This is the 1991 (2nd) edition of the 1986 book (MIT Press), considered to be the classic defense of Millianism. The nature of the information content of declarative sentences is a central topic in the philosophy of language. The natural view that a sentence like "John loves Mary" contains information in which two individuals occur as constituents is termed the naive theory, and is one that has been abandoned by most contemporary scholars. This theory was refuted originally by philosopher Gottlob (...) Frege. His argument that the naive theory did not work is termed Frege's puzzle, and his rival account of information content is termed the orthodox theory. In this detailed study, Nathan Salmon defends a version of the naive theory and presents a proposal for its extension that provides a better picture of information content than the orthodox theory gives. He argues that a great deal of what has generally been taken for granted in the philosophy of language over the past few decades is either mistaken or unsupported, and consequently, much current research is focused on the wrong set of questions. Salmon dissolves Frege's puzzle as it is usually formulated and demonstrates how it can be reconstructed and strengthened to yield a more powerful objection to the naive theory. He then defends the naive theory against the new Frege puzzle by presenting an idea that yields both a surprisingly rich and powerful extension of the naive theory and a better picture of information content than that of the original orthodox theory. Nathan Salmon is Professor of Philosophy, University of California at Santa Barbara. (shrink)

I argue that Davidson's conception of motivating reasons as belief-desire pairs suggests a model of normative reasons for action that is superior to the orthodox conception according to which normative reasons are propositions, facts, or the truth-makers of such facts.

Changing our minds isn't easy. Even when we recognize our views are disputed by intelligent and informed people, we rarely doubt our rightness. Why is this so? How can we become more open-minded, putting ourselves in a better position to tolerate conflict, advance collective inquiry, and learn from differing perspectives in a complex world? -/- Nathan Ballantyne defends the indispensable role of epistemology in tackling these issues. For early modern philosophers, the point of reflecting on inquiry was to understand (...) how our beliefs are often distorted by prejudice and self-interest, and to improve the foundations of human knowledge. Ballantyne seeks to recover and modernize this classical tradition by vigorously defending an interdisciplinary approach to epistemology, blending philosophical theorizing with insights from the social and cognitive sciences. -/- Many of us need tools to help us think more circumspectly about our controversial views. Ballantyne develops a method for distinguishing between our reasonable and unreasonable opinions, in light of evidence about bias, information overload, and rival experts. This method guides us to greater intellectual openness--in the spirit of skeptics from Socrates to Montaigne to Bertrand Russell--making us more inclined to admit that sometimes we don't have the right answers. With vibrant prose and fascinating examples from science and history, Ballantyne shows how epistemology can help us know our limits. (shrink)

During his celebrated 1922 debate with Bergson, Einstein famously proclaimed: “the time of the philosopher does not exist, there remains only a psychological time that differs from the physicist’s.” Einstein’s dictum, I maintain, has been metabolized by the natural sciences, which typically presuppose, more or less explicitly, the existence of a single, univocal, temporal substratum, ultimately determined by physics. This reductionistic assumption pervades much biological and biomedical practice. The chronological age allotted to individuals is conceived as an objective quantity, allowing (...) one to straightforwardly assign and compare the biological age of organisms. This essay argues that the standard practice of assessing the age and aging of organisms against the backdrop of a physical conception of time is problematic. This becomes especially evident in light of recent discoveries of various levels of senescence underlying the development of individual organisms—a phenomenon known as ‘age mosaicism.’ The bottom line is that the study of age and aging requires a biological conception of time, as opposed to a physical one. Einstein clearly wasn’t wrong about his operationalization of time in relativity theory. Still time may be less monolithic than he surmised. (shrink)

There are certain uses of and and or that cannot be explained by their normal meanings as truth-functional connectives, even with sophisticated pragmatic resources. These include examples such as The cops show up, and a fight will break out (‘If the cops show up, a fight will break out’), and I have no friends, or I would throw a party (‘I have no friends. If I did have friends, I would throw a party.’). We argue that these uses are indeed (...) distinct from the more ordinary uses of and and or, but that they are nonetheless related in a principled way. To explain them we give an analysis of what we call the dynamic effects of connectives, which arise in all their uses. The special uses at issue are then argued to be instances where the connectives exhibit their dynamic effects without their truth-conditional meaning. (shrink)

Many philosophers think that punishment is intentionally harmful and that this makes it especially hard to morally justify. Explanations for the latter intuition often say questionable things about the moral significance of the intent to harm. I argue that there’s a better way to explain this intuition.

Philosophers have recently come to focus on explaining the phenomenon of ​bad beliefs,​ beliefs that are apparently true and well-evidenced but nevertheless objectionable. Despite this recent focus, a consensus is already forming around a particular explanation of these beliefs’ badness called ​moral encroachment​, according to which, roughly, the moral stakes engendered by bad beliefs make them particularly difficult to justify. This paper advances an alternative account not just of bad beliefs but of bad attitudes more generally according to which bad (...) beliefs’ badness originates not in a failure of sufficient evidence but in a failure to respond adequately to reasons. I motivate this alternative account through an analogy to recent discussions of moral worth centered on the well-known grocer case from Kant’s ​Groundwork​, and by showing that this analogy permits the proposed account to generalize to bad attitudes beyond belief. The paper concludes by contrasting the implications of moral encroachment and of the proposed account for bad attitudes’ blameworthiness. (shrink)

Plant-based milk alternatives–or mylks–have surged in popularity over the past ten years. We consider the politics and consumer subjectivities fostered by mylks as part of the broader trend towards ‘plant-based’ food. We demonstrate how mylk companies inherit and strategically deploy positive framings of milk as wholesome and convenient, as well as negative framings of dairy as environmentally damaging and cruel, to position plant-based as the ‘better’ alternative. By navigating this affective landscape, brands attempt to make mylk as simultaneously palatable and (...) disruptive to the status quo. We examine the politics of mylks through the concept of palatable disruption, where people are encouraged to care about the environment, health, and animal welfare enough to adopt mylks but to ultimately remain consumers of a commodity food. By encouraging consumers to reach for “plant-based” as a way to cope with environmental catastrophe and a life out of balance, mylks promote a neoliberal ethic: they individualize systemic problems and further entrench market mechanisms as solutions, thereby reinforcing the political economy of industrial agriculture. In conclusion, we reflect on the limits of the current plant-based trend for transitioning to more just and sustainable food production and consumption. (shrink)

When central authority fails in socially crucial tasks, mutual aid, solidarity, and grassroots organization frequently arise as people take up slack on the basis of informal networks and civil society organizations. We can learn something important about the possibility of horizontal organization by studying such experiments. In this paper we focus on the rationality, care, and effectiveness of grassroots measures to respond to the pandemic and show how they illustrate core elements of anarchist thought. We do not argue for the (...) correctness of any version of anarchist politics, nor claim that the bulk of this grassroots work was done with anarchist ideas explicitly in mind. Nonetheless, the current pandemic, like many social crises before it, serves as a sort experiment in political implementation. -/- Two things have been striking in the US response to the COVID-19 pandemic: the chaos, incompetence, irrationality, and often cruel misguidedness of the centralized government response; and the rationality, care, and effectiveness of grassroots measures in many parts of the country. In this paper we focus on the latter—especially the case of Washington, DC—to illustrate core features of anarchist politics. We do not argue for the correctness of any version of anarchist politics here, but merely illustrate guiding ideas that have been a part of anarchist theory and practice for well over a century. We also do not claim that the bulk of this grassroots work was done with anarchist ideas in mind, or explicitly out of a commitment to anarchist politics. Some was, and some arises out of related ideological commitments, but most simply functions out of no more than a desire to support one another. -/- The current pandemic, like many social crises before it, rather than providing a stand-alone argument or functioning as an implementation of any political theory, serves as a sort of laboratory experiment. When central authority fails in socially crucial tasks, mutual aid, solidarity, and grassroots organization frequently arise as people take up slack on the basis of informal networks and civil society organizations. We can learn something important about the possibility of horizontal organization by studying such experiments, including how it arises through spontaneous action. If political thought is best illustrated through its implementation in practice, the functioning of grassroots individuals and organizations in a time of crisis is one way to understand the political mechanisms core to anarchist thought. (shrink)

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

According to the mainstream narrative about race, all groups have the same innate dispositions and potential, and all disparities—at least those favoring whites—are due to past or present racism. Some people who reject this narrative gravitate toward an alternative, anti-Jewish narrative, which sees recent history in terms of a Jewish/gentile conflict. The most sophisticated promoter of the anti-Jewish narrative is the evolutionary psychologist Kevin MacDonald. MacDonald argues that Jews have a suite of genetic adaptations—including high intelligence and ethnocentrism—and cultural practices (...) that lead them to undermine gentile society to advance their own evolutionary interests. He says that Jewish-designed intellectual movements have weakened gentile identity and culture while preserving Jewish identity and separatism. Cofnas recently argued that MacDonald’s theory is based on “systematically misrepresented sources and cherry-picked facts.” However, Cofnas gave short shrift to at least three key claims: Jews are highly ethnocentric, liberal Jews hypocritically advocate liberal multiculturalism for gentiles/gentile countries but racial purity and separatism for Jews/Israel, and Jews are responsible for liberalism and mass immigration to the United States. The present paper examines these claims and concludes that MacDonald’s views are not supported. (shrink)

If the laws of nature are metaphysically necessary, then it appears that miracles are metaphysically impossible. Yet Locke accepts both Essentialism, which takes the laws to be metaphysically necessary, and the possibility of miracles. I argue that the apparent conflict here can be resolved if the laws are by themselves insufficient for guaranteeing the outcome of a particular event. This suggests that, on Locke’s view, the laws of nature entail how an object would behave absent divine intervention. While other views (...) of laws also make miracles counterfactually dependent on God’s will, I show how this view is consistent with the Essentialist commitment to the view that the laws are metaphysically necessary. Further, I argue Locke’s view is a relatively attractive version of Essentialism, in part, because it allows for the possibility of miracles. (shrink)

We sometimes seek expert guidance when we don’t know what to think or do about a problem. In challenging cases concerning medical ethics, we may seek a clinical ethics consultation for guidance. The assumption is that the bioethicist, as an expert on ethical issues, has knowledge and skills that can help us better think about the problem and improve our understanding of what to do regarding the issue.The widespread practice of ethics consultations raises these questions and more:What would it take (...) to be a moral expert?Is anyone a moral expert, and if so, how could a non-expert identify one?Is it in any way problematic to accept and follow the advice of a moral expert as opposed to coming to moral conclusions on your own?What should we think and do when moral experts disagree about a practical ethical issue?In what follows, we address these theoretical and practical questions about moral expertise. (shrink)

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

Much recent work in virtue epistemology has focused on the analysis of such intellectual virtues as responsibility, conscientiousness, honesty, courage, open-mindedness, firmness, humility, charity, and wisdom. Absent from the literature is an extended examination of perseverance as an intellectual virtue. The present paper aims to fill this void. In Sect. 1, I clarify the concept of an intellectual virtue, and distinguish intellectual virtues from other personal characters and properties. In Sect. 2, I provide a conceptual analysis of intellectually virtuous perseverance (...) that places perseverance in opposition to its vice -counterparts, intransigence and irresolution. The virtue is a matter of continuing in one’s intellectual activities for an appropriate amount of time, in the pursuit of intellectual goods, despite obstacles to one’s attainment of those goods. In Sect. 3, I explore relations between intellectually virtuous perseverance and other intellectual virtues. I argue that such perseverance is necessary for the possession and exercise of several other intellectual virtues, including courage. These connections highlight the importance of perseverance in a comprehensive account of such virtues. (shrink)

Higginbotham (1986) observed that quantified conditionals have a stronger meaning than might be expected, as attested by the apparent equivalence of examples like No student will pass if he goofs off and Every student will fail if he goofs off. Higginbotham's observation follows straightforwardly given the validity of conditional excluded middle (CEM; as observed by von Fintel & Iatridou 2002), and as such could be taken as evidence thereof (e.g. Williams forthcoming). However, the empirical status of CEM has been disputed, (...) and it is invalid under many prominent theories of conditionals—notably Lewis (1973) for counterfactuals, also Kratzer (1979, 1991). More acutely, Higginbotham's observation holds even for quantified counterparts of conditionals that appear not to obey CEM (Higginbotham 2003), and the standard way of explaining (away) such apparent counterexamples to the principle, à la Stalnaker (1981), does not directly yield an account of our apparent truth-conditional intuitions about the quantified counterparts (Leslie 2009). This article provides an explanation for the latter intuitions within Stalnaker's framework, the upshot being that CEM does remain a viable explanation, in principle, for Higginbotham's observation. (shrink)

The nursing community in the United States polarized in September 2020 between Dawn Wooten's whistleblowing about forced hysterectomies at an immigration center in Georgia and the American Nurses Association's refusal to endorse a presidential candidate despite the Trump administration's mounting failures to address the public health crisis posed by the COVID‐19 pandemic. This reveals a need for more attention to political aspects of health outcome inequities. As advocates for health equity, nurses can join in recent scholarship and activism concerning the (...) political determinants of health. In this paper, we examine recent work on the political determinants of health with an aim to add two things. First, we seek to build further on the notion of “political” determinants of health by distinguishing policy and governance structures from dynamics of politicization through appeal to critical disabilities studies. Second, we seek to apply this further nuanced approach to challenge rhetorical uses of “vulnerable populations,” where this phrase serves to misrecognize systemic institutionalized forces that actively exploit and marginalize people and groups. By refocusing attention to political systems organized around and perpetuating inequitable health outcomes, nurses and other health care professionals—as well as those whom they serve—can concentrate their effort and power to act on political determinants of health in bringing about more equitable health outcomes. (shrink)

The wrong kind of reason (WKR) problem is a problem for attempts to analyze normative properties using only facts about the balance of normative reasons, a style of analysis on which the ‘Reasons First’ programme depends. I argue that this problem cannot be solved if the orthodox view of reasons is true --- that is, if each normative reason is numerically identical with some fact, proposition, or state-of-affairs. That’s because solving the WKR problem requires completely distinguishing between the right- and (...) wrong-kind reasons for an attitude. I argue that some facts give both right- and wrong-kind reasons for an attitude. Consequently, no such distinction between the two types of reasons is complete if reasons are facts or the like. I conclude by suggesting that reasons and facts are related by constitution, not identity. (shrink)

Contemporary Western culture is experiencing a heightened awareness of religious diversity. This article surveys a range of possible responses to such diversity, and distinguishes between responses that concern the salvation or moral transformation of persons (soteriological views) and those that concern the alethic or epistemic status of religious beliefs (doctrinal views). After providing a brief taxonomy of these positions and their possible relations to one another, the article focuses primarily on competing views about the truth and rationality of religious beliefs (...) (e.g., pluralism, exclusivism, and skepticism). Here a heavy emphasis is placed on arguments for and against the rationality and moral propriety of retaining one's religious beliefs in the face of disagreement. The article surveys some of the more prominent arguments from the literature on this topic and closes with suggestions for further research. (shrink)

In this essay I argue that what has been called “philosophical anarchism” in the academic literature bears little to no relationship with the historical anarchist tradition and, for this reason, ought not to be considered a genuine form of anarchism. As I will demonstrate, the classical anarchism of the nineteenth and early twentieth centuries is to be distinguished from other political theories in regarding all hierarchical institutions and relationships—including, but not limited to, the state—as incorrigibly dominative or oppressive and, for (...) this reason, immoral. Lastly, I argue that defenders of such institutions and relationships must take the challenge posed by classical anarchism seriously by engaging substantively with actual anarchist positions. (shrink)

I want to know whether Chan masters and students depicted in classical Chan transmission literature can be interpreted as asking open (or what I will call “genuine”) questions. My task is significant because asking genuine questions appears to be a decisive factor in ascertaining whether these figures represent models for dialogue—the kind of dialogue championed in democratic society and valued by promoters of interreligious exchange. My study also contributes to a more comprehensive understanding of early Chan not only by detailing (...) contrasts between contemporary interests and classical Chan, but more importantly by paying greater attention to the role language and rhetoric play in classical Chan. What roles do questions play in Chan encounter dialogues, and are any of the questions genuine? Is there anything about the conventions of the genre that keeps readers from interpreting some questions in this way? To address these topics, I will proceed as follows. First, on a global level and for critical-historical context, I survey Chan transmission literature of the Song dynasty in which encounter dialogues appear, and their role in developments of Chan/Zen traditions. Second, I zoom in on structural elements of encounter dialogues in particular as a genre. Third, aligning with the trajectory of performative analyses of Chan literature called for by Sharf and Faure, I turn to develop and criticize a performative model of questions from resources in recent analytic and continental philosophy of language and I apply that model to some questions in encounter dialogue literature. (shrink)

Some argue against coercive preventive measures on the grounds that they amount to cloaked forms of punishment. Others offer a qualified defence of such measures on the grounds that such measures have substantively different goals and purposes from punishment. Focusing on the case of civil preventive injunctions, I clear the ground and provide reasons for a third logical possibility: that coercive preventive measures are relevantly similar to punishment, but this does not itself give us a reason to oppose them. ‘Punishment’ (...) has a great deal of rhetorical force, and it thereby distracts us from the justificatory work that we need to do to specify proper restrictions on the state’s coercive powers. Whereas many commentators have proposed that legal theory provides grounds for challenging civil preventive orders, I argue for the opposite view. If we understand properly the function of civil preventive orders, we will endorse them at least in principle, and will come to rethink some central ideas in the grounding of the criminal justice processes. (shrink)

Our ability to think, argue and reason is determined by our ability to question. Questions are a vital component of critical thinking, yet we underestimate the role they play. Using Questions to Think puts questioning back in the spotlight. -/- Naming the parts of questions at the same time as we name parts of thought, this one-of-a-kind introduction allows us to see how questions relate to the definitions of propositions, premises, conclusions, and the validity of arguments. Why is this important? (...) Making the role of questions visible in thinking, reasoning, and dialogue, allows us to: -/- - Ask better questions - Improve our capability to understand an argument - Exercise vigilance in the act of questioning - Make explicit what you already know implicitly - Engage with ideas that contradict our own - See ideas in broader context -/- Breathing new life into our current approach to critical thinking, this practical, much-needed textbook moves us away from the traditional focus on formal argument and fallacy identification, combines the Kantian critique of reason with Hans-Georg Gadamer's hermeneutics and reminds us why thinking can only be understood as an answer to a question. (shrink)

Recently, Xhignesse has argued that the principle of poetic licence, which roughly states that any class of propositions is true in some possible fiction, ought to be rejected. Here, we defend PPL from Xhignesse’s objection by demonstrating that, properly understood, his purported counter-example case is either irrelevant or unproblematic. The upshot is that Xhignesse has given us no reason to reject PPL.

Much recent work in virtue epistemology has focused on the analysis of such intellectual virtues as responsibility, conscientiousness, honesty, courage, open-mindedness, firmness, humility, charity, and wisdom. Absent from the literature is an extended examination of perseverance as an intellectual virtue. The present paper aims to fill this void. In Sect. 1, I clarify the concept of an intellectual virtue, and distinguish intellectual virtues from other personal traits and properties. In Sect. 2, I provide a conceptual analysis of intellectually virtuous perseverance (...) that places perseverance in opposition to its vice-counterparts, intransigence and irresolution. The virtue is a matter of continuing in one’s intellectual activities for an appropriate amount of time, in the pursuit of intellectual goods, despite obstacles to one’s attainment of those goods. In Sect. 3, I explore relations between intellectually virtuous perseverance and other intellectual virtues. I argue that such perseverance is necessary for the possession and exercise of several other intellectual virtues, including courage. These connections highlight the importance of perseverance in a comprehensive account of such virtues. (shrink)

Drawing on social exchange theory, the present study seeks to understand how ethical leaders channel followers’ responses to positive treatment from the organization into a dutiful mindset, resulting in in-role and extra-role performance. Specifically, it examines the influence of perceived organizational support on both followers’ job performance and organizational citizenship behaviors, and the mediating effects of duty orientation on such relationships. In addition, it examines whether the mediated effects are contingent on the ethical leadership exhibited by the team leader. Based (...) on multi-source, multi-level data obtained from 233 employees in 60 teams from the Chinese public sector, we found that ethical leadership moderated the mediated relationship between perceived organizational support and follower work behaviors through duty orientation, such that this relationship was stronger in the presence of higher ethical leadership. (shrink)

Familiarity, so the saying goes, breeds contempt. But, why should familiarity breed such a negative thing as contempt, or other negative orientations? Walker Percy, it would seem, has a lot to say about human jadedness, sometimes through the very means by which we are meant to inhabit ontological intimacy. One may not care much about, say sparrows, but intuitively people seem jaded about something that matters to them in a deeper way. This chapter explores the personal or social sources of (...) jadedness: is it an individual problem only, or caused by broader cultural factors? I attempt to sketch an initial theory of jadedness, and then expand that theory by attending to Percy’s unique philosophical contributions. I will argue, that there are at least two types of jadedness—a narrow, domain-specific psychological type and a global, existential type—that share structural similarities such as volitional and epistemic inertia, an unsettled loss of meaning, a faulty assumption of epistemic completion or superiority, and a foreclosure of ontological possibilities. I then show how Percy uniquely integrates these two types of jadedness within a broader framework of what it means to be human. (shrink)

Wischik presents an extensive reply to our paper on conscientious objection, which explores the implications of distinguishing ‘medical acts’ from ‘socioclinical acts’. He provides an extensive leg...

This essay argues for the philosophical standing of Walter Benjamin’s early work and posits a deeper continuity between this early work as a philosopher and the subsequent development of his work as a writer. When these fragments are read in proper relation to each other, they reveal for the first time many of the key innovations of Benjamin as a philosopher, as well as his points of influence on Horkheimer and Adorno. His early ‘Program’ critiques the Enlightenment conception of experience (...) as a means for gaining empirical knowledge, and announces the need for a new concept of experience. Benjamin follows through on this program with a method of philosophical enquiry that is by turns fragmentary and constellational, developing a series of provisional notions of experience, which form a constellation with one another: perception, mimesis, language as a medium of experience, observation and memory. (shrink)

_ Source: _Page Count 11 Epistemic Authority: A Theory of Trust, Authority, and Autonomy in Belief. By Linda Trinkaus Zagzebski. New York: Oxford University Press, 2012. Pp. xiii +279. isbn 978–0–19–993647–2.

Selfishness is often considered a vice and selfish actions are often judged to be wrong. But sometimes we ought to do what’s best for ourselves: in a sense, we sometimes should be selfish. -/- The ethical theory known as ethical egoism states that we are always morally required to do what’s in our own self-interest. The view isn’t that we are selfish—this is psychological egoism—but that we ought to be. -/- This essay explores ethical egoism and the main arguments for (...) and against it. -/- [Note: there are links for two versions below; a 1000 Word Philosophy version and a longer version in "Introduction to Ethics: An Open Educational Resource"]. (shrink)

In “There’s No Harm in Talking,” McCarthy, Homan, and Rozier note that in recent years theological bioethicists have not felt the need to translate their insights for a broader pluralistic a...

This article offers an interpretation of a controversial aspect of Frege’s The Foundations of Arithmetic, the so-called Julius Caesar problem. Frege raises the Caesar problem against proposed purely logical definitions for ‘0’, ‘successor’, and ‘number’, and also against a proposed definition for ‘direction’ as applied to lines in geometry. Dummett and other interpreters have seen in Frege’s criticism a demanding requirement on such definitions, often put by saying that such definitions must provide a criterion of identity of a certain kind. (...) These interpretations are criticized and an alternative interpretation is defended. The Caesar problem is that the proposed definitions fail to well-define ‘number’ and ‘direction’. That is, the proposed definitions, even when taken together with the extra-definitional facts, fail to fix unique semantic extensions for ‘number’ and ‘direction’, and thereby fail to fix unique truth-values for sentences like ‘Caesar is a number’ and ‘England is a direction’. A minor modification of the criticized definitions well-defines ‘0’, ‘successor’ and ‘number’, thereby avoiding the Caesar problem as Frege understands it, but without providing any criterion of number identity in the usual sense. (shrink)