Do the rich descriptions and narrative shapings of literature provide a valuable resource for readers, writers, philosophers, and everyday people to imagine and confront the ultimate questions of life? Do the human activities of storytelling and complex moral decision-making have a deep connection? What are the moral responsibilities of the artist, critic, and reader? What can religious perspectives—from Catholic to Protestant to Mormon—contribute to literary criticism? Thirty well known contributors reflect on these questions, including iterary theorists Marshall Gregory, James Phelan, (...) and Wayne Booth; philosophers Martha Nussbaum, Richard Hart, and Nina Rosenstand; and authors John Updike, Charles Johnson, Flannery O'Connor, and Bernard Malamud. Divided into four sections, with introductory matter and questions for discussion, this accessible anthology represents the most crucial work today exploring the interdisciplinary connections between literature, religion and philosophy. (shrink)

Professor Card is not disposed to object to the main argument of my paper, which was intended to reply to Professor Lyons’ suggestion that a utilitarian cannot explain how legal rights have moral force, and at the same time to urge that the particular form of utilitarianism espoused by Professor Hare in his recent work does seem to be open to the difficulty Professor Lyons alleges. Professor Card says she is ‘not dissatisfied’ with this reasoning. I suspect that Card views (...) my criticism of Professors Lyons and Hare as part of an in-house squabble among philosophers all of whom have utilitarian leanings of one sort or another; and she is not disposed to intervene in this. She does, however, have serious reservations about utilitarian views of rights in general, and about mine in particular; her paper consists almost entirely of her statement of these reservations. I find her remarks very welcome, since they express some objections which may be widely felt, and a response to which may therefore contribute to philosophers’ thinking about these issues. (shrink)

Friendships have important influences on children's well-being and future adjustment, and interpersonal forgiveness has been suggested as a crucial means for children to maintain friendships. However, existing measures of preadolescent children's forgiveness are restricted by developmental limitations to reporting emotional responses via questionnaire and inconsistent interpretations of the term “forgive.” This paper describes development and testing of concurrent and discriminant validity of a pictorial measure of children's emotional forgiveness, the Children's Forgiveness Card Set. In Study 1, 148 Australian children aged (...) 8–13 years responded to a hypothetical transgression in which apology was manipulated and completed the CFCS and extant measures of forgiveness and socially desirable responding. Following an exploratory factor analysis to clarify the structure of the CFCS, the CFCS correlated moderately with other forgiveness measures and did not correlate with socially desirable responding. Apology predicted CFCS responding among older children. In Study 2 an exploratory factor analysis broadly replicated the structure of the CFCS among a sample of N = 198 North American children aged 5–14 years. We also fitted an exploratory bi-factor model to the Study 2 data which clarified which cards best measured general forgiveness, or positive or hostile aspects of responding to transgressions. Apology once again predicted the CFCS, this time regardless of age. The CFCS appears a potentially valid measure of children's emotional forgiveness. Potential applications and differences between explicit and latent forgiveness in children are discussed. (shrink)

Analyzing Zhuangzi’s Wild Card as presented by Brook Ziporyn, this essay aims (1) to clarify and draw out certain implications of Zhuangzi’s epistemological agnosticism and perspectivism (qua Ziporyn’s reading thereof), only (2) to problematize Zhuangzi’s response to this epistemological agnosticism and perspectivism (qua Ziporyn’s reading thereof). In turn, given the success of my argumentation, Zhuangzi will prove to be as pertinent (and unsettling) as ever.

The concept of medical futility has come to be seen in some quarters as a value-neutral trump card when dealing with issues of power and conflicting values in medicine. I argue that this concept is potentially useful, but only in a social context that provides a normative framework for its use. This social context needs to include a broad consensus about the purpose of medicine and the nature of the physician-patient relationship.

The distinctive security features of the Spanish electronic national identity card, known as Documento Nacional de Identidad electrónico, allow us to propose the usage of this cryptographic smart card in an authentication framework that can be used during the registration and login phases of internet services where the validation of the user’s age and real identity are key elements, as it is the case for example of the so-called social networks. Using this mechanism with NFC-capable devices, the identity and age (...) of the potential user can be determined, allowing or denying the access to the service based on that information. (shrink)

This paper examines social network size in contemporary Western society based on the exchange of Christmas cards. Maximum network size averaged 153.5 individuals, with a mean network size of 124.9 for those individuals explicitly contacted; these values are remarkably close to the group size of 150 predicted for humans on the basis of the size of their neocortex. Age, household type, and the relationship to the individual influence network structure, although the proportion of kin remained relatively constant at around (...) 21%. Frequency of contact between network members was primarily determined by two classes of variable: passive factors (distance, work colleague, overseas) and active factors (emotional closeness, genetic relatedness). Controlling for the influence of passive factors on contact rates allowed the hierarchical structure of human social groups to be delimited. These findings suggest that there may be cognitive constraints on network size. (shrink)

Fourth-year medical students at the University of Colorado School of Medicine distributed cards to patients in the emergency department asking, "What Worries You Most?" The patients' responses provided insight about their most pressing concerns, often unrelated to their "chief complaints.".

The selection strategies of individuals and 2-person cooperative groups were investigated in 5 concept-attainment problems. 2 types of stimulus displays were used: (a) form displays, consisting of geometric forms varying in 6 attributes with 2 levels of each, (b) sequence displays, consisting of 6 plus and/or minus signs in a row. The arrangement of cards in the stimulus displays was ordered or random. The principal results were: (a) 2-person groups used the focusing strategy more, required fewer card choices to (...) solution, and required more time than individuals; (b) form displays resulted in more use of the focusing strategy than sequence displays, with no difference in number of card choices; (c) no difference between ordered and random arrays in use of the focusing strategy or number of card choices. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

The Internet and Internet applications such as cloud computing continue to grow at an extraordinary rate, enabled by the Internet's open architecture and the vibrant lightly regulated Internet service provider (ISP) market. Proposals to hold ISPs responsible for content and software shared by their customers would dramatically constrain the openness and innovation that has been the hallmark of the Internet to date. Rather than taking the kind of approach favored by Raphael Cohen-Almagor, government should enlist the assistance of other intermediaries (...) such as credit card companies in targeted actions against illegal activities online. In addition, they should foster improved online authentication, which could support “zones of trust” on the Internet. (shrink)

Purpose Prescription stimulant use as “cognitive enhancers” has been described among undergraduate college students. However, the use of prescription stimulants among future health care professionals is not well characterized. This study was designed to determine the prevalence of prescription stimulant misuse among students at an academic health sciences center. -/- Method Electronic surveys were e-mailed to 621 medical, pharmacy, and respiratory therapy students at East Tennessee State University for four consecutive weeks in fall 2011. Completing the survey was voluntary and (...) anonymous. Surveys asked about reasons for, frequency of, and side effects of nonprescription misuse of prescription stimulants. Given the sensitive material, an opportunity to win one of ten $50 gift cards was used as an incentive. -/- Results Three hundred seventy-two (59.9%) students completed the survey from three disciplines (47.6% medical, 70.5% pharmacy, and 57.6% respiratory therapy). Overall, 11.3% of responders admitted to misusing prescription stimulants. There was more misuse by respiratory therapy students, although this was not statistically significant (10.9% medicine, 9.7% pharmacy, 26.3% respiratory therapy; P = .087). Reasons for prescription stimulant misuse included to enhance alertness/ energy (65.9%), to improve academic performance (56.7%), to experiment (18.2%), and to use recreationally/get high (4.5%). -/- Conclusions Prescription stimulant misuse was prevalent among participating students, but further research is needed to describe prevalence among future health care workers more generally. The implications and consequences of such misuse require further study across professions with emphasis on investigating issues of academic dishonesty (e.g., “cognitive enhancement”), educational quality, and patient safety or health care quality. (shrink)

In this paper, we propose a new model for development, one that transcends the North–South dichotomy and goes beyond a narrow conception of development as an economic process. This model requires a paradigm shift toward a new metaphor that develops sustainability, rather than sustains development. We conclude by defending a ‘report card on development’ as a means for evaluating how countries perform within this new paradigm.

In lieu of an abstract, here is a brief excerpt of the content:Hitler, the Holocaust, and the Tiantai Doctrine of Evil as the Good:A Response to David R. LoyBrook ZiporynIn a recent issue of this journal (vol. 54 [1]:99-103), David Loy has done me the honor of publishing his sympathetic and thoughtful review of my book Evil and/or/ as the Good: Omnicentrism, Intersubjectivity, and Value Paradox in Tiantai Buddhist Thought (Cambridge, MA: Harvard University Press, 2000). Loy has done an excellent (...) job of bringing to the forefront some of the most troubling and distinctive aspects of the Tiantai Buddhist position on evil, as expressed in particular in the works of Siming Zhili, the focus of my book. Inevitably, with the nit-picky vanity that perhaps assails every reviewee, I feel some points have been imperfectly understood or represented, but in general I want before anything else to express my gratitude to Loy for the insight and acuity with which he has handled this material, the care he has taken in reading and responding to the book, and the candor, lucidity, and forcefulness with which he has expressed a very reasonable, non-Tiantai Mahāyāna response to some of the more radical and counterintuitive Tiantai ideas.But one particularly great service Loy has done is to present a very important and necessary challenge: what would these Tiantai writers, with their bizarre ideas about the interpenetration, nay, identity, of good and evil have to say about Hitler and the Holocaust? Putting this particular topic up as a casual example to be employed in an academic discussion, in effect "making use of" the mountains of corpses in the context of an ivory-tower discussion of subtle logical and ontological hairsplitting, perhaps will strike some as being in more than questionable taste. But there are points to be made here, and it is a valid question, one that needs to be addressed—indeed, that we cannot help addressing—even when it is played as a card all the meanings of which have already been determined. Loy is quite right: these mountains of corpses are always already in play in the background of our discussions of moral doctrines, perhaps even in the interstices of our casual entertainments, and we let ourselves off too easily if we leave them in the background, as unexamined, prepackaged moral tokens, or stock bugaboos whose "use-value" in the culture has already been nonnegotiably and comfortably mapped out. This is the extreme test case that anyone who wants to talk seriously about values and ethics must face head-on. For these reasons I want to take this opportunity to extend the thought experiment and respond to this challenge, speaking for the sake of argument in the name of the Tiantai doctrine, in the hopes that this will perhaps initiate a dialogue with specialists in other systems of moral theory, who might attempt a similar experiment.To do this, however, it will be necessary to take up a few of the more general theoretical questions raised in Loy's review. The first of these concerns the relation between ultimate truth and provisional truth. Loy acknowledges that, as argued in [End Page 329] the book, the Tiantai position gives a higher status to provisional or conventional truth than most Mahāyāna Two Truths doctrines, accurately paraphrasing the conclusion that "for Tiantai, however, the provisional ends up being equal to the ultimate truth." But, on the other hand, he wishes to point out as a potential shortcoming of the Tiantai position that it seems to overstress the "highest point of view." This assertion comes in the context of a grudging attempt to make sense of the Tiantai affirmation of evil from the point of view of the general Mahāyāna Two Truths theory, thereby, in my opinion, fatally distorting the point. Loy is willing to admit "the fact that from the highest point of view every possible apprehension—including evil ones—is neither a distortion of reality nor subject to invalidation by some other more privileged perspective." This strikes Loy as problematic, and he offers his own solution: it lies in "realizing that this 'ultimate' point of view is insufficient by itself—that it always needs... (shrink)

There are indications that the interpersonal affective factor and the social deviation factor, both of which are underlying dimensions of psychopathy, have a positive and a negative relationship, respectively, with executive functioning. However, this is seldom taken into consideration in the research on the relationship between executive functioning and psychopathy, which may be an explanation for the many inconsistent results in this area as reported in the literature (e.g., Rogers, 2006). In the present study, executive functioning was studied using the (...) Wisconsin Card Sorting Test (WCST) in 53 inpatients of a Dutch forensic psychiatric clinic who were classified by means of the Psychopathy Checklist-Revised (PCL-R). Special attention was given to the relationship between the two separate factors and executive functioning. Age, educational level, and substance abuse were controlled for in the analysis. No difference was found between psychopathic (N = 17) and nonpsychopathic (N = 36) patients in the WCST scoring categories, nor was there a significant difference in the four diagnostic subgroups defined by the two factors. However, the trends observed do justify further study in this direction. (shrink)

International Archives of the History of Ideas Archives internationales d'histoire des idées, Vol. 196. -/- Introduction, S. Hutton; Nicholas of Cusa : Platonism at the Dawn of Modernity, D. Moran; At Variance: Marsilio Ficino Platonism And Heresy, M.J.B. Allen; Going Naked into the Shrine:Herbert, Plotinus and the Consructive Metaphor, S.R.L.Clark; Commenius, Light Metaphysics and Educational Reform, J. Rohls ; Robert Fludd’s Kabbalistic Cosmos, W. Schmidt-Biggeman; Reconciling Theory and Fact:The Problem of ‘Other Faiths’ in Lord Herbert and the Cambridge Platonists, D. (...) Pailin; Trinity, Community and Love: Cudworth’s Platonism and the Idea of God, L. Armour; Chaos and Order in Cudworth’s Thought, J-L. Breteau; Cudworth, Prior and Passmore on the Autonomy of Ethics, R. Attfield; Substituting Aristotle: Platonic Themes In Dutch Cartesianism, H. van Ruler; Soul, Body, And World: Plato’s Timaeus And Descartes’ Meditations, C. Wilson ; Locke, Plato and Platonism, G.A.J. Rogers; Reflections on Locke’s Platonism, V. Nuovo; The Platonism at the Core of Leibniz’s Philosophy, C. Mercer; Leibniz and Berkeley: Platonic Metaphysics and ‘The Mechanical Philosophy’, S. Brown; Which Platonism for which Modernity? A Note on Shaftesbury’s Socratic Sea-Cards, L. Jaffro; Platonism, Aesthetics and the Sublime at the Origins Of Modernity, D. Hedley. (shrink)

Philosophy &Public Affairs, Volume 47, Issue 1, Page 72-103, Winter 2019.

European Journal of Philosophy, EarlyView.

This distinction has sometimes been read as purely epistemic, resting not on things, but on our knowledge of them: there is one world, not two, though it may be apprehended in two ways. But this view is patently at odds with the text. Knowledge and opinion are δυνάμεις, "faculties," to be distinguished and defined by their objects, no less than by the state of mind they produce, and Plato clearly states that the fallibility and unclearness of opinion is rooted in (...) the relative unreality of opinables. (shrink)

The problem of computational complexity of semantics for some natural language constructions – considered in [M. Mostowski, D. Wojtyniak 2004] – motivates an interest in complexity of Ramsey quantifiers in finite models. In general a sentence with a Ramsey quantifier R of the following form Rx, yH(x, y) is interpreted as ∃A(A is big relatively to the universe ∧A2 ⊆ H). In the paper cited the problem of the complexity of the Hintikka sentence is reduced to the problem of computational (...) complexity of the Ramsey quantifier for which the phrase “A is big relatively to the universe” is interpreted as containing at least one representative of each equivalence class, for some given equvalence relation. In this work we consider quantifiers Rf, for which “A is big relatively to the universe” means “card(A) > f (n), where n is the size of the universe”. Following [Blass, Gurevich 1986] we call R mighty if Rx, yH(x, y) defines N P – complete class of finite models. Similarly we say that Rf is N P –hard if the corresponding class is N P –hard. We prove the following theorems. (shrink)

Biomedical research policy in recent years has often tried to make such research more ‘translational’, aiming to facilitate the transfer of insights from research and development to health care for the benefit of future users. Involving patients in deliberations about and design of biomedical research may increase the quality of R&D and of resulting innovations and thus contribute to translation. However, patient involvement in biomedical research is not an easy feat. This paper discusses the development of a method for involving (...) patients in biomedical research aiming to address its main challenges.After reviewing the potential challenges of patient involvement, we formulate three requirements for any method to meaningfully involve patients in biomedical research. It should enable patients to put forward their experiential knowledge, to develop a rich view of what an envisioned innovation might look like and do, and to connect their experiential knowledge with the envisioned innovation. We then describe how we developed the card-based discussion method ‘Voice of patients’, and discuss to what extent the method, when used in four focus groups, satisfied these requirements. We conclude that the method is quite successful in mobilising patients’ experiential knowledge, in stimulating their imaginaries of the innovation under discussion and to some extent also in connecting these two. More work is needed to translate patients’ considerations into recommendations relevant to researchers’ activities. It also seems wise to broaden the audience for patients’ considerations to other actors working on a specific innovation. (shrink)

This essay explores the role of informal logicand its application in the context of currentdebates regarding evidence-based medicine. This aim is achieved through a discussion ofthe goals and objectives of evidence-basedmedicine and a review of the criticisms raisedagainst evidence-based medicine. Thecontributions to informal logic by StephenToulmin and Douglas Walton are explicated andtheir relevance for evidence-based medicine isdiscussed in relation to a common clinicalscenario: hypertension management. This essayconcludes with a discussion on the relationshipbetween clinical reasoning, rationality, andevidence. It is argued that (...) informal logic hasthe virtue of bringing explicitness to the roleof evidence in clinical reasoning, and bringssensitivity to understanding the role ofdialogical context in the need for evidence inclinical decision making. (shrink)

This note deals with the prepositional uniformity principlep-UP: p x N A (p, x) x N p A (p, x) ( species of all propositions) in intuitionistic mathematics.p-UP is implied by WC and KS. But there are interestingp-UP-cases which require weak KS resp. WC only. UP for number species follows fromp-UP by extended bar-induction (ranging over propositions) and suitable weak continuity. As corollaries we have the disjunction property and the existential definability w.r.t. concrete objects. Other consequences are: there is no (...) non-trivial countable partition of;id is the only injective function from to; there are no many-place injective prepositional functions; card () is incomparable with the cardinality of all metric spaces containing at least three elements. (shrink)

In this paper I consider how thinking emerges out of human infants' relatedness towards the personal and non-personal world. I highlight the contrast between cognitive aspects and cognitive components of psychological functioning, and propose that even when thinking has become a partly separable component of the mind, affective and conative aspects inhere in its nature. I provide illustrative evidence from recent research on the developmental psychopathology of autism. In failing to adopt a developmental perspective, contemporary theorizing has displaced thinking from (...) where it is properly situated - intimately woven with feeling as well as action, and infused with qualities of interpersonal relatedness from which its structure is derived. (shrink)

A full discussion on his understanding of rights as "trump cards" which privilege the individual claim over the group policy; the critique of legal positivism; the history of a legal institution according to the analogy of a chain novel; and the insistence upon a theory of adjudication that is both constructive and yet faithful to the deepest intentions of legal documents.

Consider two entities x and y, and a relation R which holds among them. Is R’s existence accountable merely in terms of the non relational properties exhibited by x and y, once they interact? Or, is it more appropriate to say that R is independent of x and y, and these acquire sets of relational properties because of their being related through R? In case the former option obtains, the existence of relations is reducible to the relevant properties of the (...) related terms. As a consequence, some version of antirealism or eliminativism towards relations turns out to be true. Otherwise they are irreducible, and ontological analysis cannot be dispensed with relations treated as basic or primitive entities. The first section of my paper provides a framework for handling ontological facts about relations. I will address the assessment of the notions of internal and external relations by K. Mulligan. In the second section I will put my cards on the table. My purpose is to defend a Moorean approach to relations, i.e. both internal and external relations exist. I will briefly outline my methodology, and I will comment on the kind of evidence usually referred to in the debate. My view is that evolutionary research on groups behavior may play an important role. In the third section of the paper I will show that commonsense intuitions on relationships among human beings endorse an external reading of relations. My claim is supported by notorious examples drawn from literature. In the final section I will consider whether evolutionary research on human prosociality provides an empirical setting for the assessment of the commonsense understanding of (at least some) relations in terms of externality. I expand such setting to include behaviors of social animal in general (i.e., animals whose behaviors depends on groups’ hierarchy), and I advance a few reason why empirical research needs postulating the independent existence of relations. (shrink)

Infectious and parasitic diseases cause enormous health problems in the developing world whereas they leave the developed one relatively unscathed. Research and development (R&D) of drugs for diseases that mainly affect people in developing countries is limited. The problem that relatively few drugs are available for diseases that cause an enormous burden of disease in the developing world is called the 'availability problem'. In recent years, the availability problem has received quite a bit of attention. A number of proposals have (...) been fielded as to how this problem might be minimized. Wild-card patent extensions, advance market commitments, cash prizes and the Health Impact Fund are prominent examples of such proposals. These proposals can be thought of as pull-mechanisms for R&D of drugs for neglected diseases. What has been coined a 'priority review voucher' is another pull-mechanism. This paper is a critical discussion of this pull-mechanism. First, the original priority review voucher scheme, as proposed by Ridley et al. (2006), is described. A number of objections to this scheme are thereafter presented. A few amendments to the original scheme are then suggested, and it is argued that with these amendments in place, the priority review voucher scheme constitutes an attractive way of stimulating R&D of drugs for neglected diseases. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Living Alone:Solipsism in Heart of DarknessDavid Rudrum"... As if I could read the darkness."Philosophical Investigations, §635We live, as we dream—alone."1 This, Marlow's most eminently quotable aphorism, encapsulates a theme central to the outlook of modernism: what Virginia Woolf called "the loneliness which is the truth about things."2 This loneliness derives not from the absence of others—Marlow is surrounded by friends when he makes this assertion. It is a deeper (...) condition brought about by recognizing the limits of selfhood, by confronting or being confronted by them. This condition is central to Marlow's narrative predicament: he attempts to fathom the enigmatic self that is Kurtz, to understand "the tempestuous anguish of his soul" (HoD, p. 246); he is led, by this attempt, to question the nature of his own self; and, finally, he tries to relay the impenetrable essence of both these selves to the "other minds" of his narratees on the yawl Nellie. As we shall see, Marlow concedes defeat in all three of these struggles. Heart of Darkness, then, is a novel beset by the limits of subjectivity.It is also a novel which foregrounds the limits of language. Marlow concludes that we live in isolation from one another after musing on the failure of language to communicate adequately, to facilitate intersubjective understanding: "it is impossible to convey the life-sensation of any given epoch of one's existence" (HoD, p. 172), he says. [End Page 409] Conveying the meaning of his narrative to others is repeatedly written off as unattainable, and on numerous occasions Marlow, presumably wrestling with sheer wordlessness, falls silent.3 Indeed, Marlow's narrative is peppered with words highlighting the limits of language: words like "inconceivable" and "unspeakable," which F. R. Leavis famously dismissed as "overworked."Leavis described Conrad's "adjectival insistence upon inexpressible and incomprehensible mystery" as "worse than supererogatory," "tending to cheapen the tone" to a point "little short of disastrous." He concluded that Conrad was "intent on making a virtue out of not knowing what he means."4 That Leavis—a critic who fetishized "the concrete presentment of incident, setting and image" through the concrete use of words—should have failed to grasp and to value the novel's brush with wordlessness, is unsurprising (Leavis, p. 208). Nor is it surprising that two of the episodes in the novel that most clearly encounter the limits of language—Kurtz's last words and Marlow's lie about them—were written off by Leavis as examples of Conrad having a "bad patch" (Leavis, p. 208). Yet it is nevertheless instructive that a novel that insists on its linguistic and communicative limits should thus have been misread.This article reads these two issues of the limits of language and the limits of subjectivity together. To do so is to invoke a philosophical position in which language, selfhood and worldhood are interrelated, and their limits coterminous—a position found in the early thought of Ludwig Wittgenstein.ILike Marlow, Wittgenstein also sees the self as essentially isolated from other selves, and language as demarcating its limits. In his Tractatus Logico-Philosophicus, the interconnected remarks "The limits of my language mean the limits of my world" and "I am my world" delineate Wittgenstein's rethinking of the "egocentric predicament" in which, to paraphrase Marlow, we all live alone.5 This position entails a close relationship with solipsism: as Wittgenstein says, "what the solipsist means is quite correct" (TLP, 5.62)—which is not, of course, to suggest that solipsism itself is correct. The grammar of Marlow's assertion encapsulates this point. The card-carrying solipsist would assert "I live alone," but the loneliness that Marlow and Wittgenstein envisage is a [End Page 410] condition of our subjectivity that we all have in common, but cannot share. It is a transcendental solipsism.Nearly 300 years before Heart of Darkness was written, a poem by Robert Herrick anticipated some aspects of Marlow's assertion of transcendental solipsism:Dreames Here we are all, by day; By night w'are hurl'd By dreames, each one, into a sev'rall world.6This poem makes explicit something left implicit in Marlow's... (shrink)

This paper deals primarily with countable, simple, connected graphs and the following two conditions which are trivially satisfied if the graphs are finite: (a) there is an edge-recognition algorithm, i.e., an effective procedure which enables us, given two distinct vertices, to decide whether they are adjacent, (b) there is a shortest path algorithm, i.e., an effective procedure which enables us, given two distinct vertices, to find a minimal path joining them. A graph $G = \langle\eta, \eta\rangle$ with η as set (...) of vertices and η as set of edges is an α-graph if it satisfies (a); it is an ω-graph if it satisfies (b). G is called r.e. (isolic) if the sets ν and η are r.e. (isolated). While every ω-graph is an α-graph, the converse is false, even if G is r.e. or isolic. Several basic properties of finite graphs do not generalize to ω-graphs. For example, an ω-tree with more than one vertex need not have two pendant vertices, but may have only one or none, since it may be a 1-way or 2-way infinite path. Nevertheless, some elementary propositions for finite graphs $G = \langle\nu, \eta\rangle$ with $n = \operatorname{card}(\nu), e = \operatorname{card}(\eta)$ , do generalize to isolic ω-graphs, e.g., n - 1 ≤ e ≤ n(n - 1)/2. Let N and E be the recursive equivalence types of ν and η respectively. Then we have for an isolic α-tree $G = \langle\nu, \eta\rangle: N = E + 1$ iff G is an ω-tree. The theorem that every finite graph has a spanning tree has a natural, effective analogue for ω-graphs. The structural difference between isolic α-graphs and isolic ω-graphs will be illustrated by: (i) every infinite graph is isomorphic to some isolic α-graph; (ii) there is an infinite graph which is not isomorphic to any isolic ω-graph. An isolic α-graph is also called a twilight graph. There are c such graphs, c denoting the cardinality of the continuum. (shrink)

In his article ‘A Cavalry Unit in the Army of Antigonus Monophthalmus: Asthippoi’, N. G. L. Hammond argues that the reading of the manuscript R at Diodorus 19. 29. 2 should be retained and that we should read ⋯π⋯ π⋯σι δ⋯ το⋯ς τε ⋯σθ⋯ππους ⋯νομαζομ⋯νους κα⋯ τοὺς ⋯κ τ⋯ν ἄνω κατοικο⋯ντων ⋯κτακοσιο⋯ς. The readings of F and its copy X, ⋯νθ⋯ππους, and the commonly accepted conjecture of Wesseling ⋯μɸ⋯ππους, should both be abandoned. Hammond's arguments for retaining this reading are that (...) between the variant readings of R and F, R ‘is the more often correct’ ; ⋯σθ⋯ππους, the reading of R, is preferable to F's ⋯νθ⋯ππους on the principle of ‘lectio difficilior’; the ‘difficulty’ of his lectio difficilior is made less by the arguments presented by A. B. Bosworth, 245 ff.), for the restoration at several places in the text of Arrian's Anabasis the word ⋯σθ⋯ταιροι, in place of the editorial emendation of πεζ⋯ταιροι. ‘For just as asthetairoi meant an élite group of Macedonian infantrymen,’ says Hammond, ‘so asthippoi should mean an élite group of Macedonian cavalrymen.’ He then proceeds to examine the passage and its context in an attempt to find confirmation of this proposition and comes to the conclusion that Diodorus' text says that there were 800 cavalrymen, broken into two groups, the asthippoi and ‘the men from the up-country settlers’; these, though having different names, had a close relationship to each other, as is shown by their being brigaded together. Following his derivation of asthetairoi as meaning ‘townsmen-companions’, i.e. companions recruited from the towns of Upper Macedonia, he argues that asthippoi were cavalry recruited from the towns of Upper Macedonia and that τοὺς ⋯κ τ⋯ν ἄνω κατοικο⋯ντων means ‘the sons of settlers in up-country Macedonia’. These 800, says Hammond, were both among Antigonus' best troops and ‘were Macedonians from Europe’. We thus appear, on Hammond's interpretation, to have here a group of 800 Macedonian élite cavalrymen, all of whom were recruited in Upper Macedonia's townships, but of whom some were chosen to be the cavalry-equivalent of the élite ‘townsmen-companions’ by their title of ‘townsmen-cavalry’, whilst the others, similarly recruited – but perhaps of a younger generation? – had no particular distinguishing title beyond ‘sons of settlers in up-country Macedonia’.Now, while it would be exciting to be able to add another one, possibly two Macedonian cavalry units to the Macedonian army of Philip, Alexander and the Successors, there are several aspects of Hammond's arguments that, it seems to me, are less than convincing. Thus, whilst it seems beyond reasonable doubt that ⋯σθ⋯ταιροι should be retained in the text of Arrian, appearing, as it does, six times, this is not an argument that ⋯σθ⋯ππους should be read in Diodorus' text. Both it and F's reading of ⋯νθ⋯ππους are hapax legomena and it is possible that both readings are wrong. But even if we retain ⋯σθ⋯ππους as the correct reading, Hammond's explanation of its meaning is open to objection on several counts. (shrink)

Given a structure for a first-order language L, two objects of its domain can be indiscernible relative to the properties expressible in L, without using the equality symbol, and without actually being the same. It is this relation that interests us in this paper. It is called Leibniz equality. In the paper we study systematically the problem of its definibility mainly for classes of structures that are the models of some equality-free universal Horn class in an infinitary language Lκκ, where (...) κ is an infinite regular cardinal. (shrink)

We generalize two well-known model-theoretic characterization theorems from propositional modal logic to first-order modal logic. We first study FML-definable frames and give a version of the Goldblatt–Thomason theorem for this logic. The advantage of this result, compared with the original Goldblatt–Thomason theorem, is that it does not need the condition of ultrafilter reflection and uses only closure under bounded morphic images, generated subframes and disjoint unions. We then investigate Lindström type theorems for first-order modal logic. We show that FML has (...) the maximal expressive power among the logics extending FML which satisfy compactness, bisimulation invariance and the Tarski union property. (shrink)