Artificial intelligence (AI) has become nearly ubiquitous in modern society, from components of mobile applications to medical support systems, and everything in between. In societally impactful systems imbued with AI, there has been increasing concern related to opaque AI, that is, artificial intelligence where it is unclear how or why certain decisions are reached. This has led to a recent boom in research on “explainable AI” (XAI), or approaches to making AI more explainable and understandable to human users. In the (...) military domain, numerous bodies have argued that autonomous and AI-enabled weapon systems ought not incorporate unexplainable AI, with the International Committee of the Red Cross and the United States Department of Defense both explicitly including explainability as a relevant factor in the development and use of such systems. In this article, I present a cautiously critical assessment of this view, arguing that explainability will be irrelevant for many current and near-future autonomous systems in the military (which do not incorporate any AI), that it will be trivially incorporated into most military systems which do possess AI (as these generally possess simpler AI systems), and that for those systems with genuinely opaque AI, explainability will prove to be of more limited value than one might imagine. In particular, I argue that explainability, while indeed a virtue in design, is a virtue aimed primarily at designers and troubleshooters of AI-enabled systems, but is far less relevant for users and handlers actually deploying these systems. I further argue that human–machine teaming is a far more important element of responsibly using AI for military purposes, adding that explainability may undermine efforts to improve human–machine teamings by creating a prima facie sense that the AI, due to its explainability, may be utilized with little (or less) potential for mistakes. I conclude by clarifying that the arguments are not against XAI in the military, but are instead intended as a caution against over-inflating the value of XAI in this domain, or ignoring the limitations and potential pitfalls of this approach. (shrink)

A classic objection to autonomous weapon systems (AWS) is that these could create so-called responsibility gaps, where it is unclear who should be held responsible in the event that an AWS were to violate some portion of the law of armed conflict (LOAC). However, those who raise this objection generally do so presenting it as a problem for AWS as a whole class of weapons. Yet there exists a rather wide range of systems that can be counted as “autonomous weapon (...) systems”, and so the objection is too broad. In this article I present a taxonomic approach to the objection, examining a number of systems that would count as AWS under the prevalent definitions provided by the United States Department of Defense and the International Committee of the Red Cross, and I show that for virtually all such systems there is a clear locus of responsibility which presents itself as soon as one focuses on specific systems, rather than general notions of AWS. In developing these points, I also suggest a method for dealing with near-future types of AWS which may be thought to create situations where responsibility gaps can still arise. The main purpose of the arguments is, however, not to show that responsibility gaps do not exist or can be closed where they do exist. Rather, it is to highlight that any arguments surrounding AWS must be made with reference to specific weapon platforms imbued with specific abilities, subject to specific limitations, and deployed to specific times and places for specific purposes. More succinctly, the arguments show that we cannot and should not aim to treat AWS as if all of these shared all morally relevant features, but instead on a case-by-case basis. Thus, we must contend with the realities of weapons development and deployment, and tailor our arguments and conclusions to those realities, and with an eye to what facts obtain for particular systems fulfilling particular combat roles. (shrink)

Due to advances in military technology, there has been an outpouring of research on what are known as autonomous weapon systems (AWS). However, it is common in this literature for arguments to be made without first making clear exactly what definitions one is employing, with the detrimental effect that authors may speak past one another or even miss the targets of their arguments. In this article I examine the U.S. Department of Defense and International Committee of the Red Cross definitions (...) of AWS, showing that these definitions are far broader than some recognize, and that they therefore classify a much larger set of weapons as AWS. I then show that these broader views of AWS have implications for what moral and legal rules we might argue should be applied to such systems. I conclude by arguing there is a greater need for precision and clarity within AWS debates, in order to ensure that researchers are discussing the same weapon systems (autonomous or otherwise) when they argue for or against particular points. The purpose of this article is not to defend any specific view of AWS, nor to further any general endorsement or objection to such systems, but rather to show the importance of argumentative clarity in this debate. (shrink)

The principle of proportionality demands that a war (or action in war) achieve more goods than bads. In the philosophical literature there has been a wealth of work examining precisely which goods and bads may count toward this evaluation. However, in all of these discussions there is no mention of one of the most certain bads of war, namely the psychological harm(s) likely to be suffered by the combatants who ultimately must fight and kill for the purposes of winning in (...) conflict. This paper argues that harms to one’s own soldiers must be included in proportionality judgments, and goes on to argue that one of the most significant harms one’s soldiers face are the psychological stresses and traumas associated with combat. The arguments draw on a growing wealth of psychological literature exploring the connections between combatancy and psychological trauma, and highlight, in particular, the uniquely negative impact which killing has on a combatant’s mental well-being. The paper concludes that these factors place an almost certain and rather weighty negative weight in any proportionality calculations concerning wars with ground combatants who must fight “up close and personal”, and that for more remote warfighters, there is also evidence to show that they may suffer deep psychological harm as a result of their combat roles as well. The argument, however, does not attempt to demonstrate that these factors render war impermissible. Rather, it merely shows that these harms, or bads, which can be quite significant, must be factored into our considerations of proportionality. The arguments themselves are rather uncontroversial, but they bring to light an element in the moral calculus which is sadly overlooked in most discussions of the ethics of war. (shrink)

In international law and the ethics of war, there are a variety of actions which are seen as particularly problematic and presumed to be always or inherently wrong, or in need of some overwhelmingly strong justification to override the presumption against them. One of these actions is assassination, in particular, assassination of heads of state. In this essay I argue that the presumption against assassination is incorrect. In particular, I argue that if in a given scenario war is justified, then (...) assassination of the enemy state's leader is also justified, and in fact ought to be pursued as a means short of war. I defend this position on both consequential and deontic grounds, arguing that assassination is both more discriminate than war and serves to harm only those most responsible for the situation which justifies war in the first place. I conclude by arguing that a norm of assassination, far from being a destabilizing force, as some have argued, would in fact serve to reinforce international norms of rights and respect for persons by making clear that tyrants and would-be oppressors cannot hide behind military forces or notions of sovereignty to protect themselves from judgment and retribution. (shrink)

Autonomous weapons systems (AWS), sometimes referred to as “killer robots”, are receiving evermore attention, both in public discourse as well as by scholars and policymakers. Much of this interest is connected with emerging ethical and legal problems linked to increasing autonomy in weapons systems, but there is a general underappreciation for the ways in which existing law might impact on these new technologies. In this paper, we argue that as AWS become more sophisticated and increasingly more capable than flesh-and-blood soldiers, (...) it will increasingly be the case that such soldiers are “in the power” of those AWS which fight against them. This implies that such soldiers ought to be considered hors de combat, and not targeted. In arguing for this point, we draw out a broader conclusion regarding hors de combat status, namely that it must be viewed contextually, with close reference to the capabilities of combatants on both sides of any discreet engagement. Given this point, and the fact that AWS may come in many shapes and sizes, and can be made for many different missions, we argue that each particular AWS will likely need its own standard for when enemy soldiers are deemed hors de combat. We conclude by examining how these nuanced views of hors de combat status might impact on meaningful human control of AWS. (shrink)

Warfare is becoming increasingly automated, from automatic missile defense systems to micro-UAVs (WASPs) that can maneuver through urban environments with ease, and each advance brings with it ethical questions in need of resolving. Proponents of lethal autonomous weapons systems (LAWS) provide varied arguments in their favor; robots are capable of better identifying combatants and civilians, thus reducing "collateral damage"; robots need not protect themselves and so can incur more risks to protect innocents or gather more information before using deadly force; (...) robots can assess situations more quickly and do so without emotion, reducing the likelihood of fatal mistakes due to human error; and sending robots to war protects our own soldiers from harm. However, these arguments only point in favor of autonomous weapons systems, failing to demonstrate why such systems need be made *lethal*. In this paper I argue that if one grants all of the proponents' points in favor of LAWS, then, contrary to what might be expected, this leads to the conclusion that it would be both immoral and illegal to deploy *lethal* autonomous weapons, because the many features that speak in favor of them also undermine the need for them to be programmed to take lives. In particular, I argue that such systems, if lethal, would violate the moral and legal principle of necessity, which forbids the use of weapons that impose superfluous injury or unnecessary harm. I conclude by highlighting that the argument is not against autonomous weapons per se, but only against *lethal* autonomous weapons. (shrink)

Confirmation bias has been widely studied for its role in failures of reasoning. Individuals exhibiting confirmation bias fail to engage with information that contradicts their current beliefs, and, as a result, can fail to abandon inaccurate beliefs. But although most investigations of confirmation bias focus on individual learning, human knowledge is typically developed within a social structure. We use network models to show that moderate confirmation bias often improves group learning. However, a downside is that a stronger form of confirmation (...) bias can hurt the knowledge producing capacity of the community. (shrink)

This paper presents a Lewis-Skyrms signaling game that can exhibit a type of compositionality novel to the signaling game literature. The structure of the signaling game is motivated by an analogy to the alarm calls of putty-nosed monkeys (Cercopithecus nictitans). Putty-nosed monkeys display a compositional system of alarm calls with a semantics that is sensitive to the ordering of terms. This sensitivity to the ordering of terms has not been previously modeled with a Lewis-Skyrms signaling game literature. Signaling games are (...) valued for showing how communicative systems can arise with minimal learning tools. Simulation results show that basic (Roth-Erev) reinforcement learning is sufficient for the acquisition of a compositional signaling system sensitive to the ordering of terms. (shrink)

Psychiatry is rapidly adopting digital phenotyping and artificial intelligence/machine learning tools to study mental illness based on tracking participants’ locations, online activity, phone and text message usage, heart rate, sleep, physical activity, and more. Existing ethical frameworks for return of individual research results (IRRs) are inadequate to guide researchers for when, if, and how to return this unprecedented number of potentially sensitive results about each participant’s real-world behavior. To address this gap, we convened an interdisciplinary expert working group, supported by (...) a National Institute of Mental Health grant. Building on established guidelines and the emerging norm of returning results in participant-centered research, we present a novel framework specific to the ethical, legal, and social implications of returning IRRs in digital phenotyping research. Our framework offers researchers, clinicians, and Institutional Review Boards (IRBs) urgently needed guidance, and the principles developed here in the context of psychiatry will be readily adaptable to other therapeutic areas. (shrink)

Recently, Michael Huemer has defended the Principle of Phenomenal Conservatism: If it seems to S that p, then, in the absence of defeaters, S thereby has at least some degree of justification for believing that p. This principle has potentially far-reaching implications. Huemer uses it to argue against skepticism and to defend a version of ethical intuitionism. I employ a reductio to show that PC is false. If PC is true, beliefs can yield justification for believing their contents in cases (...) where, intuitively, they should not be able to do so. I argue that there are cases where a belief that p can behave like an appearance that p and thereby make it seem to one that p. (shrink)

A correct observation to the effect that a does not exist, where ‘a’ is a singular term, could be true on any of a variety of grounds. Typically, a true, singular negative existential is true on the unproblematic ground that the subject term ‘a’ designates something that does not presently exist. More interesting philosophically is a singular, negative existential statement in which the subject term ‘a’ designates nothing at all. Both of these contrast sharply with a singular, negative existential in (...) which the subject term is a name from fiction. I argue that such singular, negative existential statements are false. My account of fictional characters differs significantly from Kripke’s. It is shown that an objection to my account rests on a serious misunderstanding. Finally, a crucial aspect of the account is emphasized. (shrink)

To counter the imbalance in vaccine distribution during the COVID-19 pandemic, Albertsen and more recently Germani _et al_ have suggested a new system of taxation coined as ‘VaxTax’ that would force higher-income countries to fund the access of low-income and middle-income countries (LMICs) to new vaccines in times of pandemic. I will argue that this idea faces numerous challenges of ethical, sociopolitical and economical nature that may hinder any effort to solve the numerous health challenges that LMICs face. I argue (...) that while it is an interesting idea, it is neither sufficient nor will it ever be easily implemented because of socioeconomic or practical reasons. (shrink)

Two theses are central to recent work on the epistemology of disagreement: Conciliationism:?In a revealed peer disagreement over P, each thinker should give at least some weight to her peer's attitude. Uniqueness:?For any given proposition and total body of evidence, the evidence fully justifies exactly one level of confidence in the proposition. 1This paper is the product of full and equal collaboration between its authors. Does Conciliationism commit one to Uniqueness? Thomas Kelly 2010 has argued that it does. After some (...) scene-setting (?1), in ?2 we explain and criticize Kelly's argument, thereby defeating his larger argument that Conciliationism deserves no dialectical special treatment. But we argue further that Conciliationists are committed to a disjunction, one of whose disjuncts is Uniqueness, that amounts to an ?extremely strong and unobvious position? (??3?4). If we are correct, theorists should not treat Conciliationism as a default position in debates about the epistemic significance of disagreement. (shrink)

This book argues that Hume is a radical epistemic skeptic who gives only practical reasons for retaining belief in sensory beliefs and the deliverances of reason. He advises us to take a moderate approach to the demands of philosophy, since they sometimes diverge from the demands of life.

The concept of a proposition is important in several areas of philosophy and central to the philosophy of language. This collection of readings investigates many different philosophical issues concerning the nature of propositions and the ways they have been regarded through the years. Reflecting both the history of the topic and the range of contemporary views, the book includes articles from Bertrand Russell, Gottlob Frege, the Russell-Frege Correspondence, Alonzo Church, David Kaplan, John Perry, Saul Kripke, Hilary Putnam, Mark Richard, Scott (...) Soames, and Nathan Salmon. (shrink)

A thesis (“weak BCP”) nearly universally held among philosophers of probability connects the concepts of objective chance and metaphysical modality: Any prospect (outcome) that has a positive chance of obtaining is metaphysically possible—(nearly) equivalently, any metaphysically impossible prospect has zero chance. Particular counterexamples are provided utilizing the monotonicity of chance, one of them related to the four world paradox. Explanations are offered for the persistent feeling that there cannot be chancy metaphysical necessities or chancy metaphysical impossibilities. Chance is objective but (...) contrary to popular opinion it is also largely epistemic. Chancy necessities are analogous to necessary a posteriori truths. Philosophy and Phenomenological Research, Volume 99, Issue 3, Page 644-662, November 2019. (shrink)

In two often neglected passages of the Critique of Pure Reason, Kant submits that the Critique is a 'treatise' or a 'doctrine of method'. These passages are puzzling because the Critique is only cursorily concerned with identifying adequate procedures of argument for philosophy. In this book, Gabriele Gava argues that these passages point out that the Critique is the doctrine of method of metaphysics. Doctrines of method have the task of showing that a given science is indeed a science because (...) it possesses 'architectonic unity' – which happens when it realizes the 'idea' of a science. According to Gava's novel approach, the Critique establishes that metaphysics is capable of this unity, and his reading of the Critique from this perspective not only illuminates the central role of the Transcendental Doctrine of Method within it, but also clarifies the relationship between the different parts of the work. (shrink)

A new philosophical analysis is provided of the notorious Sleeping Beauty Problem. It is argued that the correct solution is one-third, but not in the way previous philosophers have typically meant this. A modified version of the Problem demonstrates that neither self-locating information nor amnesia is relevant to the core Problem, which is simply to evaluate the conditional chance of heads given an undated Monday-or-Tuesday awakening. Previous commentators have failed to appreciate the significance of the information that Beauty gains upon (...) waking, and which is relevant to the conditional chance of heads: de re acquaintance with the awakening itself and the non-locating knowledge that it is an experimental awakening. David Lewis and company are committed to several unjustifiable and unacceptable probability assessments. Previous commentators have in effect confused the information that Beauty undergoes this particular experimental awakening for the information that she undergoes some experimental awakening or other. Lewis in particular thereby illegitimately tips the scales both in favor of heads and in favor of Monday. The Sleeping Beauty Problem is equivalent to a ball-in-urn word problem in elementary probability theory. (shrink)

Tom Regan argues that human beings and some non-human animals have moral rights because they are “subjects of lives,” that is, roughly, conscious, sentient beings with an experiential welfare. A prominent critic, Carl Cohen, objects: he argues that only moral agents have rights and so animals, since they are not moral agents, lack rights. An objection to Cohen’s argument is that his theory of rights seems to imply that human beings who are not moral agents have no moral rights, but (...) since these human beings have rights, his theory of rights is false, and so he fails to show that animals lack rights. Cohen responds that this objection fails because human beings who are not moral agents nevertheless are the “kind” of beings who are moral agents and so have rights, but animals are not that “kind” of being and so lack rights. Regan argues that Cohen’s “kind” arguments fail: they fail to explain why human beings who are not moral agents have rights and they fail to show that animals lack rights. Since Cohen’s “kind” arguments are influential, I review and critique Regan’s objections . I offer suggestions for stronger responses to arguments like Cohen’s. (shrink)

What makes for a good education? What does one need to count as well-educated? Knowledge, to be sure. But knowledge is easily forgotten, and today's knowledge may be obsolete tomorrow. Skills, particularly in critical thinking, are crucial as well. But absent the right motivation, graduates may fail to put their skills to good use. In this book, Nathan King argues that intellectual virtues-traits like curiosity, intellectual humility, honesty, intellectual courage, and open-mindedness-are central to any education worthy of the name. (...) Further, such virtues are crucial to our functioning well in everyday life, in areas as diverse as personal relationships, responsible citizenship, civil discourse, and personal success. Our struggles in these areas often result from a failure to think virtuously. Drawing upon recent work in philosophy and psychology, King paints a portrait of virtuous intellectual character-and of the vices such a character opposes. Filled with examples and applications, this book introduces readers to the intellectual virtues: what they are, why they matter, and how we can grow in them. (shrink)

The history of Pythagoreanism is littered with different and incompatible interpretations. This observation directs this book towards a fundamentally historiographical rather than philological approach, setting out to reconstruct the way in which the tradition established Pythagoreanism s image.".

Examines transcendentalism as a distinct rhetorical genre concerned primarily and self-consciously with questions of power.

Faith Physics maintains a sublime timeless 'Supreme Consciousness' is the catalyst of all material creation as a 'great thought' via pure white 'light' in zero-point quantum fields. In the quantum wave/particle mass duality paradigm, energy itself traveling below the speed of light becomes particulate physical matter in accord with Einstein's famous equation of E=mc2. Using the natural laws of classical physics, quantum mechanics, and the dark matter/energy that composes 95% of our known universe, a Supreme Consciousness or Godhead manifests physical (...) creation from eternal quantum fields in a remarkable myriad of forms. This is an intellectually sound and spiritually satisfying ToE. (shrink)

Alonzo Church famously provided three principal competing criteria for “strict synonymy,” i.e., sameness of semantic content. These are his Alternatives (0), (1), and (2)—numbered in order of increasing course-grainedness of content. On Alternative (2), expressions are deemed strictly synonymous iff they are logically equivalent. This criterion seems hopeless as an account of the objects of propositional attitude. On Alternative (1), expressions are deemed synonymous iff they are λ-convertible. Alternative (1) also evidently conflicts with discourse about the attitudes. On Alternative (0), (...) expressions are deemed strictly synonymous iff they are “synonymously isomorphic” in Church’s sense. On Alternative (0), semantic content is so fine-grained that not even “Romeo loves Juliet” and “Juliet is loved by Romeo” qualify as strictly synonymous. A fourth alternative, here called “Alternative (3),” deems expressions strictly synonymous iff they are co-intensional, i.e., they have the same semantic extension with respect to the same possible worlds. This criterion’s notion of content is even more course grained than that of Alternative (2). Several objections to Alternative (3) are considered. (shrink)

The central theme of this important book is that we are paying the price of an arrogance that refuses to recognize mystery. The author invites the reader to enter into the argument that he holds with himself on a great number of problems. Written in the early 1950s, Marcel's discussion of these topics are remarkably contemporary, e.g.: * Our crisis is a metaphysical, not merely social, one. * What a man is depends partly on what he thinks he is, and (...) a materialistic philosophy turns men into things. * Can a man be free except in a free country? * Stoicism is no longer a workable philosophy because today pressure can be put on the mind as well as on the body. * Technical progress is not evil in itself, but a technique is a means that, regarded as an end, can become either an idol or an excuse for self-idolatry. State control of scientific research, leading to a concentration on new means of destruction, is a calamity. * Fanaticism is an opinion that refuses to argue, and so the fanatic is an enemy of truth. * The kind of unification that science is bringing about today is really an ironing out of differences, but the only valuable kind of unity is one that implies a respect for differences. * We must beware of thinking in terms of great numbers and so blinding ourselves to the reality of individual suffering. Our philosophical approach to being is made possible only by our practical approach to our neighbor. * We must encourage the spirit of fraternity and distrust the kind of egalitarianism that is based on envy and resentment. * No man however humble should feel that he cannot spread the light among his friends. No easy solution is offered, but the author conveys his own faith that ultimately love and intelligence will triumph. (shrink)

Raymond Aron and his Dialogues in an Age of Ideologies examines the thought and rhetoric of the most interesting thinker of the twentieth century of whom no one has heard. This book investigates Raymond Aron's conversations on politics during the Cold War with several of his more well-known interlocutors including Jean-Paul Sartre, Friedrich Hayek, and Charles de Gaulle. Through exploring these dialogues on the subjects of Marxism, freedom, and nationalism, we see the prudence of Aron's politics of understanding as well (...) as the emphasis he places on and virtue he demonstrates in public discourse. Through his dialogues, Aron shows us not only how to think politically but also how to engage in constructive public debate. He stands as a model for us to emulate in our own age of ideologies. (shrink)

Considered a classic in the philosophy of language movement known variously as the New Theory of Reference or the Direct-Reference Theory, as well as in the metaphysics of modal essentialism that is related to this philosophy of language. This award-winning book is based on the author’s doctoral dissertation.

Metaphysics, Mathematics, and Meaning brings together Nathan Salmon's influential papers on topics in the metaphysics of existence, non-existence, and fiction; modality and its logic; strict identity, including personal identity; numbers and numerical quantifiers; the philosophical significance of Godel's Incompleteness theorems; and semantic content and designation. Including a previously unpublished essay and a helpful new introduction to orient the reader, the volume offers rich and varied sustenance for philosophers and logicians.

Epistemic trespassers judge matters outside their field of expertise. Trespassing is ubiquitous in this age of interdisciplinary research and recognizing this will require us to be more intellectually modest.

Discussions of political obligation and political authority have long focused on the idea that the commands of genuine authorities constitute content-independent reasons. Despite its centrality in these debates, the notion of content-independence is unclear and controversial, with some claiming that it is incoherent, useless, or increasingly irrelevant. I clarify content-independence by focusing on how reasons can depend on features of their source or container. I then solve the long-standing puzzle of whether the fact that laws can constitute content-independent reasons is (...) consistent with the fact that some laws must fail to bind due to their egregiously unjust content. Finally I defend my understanding of content-independence against challenges and show why it retains a place of special importance for questions about the law and political obligation. Content-independence highlights that it is some feature of the law or law-making process in general that is supposed to generate moral obligations for citizens, not the merits of particular laws. (shrink)

One key desideratum of a theory of blame is that it be able to explain why we typically have differing blaming responses in cases involving significant degrees of luck. T.M. Scanlon has proposed a relational account of blame, and he has argued that his account succeeds in this regard and that this success makes his view preferable to reactive attitude accounts of blame. In this paper, I aim to show that Scanlon's view is open to a different kind of luck-based (...) objection. I then offer a way of understanding moral luck cases which allows for a plausible explanation of our differential blaming responses by appealing to the salience of certain relevant features of the action in question. (shrink)

In Frege’s Puzzle (1986), Salmon analyzed ‘a withholds believing p’ in terms of a ternary relation BEL of x believing a proposition p under a guise g. The proposed analysis is the following: There is a proposition guise g such that a grasps p by means of g but a does not stand in BEL to p and g. Sean Crawford has made a proposal for Millians to evade propositional guises through second-order belief. Specifically, in effect, Crawford’s proposes to analyze (...) the crucial notion of withheld belief instead as believing that one does not believe: a believes that a does not believe p. Crawford’s clever proposal thus avoids explicit quantification over guises. However, it is shown that the proposal is inadequate to avoid guises. The resulting notion is too weak to capture the relevant notion of withheld belief. (shrink)

To be a prisoner either in Plato's cave or in the Beast's castle is a form of existence no one would desire. And yet the story of Disney's Beauty and the Beast – in particular, the spell that imprisoned the Beast and his servants – is a tale as old as time. It is one's common human experience: one's recognition that he/she is shackled by ignorance and unfulfilled potential, and his/her desperate desire to escape. Unfortunately, however, breaking the chains and (...) ending the spell is no easy feat. For just as the Beast and his household companions represent a cave‐like imprisonment, Belle represents in her person the two ideals necessary to break the spell: love (which drew her to the castle to find her father) and beauty (which can compel the love of another). Love never happens without an encounter with beauty. (shrink)

The purpose of the conference "On Pythagoreanism", held in Brasilia in 2011, was to bring together leading scholars from all over the world to define the status quaestionis for the ever-increasing interest and research on Pythagoreanism in the 21st century. The papers included in this volume exemplify the variety of topics and approaches now being used to understand the polyhedral image of one of the most fascinating and long-lasting intellectual phenomena in Western history. Cornelli's paper opens the volume by charting (...) the course of Pythagorean studies over the past two centuries. The remaining contributions range chronologically from Pythagoras and the early Pythagoreans of the archaic period (6th-5th centuries BCE) through the classical, hellenistic and late antique periods, to the eighteenth century. Thematically they treat the connections of Pythagoreanism with Orphism and religion, with mathematics, metaphysics and epistemology and with politics and the Pythagorean way of life. (shrink)