We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial (...) characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)

All eyes are turned towards genomic data and models as the source of knowledge about whether human races exist or not. Will genomic science make the final decision about whether racial realism (e.g., racial population naturalism) or anti-realism (e.g., racial skepticism) is correct? We think not. We believe that the results of even our best and most impressive genomic technologies underdetermine whether bio-genomic races exist, or not. First, different sub-disciplines of biology interested in population structure employ distinct concepts, aims, measures, (...) and models, producing cross-cutting categorizations of population subdivisions rather than a single, universal bio-genomic concept of "race." Second, within each sub-discipline (e.g., conservation biology, phylogenetics), genomic results are consistent with, and map multiply to, racial realism and anti-realism. Indeed, racial ontologies are constructed conventionally, rather than discovered. We thus defend a /constructivist conventionalism/ about bio-genomic racial ontology. Choices and conventions must always be made in identifying particular kinds of groups. Political agendas, social programs, and moral questions premised on the existence of naturalistic race must accept that no scientifically grounded racial ontology is forthcoming, and adjust presumptions, practices, and projects accordingly. (shrink)

In book 10 of the Republic we find a new argument for the division of the soul. The argument’s structure is similar to the arguments in book 4 but, unlike those arguments, it centres on a purely cognitive conflict: believing and disbelieving the same thing, at the same time. The argument presents two interpretive difficulties. First, it assumes that a conflict between a belief and an appearance—e.g. disbelieving that a stick partially immersed in water is, as it appears, bent—entails a (...) conflict between beliefs. Prima facie, there is only one belief, the belief that contradicts the appearance. Second, it is unclear what parts of the soul Plato intends to divide between: some argue that it is, as in book 4, a partition between a rational and a non-rational part; others argue that it is a new partition between a higher and a lower subdivision of the rational part. This paper offers solutions to both difficulties through an analysis of what Plato means by φαινόμενα, ‘appearances’, and δόξαι, ‘beliefs’. It is argued, first, that the relevant appearances are entirely sensory but nonetheless sufficiently belief-like to (a) warrant being called δόξαι and (b) oppose, by themselves, our beliefs; there is no need for a third mental state, a belief that assents to the appearance. A second claim concerns a central line in the argument, 602e4–6, that has served as the primary evidence that the partition is within the rational part of the soul. Those who wish to avoid this conclusion generally resort to alternative, and less natural, translations of 602e4–6. It is argued that this is unnecessary: once we have correctly understood sensory appearances, we see that the standard translation of 602e4–6 in fact entails a division between a rational and a non-rational part of the soul. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

That i) there is a somehow determined chronology of Plato’s dialogues among all the chronologies of the last century and ii) this theory is subject to many objections, are points this article intends to discuss. Almost all the main suggested chronologies of the last century agree that Parmenides and Theaetetus should be located after dialogues like Meno, Phaedo and Republic and before Sophist, Politicus, Timaeus, Laws and Philebus. The eight objections we brought against this arrangement claim that to place the (...) dialogues like Meno, Phaedo and Republic both immediately after the early ones and before Parmenides and Theaetetus is epistemologically and ontologically problematic. -/- Key Words: Plato; chronology; knowledge; being; Parmenides -/- Introduction While the ancient philosophers, doxographers and commentators from Aristotle onward considered, more or less, the question of the date and arrangement of the dialogues (cf. Irwin 2008, 77 n. 69), they would not observe a firm necessity to consider the progress of Plato’s theories in dialogues, maybe because they did not think of any essential shift in there. We might be able to say, nevertheless, that the most prominent feature of the ancient attitude to Plato was its peculiar attention to the Republic and the Timaeus as the most mature works in his philosophy and also the consideration of Laws as a later work. This tendency can be discovered from the general viewpoint of the first chronologies of the early 19th century after starting to deal with the issue. That Schleiermacher observed Republic as the culmination of Plato’s philosophy and as one of the latest dialogues besides Laws and Timaeus could reflex the implicit chronology of the tradition in the first mirrors it found. Another tendency in Schleiermacher is taking the triology of Theaetetus, Sophist and Politicus as relatively early. From the last quarter of 19th century onward, stylometry helped scholars to establish a new framework to constructa new arrangement between the dialogues. Based on stylistic as well as literary findings, Campbell (1867, xxxff.) argued for the closeness of the style of Sophist and Politicus with Timaeus, Critias, Philebus and Lawsthat, especially because of the certain evidence about this last dialogue’s lateness, led to the consideration of all as late dialogues. Almost every other stylistic effort after Campbell approved the similarities between Sophist and Politicus with Timaeus, Critias, Philebus and Laws. The result of all such investigations led to a new chronology that, despite some differences, has a fixed structure in all its appearances. 1. The Standard Chronology of the Dialogues The chronologies that are now commonly accepted are mostly based on the arrangement of dialogues to three groups corresponding to three periods of Plato’s life, which became predominant after applying stylistic features in assessing the similarities between dialogues. The fact that all the stylometric considerations reached to the similar results about the date of dialogues while they were assessing different stylistic aspects helped the new chronology become prevailing not only among stylistic chronologies but also between those like Fine, Kahn and Vlastos who were inclined more to the content-based arrangements. Even this latter group could not neglect the apparently certain results of using the method of stylometry. This was the main reason, I think, that made what they called content-based chronology be under the domination of stylometry much more than they could expect. The division of the dialogues into three separate groups became something that most of the scholars took for granted so far as Kahn thinks this division 'can be regarded as a fixed point of departure in any speculation about the chronology of the dialogues' (1996, 44). Thereafter, all the chronologists are accustomed to divide the dialogues to three groups of early, middle and late corresponding to the three stages of Plato’s life. Nevertheless, some of them tried to make subdivisions among each group and introduce some of the dialogues as transitional between different periods and thus reached to a fourfold classification of the dialogues. Although theycould never achieve to a consensus about the place of some dialogues, about which we will discuss soon, the whole spirit of theirchronological arrangements is the same and thus compelling enough for us to unify all of them with the label of 'Standard Chronology of Dialogues' (SCD). We brought together some of the most famous chronologies in the table below to make a comparison easier and to show how all are approximately of the same opinion about the place of some dialogues. The following points must be noted about this table: 1. I divided the dialogues to eight groups of early, late early, transitional, early middle, late middle, post-middle, early late, and late. Although none of the chronologists applies this classification, it can be helpful to compare them. In this table, for example, if one of the chronologist’s beholds one of the dialogues as later than all the dialogues of middle group, it is considered here as late middle. Otherwise, if it is emphasized that it is after all of them, it is considered as post-middle. The same is true about the dialogues of the late group in which I regarded the first dialogues of that period as early late only in those who explicitly considered some dialogues as earlier than other ones in the late group. Though, therefore, some of the dialogues might have not been considered as forming a distinct class, they are distinguished here. A. SCD’s Early and Transitional Dialogues When we move from stylometric to content-based chronologies, the homogeneity between the dialogues of each group is more understandable. Guthrie (1975, v. 4, 50) distinguishes three groups, the first of them includes Apology, Crito, Laches, Lysis, Charmides, Euthyphro, Hippias Minor, Hippias Major, Protagoras, Gorgiasand Ion. In addition to Meno, Phaedo and Euthydems, his first group does not include Cratylus and Menexenus. Unlike Guthrie, almost all the other content-based chronologiesof our study desire to distinguish two categories inside the first group of which the latter must be considered as the transitional group leading to the dialogues of the middle period. Kahn distinguishes four groups of dialogues and arranges two of them before middle period dialogues. The first group including Apology, Crito, Ion, Hippias Minor, Gorgiasand Menexenus he calls 'early' or 'presystematic' dialogues (1998, 124). The second group he calls the 'threshold', 'pre-middle' or 'Socratic' dialogues including seven: Laches, Charmides, Lysis, Euthyphro, Protagoras, Euthydemus and Meno. Based on Vlastos’ arrangement we must distinguish Euthydemus, Hippias Major, Lysis, Menexenus and Meno as 'transitional' dialogues from the 'elenctic' dialogues that are the other dialogues of Kahn’smentioned first two groups plus the first book of theRepublic. Fine also distinguishes 'transitional' dialogues from early or 'Socratic' dialogues,but her transitional dialogues are Gorgias, Meno, Hippias Major, Euthydemus and Cratylus of which she thinks the last two dialogues are 'controversial' (2003, 1). Her Socratic dialogues are all the remaining dialogues of Kahn’s first two groups. In spite of all the differences between the mentioned chronologies, it can be seen that all of them are inclined to arrange the early dialogues in a way that: i) Besides the dialogues that are considered as late, it never includes Republic II-X, Theaetetus, Phaedrus and Parmenides. ii) It intends to consider the dialogues like Euthydemus and Hippias Majorthat look more critical as later among the earlier dialogues or as transitional group. iii) Those who do not consider Meno as a middle period dialogue place it in their second or transitional group. iv) None of the content-based chronologies considers Phaedo and Symposium as early. Stylometric chronologies also intend to put them either as last dialogues among their early ones or as middle. B. SCD’s Middle Period Dialogues Campbell listed Republic, Phaedrus, Parmenides and Theaetetus as his second group of dialogues, an idea thatwas accepted by Brandwood. Ledger’smiddle period dialogueshad Euthydemus, Symposium and Cratylus in addition to the dialogues that Campbell and Brandwood had mentioned as middle. Among content-based chronologies, Guthrie’s list of middle period dialogues did not include Parmenides but some dialogues which had been considered as early in stylometric ones: Meno, Phaedo, Republic, Symposium, Phaedrus, Euthydemus, Menexenus and Cratylus. In sofar as I know, Euthydemus and Menexenus have not been considered as middle by other content-based chronologists and Guthrie is an exception among them. That Phaedo, Phaedrus, Symposium and Republic were middle period dialogues almost all the philosophical chronologists like Kahn, Fine, Vlastos (except Rep.I), Irwin andKraut came along. The dialogues they do not string along about are Meno, Cratylus, Parmenides and Theaetetus. Those like Guthrie, Kraut and Irwin who did not consider Meno as early presumably posit it among middles. The same can be said about Cratylus in the suggested chronologies of Guthrie, Kahn, Vlastos and Kraut. Nonetheless, it is different in case of Parmenides and Theaetetus. Whereas all the mentioned stylometric chronologists like Campbell, Brandwood and Ledger set them among middle period dialogues,the philosophical chronologists, it might seem at first, did not arrive at a consensus about them. While Guthrie and Fine put them as the first dialogues of the late group, Vlastos and Kraut set them as the latest of the middle group, as well as Kahn who puts them as post-middle and amongst the late period dialogues. Regardless the way they classify their groups, their disagreement does not affect the arrangement of the dialogues: they all posit Parmenides and Theaetetus after the series of Meno, Phaedo, Phaedrus, Symposium and Republic and before Sophist, Politicus, Timaeus, Philebus and Laws. To sum up SCD’s arrangement of the middle period dialogues we can add: v) Republic and Phaedrus have been considered by all the mentioned chronologists as dialogues of the middle period. vi) All the philosophical chronologies have reached a consensus about setting Phaedo and Symposium alongside with Republic and Phaedrus as middle. vii) While Stylometric alongside some philosophic chronologists arrange Parmenides and Theaetetus among their middle period dialogues and mostly as the latest among them, other philosophical chronologists put them as the early among the late dialogues. We can conclude then that SCD intends to locate these two dialogues at the boundary between the middle and late period dialogues. -/- . (shrink)

Today's realities require medical institutions to take more careful account of intangible factors that make up an irreplaceable component of cultural characteristics. Changes in the socio-economic conditions of economic activity have led to increased attention of the management of medical institutions to the need to form a corporate style that will provide additional competitive advantages. The purpose of the study is to identify the functions and elements of the corporate style of a medical institution and its subdivisions, to find out (...) its impact on the collective consciousness and behavior of consumers of medical services and to establish requirements for its development. The methodological basis of the study is modern research on the formation of corporate style and its impact on the reputation and successful development of organizations. The main hypothesis of the study is the assumption that corporate style influences the level of recognition and authority of a medical institution. Summary of the main research material. It is proved that an authentic, working corporate style for a modern medical institution is a necessary element of its organizational culture. It is determined that the corporate style contributes to creating a positive image of a medical institution in the eyes of consumers; allows distinguishing a medical institution from other medical institutions with a similar range of services; strengthens the organizational spirit of medical staff; increases the effectiveness of advertising; and creates a favorable image of a medical institution. The originality and practical significance of the study lies in the fact that a comparative analysis of the elements of corporate style of city clinical hospitals in Dnipro, which are clearly implemented on the official pages on the Internet, was carried out. Conclusions and prospects for further research. The conducted research has made it possible to state that the considered medical institutions of the city of Dnipro do not pay the necessary attention to the formation of their own corporate style. Sporadic initiatives and events create the appearance of the existence of a corporate style of a medical institution, but do not ensure the existence of such a corporate style that would work to increase the recognition and authority of a medical institution. (shrink)

This article challenges the orthodox view that there is and can be no scientifically valid concept of race applicable to human beings by presenting a candidate scientific concept of biological race. The populationist concept of race specifies that a “race” is a subdivision of Homo sapiens—a group of populations that exhibits a distinctive pattern of genetically transmitted phenotypic characters and that belongs to an endogamous biological lineage initiated by a geographically separated and reproductively isolated founding population. The viability of (...) the PRC is shown by demonstrating its capacity to withstand a wide range of objections. A common theme is that the objections turn on misconceptions of the idea of a scientific concept of race. The final section argues that the PRC will not foster racism. (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)

Neutrosophic theory has many applications in graph theory, bipolar single valued neutrosophic graphs (BSVNGs) is the generalization of fuzzy graphs and intuitionistic fuzzy graphs, SVNGs. In this paper we introduce some types of BSVNGs, such as subdivision BSVNGs, middle BSVNGs, total BSVNGs and bipolar single valued neutrosophic line graphs (BSVNLGs), also investigate the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision BSVNGs, middle BSVNGs, total BSVNGs and BSVNLGs.

This article proposes to present, in general, the thought of the German philosopher G. W. F. Hegel about history. Using mainly the work Philosophy of History, I seek first to analyze and to explain the different modes of historical approaches elaborated by Hegel, which are: the original history, the reflective history and its subdivisions and, finally, the philosophical history. After that, I center my studies on the concept of progress or, more precisely, historical progress. According to Hegel, philosophical history appears (...) when we perceive that rationality governs the world, and therefore the actions and events that have occurred, occur and will occur are part of this rationality. Such a perception – that is, understanding that history develops and progresses according to rationality – is possible when we turn to the study of history, using it as material, and carefully observing and analyzing past historical events. According to Hegel, this historical process is the course of the spirit, constantly seeking a greater awareness of freedom and, therefore, a greater understanding of itself, because freedom is already in it, and it is not something alien, distant or external, it is in its center and is its substance. According to Hegel, nature, despite its polymorphic transformations, is only a repetitive and monotonous cycle, where there is nothing new under the sun. However, in the process of development of the spirit, that is, the spirit knowing itself, the new appears, this is progress, which, in turn, is aimed at the realization of freedom, with a view to its concretization in the State. (shrink)

L’article de Francis Dupuis-Déri propose que l’action directe constitue une voie privilégiée pour améliorer et encourager des délibérations plus égalitaires et participatives. Mon commentaire est subdivisé en deux parties. Dans un premier temps je situerai l’enjeu de la démocratie délibérative du point de vue de l’action collective. Dans un second temps je reviendrai à la thèse mise en avant par Francis Dupuis-Déri pour mettre en lumière ce qui me semble important dans son analyse. Je soulignerai par ailleurs certaines limites de (...) son texte. Cela me permettra de formuler des remarques supplémentaires au débat relatif à la portée de l’action des mouvements sociaux à l’endroit de la démocratie délibérative.Francis Dupuis-Déri’s paper suggests that direct action represents an excellent mean to enhance and encourage more egalitarian and participatory deliberations. My comment is divided into two parts. Initially I will analyze the issue of deliberative democracy in terms of collective action. In a second step I will return to the thesis put forward by Francis Dupuis-Déri and highlight what I think is important to follow. I will also emphasise some limitations of this thesis. This will allow me to make supplementary remarks in line with the scope of social movements regarding deliberative democracy. (shrink)