Richard Raatzsch en *The Apologetics o f Evil. The Case o f Yago*. Su argumento descansa fundamentalmente en otras dos tesis, a saber: [T2] que no hay motivo alguno que dé cuenta de las acciones de Yago como un todo y [T3] que Yago es s uno de esos que mantienen su corazón atento solo a (...) sí mismos. Trataré de mostrar, sin embargo, que el argumento de Raatzsch en favor de [T1-T3] es inconsistente con su defensa de Yago, por lo que concluiré que Ratzsch no puede mantener coherentemente las tres tesis. Esta conclusión se verá, no obstante, complementada con una propuesta alternativa acerca de la naturaleza del mal incondicional en la que se subraya el papel de las experiencias corporales en la articulación de lo ético. (shrink)

How should your opinion change in light of an epistemic peer's? We show that the pooling rule known as "upco" is the unique answer satisfying some natural desiderata. If your revised opinion will impact your other views by Jeffrey conditionalization, then upco is the only standard pooling rule that ensures the order in which peers are consulted makes no difference. Popular alternatives like linear pooling, geometric pooling, and harmonic pooling cannot boast the same. In fact, no alternative can that possesses (...) four minimal properties these proposals all share. (shrink)

This work is the transcript of a theological dialogue I had with ChatGPT that spanned a couple of days. I began it merely out of curiosity over how ChatGPT might respond to questions and challenges I posed. As it progressed, I became increasingly impressed with the nuance, depth, and relevance of its responses. The dialogue became, for me, something of a contemplative exercise. I still don’t know quite how to understand the ability of generative A.I. to respond with such (apparent) (...) understanding and even insight. -/- I’ve decided to post this dialogue, not only because of the puzzle it poses concerning A.I, but even more, because I believe that the theological conclusions ‘we’ arrived at have real merit. -/- In the end, the theological views expressed here echo those that I’ve expressed in other works of mine, but the expression of these views are enhanced by the way ChatGPT picks up on them, rephrases them, elaborates upon them, and often places them in the context of the classical theological tradition. -/- I might add that I have been an A.I. skeptic for some time now, concerned over the potential dangers of A.I. in general. But this dialogue, anyway, reveals its potential use as a vehicle for reflection, even profound reflection. -/- . (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)

This is the second part of my theological dialogue with ChatGPT on the meaning of God. We explore the nature of God's agency, will, goodness, the problem of evil and suffering, the meaning of sin, and the meaning and nature of the redemptive act of Christ.

Alongside existing research into the social, political and economic impacts of the Web, there is a need to study the Web from a cognitive and epistemic perspective. This is particularly so as new and emerging technologies alter the nature of our interactive engagements with the Web, transforming the extent to which our thoughts and actions are shaped by the online environment. Situated and ecological approaches to cognition are relevant to understanding the cognitive significance of the Web because of the emphasis (...) they place on forces and factors that reside at the level of agent–world interactions. In particular, by adopting a situated or ecological approach to cognition, we are able to assess the significance of the Web from the perspective of research into embodied, extended, embedded, social and collective cognition. The results of this analysis help to reshape the interdisciplinary configuration of Web Science, expanding its theoretical and empirical remit to include the disciplines of both cognitive science and the philosophy of mind. (shrink)

It is common for religiously motivated actions to be specially protected by law. Many legal theorists have asked why: what makes religion special? What makes it worthy of toleration over and above other non-religious deeply held convictions? The answer I put forward is that religions’ alleged afterlife consequences call for a principle of toleration that warrants special legal treatment. Under a Rawlsian principle of toleration, it is reasonable for those in the original position to opt for principles of justice that (...) accommodate actions with alleged afterlife consequences. And, under a utilitarian principle of toleration, a greater psychological harm is eased by such accommodations. Additionally, this alleged afterlife consequence is found in most of the religions that are thought to warrant some level of special toleration—not only do the Abrahamic religions have alleged afterlife consequences, but many eastern religions do as well, e.g. reincarnation. (shrink)

In this very brief reflection, I argue against the suggestion that consciousness may be viewed as an emergent property of matter.

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.

In this paper we compare Kierkegaard’s and Marx’s views on social reform. Then we argue that Kierkegaard’s own reasoning is consistent with the expression of neighbor-love through collective action, i.e. social reform. However, Kierkegaard’s approach to social reform would be vastly different than Marx’s. We end by reviewing several questions that Kierkegaardian social reformers would ask themselves. Our hope is that this exploration will provide helpful insights into how those who genuinely love their neighbors ought to seek the common good (...) through collective action. (shrink)

A brief reflection on the mind-body problem and its implications for the way we conceive of ourselves and live our lives.

This article explores the ambivalent relationship of neo-Aristotelian naturalism to ethical supervenience. One of the main proponents of this approach, Michael Thompson, holds a position that leads to a rejection of local ethical supervenience. It is argued that this rejection implicitly undermines a premise held by other prominent neo-Aristotelian naturalists, such as Philippa Foot or Rosalind Hursthouse, who implemented Thompson’s species-relative logic of ethical evaluations into their theories. This premise—that there is a systematic connection between the virtuous life and the (...) benefit of the individual—could be re-established if neo-Aristotelian naturalism abandoned the species-essentialist understanding of life-forms and instead accepted local ethical supervenience as an ethical frame of reference. Although this article derives its problem from the main works of the aforementioned authors, its interest lies not mainly in exegesis, but in the systematic discussion of the logical status and the functionality of the concept of life-form in neo-Aristotelian naturalism. This discussion will be enriched by the inclusion of the logical distinctions and insights from modern philosophical biology. (shrink)

How much does rationality constrain what we should believe on the basis of our evidence? According to this book, not very much. For most people and most bodies of evidence, there is a wide range of beliefs that rationality permits them to have in response to that evidence. The argument, which takes inspiration from William James' ideas in 'The Will to Believe', proceeds from two premises. The first is a theory about the basis of epistemic rationality. It's called epistemic utility (...) theory, and it says that what it is epistemically rational for you to believe is what it would be rational for you to choose if you were given the chance to pick your beliefs and, when picking them, you were to care only about their epistemic value. So, to say which beliefs are permitted, we must say how to measure epistemic value, and which decision rule to use when picking your beliefs. The second premise is a claim about attitudes to epistemic risk, and it says that rationality permits many different such attitudes. These attitudes can show up in epistemic utility theory in two ways: in the way you measure epistemic value; and in the decision rule you use to pick beliefs. This book explores the latter. The result is permissivism about epistemic rationality: different attitudes to epistemic risk lead to different choices of prior beliefs; given most bodies of evidence, different priors lead to different posteriors; and even once we fix your attitudes to epistemic risk, if they are at all risk-inclined, there is a range of different priors and therefore different posteriors they permit. (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)

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)

My aim in this paper is to identify the wrong that is done in all cases of testimonial injustice, if there is one. Miranda Fricker (2007) proposes one account of this distinctive wrong, and Gaile Pohlhaus Jr. (2014) offers another. I think neither works. Nor does an account based on giving due respect to the testifier's epistemic competence. Nor does an account based on exposing the testifier to substantial risk of harm. Rachel Fraser (2023) describes a further account, and the (...) proposal I favour is a slight amendment of this. (shrink)

Adaptive preferences give rise to puzzles in ethics, political philosophy, decision theory, and the theory of action. Like our other preferences, adaptive preferences lead us to make choices, take action, and give consent. In 'False Consciousness for Liberals', recently published in The Philosophical Review, David Enoch (2020) proposes a criterion by which to identify when these choices, actions, and acts of consent are less than fully autonomous; that is, when they suffer from what Natalie Stoljar (2014) calls an 'autonomy deficit'. (...) According to Enoch, such actions are not protected in the usual way against interference by others; there is not the same prohibition against trying to prevent someone from acting in a particular way when that action is motivated by such adaptive preferences and is an attempt to satisfy them. In this note, I raise two concerns about Enoch's criterion. (shrink)

Human biological memory systems have adapted to use technological artifacts to overcome some of the limitations of these systems. For example, when performing a difficult calculation, we use pen and paper to create and store external number symbols; when remembering our appointments, we use a calendar; when remembering what to buy, we use a shopping list. This chapter looks at the history of memory artifacts, describing the evolution from cave paintings to virtual reality. It first characterizes memory artifacts, memory systems, (...) and the two main functions such artifacts have, which are to aid individual users in completing memory tasks and as a cultural inheritance channel (section 2). It then outlines some of our first symbolic practices such as making cave paintings and figurines, and then moves on to outline several key developments in external representational systems and the artifacts that support these such as written language, numeral systems and counting devices, diagrams and maps, measuring devices, libraries and archives, photographs, analogue and digital computational artifacts, the World Wide Web, virtual reality, and smartphones (section 3). After that, it makes some brief points about the cumulative nature of the cultural evolution of memory artifacts and speculates about the possible future of memory artifacts, arguing that it is very difficult to look beyond an epistemological horizon of more than five years (section 4). (shrink)

A prominent defence of compulsory voting is based on the negative effects of a low turnout on democracy, which leads to an unequal representation of the most vulnerable citizens of our societies, since they are the least likely to vote voluntarily. This paper shows that this justification relies on the truth of an added premise – that voting is a proxy for use of political influence and power. However, the inclusion of this premise weakens the entire argument, which regains consistency (...) only through the adoption of a narrow understanding of what representation is. Introduction. (shrink)

A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.

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)

In this article, we explore the implications of opposing domains theory for developing ethical leaders. Opposing domains theory highlights a neurological tension between analytic reasoning and socioemotional reasoning. Specifically, when we engage in analytic reasoning, we suppress our ability to engage in socioemotional reasoning and vice versa. In this article, we bring together the domains of neuroscience, psychology, and ethics, to inform our theorizing around ethical leadership. We propose that a key issue for ethical leadership is achieving a healthy balance (...) between analytic reasoning and socioemotional reasoning. We argue that organizational culture often encourages too heavy a reliance on nonemotional forms of reasoning to arrive at moral judgments. As a result, leaders run the risk of suppressing their ability to pay attention to the human side of moral dilemmas and, in doing so, dehumanize colleagues, particularly subordinates, and clients. (shrink)

This analysis shows Cantor's diagonal definition in his 1891 paper was not compatible with his horizontal enumeration of the infinite set M. The diagonal sequence was a counterfeit which he used to produce an apparent exclusion of a single sequence to prove the cardinality of M is greater than the cardinality of the set of integers N.

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)

Our values change. What we value, want, desire, prefer, and how much; for nearly everyone, these will be different at different times in their life. These changes can be gradual or abrupt; they can be long-lasting or short-lived; and they can be induced by forces outside yourself or they can come from within or they can have no specific catalyst at all. Such preference change raises a number of questions for our theorising about rational choice, and these have been discussed (...) at length. In §2 and §3, I’ll outline two of these questions along with some of the putative solutions that have been proposed. But preference change also raises questions for our theorising about autonomy, and these have hardly been considered at all. In §4, I’ll outline three problems for personal autonomy; and in §5, I’ll outline one problem for political autonomy. In §6, I conclude. (shrink)

In this paper, I ask three questions of the liberal. In each, I fill in philosophical detail around a certain sort of complaint raised in current public debates about their position. In the first, I probe the limits of the liberal's tolerance for civil disobedience; in the second, I ask how the liberal can adjudicate the most divisive moral disputes of the age; and, in the third, I suggest the liberal faces a problem when there is substantial disagreement about the (...) boundaries of the rational and the reasonable. (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)

Tourism is one of the socio-economic trends that significantly contributes to the shift of the planetary system into the Anthropocene regime. At the same time, it is also a socio-cultural practice characteristic of the imperial mode of living, or consumerism. Thus, it is a form of commodification of nature, also a way of deepening social inequalities between a privileged minority of the global population and an exploited majority providing services to those whose socio-economic status allows them to travel for fun (...) and commoditised “experience”. This is not an inevitable activity, an activity in which environmental costs (carbon footprint, water footprint, energy consumption, and waste production) are necessary to ensure the basic resources of life. Tourism is therefore a form of luxury consumption. For any tourism model to be, not only, environmentally sustainable but also socially just, or at least acceptable, it would have to be accessible to all people. Ecotourism should also have to meet the criterion of a solidarity mode of living referred to as sufficiency. This is hardly conceivable in the climatic, demographic, and political regime of the Anthropocene. The latter is likely to be characterized by, among other things, mass migration of climate or environmental refugees on the one hand and climate apartheid of the states of the global North on the other. Ecotourism, accessible to an even smaller proportion of the world`s population than the current mass tourism, will thus be more likely to accentuate the social and environmental inequalities of which it is already a significant manifestation. Therefore, the question is whether the concept of ecotourism is not just another manifestation of greenwashing, i.e. an attempt to legitimize economic, social, and cultural activities that devastate the social and environmental environment. (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)

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)

A current focus of legal debate is the proper role of the courts in the interpretation of statutes and the Constitution. Are judges to look solely to the naked language of an enactment, then logically deduce its application in simple syllogistic fashion, as legal formalists had purported to do? Or may the inquiry into meaning be informed by perhaps unbridled and unaccountable judicial notions of public policy, using legal realism to best promote the general welfare? Judge Posner considers the concepts (...) of formalism and realism to be meaningful and useful in common law reasoning but in interpretation to be useless and, worse, forbidden. He analogizes unclear "orders" from a legislature to garbled battlefield communications, and argues that the duty of the recipient of those orders (the judge) is to advance as best he can the enterprise set on foot by the superiors. Case studies elaborate this thesis. Judicial decisions interpreting fixed texts, Judge Posner concludes, can be neither logically correct or incorrect, philosophically sound or unsound, until the ultimate jurist, time, has adjudged their results. (shrink)

Many welfarists wish to assign to each possible state of the world a numerical value that measures something like its moral goodness. How are we to determine this quantity? This paper proposes a contractualist approach: a legitimate measure of moral goodness is one that could be justified to each member of the population in question. How do we justify a measure of moral goodness to each individual? Each individual recognises the measure of moral goodness must be a compromise between the (...) different levels of well-being within the population. Some compromises are more reasonable than others; and some are better justifiable to a given member of the population than others. Each member recognises that the social chooser's measure of moral goodness is going to have to deviate from the well-being function of at least some of the members of the population. But we can nonetheless justify it to each of them if it doesn't deviate more than is necessary, and if the deviations from each member are given equal weighting in whatever process we use to determine it. This paper proposes that we begin with a measure of the distance from a proposed compromise to an individual's level of well-being, and then say that the moral goodness is the candidate compromise that minimizes the sum of distances from it to the individuals' levels of well-being. I describe a range of such measures of distance and show that some give utilitarianism, others different versions of prioritarianism. (shrink)

We reflect on a decade of Responsible Research and Innovation (RRI) as a discourse emerging from the European Commission (EC) 10 years ago. We discuss the foundations for RRI, its emergence during the Seventh Framework programme and its subsequent evolution during Horizon 2020. We discuss how an original vision for RRI became framed around five so-called ‘keys’: gender, open access, science communication, ethics and public engagement. We consider the prospects for RRI within the context of the EC’s Open Science agenda (...) and Horizon Europe programme, before closing with some reflections on the contribution RRI has made to debates concerning the relationship between science, innovation and society over the last decade. (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)

Purpose: This thematic literature review explores the critical role of competent writing skills in law enforcement, examining its impact on career progression, agency reputation, and legal proceedings. The purpose is to synthesize existing literature to identify research gaps and suggest directions for future studies. Methods: Google Scholar, ERIC, and the Jerry Falwell Library searches were conducted to capture a broad range of studies involving police report writing, its impact on officers, law enforcement agencies, and the criminal justice system, and writing (...) improvement strategies. Although not required for this review, the work followed PRISMA-ScR guidelines. Results: The initial search yielded numerous qualitative and quantitative studies. This review categorizes the findings into themes of the importance of writing proficiency, the influence of organizational culture, training and education, and technological integration, highlighting the variability and scope of the existing literature. Conclusions: The review shows the need for well-structured research to substantiate the factors contributing to effective law enforcement report writing. It recommends areas for in-depth exploration in future systematic reviews or primary studies, especially longitudinal studies on the effects of targeted training programs, organizational culture shifts, and technological integration on writing proficiency. Application in Law Enforcement: For trainers and instructors, integrating comprehensive report writing programs into training for law enforcement officers can enhance professional skills and accountability. Effective report writing improves documentation accuracy, supports legal proceedings, and enhances career progression. Incorporating targeted report writing training can holistically enhance the performance and professionalism of law enforcement officers. (shrink)

We reflect on a decade of Responsible Research and Innovation (RRI) as a discourse emerging from the European Commission (EC) 10 years ago. We discuss the foundations for RRI, its emergence during the Seventh Framework programme and its subsequent evolution during Horizon 2020. We discuss how an original vision for RRI became framed around five so-called ‘keys’: gender, open access, science communication, ethics and public engagement. We consider the prospects for RRI within the context of the EC’s Open Science agenda (...) and Horizon Europe programme, before closing with some reflections on the contribution RRI has made to debates concerning the relationship between science, innovation and society over the last decade. (shrink)

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (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)

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)

The aim of this paper is to emphasize the fact that for all finitely-many-valued logics there is a completely systematic relation between sequent calculi and tableau systems. More importantly, we show that for both of these systems there are al- ways two dual proof sytems (not just only two ways to interpret the calculi). This phenomenon may easily escape one’s attention since in the classical (two-valued) case the two systems coincide. (In two-valued logic the assignment of a truth value and (...) the exclusion of the opposite truth value describe the same situation.). (shrink)

In a study drawing from both evolutionary biology and the social sciences, evidence and argument is assembled in support of the comprehensive appli- cation of selfish gene theory to the human population. With a focus on genes giving rise to characteristically-human cooperation (“cooperative genes”) in- volving language and theory of mind, one may situate a whole range of pat- terned behaviour—including celibacy and even slavery—otherwise seeming to present insuperable difficulties. Crucially, the behaviour which tends to propa- gate the cooperative genes (...) may be “at cost” to the genes of some who may be party to the cooperation itself. Explanatory insights are provided by Trivers’ parent-offspring conflict theory, Lack’s principle, and Hamilton’s kin selec- tion mechanism. A primary observation is that cooperation using language and theory of mind is itself interdependent with full human conceptualization of a world of objects and of themselves as embodied beings. Human capaci- ties inhering in, or arising out of, the ability to cooperate are also responsible for a vitally important long-term process, the domestication of animals and p- lants. The approach illuminates the difference between animal and human sexual behaviour, and the emergence of kinship systems. Again, recent pat- terns of population growth become much more explicable. It is argued that the gene is the single controlling replicator; the notion of the meme as a sec- ond independent replicator is flawed. (shrink)

A teaching document I've used in my courses on truth and on incompleteness. Aimed at students who have a good grasp of basic logic, and decent math skills, it attempts to give them the background they need to understand a proper statement of the classic results due to Gödel and Tarski, and sketches their proofs. Topics covered include the notions of language and theory, the basics of formal syntax and arithmetization, formal arithmetic (Q and PA), representability, diagonalization, and the incompleteness (...) and undefinability theorems. (shrink)

On what basis should we embrace a religious belief? In this article I argue that religious faith should be viewed, not as a conclusion we arrive at after reviewing the evidence, but as an existential decision we make through which we define ourselves.

This is a completely informal presentation of the ideas behind the diagonal lemma. One really can't see this important result from too many different angles. This one aims at getting the main idea across. (For the cognoscenti, it is in the spirit of Quine's treatment in terms of "appended to its own quotation".).

In the first half of this paper, I argue that group belief ascriptions are highly ambiguous. What's more, in many cases, neither the available contextual factors nor known pragmatic considerations are sufficient to allow the audience to identify which of the many possible meanings is intended. In the second half, I argue that this ambiguity often has bad consequences when a group belief ascription is heard and taken as testimony. And indeed it has these consequences even when the ascription is (...) true on the speaker's intended interpretation, when the speaker does not intend to mislead and indeed intends to cooperatively inform, and when the audience incorporates the evidence from the testimony as they should. I conclude by arguing that these consequences should lead us to stop using such ascriptions. (shrink)

This paper attempts to address the question what logical strength theories of truth have by considering such questions as: If you take a theory T and add a theory of truth to it, how strong is the resulting theory, as compared to T? It turns out that, in a wide range of cases, we can get some nice answers to this question, but only if we work in a framework that is somewhat different from those usually employed in discussions of (...) axiomatic theories of truth. These results are then used to address a range of philosophical questions connected with truth, such as what Tarski meant by "essential richness" and the so-called conservativeness argument against deflationism. -/- This draft dates from about 2009, with some significant updates having been made around 2011. Around then, however, I decided that the paper was becoming unmanageable and that I was trying to do too many things in it. I have therefore exploded the paper into several pieces, which will be published separately. These include "Disquotationalism and the Compositional Principles", "The Logical Strength of Compositional Principles", "Consistency and the Theory of Truth", and "What Is Essential Richness?" You should probably read those instead, since this draft remains a bit of a mess. Terminology and notation are inconsistent, and some of the proofs aren't quite right. So, caveat lector. I make it public only because it has been cited in a few places now. (shrink)

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)