I argue that culpable ignorance can be irreducibly collective. In some cases, it is not fair to expect any individual to have avoided her ignorance of some fact, but it is fair to expect the agents together to have avoided their ignorance of that fact. Hence, no agent is individually culpable for her ignorance, but they are culpable for their ignorance together. This provides us with good reason to think that any group that is culpably ignorant in this irreducibly collective (...) sense is non-distributively collectively responsible for subsequent unwitting acts and consequences. (shrink)

Does DBS change a patient’s personality? This is one of the central questions in the debate on the ethics of treatment with Deep Brain Stimulation (DBS). At the moment, however, this important debate is hampered by the fact that there is relatively little data available concerning what patients actually experience following DBS treatment. There are a few qualitative studies with patients with Parkinson’s disease and Primary Dystonia and some case reports, but there has been no qualitative study yet with patients (...) suffering from psychiatric disorders. In this paper, we present the experiences of 18 patients with Obsessive-Compulsive Disorder (OCD) who are undergoing treatment with DBS. We will also discuss the inherent difficulties of how to define and assess changes in personality, in particular for patients with psychiatric disorders. We end with a discussion of the data and how these shed new light on the conceptual debate about how to define personality. (shrink)

Collective moral agents can cause their own moral incapacity. If an agent is morally incapacitated, then the agent is exempted from responsibility. Due to self-induced moral incapacity, corporate responsibility gaps resurface. To solve this problem, I first set out and defend a minimalist account of moral competence for group agents. After setting out how a collective agent can cause its own moral incapacity, I argue that self-induced temporary exempting conditions do not free an agent from diachronic responsibility once the agent (...) regains its moral faculties. For collective agents, any exempting condition is potentially temporary due to the ‘malleability’ of their constitution. Therefore, in cases of self-induced moral incapacity and subsequent wrongdoing, unlike individuals, every collective agent can be (made) morally responsible for its actions even though it did not qualify as a moral agent at the time of wrongdoing. Hence, this is no reason for skepticism concerning corporate responsibility. (shrink)

According to the traditional Western concept of freedom, the ability to exercise free will depends on the availability of options and the possibility to consciously decide which one to choose. Since neuroscientific research increasingly shows the limits of what we in fact consciously control, it seems that our belief in free will and hence in personal autonomy is in trouble. -/- A closer look at the phenomenology of Obsessive-Compulsive Disorder (OCD) gives us reason to doubt the traditional concept of freedom (...) in terms of conscious control. Patients suffering from OCD experience themselves as unfree. The question is whether their lack of freedom is due to a lack of will power. Do they have too little conscious control over their thoughts and actions? Or could it be the opposite: are they exerting too much conscious control over their thoughts and actions? -/- In this chapter, we will argue that OCD patients testify to the general condition that exercising an increased conscious control over actions can in fact diminish the sense of agency rather than increase the experience of freedom. The experiences of these patients show that the traditional conception of freedom in terms of ‘free will’ has major shortcomings. There is an alternative, however, to be found in the work of Hannah Arendt. She advocates a conception of freedom as freedom in action. Combined with phenomenological insights on action, Arendt’s account of freedom helps us to get a more adequate understanding of the role of deliberation in the experience of freedom. We argue that the experience of freedom depends on the right balance between deliberate control and unreflective actions. (shrink)

In this chapter we give an overview of current and historical conceptions of the nature of obsessions and compulsions. We discuss some open questions pertaining to the primacy of the affective, volitional or affective nature of obsessive-compulsive disorder (OCD). Furthermore, we add some phenomenological suggestions of our own. In particular, we point to the patients’ need for absolute certainty and the lack of trust underlying this need. Building on insights from Wittgenstein, we argue that the kind of certainty the patients (...) strive for is unattainable in principle via the acquisition of factual knowledge. Moreover, we suggest that the patients’ attempts to attain certainty are counter-productive as their excessive conscious control in fact undermines the trust they need. (shrink)

People suffering from Obsessive-Compulsive Disorder (OCD) do things they do not want to do, and/or they think things they do not want to think. In about 10 percent of OCD patients, none of the available treatment options is effective. A small group of these patients is currently being treated with deep brain stimulation (DBS). Deep brain stimulation involves the implantation of electrodes in the brain. These electrodes give a continuous electrical pulse to the brain area in which they are implanted. (...) It turns out that patients may experience profound changes as a result of DBS treatment. It is not just the symptoms that change; patients rather seem to experience a different way of being in the world. These global effects are insufficiently captured by traditional psychiatric scales, which mainly consist of behavioural measures of the severity of the symptoms. In this article we aim to capture the changes in the patients’ phenomenology and make sense of the broad range of changes they report. For that we introduce an enactive, affordance-based model that fleshes out the dynamic interactions between person and world in four aspects. The first aspect is the patients’ experience of the world. We propose to specify the patients’ world in terms of a field of affordances, with the three dimensions of broadness of scope (‘width’ of the field), temporal horizon (‘depth’), and relevance of the perceived affordances (‘height’). The second aspect is the person-side of the interaction, that is, the patients’ self-experience, notably their moods and feelings. Thirdly, we point to the different characteristics of the way in which patients relate to the world. And lastly, the existential stance refers to the stance that patients take towards the changes they experience: the second-order evaluative relation to their interactions and themselves. With our model we intend to specify the notion of being in the world in order to do justice to the phenomenological effects of DBS treatment. (shrink)

In this essay I explore the resources Thomas Aquinas provides for enquiries concerning the psychological abilities of nonhuman animals. I first look to Aquinas’s account of divine, angelic, human, and nonhuman animal naming, to help us articulate the contours of a ‘critical anthropocentrism’ that aims to steer clear of the mistakes of a na¨ıve anthropocentrism and misconceived avowals to entirely eschew anthropocentrism. I then address the need for our critical anthropocentrism both to reject the mental-physical dichotomy endorsed by ‘folk psychology’ (...) and to articulate a more adequate ‘commonsense psychology’ that acknowledges most embodied animal behavior is observable psychological behavior. Next, I argue that we can develop Aquinas’s doctrine of estimation and conation to formulate an account of nonhuman animal action that more adequately characterizes the purposeful behaviors of nonhuman animals. To do so, we first need to recognize a wider range of nonhuman animal behaviors that are captured by Aquinas’s ‘estimative sense’, and that all of these behaviors are specified by a finite variety of particular goods confined to the animals’ environmental niches. But we also need to supplement Aquinas’s account of human and nonhuman animal agency by exploring the ontogeny and ecology of how humans and other animals become attuned to affordances within these different environmental niches. I argue that we should look to Aquinas’s account of nonhuman animal capacities in ST I-II 6-17 for subtle insights that can expand our understanding of how nonhuman animals engage in purposeful behavior by exercising analogous nonrational and imperfectly voluntary forms of intention, deliberation, choice, execution, and enjoyment. I conclude with an outline for how future enquiry can seek to explain the nonrational purposeful problem-solving competencies of chimps, canines, corvids, cetaceans, cephalopods, and other nonhuman animal species. (shrink)

Deep Brain Stimulation (DBS) is a relatively new, experimental treatment for patients suffering from treatment-refractory Obsessive Compulsive Disorder (OCD). The effects of treatment are typically assessed with psychopathological scales that measure the amount of symptoms. However, clinical experience indicates that the effects of DBS are not limited to symptoms only: patients for instance report changes in perception, feeling stronger and more confident, and doing things unreflectively. Our aim is to get a better overview of the whole variety of changes that (...) OCD patients experience during DBS treatment. For that purpose we conducted in-depth, semi-structured interviews with 18 OCD patients. In this paper, we present the results from this qualitative study.We list the changes grouped in four domains: with regard to (a) person, (b) (social) world, (c)characteristics of person-world interactions, and (d) existential stance. We subsequently provide an interpretation of these results. In particular, we suggest that many of these changes can be seen as different expressions of the same process; namely that the experience of anxiety and tension gives way to an increased basic trust and increased reliance on one’s abilities. We then discuss the clinical implications of our findings, especially with regard to properly informing patients of what they can expect from treatment, the usefulness of including CBT in treatment, and the limitations of current measures of treatment success. We end by making several concrete suggestions for further research. (shrink)

We propose to understand social affordances in the broader context of responsiveness to a field of relevant affordances in general. This perspective clarifies our everyday ability to unreflectively switch between social and other affordances. Moreover, based on our experience with Deep Brain Stimulation for treating obsessive-compulsive disorder (OCD) patients, we suggest that psychiatric disorders may affect skilled intentionality, including responsiveness to social affordances.

This article, the second of a two-part essay, outlines a solution to certain tensions in Thomist philosophical anthropology concerning the interaction of the human person’s immaterial intellectual or noetic operations with the psychosomatic sensory operations that are constituted from the formal organization of the nervous system. Continuing with where the first part left off, I argue that Thomists should not be tempted by strong emergentist accounts of mental operations that act directly on the brain, but should maintain, with Aquinas, that (...) noetic operations directly interact with psychosomatic operations. I develop a Thomist account of noetic–psychosomatic interactions that expands upon the first part’s rapprochement between the new mechanist philosophy of neuroscience and psychology and hylomorphic animalism. I argue that noetic–psychosomatic interactions are best understood as analogous to the way diverse higher and lower order psychosomatic powers interact by actualizing, coordinating, and directing the operations of other psychosomatic powers. I draw on James Ross’s arguments for the immateriality of intellectual operations as realizing definite pure functions in order to elucidate the way noetic operations uniquely actualize, coordinate, and direct the psychosomatic operations they interact with. I conclude with a conjectural sketch of how this presentation of Thomist philosophical anthropology understands the noetic and psychosomatic deficits brought about by damage to the nervous system. (shrink)

This paper investigates agents’ blameworthiness when they are part of a group that does harm. We analyse three factors that affect the scope of an agent’s blameworthiness in these cases: shared intentionality, interpersonal influence, and common knowledge. Each factor involves circumstantial luck. The more each factor is present, the greater is the scope of each agent’s vicarious blameworthiness for the other agents’ contributions to the harm. We then consider an agent’s degree of blameworthiness, as distinct from her scope of blameworthiness. (...) We suggest that an agent mostly controls her degree of blameworthiness—but even here, luck constrains what possible degrees of blameworthiness are open to her. (shrink)

I argue that agents can have duties to cooperate with one another if this increases their combined efficiency and/or efficacy in addressing ongoing collective moral problems. I call these duties cooperative duties of efficiency and efficacy. I focus particularly on collective agents and how agents ought to reason and act in the face of global moral problems. After setting out my account, I argue that a subset of cooperative duties of efficiency and efficacy of collective agents are duties of justice (...) in virtue of the roles these agents have taken up. (shrink)

Although the enactive approach has been very successful in explaining many basic social interactions in terms of embodied practices, there is still much work to be done when it comes to higher forms of social cognition. In this article, we discuss and evaluate two recent proposals by Shaun Gallagher and Daniel Hutto that try to bridge this ‘cognitive gap’ by appealing to the notion of narrative practice. Although we are enthusiastic about these proposals, we argue that (i) it is difficult (...) to see them as continuous with the enactivist notion of direct coupling, and (ii) the failure to account for folk psychological action interpretation suggests that the enactive approach should adopt a broader notion of coupling. (shrink)

According to some collectivists, purposive groups that lack decision-making procedures such as riot mobs, friends walking together, or the pro-life lobby can be morally responsible and have moral duties. I focus on plural subject- and we-mode-collectivism. I argue that purposive groups do not qualify as duty-bearers even if they qualify as agents on either view. To qualify as a duty-bearer, an agent must be morally competent. I develop the Update Argument. An agent is morally competent only if the agent has (...) sufficient positive and negative control over updating their goal-seeking states. Positive control involves the general ability to update one’s goal-seeking states, whereas negative control involves the absence of other agents with the capacity to arbitrarily interfere with updating one’s goal-seeking states. I argue that even if purposive groups qualify as plural subjects or we-mode group agents, these groups necessarily lack negative control over updating their goal-seeking states. This creates a cut-off point for groups as duty-bearers: Organized groups may qualify as duty-bearers, whereas purposive groups cannot qualify as duty-bearers. (shrink)

We whole-heartedly agree with Mecacci and Haselager(2014) on the need to investigate the psychosocial effects of deep brain stimulation (DBS), and particularly to find out how to prevent adverse psychosocial effects. We also agree with the authors on the value of an embodied, embedded, enactive approach (EEC) to the self and the mind–brain problem. However, we do not think this value primarily lies in dissolving a so-called “maladaptation” of patients to their DBS device. In this comment, we challenge three central (...) claims of the authors on the basis of our direct experience with psychosocial effects of DBS in 45 obsessive- compulsive disorder (OCD) patients treated at the AMC in Amsterdam, The Netherlands, and our indepth qualitative interviews with 18 of them (de Haan et al. 2013). We end our comment by sketching out our perspective on the practical merits of an EEC approach to DBS. (shrink)

Many philosophers accept the idea that there are duties to promote or create just institutions. But are the addressees of such duties supposed to be individuals – the members of the citizenry? What does it mean for an individual to promote or create just institutions? According to the ‘Simple View’, the citizenry has a collective duty to create or promote just institutions, and each individual citizen has an individual duty to do their part in this collective project. The simple view (...) appears to work well with regard to – you guessed it – ‘simple’ scenarios but it is riddled with further questions and problems. In this chapter, we raise five problems for the Simple View: (a) We suggest that one cannot develop a view concerning the citizenry’s duty to promote just institutions in isolation from a conception of the ontological relationship between the state and its citizens; (b) We argue that it is not obvious that the citizenry is the right entity to be attributed duties in the first place; (c) We show that a plausible account of collective duties to promote just institutions must not remain silent on the complexities and difficulties amorphous, unorganized group face in vis-à-vis collective action; (d) We contend that without allocation principles for contributory duties amongst the citizenry, or – alternatively – a method for practical deliberation that is action-guiding in collective action contexts, the claim that the citizens have a collective duty to promote just institutions remains moot; and, finally, (e) We demonstrate that the problem of reasonable disagreement is a serious threat to a collective duty to promote or create just institutions – it potentially undermines such a duty altogether and allows for conflicting contributory duties amongst the citizenry. We hope that our discussion will ultimately help improve existing theories and conceptual frameworks with a view to better understanding citizens’ obligations to promote justice under non-ideal conditions. (shrink)

Thomas Aquinas consistently defended the thesis that the separated rational soul that results from a human person’s death is not a person. Nevertheless, what has emerged in recent decades is a sophisticated disputed question between “survivalists” and “corruptionists” concerning the personhood of the separated soul that has left us with intractable disagreements wherein neither side seems able to convince the other. In our contribution to this disputed question, we present a digest of an unconsidered middle way: the separated soul is (...) an incomplete person. (shrink)

I am tasked with addressing philosophical hazards in the neuroscientific study of religion. As a philosopher concerned with the well-being of neuroscientists studying religion, I am inclined to begin with the philosophical hazards of philosophy. I am well aware of the extraordinary difficulties of both tasks, for the hazards are many and it is easy to miss the forest for the trees or the trees for the forest. Instead of focusing on one issue in great detail, I shall hang a (...) number of warning signs around a forest of issues that identify various philosophical hazards which deserve particular caution when it comes to neuroscience and religion. Since I am aiming for breadth over depth, my brief remarks on each issue shall be synoptic, non-exhaustive, contentious and suggestive for additional consideration and reflection. To redress such deficits, I have provided references for further reading. (shrink)

This paper will argue that the order and the unity of St. Thomas Aquinas’s five ways can be elucidated through a consideration of St. Thomas’s appropriation of an Avicennian insight that he used to order and unify the wisdom of the Aristotelian and Abrahamic philosophical traditions towards the existence of God. I will begin with a central aporia from Aristotle’s Metaphysics. Aristotle says that the science of first philosophy has three different theoretical vectors: ontology, aitiology, and theology. But how can (...) all three be united into a single Aristotelian science? In his Metaphysics of the Healing, Avicenna resolved the impasse by taking the ontological vector as the subject of metaphysics. He then integrated the question of the four first causes into the penultimate stage of his demonstration for the existence of God, thereby placing aitiological and theological questions among the ultimate concerns of a unified Aristotelian metaphysics. In the five ways, St. Thomas integrated Avicenna’s Aristotelian search for the first four causes into the last four of his five ways, by showing that each of the four aitiological orders terminate in an ultimate first cause that we call God. Finally, by appending the proof from the Physics to the beginning of the five ways, St. Thomas was able to show that the ultimate aim of both natural philosophy and metaphysics is the divine first principle, which is the beginning and subject of sacra doctrina. (shrink)

Is it necessary for all Christians – including Christians who are metaphysicians with demonstrative knowledge of God’s existence – to hold by faith that God exists? I shall approach this apparently straightforward question by investigating two opposing lines of interpretation of Thomas Aquinas’s own response to this question. I shall begin with two texts from Thomas that motivate two incompatible theses concerning Thomas’s doctrine of the harmony of faith and reason with respect to the existence of God. Next, I shall (...) clarify the salient points of disagreement between these two interpretations of faith and reason in Thomas Aquinas before examining dialectically a number of arguments in favor and against the respective theses of these two interpretations. In the final section I shall argue that the results of our dialectical inquiry reveal that the initial disagreement between the two positions is not irresolvable. Accordingly, I shall conclude by proposing two revised versions of the initial theses that emphasize the compatibility of these two interpretations of Thomas Aquinas’s doctrine of the harmony of faith and reason. (shrink)

In this paper, we focus on the moral responsibility of organized groups in light of historicism. Historicism is the view that any morally responsible agent must satisfy certain historical conditions, such as not having been manipulated. We set out four examples involving morally responsible organized groups that pose problems for existing accounts of historicism. We then pose a trilemma: one can reject group responsibility, reject historicism, or revise historicism. We pursue the third option. We formulate a Manipulation Condition and a (...) Guarding Condition as addendums to historicism that are necessary to accommodate our cases of group responsibility. (shrink)

The idea that human cognition is, or can be understood as, a form of computation is a useful conceptual tool for cognitive science. It was a foundational assumption during the birth of cognitive science as a multidisciplinary field, with Artificial Intelligence (AI) as one of its contributing fields. One conception of AI in this context is as a provider of computational tools (frameworks, concepts, formalisms, models, proofs, simulations, etc.) that support theory building in cognitive science. The contemporary field of AI, (...) however, has taken the theoretical possibility of explaining human cognition as a form of computation to imply the practical feasibility of realising human(-like or -level) cognition in factual computational systems, and the field frames this realisation as a short-term inevitability. Yet, as we formally prove herein, creating systems with human(-like or -level) cognition is intrinsically computationally intractable. This means that any factual AI systems created in the short-run are at best decoys. When we think these systems capture something deep about ourselves and our thinking, we induce distorted and impoverished images of ourselves and our cognition. In other words, AI in current practice is deteriorating our theoretical understanding of cognition rather than advancing and enhancing it. The situation could be remediated by releasing the grip of the currently dominant view on AI and by returning to the idea of AI as a theoretical tool for cognitive science. In reclaiming this older idea of AI, however, it is important not to repeat conceptual mistakes of the past (and present) that brought us to where we are today. (shrink)

The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...) of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation. (shrink)

The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...) and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)

This paper has a twofold aim. On the one hand, we will discuss the much debated question of the source of normativity (which traditionally has nature and practical reason as the two main contenders to this role) and propose a new answer to it. Second, in answering this question, we will present a new account of practical wisdom, which conceives of the ethical virtues as ultimately unified in the chief virtue of phronesis, understood as ethical expertise. To do so, we (...) will first criticize the main current view of phronesis and its bearer (the phronimos), then offer another view of the nature of phronesis and of its relation to the other ethical virtues. Our proposal should not be intended as an interpretation of Aristotle’s own view; rather, it should be seen as a broadly Aristotelian theoretical proposal, which we believe can satisfyingly address most of the problems that afflict the more traditional accounts of practical wisdom. In section 2 of this paper, after criticizing first-nature naturalistic views of moral virtue, we take practical reason to be the cornerstone of second-nature naturalistic views; in section 3, we will outline criticisms to which, in our view, the traditional views of phronesis are ill-suited to respond, and, in section 4, we will outline our view of phronesis as ethical expertise – a view which in our view is immune to the above-mentioned criticisms – by spelling out the three main tenets of phronesis as ethical expertise: a conceptual thesis, an epistemic thesis, and the educational implications of the two. Finally, we will support our proposal with some empirical evidence taken from cognitive science. (shrink)

According to the received view, genuine mathematical justification derives from proofs. In this article, I challenge this view. First, I sketch a notion of proof that cannot be reduced to deduction from the axioms but rather is tailored to human agents. Secondly, I identify a tension between the received view and mathematical practice. In some cases, cognitively diligent, well-functioning mathematicians go wrong. In these cases, it is plausible to think that proof sets the bar for justification too high. I then (...) propose a fallibilist account of mathematical justification. I show that the main function of mathematical justification is to guarantee that the mathematical community can correct the errors that inevitably arise from our fallible practices. (shrink)

Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for a (...) taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations. I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading. (shrink)

The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used (...) in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect different pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a specific practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology. (shrink)

The aim of this article is to explain why knot diagrams are an effective notation in topology. Their cognitive features and epistemic roles will be assessed. First, it will be argued that different interpretations of a figure give rise to different diagrams and as a consequence various levels of representation for knots will be identified. Second, it will be shown that knot diagrams are dynamic by pointing at the moves which are commonly applied to them. For this reason, experts must (...) develop a specific form of enhanced manipulative imagination, in order to draw inferences from knot diagrams by performing epistemic actions. Moreover, it will be argued that knot diagrams not only can promote discovery, but also provide evidence. This case study is an experimentation ground to evaluate the role of space and action in making inferences by reasoning diagrammatically. (shrink)

Criteria of acceptability for mathematical proofs are field-dependent. In topology, though not in most other domains, it is sometimes acceptable to appeal to visual intuition to support inferential steps. In previous work :829–842, 2014; Lolli, Panza, Venturi From logic to practice, Springer, Berlin, 2015; Larvor Mathematical cultures, Springer, Berlin, 2016) my co-author and I aimed at spelling out how topological proofs work on their own terms, without appealing to formal proofs which might be associated with them. In this article, I (...) address two criticisms that have been raised in Tatton-Brown against our approach: that it leads to a form of relativism according to which validity is equated with social agreement and that it implies an antiformalizability thesis according to which it is not the case that all rigorous mathematical proofs can be formalized. I reject both criticisms and suggest that our previous case studies provide insight into the plausibility of two related but quite different theses. (shrink)

Mathematical diagrams are frequently used in contemporary mathematics. They are, however, widely seen as not contributing to the justificatory force of proofs: they are considered to be either mere illustrations or shorthand for non-diagrammatic expressions. Moreover, when they are used inferentially, they are seen as threatening the reliability of proofs. In this paper, I examine certain examples of diagrams that resist this type of dismissive characterization. By presenting two diagrammatic proofs, one from topology and one from algebra, I show that (...) diagrams form genuine notational systems, and I argue that this explains why they can play a role in the inferential structure of proofs without undermining their reliability. I then consider whether diagrams can be essential to the proofs in which they appear. (shrink)

The distinction between propositional and doxastic justification is well-known among epistemologists. Propositional justification is often conceived as fundamental and characterized in an entirely apsychological way. In this chapter, I focus on beliefs based on deductive arguments. I argue that such an apsychological notion of propositional justification can hardly be reconciled with the idea that justification is a central component of knowledge. In order to propose an alternative notion, I start with the analysis of doxastic justification. I then offer a notion (...) of propositional justification, intersubjective propositional justification, that is neither entirely apsychological nor idiosyncratic. To do so, I argue that to be able to attribute propositional justification to a subject, we have to consider her social context as well as broad features of our human cognitive architecture. (shrink)

If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. Their ability to (...) recognize whether a putative proof is correct is not infallible. In most cases, disagreement over the correctness of a putative proof is, however, evanescent. Once an error is spotted and communicated, the disagreement disappears. But this is not always the case. Sometimes it is recalcitrant; that is, it persists over time. In order to zoom in on this type of disagreement and explain its very possibility, we focus on a single case study: a decades-long (1921-1949) controversy between Federigo Enriques and Francesco Severi, two prominent exponents of the Italian school of algebraic geometry. We suggest that the instability of the mathematical community to which they belonged can be explained by the gap between an abstract criterion of rigor and local criteria of acceptability. It is this instability that made the existence of recalcitrant disagreement over putative proofs possible. We do not condemn speculative mathematics but rather its pretense of being rigorous mathematics. In this respect, we show that the overly self-confident Severi and the more intuitive, visionary Enriques had a completely different attitude. (shrink)

Giacomo Leopardi, a major Italian poet of the nineteenth century, was also an expert in evil to whom Schopenhauer referred as a “spiritual brother.” Leopardi wrote: “Everything is evil. That is to say, everything that is, is evil; that each thing exists is an evil; each thing exists only for an evil end; existence is an evil.” These and other thoughts are collected in the Zibaldone, a massive collage of heterogeneous writings published posthumously. Leopardi’s pessimism assumes a polished form in (...) his literary writings, such as Dialogue between Nature and an Islander (1824)—an invective against nature and the suffering of creatures within it. In his last lyric, Broom, or the flower of the desert (1836), Leopardi points to the redeeming power of poetry and to human solidarity as placing at least temporary limits on the scope of evil. (shrink)

According to a widely held view in the philosophy of mathematics, direct inferential justification for mathematical propositions (that are not axioms) requires proof. I challenge this view while accepting that mathematical justification requires arguments that are put forward as proofs. I argue that certain fallacious putative proofs considered by the relevant subjects to be correct can confer mathematical justification. But mathematical justification doesn’t come for cheap: not just any argument will do. I suggest that to successfully transmit justification an argument (...) must satisfy specific standards, some of which are social. I contrast my view with Huemer’s inferential conservatism, which makes mathematical justification too easy to get. Although in this article I focus on mathematical inferential beliefs, the view on offer generalizes to other inferential beliefs. (shrink)

The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th-century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive conception of (...) rigor and intuition. Unlike what is often assumed today, from their perspective, rigor is neither opposed to intuition nor understood as a unitary phenomenon – Enriques distinguishes between small-scale rigor and large-scale rigor and Severi between formal rigor and substantial rigor. Finally, we turn to the notion of mathematical objectivity. We draw from our case study in order to advance a multi-dimensional analysis of objectivity. Specifically, we suggest that various types of rigor may be associated with different conceptions of objectivity: namely, objectivity as faithfulness to facts and objectivity as intersubjectivity. (shrink)

Paying attention to the inner workings of mathematicians has led to a proliferation of new themes in the philosophy of mathematics. Several of these have to do with epistemology. Philosophers of mathematical practice, however, have not (yet) systematically engaged with general (analytic) epistemology. To be sure, there are some exceptions, but they are few and far between. In this chapter, I offer an explanation of why this might be the case and show how the situation could be remedied. I contend (...) that it is only by conceiving the knowing subject(s) as embodied, fallible, and embedded in a specific context (along the lines of what has been done within social and feminist epistemology) that we can pursue an epistemology of mathematics sensitive to actual mathematical practice. I further suggest that this reconception of the knowing subject(s) does not force us to abandon the traditional framework of epistemology in which knowledge requires justified true belief. It does, however, lead to a fallible conception of mathematical justification that, among other things, makes Gettier cases possible. This shows that topics considered to be far removed from the interests of philosophers of mathematical practice might reveal to be relevant to them. (shrink)

Computational tools might tempt us to renounce complete cer- tainty. By forgoing of rigorous proof, we could get (very) probable results for a fraction of the cost. But is it really true that proofs (as we know and love them) can lead us to certainty? Maybe not. Proofs do not wear their correct- ness on their sleeve, and we are not infallible in checking them. This suggests that we need help to check our results. When our fellow mathematicians will be (...) too tired or too busy to scrutinize our putative proofs, computer proof assistants could help. But feeding a mathematical argument to a computer is hard. Still, we might be willing to undertake the endeavor in view of the extra perks that formalization may bring—chiefly among them, an enhanced mathematical understanding. (shrink)

John P. Burgess is the John N. Woodhull Professor of Philosophy at Princeton University. He obtained his Ph.D. from the Logic and Methodology program at the University of California at Berkeley under the supervision of Jack H. Silver with a thesis on descriptive set theory. He is a very distinguished and influential philosopher of mathematics. He has written several books: A Subject with No Object (with G. Rosen, Oxford University Press, 1997), Computability and Logic (with G. Boolos and R. Jeffrey, (...) 5th ed., Cambridge University Press, 2007), Fixing Frege (Princeton University Press, 2005), Mathematics, Models, and Modality (Cambridge University Press, 2007), Philosophical Logic (Princeton University Press, 2009), Truth (with A. G. Burgess, Princeton University Press, 2011), Saul Kripke: Puzzles & Mysteries (Polity Press, 2012), Rigor & Structure (Oxford University Press, 2015), and Set Theory (Cambridge Elements, Forthcoming). In this interview, Professor Burgess talks about how his interests in mathematics and philosophy developed and relate to each other. He then answers questions about specific themes of his philosophical work, with a focus on issues pertaining to philosophy of mathematics. (shrink)

In this chapter, we will offer a sketch of the state of the art as concerns existing accounts of virtue acquisition in relation to automaticity. In particular, we will focus on the so-called “skill model,” which we aim to improve by questioning its rather common underlying dualistic picture of the mind. Then we will propose an account of skillful emotions by identifying the features that make them both automatic and embedded in an intelligent practice. Finally, we will show how this (...) view can help the skill model by offering a better description of emotion shaping in virtue acquisition. By doing so, we will contend that emotions contribute autonomously and actively to the skillfulness of the habits in which they are embedded. (shrink)

Rigorous proof is supposed to guarantee that the premises invoked imply the conclusion reached, and the problem of rigor may be described as that of bringing together the perspectives of formal logic and mathematical practice on how this is to be achieved. This problem has recently raised a lot of discussion among philosophers of mathematics. We survey some possible solutions and argue that failure to understand its terms properly has led to misunderstandings in the literature.

In the last few decades, the historiographical categories rationalism and empiricism have been criticized for their limitations to explain the complex positions and the links held by the philosophers tradiotnally attached to them. This narrative was firstly conceived by Kantian German historians and began to become standard at the turn of the twentieh century. Nonetheless, nineteenth-century French historiography developed other narratives by which early modern philosophers were classified according to alternative criteria. In the first edition of Histoire comparée des systémes (...) de philosophie (1804), Joseph-Marie Degérando distinguishes three first-order early modern schools founded by Bacon, Descartes and Leibniz, respectively. Degérando introduces the empiricism and rationalism distinction as one among others, and not as the fundamental one. In addition, he separates empiricism from experimental philosophy. The last one, along with speculative philosophy, is said to conciliate senses and reason. As a result, this account offers philosophical groupings different from those constructed by the standard narrative. Furthermore, it draws on labels and classification criteria which were part of the early modern philosophical discourse. (shrink)

La idea de que la tarea de la ciencia consiste en dar cuenta de las leyes de la naturaleza comenzó a establecerse durante el siglo XVII mientras se estaba delineando la nueva imagen de la ciencia y de la naturaleza. Si bien distintos estudios historiográficos coinciden en situar el origen del concepto moderno de ley de la naturaleza en este siglo, sus interpretaciones son divergentes en varios sentidos. En este trabajo, me dedicaré en primer lugar a repasar brevemente y analizar (...) en forma crítica los resultados de estos estudios historiográficos, agrupándolos en cuatro grandes líneas de lectura. En segundo lugar y a modo de conclusión a partir de lo arrojado por esos estudios, enumeraré los factores fundamentales que considero ineludibles para realizar un abordaje historiográfico satisfactorio y completo de este problema. (shrink)

The occasion for this dialogue on Elisabeth Anscombe’s legacy for twenty-first-century ethics came with the publication in Italian of the collection of her ethical writings (G. E. M. Anscombe, Scritti di etica con un saggio di Peter Geach, a cura di S. Cremaschi, Morcelliana, Brescia 2022). In addition to making Anscombe’s ethical writings accessible to the Italian public, the book brings together her contribution to practical philosophy to its full extent for the first time. Vaccarezza's essay discusses Anscombe’s critique of (...) the modern law-based view of ethics. Magri’s contribution focuses on Anscombe’s anti-anti-naturalism, aiming to unearth the twofold agenda in her project of meta-critique of modern moral philosophy. De Anna's paper sets out to examine the role of Wittgensteinian ways of thinking in Anscombe’s proposed restructuring of modern ethics. (shrink)

Os escritos de Francis Bacon dedicados à filosofia abundam em imagens, metáforas, comparações e alegorias destinadas a ilustrar e apresentar com eloquência suas ideias. Solidamente formado na cultura humanista de seu tempo, Bacon adotou com destreza os recursos da retórica e nutriu-se de um amplo espectro da literatura clássica greco-latina, assim como também dos escritos bíblicos. Em especial, a mitologia clássica (a que dedicou seu De sapientia veterum (1609) - Da sabedoria dos antigos) foi um de seus recursos predilteos na (...) hora de valer-se de alegorias para tornar acessível a um público amplo e não especializado os conteúdos mais inovadores, profundos e abstrusos de sua filosofia.1 Tudo isso converte algumas de suas obras em excelentes peças da literatura filosófica, nas quais Bacon põe em prática sua grande plasticidade como escritor, que, delicadamente e sem tropeços, transporta seus leitores da beleza da poesia e fantasia para os conceitos mais abstratos, sempre em busca de representar suas ideias filosóficas e de transformar a realidade por meio delas. Neste texto, apresentarei brevemente algumas das imagens pelas quais ele quis retratar aspectos fundamentais do seu projeto de restauração do saber. (shrink)

One of the main philosophical works by Alexander of Aphrodisias, De principiis, is lost in its original Greek text, but it is preserved in three extant Medieval Semitic versions, one in Syriac and two in Arabic, which were written in the Near East between 500 and 950 AD. These versions are not totally identical and, as we have shown in 2012, they are in a rather complex textual relationship. As we will show in this article, a tentative reconstruction of the (...) lost text should be based upon an attentive and point‑to‑point comparative analysis of some aspect of all three versions. We have tentatively called the abore way “critical translation”. (shrink)

¿Qué entendemos hoy por canon en el ámbito de la filosofía? El sentido más habitual de esta palabra remite a una lista o catálogo de autores y de textos que se consideran fundamentales con respecto a un determinado recorte de la filosofía y a veces a la filosofía en su totalidad. Este sentido de canon, por extensión, suele tener una connotación de norma, precepto o regla, en la medida en que la lista de obras o autores es juzgada como necesaria (...) para alcanzar un conocimiento o dominio de la filosofía. Está ligado con la formación de los filósofos en el marco de una institución de enseñanza. El propósito de este trabajo es deconstruir este sentido de canon, considerando sus elementos como piezas de un modelo que puede armarse, desarmarse y rearmarse. Antes de esta deconstrucción, será necesario hablar del lugar donde se construye y delinear cuáles son sus rasgos definitorios, incluyendo sus modos de construcción y reproducción. A ello estará dedicada la primera sección de este texto. Las tres secciones que siguen se concentrarán en cada de las piezas básicas que constituyen los cánones filosóficos: los autores, las obras y los temas. (shrink)