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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...) in Chapter 2 shows that a completeness proof for propositional logic was found by Hilbert and his assistant Paul Bernays already in 1917--18, and that Bernays's contribution was much greater than is commonly acknowledged. Aside from logic, the main technical contribution of Hilbert's Program are the development of formal mathematical theories and proof-theoretical investigations thereof, in particular, consistency proofs. In this respect Wilhelm Ackermann's 1924 dissertation is a milestone both in the development of the Program and in proof theory in general. Ackermann gives a consistency proof for a second-order version of primitive recursive arithmetic which, surprisingly, explicitly uses a finitistic version of transfinite induction up to www . He also gave a faulty consistency proof for a system of second-order arithmetic based on Hilbert's &egr;-substitution method. Detailed analyses of both proofs in Chapter 3 shed light on the development of finitism and proof theory in the 1920s as practiced in Hilbert's school. ;In a series of papers, Charles Parsons has attempted to map out a notion of mathematical intuition which he also brings to bear on Hilbert's finitism. According to him, mathematical intuition fails to be able to underwrite the kind of intuitive knowledge Hilbert thought was attainable by the finitist. It is argued in Chapter 4 that the extent of finitistic knowledge which intuition can provide is broader than Parsons supposes. According to another influential analysis of finitism due to W. W. Tait, finitist reasoning coincides with primitive recursive reasoning. The acceptance of non-primitive recursive methods in Ackermann's dissertation presented in Chapter 3, together with additional textual evidence presented in Chapter 4, shows that this identification is untenable as far as Hilbert's conception of finitism is concerned. Tait's conception, however, differs from Hilbert's in important respects, yet it is also open to criticisms leading to the conclusion that finitism encompasses more than just primitive recursive reasoning. (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)

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)

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)

In numerous places in his Ethics and Politics, Aristotle associates political justice (or ruling in turns) and the regime of polity. I argue that there is a necessary connection between political justice and polity due to their origins in political mixing. Aristotle is the first to discover political justice and polity because his predecessors had thought that the elements which they combine -- excellence and equality in the case of political justice, and oligarchy and democracy in the case of polity (...) -- were antithetical. The novelty of Aristotle's 'discoveries' points to their connection, namely that both originate in the political mixing of elements. This article examines such political mixing in detail and shows how an institutional arrangement such as ruling in turns can be adapted to different regime-types. (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)

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)

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)

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)

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)

The relationship between nature and normativity in Aristotle’s practical philosophy is problematic. On the one hand, Aristotle insists that ethical virtue arises through the habitual repetition of ethically good actions, and thus no one is good or virtuous by nature. Phusikê aretê or “natural virtue” is more like cleverness (demotes) than prudence (phronêsis) and it can result in wrong actions. Yet on the other hand, at times Aristotle appears to use nature to justify normative claims. Thus the problem with Aristotle’s (...) use of the notion of nature in his practical philosophy is that in some instances what is natural seems to be ethically neutral, but in other instances it seems to set the standard for human perfection. Modern Aristotle exegetes have sometimes argued that Aristotle must, consciously or not, be using the term “nature” in at least two different senses here. To use the language of Julia Annas, when Aristotle talks about “natural virtue” in the sense of the talents or abilities which one possesses from birth, he has in mind the notion of “mere nature,” but when he discusses the perfections which a virtuous individual enjoys by his or her nature, Aristotle has in mind the notion of nature as an “ethical ideal.” I would like to suggest an alternative solution to the problem of reconciling Aristotle’s different senses of nature in his Ethics. In Nicomachean Ethics V.7, Aristotle claims that political justice {to dikaion politikon) possesses a “natural” {phusikon) part and a “conventional” {nomikori) part. Aristotle claims that both nature and convention admit of variation, and his language suggests that the two are ultimately parts which need to be interwoven or combined. Scholars who have struggled with Aristotle’s apparently disparate senses of the idea of nature have assumed that nature is an ethical ideal which can be separated from and serve as a guide for that which is merely conventional. I argue that when Aristotle invokes what is “natural” as a norm, he does so under the assumption that the natural component of a norm is ultimately separable from its conventional part only in abstraction. Just like the syllable “BA” is not reducible to the letters “b” and “a,” but instead is a whole greater than its two parts, political justice is a composite unity of nature and convention which, in unifying the two parts, transforms them. (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)

Numerous ancient sources attest that Artemisia of Halicarnassus, a fifth-century BCE tyrant whose polis came under Persian rule in 524 BCE, figures prominently in Xerxes’ naval campaign against Greece. At least since Pompeius Trogus’ first-century BCE Philippic History, interpretations of Artemisia have juxtaposed her “virile courage” (uirilem audaciam) with Xerxes’ “womanish fear” (muliebrem timorem) primarily as a means of belittling the effeminate non-Greeks. My paper argues that although Herodotus is aware of such interpretations of Artemisia, he depicts her primarily as (...) an excellent counsel, a woman who is not only brave in battle, but who is a wonder primarily because of her intellectual excellences in deliberative rhetoric and “geo-political” strategy in the Greco-Persian world. (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)

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.

Topical bibliography of Aristotle's Politics, organized by books/subjects within the Politics.

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)

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)

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)

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)

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)

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)

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)

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)

Aeschylus’ Persians dramatically represents the Athenian victory at Salamis from the perspective of the Persian royal court at Susa. Although the play is in some sense a patriotic celebration of the Athenian victory and its democracy, nonetheless in both form and function it is a tragedy that generates sympathy for the suffering of its main character, Xerxes. Although scholars have argued whether the play is primarily patriotic or tragic, I argue that the play purposively provides both patriotic and tragic elements (...) in such a fashion as to invite its audience to reflect on the ramifications of Persia’s failed empire for Athens’ own nascent Delian League, which even in 472 was showing imperialistic tendencies. I argue that Aeschylus’ political theory in Persians is aporetic in the sense that its careful balance between patriotism and anti-imperialism generates an impasse which members of the play’s audience are thus given the occasion to puzzle over. (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 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)

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.

An introductory textbook on metalogic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. The audience is undergraduate students with some background in formal logic.

The opening words of the second book of Aristotle’s Nicomachean Ethics are as familiar as any in his corpus: Excellence of character results from habituation [ethos]—which is in fact the source of the name it has acquired [êthikê], the word for ‘character-trait’ [êthos] being a slight variation of that for ‘habituation’ [ethos]. This makes it quite clear that none of the excellences of character [êthikê aretê] comes about in us by nature; for no natural way of being is changed through (...) habituation [ethizetai]. Equally familiar, unfortunately, is the characterization of Aristotle’s notion of character formation as a form of habituation by means of the repetition of actions which results in a “habit” in the same way that a weight lifter produces muscles through the repetition of exertions. As a 19th century commentator remarked on the passage above, “[insert Grant].” From a Socratic perspective, such a view of becoming good seems hopelessly rigid and unconnected to the intellectual development which knowledge of the good requires. Habit and habituation in Aristotle seem eminently familiar and eminently unphilosophical. Such a view would be mistaken on at least three counts. First, the notion of character formation (to use the broadest possible term for the phenomenon of habituation) in Aristotle is significantly more complicated than the notion that through habituation one develops good habits which are what we mean by ethical virtue. Although character formation includes the development of proper emotional responses, such as taking pleasure in what is fine and being repulsed by what is shameful, it is equally concerned with cognitive development independent of the intellectual virtues. Second, although Aristotle’s terms for “ethics” (êthica), character-trait (êthos), and habituation (ethos, ethismos, or ethizetai) are linguistically and conceptually interrelated, his notion of “ethical state” (hexis) is both linguistically and conceptually quite distinct from the notion of “habit,” at least as we use that term today. As one Aristotle translator has put it, “A hexis is not only not the same thing as a habit, but is almost exactly its opposite.” For Aristotle, a hexis is a dynamic equilibrium which, although always productive of virtuous actions, is nonetheless the basis for being virtuous in varied circumstances. Thirdly, once Aristotle’s notion of a character state is retrieved from its false association with “habit” and repetitive habituation, one sees that its apparent divorce from practical reason is more a fixture of Aristotle’s analytical method and its connotations of inflexibility or fixedness are in fact antithetical to Aristotle’s description of ethical virtue. Rather than view ethical “character” in its Greek etymological sense as an indelibly fixed or engraved mark or stamp (charactêr) upon one’s soul, Aristotle’s notion of ethical character (êthos) or virtue (aretê) captures the notion of a virtuoso who is responsive in an excellent fashion to what reason perceives in particular and changing circumstances. (shrink)