I propose a novel metaphysical explanation of identity and distinctness facts called the Modal Proposal. According to the Modal Proposal, for each identity fact – that is, each fact of the form a=b – that fact is metaphysically explained by the fact that it is necessary that the entities involved are indiscernible, and for each distinctness fact –that is, each fact of the form a≠b – that fact is metaphysically explained by the fact that it is possible for the entities (...) involved to be discernible. I argue that the Modal Proposal has greater payoffs at less cost than any of its competitors. It gives simple, uniform, and intuitive explanations of identity and distinctness that conserve longstanding philosophical insights about identity that go back to Leibniz. It does this while making our fundamental base more parsimonious, determining whether controversial cases of identity or distinctness are possible, and expanding our understanding of these central philosophical relations. It does all this while avoiding controversial ontological commitments. (shrink)

Initially, you judge that p. You then learn that most experts disagree. All things considered, you believe that the experts are probably right. Still, p continues to seem right to you, in some sense. You don’t yet see what, if anything, is wrong with your original reasoning. In such a case, we’ll say that you are ‘inclined’ toward p. This paper explores various roles that this state of inclination can play, both within epistemology and more broadly. Specifically, it will be (...) argued that: (i) inclinations can promote the accuracy of inquiring groups; (ii) they can support rational participation within philosophy despite pervasive disagreement; (iii) they allow us to make sense of an important way in which two people can continue to disagree even after they ‘conciliate’; (iv) inclinations carry information about individuals’ independent judgments and for this reason must be accounted for when updating on the opinions of others; (v) inclinations are connected to understanding in a way that belief is not; (vi) and awareness of the inclination-belief distinction enables us to respond to a provocative challenge purporting to show that critical thinking, or ‘thinking for oneself’, typically reduces expected accuracy and hence should be discouraged. (shrink)

Six people are in trouble. We can save five of them or just the sixth. What should we do? John Taurek (1977) defends a radical view: We are not required to save the greater number. Taurek's paper has persuaded some. But even the unpersuaded agree that Taurek poses a deep and important challenge: From where does the priority of the many derive? It seems difficult, or even impossible, to convince someone who denies the importance of the numbers... to care about (...) the numbers. That’s what this paper aims to do. It will argue that the priority of the many follows, with minimal other assumptions, from something all should accept: the modest premise that if we can improve one person's chance of survival—without affecting anyone else—we should. (shrink)

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

Should we believe our controversial philosophical views? Recently, several authors have argued from broadly conciliationist premises that we should not. If they are right, we philosophers face a dilemma: If we believe our views, we are irrational. If we do not, we are not sincere in holding them. This paper offers a way out, proposing an attitude we can rationally take toward our views that can support sincerity of the appropriate sort. We should arrive at our views via a certain (...) sort of ‘insulated’ reasoning – that is, reasoning that involves setting aside certain higher-order worries, such as those provided by disagreement – when we investigate philosophical questions. (shrink)

Prevailing opinion—defended by Jason Brennan and others—is that voting to change the outcome is irrational, since although the payoffs of tipping an election can be quite large, the probability of doing so is extraordinarily small. This paper argues that prevailing opinion is incorrect. Voting is shown to be rational so long as two conditions are satisfied: First, the average social benefit of electing the better candidate must be at least twice as great as the individual cost of voting, and second, (...) the chance of casting the decisive vote must be at least 1/N, where N stands for the number of citizens. It is argued that both of these conditions are often true in the real world. (shrink)

Eco-Rational Education proposes an educational response to climate change, environmental degradation, and desctructive human relations to ecology through the delivery of critical land-responsive environmental education. -/- The book argues that education is a powerful vehicle for both social change and cultural reproduction. It proposes that the prioritisation and integration of environmental education across the curriculum is essential to the development of ecologically rational citizens capable of responding to the environmental crisis and an increasingly changing world. Using philosophical analysis, particularly environmental (...) philosophy, pragmatism, and ecofeminism, the book develops an understanding of contemporary issues in education, especially inquiry-based learning as pedagogy, diversifying knowledge, environmental and epistemic justice, climate change education, and citizenship education. -/- Eco-Rational Education will be of interest to researchers and post-graduate students of social and political philosophy, educational philosophy, as well as environmental philosophy, ethics, and teacher education. (shrink)

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...) primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)

This paper is about how to aggregate outside opinion. If two experts are on one side of an issue, while three experts are on the other side, what should a non-expert believe? Certainly, the non-expert should take into account more than just the numbers. But which other factors are relevant, and why? According to the view developed here, one important factor is whether the experts should have been expected, in advance, to reach the same conclusion. When the agreement of two (...) (or of twenty) thinkers can be predicted with certainty in advance, their shared belief is worth only as much as one of their beliefs would be worth alone. This expectational model of belief dependence can be applied whether we think in terms of credences or in terms of all-or-nothing beliefs. (shrink)

Place-based education is founded on the idea that the student’s local community is one of their primary learning resources. Place-based education’s underlying educational principle is that students need to first have an experiential understanding of the history, culture, and ecology of the environment in which they are situated before tackling broader national and global issues. Such attempts are a step in the right direction in dealing with controversial issues in a democracy by providing resources for synthesising curriculum though theory (curriculum (...) content, including traditional subjects) and practice (practical learning as experiential education). Nevertheless, many place-based accounts discount Indigenous conceptions of place, which are integral to Indigenous ways of knowing, being and doing, especially in relation to the ontological relationship to Land and Country. Indigenous philosophy has the potential to inform what place-based education means by students developing a ‘sense of place’ when engaging with local communities as their ‘own’ place. In this article we re-imagine the community of inquiry as a place-responsive pedagogy by learning from Indigenous philosophy, and recentring Indigenous notions of place in experiential learning. In addition to exploring the pedagogical potential of a place-responsive account of the community of inquiry, we look to the implications for teacher preparation. (shrink)

At first glance, it looks like Aristotle can’t make up his mind about the ethical or moral status of non-human animals in his ethical treatises. Somewhat infamously, the Nicomachean Ethics claims that “there is neither friendship nor justice towards soulless things, nor is there towards an ox or a horse” (EN 8.11.1161b1–2). Since Aristotle thinks that friendship and justice are co-extensive (EN 8.9.1159b25–32), scholars have often read this passage to entail that humans have no ethical obligations to non-human animals. By (...) contrast, although the Eudemian Ethics denies that non-human animals can participate in “primary” friendships, EE 7.2 claims that “the other kinds of friendship are also found among animals; and it is evident that utility is present to some extent among them both in relation to humankind, in the case of tame animals, and in relation to each other” (EE 7.2.1236b3–11). Does the Nicomachean account of non-human animals contradict that of the Eudemian Ethics? Ultimately, I believe the Nicomachean account is consistent with the Eudemian account. Nonetheless, I argue that Aristotle’s treatment of non-human animals differs significantly in the two texts. My chapter explores this difference in greater detail and considers the ramifications of such a difference for our understanding of Aristotle’s place in the philosophical tradition concerning the ethical status of non-human animals. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...) successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s. (shrink)

Conciliationism faces a challenge that has not been satisfactorily addressed. There are clear cases of epistemically significant merely possible disagreement, but there are also clear cases where merely possible disagreement is epistemically irrelevant. Conciliationists have not yet accounted for this asymmetry. In this paper, we propose that the asymmetry can be explained by positing a selection constraint on all cases of peer disagreement—whether actual or merely possible. If a peer’s opinion was not selected in accordance with the proposed constraint, then (...) it lacks epistemic significance. This allows us to distinguish the epistemically significant cases of merely possible disagreement from the insignificant ones. (shrink)

There is a well-known moral quandary concerning how to account for the rightness or wrongness of acts that clearly contribute to some morally significant outcome – but which each seem too small, individually, to make any meaningful difference. One consequentialist-friendly response to this problem is to deny that there could ever be a case of this type. This paper pursues this general strategy, but in an unusual way. Existing arguments for the consequentialist-friendly position are sorites-style arguments. Such arguments imagine varying (...) a subject’s predicament bit by bit until it is clear that a relevant difference has been achieved. The arguments offered in this paper are structurally different, and do not rely on any sorites series. For this reason, they are not vulnerable to objections that have been leveled against the sorites-style arguments. (shrink)

Pascal famously wrote that Plato and Aristotle “ont écrit de politique c'était comme pour régler un hôpital de fous.” I argue that the best way of understanding Aristotle’s political thought is to see that although Pascal may be right about Plato, he is completely wrong about Aristotle—and that that difference in their political philosophies may provide resources for challenges we face today. The first five chapters of the book argue that Aristotle envisions the paradigmatic case in which the ethical virtue (...) of justice operates as that between citizens within one and the same political community. Just like the virtue of courage is one that paradigmatically applies to a citizen-solider defending his polis, the virtue of justice applies to the citizen-jurist and the citizen-assemblyman, exercising the virtue within the domains of the assembly and the law-courts. The last three chapters argue that Aristotle conceives of justice as an institutional characteristic paradigmatically in the case of politeiai, both in how they are governed and which citizens they incorporate into the governing of the political community. The final chapter maps out how Aristotle understands justice in three domains that are significantly different than paradigmatic citizen roles. I look at what place, if any, Aristotle has for justice between human and non-human animals, within the household (specifically, towards slaves, children, and female spouses), and between poleis (or “inter-nationally”). (shrink)

What should a person do when, through no fault of her own, she ends up believing a false moral theory? Some suggest that she should act against what the false theory recommends; others argue that she should follow her rationally held moral beliefs. While the former view better accords with intuitions about cases, the latter one seems to enjoy a critical advantage: It seems better able to render moral requirements ‘followable’ or ‘action-guiding.’ But this tempting thought proves difficult to justify. (...) Indeed, whether it can be justified turns out to depend importantly on the rational status of epistemic akrasia. Furthermore, it can be argued, from premises all parties to the moral ignorance debate should accept, that rational epistemic akrasia is possible. If the argument proves successful, it follows that a person should sometimes act against her rationally held moral convictions. (shrink)

Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.

Classical Sparta is an enigma in many ways, but for ancient and contemporary political theorists it is especially intriguing insofar as its politeia (or its educational/political/social system or “constitution”) produced a city-state that was both the hegemon of all other Greek city-states, for instance during the 5th century Persians wars, but was also ignobly defeated by Thebes at the battle of Leuctra in 371, slightly more than a century later, after which its hegemony collapsed and its subject population of helots (...) won a war of emancipation. How did Sparta field citizen-soldiers in the 5th century who were without parallel in their bravery and military prowess? And why did Sparta, perhaps under the same politeia, collapse just over a century later? Xenophon, Plato, Aristotle, and Plutarch searched for answers to such questions in the Spartan public educational program, its mixed constitutions, and its apparently militaristic goal and orientation. Such 4th century intellectuals (and Plutarch, writing in the 1st century CE) debated whether Sparta’s collapse was the result of deep-rooted problems within its Lycurgan constitution or in Sparta’s subsequent departure from that constitution; there also is significant debate concerning the education and roles of women within Spartan society. (shrink)

Jaspers’s binary distinction between understanding and explanation has given way first to a proliferation of explanatory levels and now, in John Campbell’s recent work, to a conception of explanation with no distinct levels of explanation and no inbuilt rationality requirement. I argue that there is still a role for understanding in psychiatry and that is to demystify the assumption that the states it concerns are mental. This role can be fulfilled by placing rationality at the heart of understanding without a (...) commitment to the attempt to use rationality to shed light on interpretation and mindedness as though from outside those notions. Delusions still present a significant challenge to philosophical attempts at understanding, but this merely reflects the genuine clinical difficulties such states present. (shrink)

In The Boundary Stones of Thought, Rumfitt defends classical logic against challenges from intuitionistic mathematics and vagueness, using a semantics of pre-topologies on possibilities, and a topological semantics on predicates, respectively. These semantics are suggestive but the characterizations of negation face difficulties that may undermine their usefulness in Rumfitt’s project.

Roger White (2015) sketches an ingenious new solution to the problem of induction. He argues from the principle of indifference for the conclusion that the world is more likely to be induction- friendly than induction-unfriendly. But there is reason to be skeptical about the proposed indifference-based vindication of induction. It can be shown that, in the crucial test cases White concentrates on, the assumption of indifference renders induction no more accurate than random guessing. After discussing this result, the paper explains (...) why the indifference-based argument seemed so compelling, despite ultimately being unsound. (shrink)

Il est communément admis, aussi bien par les spécialistes que les non-spécialistes de la Grèce antique, qu'Aristote considère le barbaros ou l'autre Non-Grec comme radicalement distinct des Grecs (peut-être même racialement) et intrinsèquement inférieur à eux. Cette idée puise sa source dans ses remarques sur l'esclavage, sur les institutions politiques non grecques, sur les caractères naturels ou ethniques. Mais l’idée la plus répandue manque de nuance, et est souvent affirmée à tort en faisant l’économie d’un examen attentif des bases textuelles. (...) Cet article, qui est une sous-section d'un essai plus vaste sur les institutions politiques non-grecques (comme le traitement par Aristote de la politeia de Carthage dans Politique 2.11), soutient qu'Aristote ne distingue pas catégoriquement (et encore moins racialement) les Grecs et les Non-Grecs, ni n’approuve l’assertion selon laquelle les Grecs sont supérieurs aux non-Grecs. En effet, Aristote s'appuie régulièrement sur des institutions politiques non-grecques dans sa propre formulation de la meilleure constitution. (shrink)

Professor Garver’s “Living Well and Living Together” sheds light on one of the more confusing sections in Aristotle’s Politics, namely the discussion of the best way of life for individuals and city in Politics VII.1-3. At a distance, the conclusion of Aristotle’s remarks seem relatively clear: He endorses the claim that the most choice-worthy life and happiness of a city and an individual are the same. Further, the implications of such a claim for Aristotle’s political philosophy also seem clear: Aristotle’s (...) view of an “internally active” city amounts to a thorough critique of expansionist imperialism. But how these two surface level views—the best way of life for a city and the critique of imperialism—fit together is less than perspicuous. Garver’s paper goes after this text through the lens of two problems. First, Aristotle apparently argues from the nature of the best way of life or happiness for an individual to the best way of life for a city. But as Aristotle himself points out in his critique of the Republic, such an argument seems in danger of falling into a fallacy of composition. In response to such a perceived fallacy, Garver argues that Aristotle incorporates into his argument a third thing—what is the best life for a citizen or what Garver calls “common life” (p. 5, 6, of Garver’s text)—which mediates between the best life for a separate individual and for the city. As Garver puts it at one point “the best life for the citizen will be our means for discovering those [other] two” (p. 5, Garver’s text). The second problem which Garver raises concerns Aristotle’s apparent inference from energeiai to dunameis. Aristotle’s argument in Politics VII.1-3 begins from the claim that a city and individual have the same kind of happiness—namely, a sort of energeia—and extends to a claim about the structure which serves as the basis of that activity. The problem, according to Garver, is that “the virtues of the state cannot be energeiai of that part of its soul, because states don’t have souls” (p. 6, Garver’s text). The comparison between city and individual works—if it does work—only if “the psychological aspects of the virtue central to the Ethics become politically irrelevant” (p. 7, Garver’s text). Thus, Garver suggests that Aristotle’s comparison of city and individual comes at a cost, viz. that “Aristotle can talk about states being virtuous and happy only because of this psychological superficiality” (p. 9, Garver’s text). (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions of (...) the connectives in question. (shrink)

At least since Foster (2002), scholars interested in Aristotle’s views about environmental ethics have focused primarily upon his teleological account of non-human animals as the basis for an Aristotelian environmental virtue ethics. But although Aristotle’s scientific account of non-human animals can serve as the basis for a form of environmental ethics akin to “nature preservation,” one finds in his account of “household management” (or oikonomikē) a very different sort of environmental ethic, one that looks much more like a form of (...) “nature conservation.” My paper argues that for Aristotle, oikonomikē is indeed both “environmental” and an “ethic.” The first part of my chapter shows that oikonomikē is fundamentally environmental insofar as it concerns what Aristotle in Politics 1.8 calls “property acquisition in accord with nature” or “true wealth” (Pol. 1.8.1256b26–27, 30–31), namely the prudential use of natural resources in a way that recognizes the dependence of ways of life upon different habitats or environments. The second part of my chapter shows that oikonomikē is also an “ethic” insofar as it embeds three different kinds of limit on the use of animate and inanimate natural resources, namely that natural resource use is subordinate to expertise about the happiness of the political community (or what Aristotle calls “politics” [πολιτική]); that natural resource use, as an instrumental good, is limited and governed by the craft or expertise of oikonomikē; and that notions of unlimited commercial “wealth acquisition” (χρηματιστική) are based on ethically problematic ways of life. After showing that Aristotle’s account of oikonomikē is indeed an environmental ethic, the third part of my chapter considers the objection that oikonomikē is a weak environmental ethic insofar as it is exploitatively or axiological anthropocentric. I respond that Aristotle’s account of non-human animal domestication provides conceptual resources for thinking about non-human animals as subordinate members in one’s ecological-political community, especially with respect to his invocation of the craft analogy (in the example of shepherds) and inter-species utility friendships. Although Aristotle has multiple sources relevant for understanding environmental ethics, his account of oikonomikē is both a neglected source and a potentially fruitful one. (shrink)

In the Symposium, Plato has Socrates claim that the priestess Diotima once claimed that Eros is a lover of wisdom or someone who is “in between wisdom and ignorance. In fact, you see, none of the gods loves wisdom or wants to become wise—for they are wise—and no one else who is wise loves wisdom.” Perhaps the best starting point for understanding the philosophy of Aristotle is that in principle, he rejects Diotima’s etymological wordplay that claims that philosophy implies an (...) absence of wisdom. At the heart of Aristotle’s philosophy is the claim not only that all humans desire to know, but also that human animals (and indeed some non-human animals) are capable of understanding the world and its contents in a broad array of epistemic capacities, including veridical perception, artisanal expertise, theoretical science, practical wisdom, and, indeed, even σοφία itself of the highest objects of cognition, namely the nature of the gods (Metaph. 1.1.980a22–981b7). My chapter explores the philosophy of Aristotle in five different parts. Part I examines the “organon” or linguistic and logical tool-kit that analyzes human reasoning from the most basic components of a proposition up through syllogistic presentation of the causes that explain what research has uncovered. Parts II and III of the chapter explore the main contours of Aristotle’s “theoretical sciences”—what today we call natural science, metaphysics, and theology. Part IV of the chapter examines what the Nicomachean Ethics calls “the philosophy of human things,” namely the study of ethics and politics. Finally, Part V looks at how Aristotle and his school systemized two different fields of human study, namely that of artistic mimesis or the art of poetry, and deliberative, judicial, and epidictic oratory or the art of rhetoric. (shrink)

Aristotle’s Politics is a study of the political institutions of the 4th C. Mediterranean world, including both Greek communities (like Athens and Sparta) and non-Greek communities (like Persia and Carthage). The work is foundational for a number of modern scholarly disciplines such as political science, political theory, ancient history, and ancient philosophy; thus, the work annually is the subject of a robust number of scholarly studies (on average, about four monographs and 25 journal articles and book chapters per year). This (...) chapter reviews scholarship on the Politics, focusing on work produced since 2010. The chapter first reviews general introductions, editions, and interpretative strategies for understanding the Politics. It then reviews major subsections or conceptual issues within the Politics. The chapter concludes with a review of major trends in scholarship and suggestions for future scholarly directions in understanding Aristotle’s Politics. (shrink)

It gives me great pleasure and honor to introduce myself as the incoming Editor-in-Chief of Polis: The Journal for Ancient Greek and Roman Political Thought. For the last decade I have served as an Associate Editor and the Book Review Editor of the journal. I am very excited about charting new paths for the journal, while continuing to publish first-rate scholarship in our area strengths. Although ‘polis’ is a Greek word that identifies a specific Greek historical political institution, in many (...) important ways the culture of Greek political thought interacted with the political culture of Regal, Republican, and Imperial Rome through Greek settlements in the Western Mediterranean, Roman military conquest, and cultural Hellenization. In the last year the editorial staff of Polis decided to expand the domain of our journal to include scholarship on Roman political thought and Greek-language political thought from the Hellenistic and Roman Imperial periods. Although Polis has been publishing reviews of books devoted to these new domains for several issues, it is quite gratifying to publish an entire special issue, edited by Grant Nelsestuen and Associate Editor Daniel Kapust, devoted to Roman political thought. Additional articles on Roman political thought are in the journal’s publication queue and we look forward to becoming an important venue for the publication of original scholarship and book reviews on Roman political thought and its subsequent reception, along with our original remit for Greek political thought and its reception. The editorial staff of Polis has undergone a number of changes in conjunction with my new role. First and foremost, my mentor and predecessor Kyriakos Demetriou has retired from the position of Editor-in-Chief and become a member of our Editorial Board. I have had the privilege of working with Kyriakos for over 15 years, during which time he transformed the newsletter of the Society for Ancient Greek Political Thought into a pre-eminent peer-reviewed academic journal. I may only hope 15 years from now, that Polis has continued to grow as a source for landmark scholarship on Greek and Roman political thought. During the editorial transition, Associate Editors Rosanna Lauriola and Essam Safty have left our editorial staff. We are grateful for their service to the journal and wish them well in their scholarly endeavors. Finally, I am pleased to announce several additions to our editorial staff. Dimitri El Murr, Professor of Ancient Philosophy at the Ecole Normale Supérieure (Université Paris Sciences et Lettres), has joined the journal as an Associate Editor responsible for the refereeing and editing of Francophone submissions to Polis. Demetra Kasimis, Assistant Professor of Political Science at the University of Chicago, has joined as an Associate Editor responsible for the refereeing of submissions on the political aspects of Greek literature (such as epic, tragedy, and comedy). Matthew Simonton, Associate Professor of History at Arizona State University, has joined the journal as an Associate Editor and Book Review Editor. Finally, Dr. Alexandra Wilding has joined our editorial staff as the journal’s copy-editor. Learn from and enjoy the scholarship of our current issue. Submit to Polis your scholarship on ancient Greek and Roman political thought. Be a part of the future of Polis. Thornton Lockwood Editor-in-Chief. (shrink)

In Nicomachean Ethics V.6 Aristotle contrasts political justice with household justice, paternal justice, and despotic justice. My paper expands upon Aristotle’s sometimes enigmatic remarks about political justice through an examination of his account of justice within the oikia or ‘household’. Understanding political justice requires explicating the concepts of freedom and equality, but for Aristotle, the children and wife within the household are free people even if not citizens, and there exists proportionate equality between a husband and wife. Additionally, Aristotle’s articulation (...) and defence of political justice arises out of his examination of despotic justice in the first book of the Politics. Not only are the polis and the oikia similar insofar as they are associations, but Nicomachean Ethics VIII.9–11 suggests they are even isomorphic with respect to justice and friendship. Thus, in this paper I explore the relationships between father and son, husband and wife, master and slave, and between siblings in order to see what they tell us about Aristotle’s understanding of freedom, equality, and justice. (shrink)

Although there is much scholarship on Aristotle’s account of friendship (φιλία), almost all of it has focused on inter-personal relationships between human animals. Nonetheless, in both Aristotle’s ethical and zoological writings, he documents the intra- and inter-species friendship between many kinds of animals, including between human and non-human animals. Such non-human animal friendships establish both an indirect basis for establishing moral ties between humans and non-human animals (insofar as we respect their capacity to love and befriend others) and a direct (...) basis for establishing such ties (insofar as Aristotle provides a framework for thinking about utility and pleasure friendships between human and non-human animals). My paper defends Aristotle’s limitation of inter-species friendships to only utility and pleasure friendships and responds to scholars who claim that Aristotle recognizes no moral ties between human and non-human animals. (shrink)

Aristotle of Stagira (384–322 BCE) originates the study of zoology and political science. But whereas his zoology identifies a continuum between human and non-human animals, in his political and ethical works he appears to view human and non-human animals as different in kind in order to illustrate the superiority of the former and justify the instrumental use of the latter. For instance, Aristotle’s account of the virtue of moderation (namely that which concerns how humans experience pleasure) depicts non-human animals as (...) predators who only view other animals as a meal and immoderate human animals as beast-like and disgraceful because they act, “not insofar as they are human beings but insofar as they are animals” (EN 3.10.1118b2–3). Nonetheless, Aristotle wrote another ethical treatise, the Eudemian Ethics, that offers discussions that parallel those in the Nicomachean Ethics but that eschew negative characterizations of non-human animals—as if Aristotle had excised all such negative depictions of non-human animals from the Eudemian text on rhetorical grounds. I argue that the reason that Aristotle treats pleasure so differently is the result of his contrast between ethics as a function of political science (as found in the Nicomachean Ethics) and a “non-political” ethical reflection (as found in the Eudemian Ethics) that is more in line with Aristotle the zoologist. (shrink)

Although there is much scholarship on Aristotle’s account of friendship (φιλία), almost all of it has focused on inter-personal relationships between human animals. Nonetheless, in both Aristotle’s ethical and zoological writings, he documents the intra- and inter-species friendship between many kinds of animals, including between human and non-human animals. Such non-human animal friendships establish both an indirect basis for establishing moral ties between humans and non-human animals (insofar as we respect their capacity to love and befriend others) and a direct (...) basis for establishing such ties (insofar as Aristotle provides a framework for thinking about utility and pleasure friendships between human and non-human animals). My paper defends Aristotle’s limitation of inter-species friendships to only utility and pleasure friendships and responds to scholars who claim that Aristotle recognizes no moral ties between human and non-human animals. (shrink)

Aristotle's account of natural slavery appears to be internally inconsistent concerning whether slavery is advantageous to the natural slave. Whereas the Politics asserts that slavery is beneficial to the slave, the ethical treatises deny such a claim. Examination of Aristotle's arguments suggests a distinction which resolves the apparent contradiction. Aristotle distinguishes between the common benefit between two people who join together in an association And the same benefit which exists between a whole and its parts. Master and slave share no (...) common benefit, but instead the slave receives the same benefit a master does, albeit only through participation in the master as a part within a whole. Although Aristotle's distinction hardly justifies his doctrine of slavery, it saves Aristotle from one alleged internal inconsistency and sheds light on what Aristotle means by association and the common good. (shrink)

Aristotle’s discussions of natural slavery, ‘barbarian kingship’, and the natural characteristics of barbarians or non-Greeks are usually read as calling into question the intellectual, ethical, and political accomplishments of non-Greeks. Such accounts of non-Greek inferiority or inability to self-govern also appear to presuppose a climatic or environmental account that on the whole would imply severe limitations on the possibility of political flourishing for peoples living outside the Greek Mediterranean basin. In light of such accounts, it is somewhat astounding to find (...) Aristotle praising the social and political institutions of Carthage within his discussion of the best constitution in the second book of the Politics. In the 4th century BCE, Carthage (modern day Tunis) was a Phoenician commercial empire that culturally and linguistically was Semitic and clearly non-Greek. That Aristotle contrasts Carthage, a non-Greek polis, favorably with both Sparta and Crete undermines both the claim that Aristotle embraced a categorical opposition between Greeks and non-Greeks and the claim that he was dismissive of the achievements of non-Greeks. (shrink)

Cicero’s ethical and political writings present a detailed and sophisticated philosophy of just war, namely an account of when armed conflict is morally right or wrong. Several of the philosophical moves or arguments that he makes, such as a critique of “Roman realism” or his incorporation of the ius fetiale—a form of archaic international law—are remarkable similar to those of the contemporary just war philosopher Michael Walzer, even if Walzer is describing inter-state war and Cicero is describing imperial war. But (...) if it is clear that Walzer presents a detailed philosophy of just war, then I argue we should draw the same conclusion for Cicero. The result is a deeper appreciation of the insight and novelty of Cicero’s view of just war. The paper concludes by arguing against the claim that Cicero’s philosophy of just war is derivative from the Stoic philosopher Panaetius, whom Cicero drew upon in the organization of his On Duties. Just as Walzer’s Just and Unjust Wars was written in response to America’s war in Vietnam, Cicero’s just war philosophy was written in response to the wars (both civil and external) of Gaius Caesar. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

On some accounts of vagueness, predicates like “is a heap” are tolerant. That is, their correct application tolerates sufficiently small changes in the objects to which they are applied. Of course, such views face the sorites paradox, and various solutions have been proposed. One proposed solution involves banning repeated appeals to tolerance, while affirming tolerance in any individual case. In effect, this solution rejects the reasoning of the sorites argument. This paper discusses a thorny problem afflicting this approach to vagueness. (...) In particular, it is shown that, on the foregoing view, whether an object is a heap will sometimes depend on factors extrinsic to that object, such as whether its components came from other heaps. More generally, the paper raises the issue of how to count heaps in a tolerance-friendly framework. (shrink)

David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...) little attention, and on a number of philosophical reconstructions of the viewpoint (in particular, by Hand, Kitcher, and Tait). (shrink)

Education as identity formation in Western-style liberal-democracies relies, in part, on neutrality as a justification for the reproduction of collective individual identity, including societal, cultural, institutional and political identities, many aspects of which are problematic in terms of the reproduction of environmentally harmful attitudes, beliefs and actions. Taking a position on an issue necessitates letting go of certain forms of neutrality, as does effectively teaching environmental education. We contend that to claim a stance of neutrality is to claim a position (...) beyond criticism. In the classroom this can also be an epistemically damaging position to hold. To further explore the problem of neutrality in the classroom, and to offer a potential solution, we will look to the philosophical community of inquiry pedagogy, and advocate for the addition of place-based education; a form of experiential education that promotes learning in local communities in which the school is situated, each with its own history, culture, economy and environment. However, how we understand ‘place’ is fundamental to understanding the potential of place-based education in giving students a ‘sense of place’—how they perceive a place, which includes place attachment and place meaning. To this end, we look to Indigenous understandings of Place and social reconstruction learning to inform place-based pedagogies. Doing so, we hold, opens a pathway to ethical education. (shrink)

The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...) and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

I have sought to keep a running tabulation of all books, edited collections, translations, and journal articles which are primarily devoted to Aristotle’s ethical and political writings (including their historical reception but excluding neo-Aristotelian virtue ethics). Criteria for inclusion in this bibliography are: (1) published after January 1, 2021 (including pre-publication articles assigned a DOI); (2) devoted to one of Aristotle’s ethical or political works (e.g., Pol, EN, EE, MM, Athenian Constitution, Protrepticus); and/or (3) devoted to ethical or political concepts (...) examined elsewhere in Aristotle’s corpus (e.g., Rhetoric, Poetics, zoological treatises, etc.). I encourage scholars to alert me about published works that I have omitted or listed incorrectly. (shrink)

Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then (...) describe three additional empirical studies that investigate further claims in the literature on vagueness: the hypothesis that speakers confuse ‘P’ with ‘definitely P’, the relative persuasiveness of different formulations of the inductive premise of the Sorites, and the interaction of vague predicates with three different forms of negation. (shrink)

The purpose of Aristotle's discussion of political justice (τό πολιὸν[unrepresentable symbol]δν δί[unrepresentable symbol]αιον) in "EN" V.6-7 has been a matter of dispute. Although the notion of political justice which Aristotle seeks to elucidate is relatively clear, namely the notion of justice which obtains between free and equal citizens living within a community aiming at self-sufficiency under the rule of law, confusion arises when one asks how political justice relates to the other kinds of justice examined in "EN" V. Is political (...) justice a highly determinate subdivision of justice which Aristotle examines alongside the other varieties of particular justice analyzed in "EN" V.2-5? Or is political justice related to the analysis of ethical agency which follows in "EN" V.8-11? The question is complicated by the fact that the passage in question -- "EN" V 1134a17-1135a15 -- has occasioned much speculation about textual dislocations and has been incorporated into chapter divisions differently according to the two prevalent modern editorial divisions of the Ethics. To resolve these problems, I argue that Aristotle's account of political justice is situated within an extended aporetic analysis which begins in "EN" V.6 and extends through "EN" V.8. Aristotle introduces the notion of political justice within the extended analysis concerning the ascription of character states because calling someone just or unjust presupposes that the person is a fully mature ethical agent, but anyone capable of political justice possesses such agency. Once the extended argument in the second half of "EN" V is properly understood, it appears that the received text is not in need of emendation. To further support my claim that Aristotle's account of political justice introduces a new inquiry which is not analogous to the analyses of particular justice in the first half of "EN" V, I compare political justice to the other species of justice. (shrink)

Scholars have disagreed on whether Cicero’s De Amicitia is a philosophically serious or even coherent work. Such criticisms, I believe, can be met by an examination of the successive accounts of friendship that the character of Gaius Laelius provides in the dialogue. I argue that the dialogue offers three such accounts of friendship which taken together provide a comprehensive and coherent account of friendship. Further, I defend Cicero’s account against criticisms that Aulus Gellius had raised in the 2nd century CE (...) (criticisms that have been repeated to the modern day). The problem of defining friendship is a thread that brings unity to the entire dialogue and shows Cicero philosophizing about both the origins of friendship and its dissolution, especially when the bonds of friendship are in tension with obligations to the political community. (shrink)

Leading digital platform providers such as Google and Uber construct marketplaces in which algorithms set prices. The efficiency-maximising free market credentials of this approach are touted by the companies involved and by legislators, policy makers and marketers. They have also taken root in the public imagination. In this article we challenge this understanding of algorithmically constructed marketplaces. We do so by returning to Hayek’s (1945) classic defence of the price mechanism, and by arguing that algorithmically-mediated price mechanisms do not, and (...) probably cannot, accumulate and signal that same kinds of knowledge that Hayek felt were essential to effective market governance. Indeed, we argue that algorithmically-constructed marketplaces are closer to, though distinct from, the central planning model that Hayek critiqued. Regardless of how you feel about Hayek’s argument, this has important consequences for how we respond to the rise of algorithmic governance tools in both markets and elsewhere. (shrink)

Martha Nussbaum has provided a sustained critique of Cicero’s De officiis (or On Duties), concerning what she claims is Cicero’s incoherent distinction between duties of justice, which are strict, cosmopolitan, and impartial, and duties of material aid, which are elastic, weighted towards those who are near and dear, and partial. No doubt, from Nussbaum’s cosmopolitan perspective, Cicero’s distinction between justice and beneficence seems problematic and lies at the root of modern moral failures to conceptualize adequately our obligations in situations of (...) famine and global inequality. And yet a careful reading of Cicero’s On Duties shows many duties that appear to be partial. It is hard to believe that Cicero’s discussion of these “partial duties” was a mere oversight or omission on his part. Rather, Cicero seemed to have no problem endorsing what I will call the “partial coherence” of duties in the work—namely, the claim that asserting that duties are exhaustively partial or impartial is a false dichotomy. With the help of conceptual analysis by Richard Kraut, my paper aims to establish and defend Cicero’s “partial coherence” against Nussbaum’s criticisms. (shrink)

Scholarship on Aristotle’s NICOMACHEAN ETHICS (hereafter “the Ethics”) flourishes in an almost unprecedented fashion. In the last ten years, universities in North America have produced on average over ten doctoral dissertations a year that discuss the practical philosophy that Aristotle espouses in his Nicomachean Ethics, Eudemian Ethics, and Politics. Since the beginning of the millennium there have been three new translations of the entire Ethics into English alone, several more that translate parts of the work into English and other modern (...) languages, and half a dozen collections of new articles discussing Aristotle’s Ethics. Such an outpouring of scholarship has produced an almost unmanageable wave of books, articles, and reviews. Through my topical bibliography, I seek to organize this wealth of scholarly writing so as to make it manageable both to scholars working across the disciplines of philosophy, classics, history, and politics, and to scholars pursuing theses on specific topics within the Ethics. The bibliography takes as its model and is much indebted to that compiled by Barnes, Schofield, and Sorabji in their Articles on Aristotle, Volume 2: Ethics and Politics (1977), which was further updated and incorporated into the complete bibliography to all of Aristotle’s writings in Barnes’s Cambridge Companion to Aristotle (1995). Although I have taken guidance from their model, my bibliography differs in one main respect. Whereas Barnes et al. were more selective and annotated their bibliography, I have been more comprehensive in my inclusion of items. I have sought to include all books and journal articles concerned with the Ethics written in English over the last 120 years; additionally, I have sought to include representative and central works of scholarship written on the Ethics in French, German, and Italian during the same period of time. (shrink)

이 책자는 형식 논리의 일종인 양상논리에 입문하고 싶으신 분들을 위한 짧은 교재입니다. “양상논리 맛보기” 라는 말마따나, 이 책자는 양상논리에 관심은 있지만 아직 본격적으로 공부를 시작하진 않은 분들께서 ‘맛보기’를 하기에 적합한 안내 책자입니다. 아무쪼록 이 책자가 양상논리를 공부해나가시는데 유용한 첫 발판이 될 수 있기를 바랍니다. / This booklet is a Korean adaptation and translation of Part VIII of forall x: Calgary (Fall 2021 edition), which is intended to be introductory material for modal logic. The original text is based on Robert Trueman's (...) A Modal Logic Primer, which is revised and expanded by Richard Zach and Aaron Thomas-Bolduc in forall x: Calgary. (forall x: Calgary is based on forall x: Cambridge by Tim Button, which is in turn based on forall x by P. D. Magnus, and also includes material from forall x: Lorain County Remix by Cathal Woods and J. Robert Loftis.) This booklet is licensed under a Creative Commons Attribution 4.0 license. (shrink)

A textbook for modal and other intensional logics based on the Open Logic Project. It covers normal modal logics, relational semantics, axiomatic and tableaux proof systems, intuitionistic logic, and counterfactual conditionals.