Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, ready to (...) meet them, who have explicitly invoked virtues in discussing what is necessary for a mathematician to succeed. In both ethics and epistemology, virtue theory tends to emphasize character virtues, the acquired excellences of people. But people are not the only sort of thing whose excellences may be identified as virtues. Theoretical virtues have attracted attention in the philosophy of science as components of an account of theory choice. Within the philosophy of mathematics, and mathematics itself, attention to virtues has emerged from a variety of disparate sources. Theoretical virtues have been put forward both to analyse the practice of proof and to justify axioms; intellectual virtues have found multiple applications in the epistemology of mathematics; and ethical virtues have been offered as a basis for understanding the social utility of mathematical practice. Indeed, some authors have advocated virtue epistemology as the correct epistemology for mathematics (and perhaps even as the basis for progress in the metaphysics of mathematics). This topical collection brings together several of the researchers who have begun to study mathematical practices from a virtue perspective with the intention of consolidating and encouraging this trend. (shrink)

This paper considers the relation between the sources of normativity, reasons, and normative conflicts. It argues that common views about how normative reasons relate to their sources have important consequences for how we can understand putative normative conflicts.

This entry summarizes arguments for and against the thesis that knowledge entails belief.

Virtue theories have lately enjoyed a modest vogue in the study of argumentation, echoing the success of more far-reaching programmes in ethics and epistemology. Virtue theories of argumentation (VTA) comprise several conceptually distinct projects, including the provision of normative foundations for argument evaluation and a renewed focus on the character of good arguers. Perhaps the boldest of these is the pursuit of the fully satisfying argument, the argument that contributes to human flourishing. This project has an independently developed epistemic analogue: (...) eudaimonistic virtue epistemology. Both projects stress the importance of widening the range of cognitive goals beyond, respectively, cogency and knowledge; both projects emphasize social factors, the right sort of community being indispensable for the cultivation of the intellectual virtues necessary to each project. This paper proposes a unification of the two projects by arguing that the intellectual good life sought by eudaimonistic virtue epistemologists is best realized through the articulation of an account of argumentation that contributes to human flourishing. (shrink)

Virtue theories of argumentation (VTA) emphasize the roles arguers play in the conduct and evaluation of arguments, and lay particular stress on arguers’ acquired dispositions of character, that is, virtues and vices. The inspiration for VTA lies in virtue epistemology and virtue ethics, the latter being a modern revival of Aristotle’s ethics. Aristotle is also, of course, the father of Western logic and argumentation. This paper asks to what degree Aristotle may thereby be claimed as a forefather by VTA.

Andrews argues for a pluralistic folk psychology that employs different kinds of practices and different kinds of cognitive tools (including personality trait attribution, stereotype activation, inductive reasoning about past behavior, and ...

Douglas Walton’s multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.

According to an influential idea in the philosophy of set theory, certain mathematical concepts, such as the notion of a well-order and set, are indefinitely extensible. Following Parsons (1983), this has often been cashed out in modal terms. This paper explores instead an extensional articulation of the idea, formulated in higher-order logic, that flat-footedly formalizes some remarks of Zermelo. The resulting picture is incompatible with the idea that the entire universe can be well-ordered, but entirely consistent with the idea that (...) the sets of any set-theoretic universe can be. (shrink)

The dependence solution claims that God’s foreknowledge is no threat to our freedom because God’s foreknowledge depends (in a relevant sense) on our actions. The assumption here is that those parts of the world which depend on our actions are no threat to the freedom of those actions. Recently, Taylor Cyr has presented a case which challenges this assumption. Moreover, since the case is analogous to the case of God’s foreknowledge, it would seem to establish that, even if God’s foreknowledge (...) somehow depends on our actions, our freedom is still threatened. This paper defends the dependence solution, first, by offering an error theory for the intuitions that drive Cyr’s case and, second, by pointing out some arguably mysterious implications of accepting those intuitions. These points taken in conjunction show that Cyr’s case, although quite fascinating, is not as challenging as it might at first seem. (shrink)

Wittgenstein's farcical clash with literary critic F. R. Leavis over the analysis of Empson's poem "Legal Fiction" is well known to devotees of Wittgenstein's life (Ludwig Wittgenstein: Personal Recollections (1981), edited by Rush Rhees, Oxford: Basil Blackwell, 80). Less well known is the value of studying Empson's artistic and intellectual achievement as part of the wider cultural background for the appreciation of Wittgenstein's views and influence, early and late. This talk sketches some diverting byways awaiting further exploration. A recurrent theme (...) is contradiction. (shrink)

Commentators typically neglect the distinct nature and role of hope in Kant’s system, and simply lump it together with the sort of Belief that arises from the moral proof. Kant himself is not entirely innocent of the conflation. Here I argue, however, that from a conceptual as well as a textual point of view, hope should be regarded as a different kind of attitude. It is an attitude that we can rationally adopt toward some of the doctrines that are not (...) able to be proved from within the bounds of mere reason – either theoretical or practical. This does not mean that hope is unconstrained; there are rational limits, as we shall see. In fact one of my central claims here is that a crucial difference between knowledge, rational Belief, and rational hope is that they are governed by different modal constraints; section II discusses those constraints and the kind of modality involved. In section III, I return to Religion and offer what I take to be Kant’s account of the main objects of rational hope in that text – namely, “alleged outer experiences (miracles)”;a “supposed inner experience(effect of grace)”;and a future collective experience (the construction of a truly ethical society). (shrink)

In their article, Thom Scott‐Phillips, Stefaan Blancke, and Christophe Heintz do a commendable job summarizing the position and misunderstandings of “cultural attraction theory” (CAT). However, they do not address a longstanding problem for the CAT framework; that while it has an encompassing theory and some well‐worked out case studies, it lacks tools for generating models or empirical hypotheses of intermediate generality. I suggest that what the authors diagnose as misunderstandings are instead superficial interpretive errors, resulting from researchers who have attempted (...) to extract generalizable hypotheses from CAT and bring them into contact with the analytical and inferential models of contemporary cultural evolutionary research. (shrink)

A satisfactory theory of linguistic communication must explain how it is that, through the interpersonal exchange of auditory, visual, and tactile stimuli, the communicative preconditions for the acquisition of testimonial knowledge regularly come to be satisfied. Without an account of knowledge-yielding communication this success condition for linguistic theorizing is left opaque, and we are left with an incomplete understanding of testimony, and communication more generally, as a source of knowledge. This paper argues that knowledge-yielding communication should be modelled on knowledge (...) itself. It is argued that knowledge-yielding communication occurs iff interlocutors coordinate on truth values in a non-lucky and non-deviant way. This account is able to do significant explanatory work: it sheds light on the nature of referential communication, and it allows us to capture, in an informative way, the sense in which interlocutors must entertain similar propositions in order to communicate successfully. (shrink)

I want to say something about the sort of arguments that it is possible to lose, and whether losing arguments can be done well. I shall focus on losing philosophical arguments, and I will be talking about arguments in the sense of acts of arguing. This is the sort of act that one can perform on one’s own or with one other person in private. But in either of these cases it is difficult to win—or to lose. So I shall (...) concentrate on arguments with audiences. We may think of winning or losing such arguments in terms of whether the audience is convinced. Of course, this doesn’t necessarily have anything to do with who is in the right. That means that there are two sorts of loser: real losers, who lose the argument deservedly, because they are in the wrong, and mere losers, who lose the argument undeservedly, because they are in the right. Hence there must also be two sorts of winner: real winners, who win the argument deservedly, because they are in the right, and mere winners, who win the argument undeservedly, because they are in the wrong. An optimal outcome for arguments with losers would be if all the losers are real losers. (shrink)

In this chapter, I present and explore various arguments for skepticism that are related to memory. My focus will be on the aspects of the arguments that are unique to memory, which are not shared, for example, by the more often explored skeptical arguments related to perception. -/- Here are some interesting upshots. First, a particular problem for justifiably concluding that one's memory is reliable is that any reasoning in favor of this conclusion will either result in epistemically circularity or (...) not be sufficient to justify the conclusion. Second, since many beliefs stored in memory do not appear to be based on evidence, it might also appear to follow that they are not justified. Third, although many stored memory beliefs are not based on stored memory experiences in the same way that perceptual beliefs are based on perceptual experiences, skeptical scenarios loom just as problematically for memory beliefs as they do for perceptual beliefs. (shrink)

In tradition linked to Aristotle and Kant, many contemporary philosophers treat practical and theoretical normativity as two genuinely distinct domains of normativity. In this paper I consider the question of what it is for normative domains to be distinct. I suggest that there are two different ways that the distinctness thesis might be understood and consider the different implications of the two different distinctness theses.

This chapter articulates two concerns that Karl Jaspers raised (with Hannah Arendt) about the common practice of viewing moral evil as unintelligible. The first is that this involves exoticizing the act and/or perpetrator in such a way that moral condemnation becomes difficult. The second is that it can lead us to treat the perpetrator, place, or victim as tainted or stained by a force whose motives we cannot grasp; this in turn can lead to magical thinking about evil as somehow (...) contagious or contaminating. After distinguishing some of the main categories of evil discussed in the western tradition, I examine ways in which moral evil, in particular, has been characterized as unintelligible, and try to discern which of them raises these Jaspersian concerns. I argue that there are at least two conceptions of “radical evil”—not the Kantian one, but the ones articulated by Hannah Arendt—that do so. (shrink)

I show in this paper why the universality of quantum mechanics at all scales, which implies the possibility of Schrodinger's Cat and Wigner's Friend thought experiments, cannot be experimentally confirmed, and why macroscopic superpositions in general cannot be observed or measured, even in principle. Through the relativity of quantum superposition and the transitivity of correlation, it is shown that from the perspective of an object that is in quantum superposition relative to a macroscopic measuring device and observer, the observer is (...) already sufficiently well correlated to the measuring device that once the object correlates to the measuring device, there is no time period in which the observer can perform an appropriate interference experiment to show that the measuring device is in a superposition. (shrink)

David Albert has recently argued that classical electromagnetic theory (EM) is not time reversal invariant (non-TRI), while David Malament rejects this argument and maintains the orthodox result, that EM is TRI. Both Albert's and Malament's arguments are analysed, and both are found wanting in certain respects. It is argued here that the result really depends on the choice of theoretical ontology choosen to interpret EM theory, and there is more than one plausible choice. Albert and Malament have choosen different plausible (...) ontologies; but neither shows that their choice of interpretation is definitive. Deeper principles about this choice are examined. The extension to EM theory with magnetic monopoles is also examined. It is concluded that, despite certain flaws in his account, Albert's analysis does reveal serious problems in the orthodox account, which Malament's response does not adequately address. (shrink)

This article discusses the following question: what epistemic relation must audiences bear to the content of assertions in order to gain testimonial knowledge? There is a brief discussion of why this issue is of importance, followed by two counterexamples to the most intuitive answer: that in order for an audience to gain testimonial knowledge that p they must know that the speaker has asserted p. It is then suggested that the argument generalises and can be made to work on different (...) sets of assumptions about the conditions for knowledge, and the conditions under which a proposition is asserted. (shrink)

This essay presents the framework for the foundational axiom and conceptual underpinnings of mathematics and how they are applied.

The assertion by Yu and Nikolic that the delayed choice quantum eraser experiment of Kim et al. empirically falsifies the consciousness-causes-collapse hypothesis of quantum mechanics is based on the unfounded and false assumption that the failure of a quantum wave function to collapse implies the appearance of a visible interference pattern.

The possibility of algorithmic consciousness depends on the assumption that conscious states can be copied or repeated by sufficiently duplicating their underlying physical states, leading to a variety of paradoxes, including the problems of duplication, teleportation, simulation, self-location, the Boltzmann brain, and Wigner’s Friend. In an effort to further elucidate the physical nature of consciousness, I challenge these assumptions by analyzing the implications of special relativity on evolutions of identical copies of a mental state, particularly the divergence of these evolutions (...) due to quantum fluctuations. By assuming the supervenience of a conscious state on some sufficient underlying physical state, I show that the existence of two or more instances, whether spacelike or timelike, of the same conscious state leads to a logical contradiction, ultimately refuting the assumption that a conscious state can be physically reset to an earlier state or duplicated by any physical means. Several explanatory hypotheses and implications are addressed, particularly the relationships between consciousness, locality, physical irreversibility, and quantum no-cloning. (shrink)

Профессиональная деятельность вполне развитого образованного человека, использующего по максимуму свой интеллект и знания на работе, остается, как правило, вне круга интересов современной философии сознания, которая анализирует главным образом элементарные мысли и действия. В данной работе предлагается единый подход к описанию как простейших, так и чрезвычайно сложных действий на основе синтетического концепта «мыследействие», объединяющего как ментальные, так и внешние аспекты действий. Генезис нового понятия рассматривается в свете холистических парадигм экстернализма и энактивизма. Professional activity of a fully developed educated individual getting the (...) most out of his knowledge and intellect at work has attracted as of yet little interest in modern cognitive science and philosophy of mind, whereas the main focus is on the analysis of elementary thoughts and actions. In this paper I propose a unified approach to both elementary and very complex actions based on a concept of “action-thoughts”, in which mental and physical aspects of actions are fused together. The genesis of this novel concept is presented in the light of holistic paradigms of externalism and enactivism. (shrink)

My aim in this paper is to explore different ways of understanding Kant’s Formula of Humanity as a formal principle. I believe that a formal principle for Kant is a principle that is constitutive of some domain of cognition or rational activity. It is a principle that both constitutively guides that activity and serves as its internal regulative norm. In the first section of this essay, I explain why it is desirable to find a way to understand the Formula of (...) Humanity as a formal principle in this sense. In sections II and III I discuss two interpretive approaches to Kant’s idea that rational nature or humanity is an end in itself, both of which may be construed as treating the Formula of Humanity as a formal principle. By focusing on the notion of formal principle, I hope to raise a set of issues about how to understand the idea of rational nature or humanity as an end in itself, and about the relation of the Formula of Humanity [FH] to the Formula of Universal Law [FUL]. I do not resolve the issues in this paper, though I briefly sketch some resolution at the end. (shrink)

In this review article of Dan Hutto's bok Folk Psychological Narratives: The Sociocultural Basis of Understanding Reasons, I argue that we can take a functional approach to FP that identifies it with the practice of explaining behaviour -- that is, we can understand folk psychology as having the purpose of explaining behaviour and promoting social cohesion by making others’ behaviour comprehensible, without thinking that this ability must be limited to those with linguistic abilities. One reason for thinking that language must (...) be implicated in FP explanations arises from the history of theorizing about the nature of scientific explanation. I will show that there are other models of explanation that are free from the metaphysical linguistic baggage of the traditional models, and argue that such models can be profitably used to make sense of an explanation-centred FP that need not involve the attribution of propositional attitudes or a functioning linguistic competence. Further, I will argue that there is evidence that pre-linguistic human children engage in explanatory practices, and that some of these explanations may be seen as narrative explanations in an important sense. (shrink)

The universality assumption (“U”) that quantum wave states only evolve by linear or unitary dynamics has led to a variety of paradoxes in the foundations of physics. U is not directly supported by empirical evidence but is rather an inference from data obtained from microscopic systems. The inference of U conflicts with empirical observations of macroscopic systems, giving rise to the century-old measurement problem and subjecting the inference of U to a higher standard of proof, the burden of which lies (...) with its proponents. This burden remains unmet because the intentional choice by scientists to perform interference experiments that only probe the microscopic realm disqualifies the resulting data from supporting an inference that wave states always evolve linearly in the macroscopic realm. Further, the nature of the physical world creates an asymptotic size limit above which interference experiments, and verification of U in the realm in which it causes the measurement problem, seem impossible for all practical purposes if nevertheless possible in principle. This apparent natural limit serves as evidence against an inference of U, providing a further hurdle to the proponent’s currently unmet burden of proof. The measurement problem should never have arisen because the inference of U is entirely unfounded, logically and empirically. (shrink)

A short encyclopaedia entry on John Broome.

In the science of consciousness, it’s oftentimes assumed that some creatures (or mental states) are more conscious than others. But in recent years, a number of philosophers have argued that the notion of degrees of consciousness is conceptually confused. This paper (1) argues that the most prominent objections to degrees of consciousness are unsustainable, (2) examines the semantics of ‘more conscious than’ expressions, (3) develops an analysis of what it is for a degreed property to count as degrees of consciousness, (...) and (4) applies the analysis to various theories of consciousness. I argue that whether consciousness comes in degrees ultimately depends on which theory of consciousness turns out to be correct. But I also argue that most theories of consciousness entail that consciousness comes in degrees. (shrink)

A response to critical commentaries. Crookston begins her commentary by noting that my book would have been better with answers to “the following three questions: (1) Why is the harm principle the right principle upon which to base a theory of toleration? (2) How is Cohen thinking of the concept of volenti? (p. x ) Is interference (i.e., the abandonment of toleration) ever morally required by the harm principle?” (p. x ). She is right, and I address these questions below (...) in Sections 2, 3, and 4. That is the bulk of this essay. I then turn to Kelley's issues in Sections 6, 7, and 8; these have to do with “the link between toleration and relativism,” the way I distinguish “the concepts of toleration and endurance,” and a “question about moral toleration” (p. x ). Despite much agreement, there are points of contention and I try to make my position clearer in response . (shrink)

This paper introduces and argues for contrastivism about intentions. According to contrastivism, intention is not a binary relation between an agent and an action. Rather, it is a ternary relation between an agent, an action, and an alternative. Contrastivism is introduced via a discussion of cases of known but (apparently) unintended side effects. Such cases are puzzling. They put pressure on us to reject a number of highly compelling theses about intention, intentional action, and practical reason. And they give rise (...) to a puzzle about rather than constructions such as ‘I intend to φ rather than ψ’: In side effect cases it can seem wrong to claim that the subject intends to φ, yet acceptable to claim that they intend to φ rather than ψ. This cries out for explanation. Contrastivism provides a unified response to all of these problems. (shrink)

We live in a market system with much economic inequality. This may not be an essential characteristic of market systems but seems historically inevitable. How we should evaluate it, on the other hand, is contentious. I propose that bleeding heart libertarianism provides the best diagnosis and prescription.

Most elpistologists now agree that hope for a specific outcome involves more than just desire plus the presupposition that the outcome is possible. This paper argues that the additional element of hope is a disposition to focus on the desired outcome in a certain way. I first survey the debate about the nature of hope in the recent literature, offer objections to some important competing accounts, and describe and defend the view that hope involves a kind of focus or attention. (...) I then suggest that this account makes sense of the intuitive thought that there are moral and pragmatic norms on hope that go beyond the norms on desires and modal presuppositions. I conclude by considering some key questions. (shrink)

A widely circulated list of spurious proof types may help to clarify our understanding of informal mathematical reasoning. An account in terms of argumentation schemes is proposed.

Perception is riddled with cases of reliable misperception. These are cases in which a perceptual state is tokened inaccurately any time it is tokened under normal conditions. On the face of it, this fact causes trouble for theories that provide an analysis of perceptual content in non-semantic, non-intentional, and non-phenomenal terms, such as those found in Millikan (1984), Fodor (1990), Neander (2017), and Schellenberg (2018). I show how such theories can be extended so that they cover such cases without giving (...) up their core commitments. (shrink)

The problem of colour exclusion is not fatal to Ludwig Wittgenstein’s early philosophy, nor was it the catalyst for his later philosophy. The remarks in the Tractatus about the impossibility of the simultaneous occurrence of two colours at a point in the visual field sit comfortably with the remarks in the rest of the book, the discussion of mathematical physics above all. Furthermore Wittgenstein’s second thoughts about the impossibility were a consequence, not the cause, of the subsequent turn in his (...) philosophy. (shrink)

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system’s interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those that use interpretive rules to map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three independent ways in which (...) a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically. (shrink)

The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in order (...) to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia. (shrink)

Recent debates in the interpretation of Kant’s theoretical philosophy have focused on the nature of Kantian intuition and, in particular, on the question of whether intuitions depend for their existence on the existence of their objects. In this paper we show how opposing answers to this question determine different accounts of the nature of Kantian cognition and we suggest that progress can be made on determining the nature of intuition by considering the implications different views have for the nature of (...) cognition. (shrink)

The new evil demon problem is often considered to be a serious obstacle for externalist theories of epistemic justification. In this paper, I aim to show that the new evil demon problem also afflicts the two most prominent forms of internalism: moderate internalism and historical internalism. Since virtually all internalists accept at least one of these two forms, it follows that virtually all internalists face the NEDP. My secondary thesis is that many epistemologists – including both internalists and externalists – (...) face a dilemma. The only form of internalism that is immune to the NEDP, strong internalism, is a very radical and revisionary view – a large number of epistemologists would have to significantly revise their views about justification in order to accept it. Hence, either epistemologists must accept a theory that is susceptible to the NEDP or accept a very radical and revisionary view. (shrink)

Critical comments on David Papineau's idea that people find physicalism about phenomenal consciousness unbelievable because they commit what he calls the 'antipathetic fallacy'.

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This is part 1 on a paper whose final variation of parts shall be titled,”The Universal Theory of Existence: The Sashu, Pharaohs, and the al-Mahdī”. The first part of this series sets the premise for a proposed ”Theory of Everything” that will be the foundation for encompassing many different topics. Since, the beginning of time, a singularity existed. This singularity is what we call an origin point of everything. Beyond, this origin point for time is different depending on position, being (...) outside of the singularity, or the idea that multiple universes exists with different time dilation, and likely different laws. Existence in essence is centered around the idea of what is prior to the origin point of time, and in theory, what is the space-time complexity together, in regards to how civilization come to be. From a physics standpoint, there are multiple theories around this. For starters, the author of this paper coined QSOPR Theorem, MDQBT, QSICT, and how this relates to Time/Multiverse Dilation and Origin Points. Quantum Similarity on a molecular, atomic, theoretical, and chemical level is one of these vast things humanity should be trying to explore. (shrink)