Artificial intelligence systems have been widely applied to various contexts, including high-stake decision processes in healthcare, banking, and judicial systems. Some developed AI models fail to offer a fair output for specific minority groups, sparking comprehensive discussions about AI fairness. We argue that the development of AI systems is marked by a central paradox: the less participation one stakeholder has within the AI system’s life cycle, the more influence they have over the way the system will function. This means that (...) the impact on the fairness of the system is in the hands of those who are less impacted by it. However, most of the existing works ignore how different aspects of AI fairness are dynamically and adaptively affected by different stages of AI system development. To this end, we present a use case to discuss fairness in the development of corporate wellness programs using smart wearables and AI algorithms to analyze data. The four key stakeholders throughout this type of AI system development process are presented. These stakeholders are called service designer, algorithm designer, system deployer, and end-user. We identify three core aspects of AI fairness, namely, contextual fairness, model fairness, and device fairness. We propose a relative contribution of the four stakeholders to the three aspects of fairness. Furthermore, we propose the boundaries and interactions between the four roles, from which we make our conclusion about the possible unfairness in such an AI developing process. (shrink)

Intellectual humility, I argue in this paper, is a cluster of strong attitudes directed toward one's cognitive make-up and its components, together with the cognitive and affective states that constitute their contents or bases, which serve knowledge and value-expressive functions. In order to defend this new account of humility I first examine two simpler traits: intellectual self-acceptance of epistemic limitations and intellectual modesty about epistemic successes. The position defended here addresses the shortcomings of both ignorance and accuracy based accounts of (...) humility. (shrink)

In this paper I provide an account of two forms of intellectual arrogance which cause the epistemic practices of conversational turn-taking and assertion to malfunction. I detail some of the ethical and epistemic harms generated by intellectual arrogance, and explain its role in fostering the intellectual vices of timidity and servility in other agents. Finally, I show that arrogance produces ignorance by silencing others (both preventing them from speaking and causing their assertions to misfire) and by fostering self-delusion in the (...) arrogant themselves. (shrink)

Intellectual servility is a vice opposing proper pride about one's intellectual achievements. Intellectual timidity is also a vice; it is manifested in a lack of proper concern for others’ esteem. This paper offers an account of the nature of these vices and details some of the epistemic harms that flow from them. I argue that servility, which is often the result of suffering humiliation, is a form of damaged self-esteem. It is underpinned by attitudes serving social-adjustive functions and causes ingratiating (...) behaviors. Timidity, which is habituated through self-silencing, is underpinned by negative attitudes toward the intellectual worth of the self, which serve a defensive function. Like servility, timidity is an obstacle to the acquisition and transmission of knowledge and especially knowledge about oneself. (shrink)

In this paper I offer an original account of intellectual modesty and some of its surrounding vices: intellectual haughtiness, arrogance, servility and self-abasement. I argue that these vices are attitudes as social psychologists understand the notion. I also draw some of the educational implications of the account. In particular, I urge caution about the efficacy of direct instruction about virtue and of stimulating emulation through exposure to positive exemplars.

This article argues that intellectual character vices involve non-instrumental motives to oppose, antagonise, or avoid things that are epistemically good in themselves. This view has been the recent target of criticism based on alleged counterexamples presenting epistemically vicious individuals who are virtuously motivated or at least lack suitable epistemically bad motivations. The paper first presents these examples and shows that they do not undermine the motivational approach. Finally, having distinguished motivating from explanatory reasons for belief and action, it argues that (...) our epistemic practice of vice attribution supplies evidence in favour of motivational accounts of vice. (shrink)

Theories of assertion must explain how silencing is possible. This chapter defends an account of assertion in terms of normative commitments on the grounds that it provides the most plausible analysis of how individuals might be silenced when attempting to make assertions. The chapter first offers an account of the nature of silencing and defends the view that it can occur even in contexts where speakers’ communicative intentions are understood by their audience. Second, it outlines some of the normative commitments (...) characteristic of assertion when used in the speech act of telling;. This commitment view of assertion is then used to explain silencing as a matter of being deprived of the ability to make some of the commitments one is trying to acquire. Finally, the main rivals of the commitment view of assertion endorsed here are shown to be unable to account for silencing, at least when they are considered in their purest form. (shrink)

In this chapter, after a review of some existent empirical and philosophical literature that suggests that human beings are essentially incapable of changing their mind in response to counter-evidence, I argue that motivation makes a significant difference to individuals’ ability rationally to evaluate information. I rely on empirical work on group deliberation to argue that the motivation to learn from others, as opposed to the desire to win arguments, promotes good quality group deliberation. Finally I provide an overview of some (...) epistemic virtues and vices crucial to the politico-epistemic activities of arguing, debating, and listening to a contrary point of view. (shrink)

Arrogance has widespread negative consequences for epistemic practices. Arrogant people tend to intimidate and humiliate other agents, and to ignore or dismiss their views. They have a propensity to mansplain. They are also angry. In this paper I explain why anger is a common manifestation of arrogance in order to understand the effects of arrogance on debate. I argue that superbia (which is the kind of arrogance that is my concern here) is a vice of superiority characterised by an overwhelming (...) desire to diminish other people in order to excel and by a tendency to arrogate special entitlements for oneself, including the privilege of not having to justify one’s claims. (shrink)

The article advances a new way of thinking about classifications in general and the classification of mental disorders in particular. By applying insights from measurement practice to the context of classification, I defend a notion of epistemic accuracy that allows one to evaluate and improve classifications by comparing different classifying methods to each other. Progress in classification arises from the mutual development of classification systems and classifying methods. Based on this notion of accuracy, the article illustrates with an example how (...) psychiatric classifications can be improved via circumscribed comparisons of different perspectives on mental disorders, without relying on complete models of their complex aetiology. When applying this strategy, the traditional opposition between symptom-based and causal approaches is of little consequence for making progress in the epistemic accuracy of psychiatric classification. (shrink)

There is much of interest in Cassam’s ground-breaking Vices of the Mind. This discussion focuses exclusively on one aspect of his view, namely, his account of what it takes to be properly criticisable or blameworthy for one’s epistemic vices. This critical discussion consists of two sections. The first provides an overview of Cassam’s account of responsibility and criticisability for intellectual vices. The second raises a problem for that account whose formulation is due to Battaly and proposes a solution which, at (...) least in part, could also be adopted by Cassam himself if he were prepared to make some small changes to his view. This solution generates a highly disjunctive account of criticisability and responsibility for possessing an epistemic vice. Although such heterogeneity might seem wholly unsatisfactory, it receives a plausible explanation when the account is put within the context of a Strawsonian approach to the practice of holding people responsible for their epistemic vices. (shrink)

Anger dominates debates in the public sphere. In this article I argue that there are diverse forms of anger that merit different responses. My focus is especially on two types of anger that I label respectively arrogant and resistant. The first is the characteristic defensive response of those who unwarrantedly arrogate special privileges for themselves. The second is often a source of insight and a form of moral address. I detail some discursive manifestations of these two types of anger. I (...) show that arrogant anger is responsible for attempts to intimidate and humiliate others with whom one disagrees. Whilst resistant anger can be intimidating, it is also essential in communicating moral demands. (shrink)

It is a common opinion that chance events cannot be understood in causal terms. Conversely, according to a causal view of chance, intersections between independent causal chains originate accidental events, called “coincidences.” The present paper takes into proper consideration this causal conception of chance and tries to shed new light on it. More precisely, starting from Hart and Honoré’s view of coincidental events, this paper furnishes a more detailed account on the nature of coincidences, according to which coincidental events are (...) hybrids constituted by ontic components, that is the intersections between independent causal chains, plus epistemic aspects; where by “epistemic” we mean what is related, in some sense, to knowledge: for example, access to information, but also expectations, relevance, significance, that is psychological aspects. In particular, this paper investigates the role of the epistemic aspects in our understanding of what coincidences are. In fact, although the independence between the causal lines involved plays a crucial role in understanding coincidental events, that condition results to be insufficient to give a satisfactory definition of coincidences. The main target of the present work is to show that the epistemic aspects of coincidences are, together with the independence between the intersecting causal chains, a constitutive part of coincidental phenomena. Many examples are offered throughout this paper to enforce this idea. This conception, despite—for example—Antoine Augustine Cournot and Jacques Monod’s view, entails that a pure objectivist view about coincidences is not tenable. (shrink)

With the progress of artificial intelligence, the digitalization of the lifeworld, and the reduction of the mind to neuronal processes, the human being appears more and more as a product of data and algorithms. Thus, we conceive ourselves “in the image of our machines,” and conversely, we elevate our machines and our brains to new subjects. At the same time, demands for an enhancement of human nature culminate in transhumanist visions of taking human evolution to a new stage. Against this (...) self-reification of the human being, the present book defends a humanism of embodiment: our corporeality, vitality, and embodied freedom are the foundations of a self-determined existence, which uses the new technologies only as means instead of submitting to them. The book offers an array of interventions directed against a reductionist naturalism in various areas of science and society. As an alternative, it offers an embodied and enactive account of the human person: we are neither pure minds nor brains, but primarily embodied, living beings in relation with others. This general concept is applied to issues such as artificial intelligence (AI), transhumanism and enhancement, virtual reality, neuroscience, embodied freedom, psychiatry, and finally to the accelerating dynamics of current society which lead to an increasing disembodiment of our everyday life. The book thus applies cutting-edge concepts of embodiment and enactivism to current scientific, technological, and cultural tendencies that will crucially influence our society’s development in the twenty-first century. (shrink)

This book brings together papers from a conference that took place in the city of L'Aquila, 4–6 April 2019, to commemorate the 10th anniversary of the earthquake that struck on 6 April 2009. Philosophers and scientists from diverse fields of research debated the problem that, on 6 April 1922, divided Einstein and Bergson: the nature of time. For Einstein, scientific time is the only time that matters and the only time we can rely on. Bergson, however, believes that scientific time (...) is derived by abstraction, even in the sense of extraction, from a more fundamental time. The plurality of times envisaged by the theory of Relativity does not, for him, contradict the philosophical intuition of the existence of a single time. But how do things stand today? What can we say about the relationship between the quantitative and qualitative dimensions of time in the light of contemporary science? What do quantum mechanics, biology and neuroscience teach us about the nature of time? The essays collected here take up the question that pitted Einstein against Bergson, science against philosophy, in an attempt to reverse the outcome of their monologue in two voices, with a multilogue in several voices. (shrink)

The paper argues that thumos, which is never explicitly mentioned as a part of the soul in the Symposium, plays a major role in the dialogue. In light of the Republic’s characterization of thumos as the source of emotions such as of love of honor, love of victory, admiration for courage, shame, anger, and the propensity to become indignant at real or imaginary wrongs, the paper argues that both Phaedrus’ speech and the speech of Alcibiades are shaped by thumoeidetic motivations. (...) While Phaedrus’ stress on shame, honor, glory and courage aims at proving that Eros inspires virtue, the speech of Alcibiades shows that thumoeidetic motivations are not sufficient to shape a noble character. The dependence on recognition, the ambiguous role played by shame, and the tension between what is admirable and what just happens to be admired are implicit shortcomings in Phaedrus’ speech. When the same themes come back in Alcibiades’ speech they work as negative counterpoints to Phaedrus’ main arguments. Alcibiades’ obsession with power and victory dominates his ambivalent encomium of Socrates. The speech does not reveal who Socrates really is. Rather, it shows how the philosophical life can be misunderstood when reason’s best ally takes over in the souls of men. (shrink)

The present dissertation investigates certain facets of the logical structure of oughts – where “ought” is used as a noun, roughly meaning obligation. I do so by following two lines of inquiry. The first part of the thesis places oughts in the context of practical rationality. The second part of the thesis concerns the inference rules governing arguments about oughts, and specifically the inference rule of Reasoning by Cases. These two lines of inquiry, together, aim to expound upon oughts in (...) rationality and reasoning. The methodology used in this dissertation is the one of philosophical logic, in which logical, qualitative models are developed to support and foster conceptual analysis. The dissertation consists of four main chapters. The first two chapters are devoted to the role of oughts in practical rationality. I focus on the so-called Enkratic principle of rationality, which – in its most general formulation – requires that if an agent believes sincerely and with conviction that she ought to do X, then she intends to X. I develop a logical framework to investigate the (static and dynamic) relation between those oughts believed by the agent and her intentions. It is shown that, under certain minimal assumptions, the Enkratic principle of rationality is a principle of limited validity. The following two chapters of the dissertation constitute a study of the classical inference rule of Reasoning by Cases, which – in its simplest form – moves from the premises “A or B”, “if A then C” and “if B then C” to the conclusion “C”. Recent literature has called the validity of Reasoning by Cases into question, with the most influential counterexample being the so-called Miners’ Puzzle – an instance of Reasoning by Cases where “C” involves oughts. I provide a unifying explanation of why the Miners’ Puzzle emerges. It is shown that, within specific boundaries, Reasoning by Cases is a valid inference rule. (shrink)

In this paper I offer an innovative interpretation of Nietzsche's metaethical theory of value which shows him to be a kind of constitutivist. For Nietzsche, I argue, valuing is a conative attitude which institutes values, rather than tracking what is independently of value. What is characteristic of those acts of willing which institute values is that they are owned or authored. Nietzsche makes this point using the vocabulary of self-mastery. One crucial feature of those who have achieved this feat, and (...) have consequently become agents, is that they possess a diachronic or long will and are consequently capable of the rational governance of future behaviour. The possession of a will of this sort is crucial because it is a necessary condition for engaging in temporally unified activities which are a requisite of authorship. Nietzsche, I argue, makes these points in his doctrine of eternal recurrence which provides a test that acts of will must pass to count as laws. In the final section of the paper I argue for the superiority of this interpretation over some of its competitors. (shrink)

This paper focuses on the Enkratic principle of rationality, according to which rationality requires that if an agent sincerely and with conviction believes she ought to X, then X-ing is a goal in her plan. We analyze the logical structure of Enkrasia and its implications for deontic logic. To do so, we elaborate on the distinction between basic and derived oughts, and provide a multi-modal neighborhood logic with three characteristic operators: a non-normal operator for basic oughts, a non-normal operator for (...) goals in plans, and a normal operator for derived oughts. We prove two completeness theorems for the resulting logic, and provide a dynamic extension of the logic by means of product updates. We illustrate how this setting informs deontic logic by considering issues related to the filtering of inconsistent oughts, the restricted validity of deontic closure, and the stability of oughts and goals under dynamics. (shrink)

In this paper I argue that in Western contemporary societies testimony is structured by norms of reciprocation and thus is best understood as involving the exchange of gifts rather than, as philosophers and game theorists have tended to presume, market transactions. My argument is based on an initial analysis of the reactive attitudes that are exhibited in testimonial exchanges. I highlight the central role played by the reciprocating attitudes of gratitude and gratification respectively in the recipient and the donor of (...) testimony. This analysis leads to an account of the speech act of telling that is the primary vehicle of testimony. Telling, I argue, is a commissive but it is not, as it is usually presumed, akin to promising. Instead, its nature is that of an offer of a gift. Finally, I develop an account of the norms of trust and trustfulness as reciprocating social norms. I show that adopting these norms provides a particularly effective solution of the problem of cooperation. The solution is particularly effective because it incentivises both the sharing of epistemic goods and the acquisition of further such goods so that one is able to share them. (shrink)

The paper reviews the philosophical literature on the epistemology of modelling in contemporary economics. In particular, it focuses on open questions concerning the epistemic role of models, the validity of inferences from the models to the world, and the legitimacy of their use for purposes of explanation, prediction and intervention.

Why do some people become WNBA champions or Olympic gold medalists and others do not? What is ‘special’ about those very few incredibly skilled athletes, and why do they, in particular, get to be special? In this paper, I attempt to make sense of the relationship that there is, in the case of sports champions, between so-called ‘talent’, i.e. natural predisposition for particular physical activities and high-pressure competition, and practice/training. I will articulate what I take to be the ‘mechanism’ that (...) allows certain people to rise to the Olympus of athletic excellence, and what being part of this elite club ‘feels like’. My proposal is based on the idea that so-called talent and practice interact in complex and unsystematic ways. I will also argue that becoming a top athlete involves undergoing a special kind of transformation, which makes such people qualitatively different from any ‘normal’ sport amateur, even when the difference might not be immediately visible to the ‘untrained’ eye. (shrink)

A number of philosophers have defended the view that seemingly intellectually arrogant behaviours are epistemically beneficial. In this chapter I take issue with most of their conclusions. I argue, for example, that we should not expect steadfastness in one's belief in the face of contrary evidence nor overconfidence in one’s own abilities to promote better evaluation of the available evidence resulting in good-quality group-judgement. These features of individual thinkers are, on the contrary, likely to lead groups to end up in (...) stalemates and to polarise over issues. It is true that groups benefit from including members that, prior to discussion, hold diverse views. But disagreement benefits group judgement only when it is transient, rather than entrenched. That is, groups reach better quality conclusions when a number of diverse opinions are disseminated and evaluated fairly before reaching a consensus. If this is right, it would seem that individual qualities, such as open-mindedness and even-handedness about the epistemic value of opinions other than one's own, rather than steadfastness or overconfidence are conducive to better quality group judgement. (shrink)

This article presents a few research findings related to the Geomantia attributed to William of Moerbeke. It consists of three sections: The first provides evidence for the classification of the Geomantia within the genre of the medieval compilations. The second includes a comparison of the Geomantia with the Ars geomantie nova of Batholomew of Parma and a few considerations on the datation of the treatise attributed to Moerbeke, based on this assessment. The third brings to the attention of scholars an (...) unpublished marginal note concerning the date of composition of the Geomantia. (shrink)

This volume brings together new work on the logic and ontology of plurality and a range of recent articles exploring novel applications to natural language semantics. The contributions in this volume in particular investigate and extend new perspectives presented by plural logic and non-standard mereology and explore their applications to a range of natural language phenomena. Contributions by P. Aquaviva, A. Arapinis, M. Carrara, P. McKay, F. Moltmann, O. Linnebo, A. Oliver and T. Smiley, T. Scaltsas, P. Simons, and B.-Y. (...) Yi . (shrink)

The current and the next issues of “Spazio Filosofico”, both devoted to Festival (Festival I and II respectively), are dedicated to Ugo Perone on the occasion of his 70th birthday. Perone’s friends and colleagues have chosen to celebrate his birthday in a philosophical way, namely, with a reflection on the concept of festival/holiday [festa] and its meaning for us today. Thrifty spirits might object that a journal issue is like a gift – one is enough. Are these not times of (...) economic crisis? There is no real festival, however, without a Zugabe: without an addition, an encore, or a supplement. Hence, two issues, both devoted to a single concept. The choice of the theme has not been accidental – the concept of “festival/holiday” plays in fact an important role in Perone’s thought. In an essay that is often quoted in various contributions to the two issues, Perone understands the pair of concepts “ultimate/penultimate,” which has been discussed by Dietrich Bonhoeffer, in terms of “holidays/everydayness.” For Bonhoeffer, God is present not where human abilities fail but rather “at the center of the village.” Likewise, for Perone, the square, which is the “symbol for the holiday time,” is the center of town. It is even, “at the same time, the center of town and its interruption.” . (shrink)

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".).

The insightful commentaries to our contribution "Education as the Social Cultivation of Intellectual Virtue" (in 'Social Virtue Epistemology', (eds.) M. Alfano, C. Klein & J. de Ridder, Routledge 2022) offered by Alessandra Tanesini and Lani Watson highlight some important aspects of the work that philosophers, education theorists, and educators should carry out to strengthen the theoretical and practical advantages of the educational approach we have proposed. This commentary briefly addresses a few points that could set the grounds for future (...) investigations on intellectual virtue-based approaches to education and their social dimensions. (shrink)

In this paper we propose to present from a new perspective some loci comunes of traditional logic. More exactly, we intend to show that some hypothetico-disjunctive inferences (i.e. the complex constructive dilemma, the complex destructive dilemma, the simple constructive dilemma, the simple destructive dilemma) and two hypothetico-categorical inferences (namely modus ponendo-ponens and modus tollendo-tollens) particularize two more abstract inferential structures: the constructive n-lemma and the destructive nlemma.

Příspěvek přináší základní matematické zakotvení pojmů „teorie chaosu". Představuje klíčové vlastnosti modelů chaotického chování dynamického systému s ohledem na explanační a prediktivní sílu modelů. Z pozice filosofie vědy podrobuje analýze především reprezentační aspekty modelů chaotické dynamiky systému. Nejzajímavějším aspektem těchto modelů je přísné omezení jejich reprezentační úlohy s ohledem na splnění podmínky hyperbolicity nutné pro platnost stínového lemma.

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships between (...) various cut-conditions in the absence of finitariness or of monotonicity. (shrink)

Chains of causes appear when the existence of God is discussed. It is claimed by some that these chains must be finite and terminated by God. But these chains seem endless through our knowledge search. This endlessness for the physical reasons for any world event expresses the greatness and complexity of God’s creation and so the transcendence of God. So, only we can put our hands on physical reasons in an endless forage for knowledge. Yet, the endlessness of the physical (...) causes chains confirms the existence of God, and this is what our paper tries using Zorn’s lemma, an equivalent for one of the most celebrated axioms of mathematics, the Axiom of Choice. (shrink)

The current literature on norms of inquiry features two families of norms: norms that focus on an inquirer’s ignorance and norms that focus on the question’s soundness. I argue that, given a factive conception of ignorance, it’s possible to derive a soundness-style norm from a version of the ignorance norm. A crucial lemma in the argument is that just as one can only be ignorant of a proposition if the proposition is true, so one can only be ignorant with (...) respect to a question if the question is sound. (shrink)

No False Lemmas (NFL) says: necessarily, S’s belief that p is knowledge only if it is not inferred from any falsehood. Its proponents argue that alleged counterexamples to NFL are really cases of knowledge despite falsehood, wherein the false premise is inessential to the inference; perhaps some nearby truth does the justificatory heavy-lifting. We argue that there can be cases of inferential knowledge from a blindspot premise. Given that in such cases the relevant falsehood is essential to the inference, one (...) cannot employ the knowledge despite falsehood strategy to defend NFL. We conclude by discussing how cases of knowledge from blindspots exemplify one way in which we can gain inferential knowledge defectively or non-ideally. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free topology) (...) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

This paper presents a formalization of the classical proof of completeness in Henkin-style developed by Troelstra and van Dalen for intuitionistic logic with respect to Kripke models. The completeness proof incorporates their insights in a fresh and elegant manner that is better suited for mechanization. We discuss details of our implementation in the Lean theorem prover with emphasis on the prime extension lemma and construction of the canonical model. Our implementation is restricted to a system of intuitionistic propositional logic (...) with implication, conjunction, disjunction, and falsity given in terms of a Hilbert-style axiomatization. As far as we know, our implementation is the first verified Henkin-style proof of completeness for intuitionistic logic following Troelstra and van Dalen's method in the literature. (shrink)

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing (...) Lemma and Dunn's Theorem in 3-Valued Logic. (shrink)

I this paper I give minimal axioms for the ontology of time, especially A-theories and B-theories and I derive philosophically interesting lemmas. The exercise is set-theoretical, defining all notions and indicating assumptions and philosophical points of disagreement, while being easy to translate to other formal expressions . The issue of a logic for A-theories of time is treated towards the end, where I sketch ‘copresent’ operators for capturing the idea of temporal passage. The main conclusion will be that, while circularity (...) threatens both families of theories, the growing block theory (belonging to the A-theory) is the least objectionable philosophically. (shrink)

The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. This (...) undecidability result is proved directly from the notion itself of an effective procedure, without reliance on any (partly) mathematical lemma, conjecture, or thesis invoking recursiveness or Turing-computability. In fact, there is no reliance on anything very mathematical. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of an effective procedure. Though the result that effectiveness is undecidable is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure invariably terminates with the correct verdict. (shrink)

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I prove (...) that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the 'circularity dependence' of paradoxes, which was introduced by Hsiung (2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König's infinity lemma. In contrast, this paper also shows that Yablo's paradox and its nested variant are non-self-referential, and neither McGee's paradox nor the omega-cycle liar paradox has circularity dependence. (shrink)

The purpose of this note is to present a strong form of the liar paradox. It is strong because the logical resources needed to generate the paradox are weak, in each of two senses. First, few expressive resources required: conjunction, negation, and identity. In particular, this form of the liar does not need to make any use of the conditional. Second, few inferential resources are required. These are: (i) conjunction introduction; (ii) substitution of identicals; and (iii) the inference: From ¬(p (...) ∧ p), infer ¬ p. It is, interestingly enough, also essential to the argument that the ‘strong’ form of the diagonal lemma be used: the one that delivers a term λ such that we can prove: λ = ¬ T(⌈λ⌉); rather than just a sentence Λ for which we can prove: Λ ≡ ¬T(⌈Λ⌉). The truth-theoretic principles used to generate the paradox are these: ¬(S ∧ T(⌈¬S⌉); and ¬(¬S ∧ ¬T(⌈¬S⌉). These are classically equivalent to the two directions of the T-scheme, but they are intuitively weaker. The lesson I would like to draw is: There can be no consistent solution to the Liar paradox that does not involve abandoning truth-theoretic principles that should be every bit as dear to our hearts as the T-scheme. So we shall have to learn to live with the Liar, one way or another. (shrink)

The copy provided on ths site is a late draft. It provides a philosophical argument for the view that by and large it is morally wrong to buy shares in a company that is behaving badly unless you (if necessary acting together with others) are able and willing to prevent the misbehaviour. A key lemma in my argument concerns a chain of authorisation from the shareholders to the company's board to the CEO -- one in virtue of which shareholders (...) are ultimately responsible for major patterns of wrongdoing by the company. (shrink)

In his “A new argument for evidentialism” (Shah, Philos Q 56(225): 481–498, 2006 ), Nishi Shah argues that the best explanation of a feature of deliberation whether to believe that p which he calls transparency entails that only evidence can be reason to believe that p. I show that his argument fails because a crucial lemma that his argument appeals to cannot be supported without assuming evidentialism to be true in the first place.