This study examines the roles of environmental strategy and accounting in corporate carbon performance, as measured by the Greenhouse Gas (GHG) Protocol. A novel interaction model is developed based on legitimacy theory and natural-resource dependence theory to capture the interaction between environmental strategy and accounting. An international sample of 3322 firms from 73 countries is used in the analysis, based on a panel data design for 17 years (2005–2022). The empirical findings reveal an overall reactive role of these environmental initiatives (...) in relation to carbon performance. The marginal effect analysis shows that environmental accounting favourably moderates the effect of environmental strategic functions on carbon performance, indicating that the former facilitates the translation of the latter into practice. Similarly, environmental strategic initiatives improve the impact of environmental accounting information on carbon performance. The main contribution of this study stems from methodologically demonstrating how the synergy between environmental strategic initiatives and environmental information mechanisms can translate into improved carbon performance. This finding has multiple societal, practical and research implications. The interaction effect evidence can be viewed as consistent with recent trends of integrated approaches to thinking and reporting, where interrelated phenomena are integrated into operational and reporting contexts to improve efficiency. This can be of interest to policymakers, investors, corporate managers and providers of assurance services related to carbon performance. (shrink)

International marketing practices, embedded in a strong ethical doctrine, can play a vital role in raising the standards of business conduct worldwide, while in no way compromising the quality of services or products offered to customers, or surrendering the profit margins of businesses. Adherence to such ethical practices can help to elevate the standards of behavior and thus of living, of traders and consumers alike. Against this background, this paper endeavors to identify the salient features of the Islamic framework of (...) International Marketing Ethics. In particular, it highlights the capabilities and strengths of this framework in creating and sustaining a strong ethical international marketing culture. At the heart of Islamic marketing is the principle of value-maximization based on equity and justice (constituting just dealing and fair play) for the wider welfare of the society. Selected key international marketing issues are examined from an Islamic perspective which, it is argued, if adhered to, can help to create a value-loaded global ethical marketing framework for MNCs in general, and establish harmony and meaningful cooperation between international marketers and Muslim target markets in particular. (shrink)

The question posed is whether the optimization methods of calculus that are often used in social and scientific analyses offer an appropriate analytical approach to analyze problems that are immersed in systemic complexity and its consequences. This paper refers to the portfolio of such complex problems belonging to social and scientific forces. We refer to such a complex combination by the term ‘socio-scientific’. In the study of socio-scientific complexity, dynamic preferences, intricate decisions, and uncertain behavior, endogenous relations and systemic perturbations (...) abound. The arguments presented in this paper establish that the methodological approach of optimization and steady-state equilibrium turns out to be nicety rather than objectivity in the presence of complexity. Complex situations of the socio-scientific universe cause perturbations in the variables; there explaining complexity formed by the social embedding of variables. Indeed, human individuals, institutions and governments, and society at large are complex interrelated entities. Therefore, complex interrelations caused by social embedding remain submerged in social perturbations. However, interactions arising from social embedding also generate endogenous and complex relations. The contribution of this paper is in the area of endogenous learning in the wellbeing objective criterion function. The interrelationships between the emergent cognitive variables now cause interactive embedding, complexity, and social perturbations. Yet such perturbations are not altogether uncontrollable. They can be and need to be controlled for the purposes of social explanation—hence demanding predictability—even as the complex nature of evolutionary systemic learning proceeds. The controllability problem of extreme perturbations leads us to formalize a mathematical methodology to study controllable perturbations while avoiding extreme forms of perturbations in socio-scientific theory. (shrink)

The main aim of this paper is to assess the level of knowledge, attitude and practice of university teachers regarding plagiarism in Bangladesh. An online questionnaire consisted of 20 knowledge questions, 23 attitude items, and 18 practice questions was created using Google Forms. The link to the questionnaire was sent via email to university teachers. The total correct answers for knowledge and practice questions, and the total attitude score were converted to percentile scores and categorized accordingly as poor ( mean (...) + 1 SD). Bivariate analyses were conducted to compare the total knowledge, attitude and practice scores based on demographic and academic variables. Multiple linear regressions were used to identify the association between knowledge, attitude and practice scores, and other covariates. The findings revealed an average level of knowledge, attitude and practice regarding plagiarism among the majority of university teachers. The knowledge, attitude and practice scores were significantly higher for teachers who attended academic writing workshops compared to those who did not attend such events. Demographic and academic variables did not impact knowledge and attitude scores. However, the number of papers published in the last two years and their indexing in Web of Science (WoS) or Scopus significantly impacted attitude and knowledge scores. The multiple regression analyses showed that the practice score was significantly associated with age, highest education, and knowledge. (shrink)

The food security of more than half of the world’s population depends on rice production which is one of the key objectives of precision agriculture. The traditional rice almanac used astronomical and climate factors to estimate yield response. However, this research integrated meteorological, agro-chemical, and soil physiographic factors for yield response prediction. Besides, the impact of those factors on the production of three major rice ecotypes has also been studied in this research. Moreover, this study found a different set of (...) those factors with respect to the yield response of different rice ecotypes. Machine learning algorithms named Extreme Gradient Boosting and Support Vector Regression have been used for predicting the yield response. The SVR shows better results than XGBoost for predicting the yield of the Aus rice ecotype, whereas XGBoost performs better for forecasting the yield of the Aman and Boro rice ecotypes. The result shows that the root mean squared error of three different ecotypes are in between 9.38% and 24.37% and that of R-squared values are between 89.74% and 99.13% on two different machine learning algorithms. Moreover, the explainability of the models is also shown in this study with the help of the explainable artificial intelligence model called Local Interpretable Model-Agnostic Explanations. (shrink)

In this study, we examine investor and firm response to the California Transparency in Supply Chains Act of 2010. The CTSCA requires large retail and manufacturing firms to disclose efforts to eradicate slavery and human trafficking from their supply chains and is a rare example of mandated corporate social responsibility disclosure. Based on a sample of 105 retail companies subject to the CTSCA, we find a significant negative market reaction to the passing of the CTSCA. Furthermore, we find that the (...) reaction is significantly more negative for larger firms and companies facing greater supply chain risks, suggesting that investors place a negative value on exposure to legitimacy threats in the social domain. With respect to company disclosure response, we document relatively high compliance with the legislation, although we also find that the disclosure response appeared to be more symbolic than substantive in nature. Finally, our analysis indicates that both disclosure choice and disclosure extensiveness were significantly higher for the high-supply chain risk companies, suggesting that the response was influenced by concerns with strategic legitimation. Overall, the limited quality of disclosure suggests that, without additional rules and guidance, mandates alone may not lead to meaningful social disclosure. (shrink)

This study examines the influence of the COVID-19 crisis on academic expectations among international students from north-western China. According to past studies, academic expectations are multifaceted, making it critical to test the methods employed to assess this fundamental trait. The outbreak of COVID-19 has resulted in various significant changes in education, which have shifted from traditional to online or mixed formats. As a result, examining international students' academic expectations along with their interactions with adopted technologies is a topic that addresses (...) the current situation and issues. A mixed approach, comprising two different instruments, was followed to achieve this primary objective. While a survey with a questionnaire was undertaken with 551 international students, divided into two groups, ten students were interviewed during and after the lockdowns. The findings revealed that COVID-19 had a significant impact on the academic expectations of students as well as many elements such as training for employment, personal and social development, international student mobility, motivation, social pressure, and social interaction with the help of supporting technologies. In terms of gender, men outperformed women in motivation, social interaction, training for employment, and personal and social development factors. Similarly, as per the grade variable, the same higher trend was seen in postgraduates. Based on these findings, a set of recommendations was put forward. In the future, technology will be helpful in China's educational sector, such as online group collaboration, open education, managing student retention, and supervising teachers' recruitment. (shrink)

Dignity represents the essence of nursing care; hence, nurses are professionally responsible for promoting understanding about the promotion, provision, and preservation of every patient’s dignity, while considering contextual differences. The aim of this study was to explore the factors that influence, promote, or compromise patient dignity. A purposeful sample of 14 participants with hospitalization experience was chosen, and individual in-depth semi-structured interviews were conducted for data collection. Using inductive content analysis, the themes and subthemes related to factors influencing patients’ dignity (...) were explored: “persona” (“personal beliefs” and “personal characteristics”), “communication behaviors” (“verbal interaction,” “body language,” “compassionate behavior,” and “devoting enough time”), and “staff conduct” (“professional commitment,” “adequate human resources,” and “staff’s proficiency and competency”). The findings revealed that it is essential to expand nurses’ insights and knowledge about preserving patients’ dignity and the factors that influence these. Recognizing and focusing on these factors will help nurses to establish practical measures for preserving and promoting patients’ dignity and providing more dignified care at the bedside. (shrink)

Avicenna introduces the primary propositions as the most fundamental principles of knowledge. However, as far as we are aware, Avicenna’s primaries have not yet been independently studied. Nor do Avicenna scholars agree on how to characterize them in the language of contemporary philosophy. It is well-known that the primaries are indemonstrable; nonetheless, it is not clear what the genealogy of the primaries is, how, epistemologically speaking, they can be distinguished from other principles, what their phenomenology is, what the cause of (...) the assent to them is, how to explain the relationship between the ‘innate [nature] of the intellect’ and the primaries and, finally, back to their indemonstrability, in what sense they are ‘indemonstrable’. We will try to fill this gap. As a corollary, we will explain why Gutas’s view [Gutas, Dimitri.... (shrink)

Nielsen Busch and Mjaaland (2023) raise important considerations, but confuse certain critical issues and overlook others, and questions emerge about how these decisions should be made in our socie...

This paper aims at investigating comparatively the ethical orientation of information technology professionals in the Middle East and the United States. It tests for attitudes toward and awareness of ethically-related issues, namely intellectual property, privacy and other general ethical IT aspects. In addition, through a comparison between the two regions, this paper intends to examine whether differences in IT professional demographics and characteristics, including gender and academic level, have any impact on attitudes to business ethics. A ttest is used to (...) establish significant differences between the targeted samples, while an ANOVA F-test is conducted to determine significant differences among the sample countries on a group basis. The results show a general awareness of ethical issues concerning information technology, and no significant differences are found between the two samples. However, different ethical attitudes are reported among respondents in terms of their reactions to the targeted IT ethical aspects. On an individual sample basis, the results about gender support the claim that male and female respondents are different, while mixed results are revealed for the influence of academic level on attitudes towards IT ethics. For intellectual property, the results are significant regarding ethical attitude differences between Middle-Eastern professionals and their counterparts in the US, while no significance differences are reported in terms of privacy. (shrink)

Concept originalism, recently introduced and defended by Sainsbury and Tye, Tye, and Sainsbury, holds that “atomic concepts are to be individuated by their historical origins, as opposed to their semantic or epistemic properties”. The view is immune to Gareth Evans’s “Madagascar” objection to the Causal Theory of Reference since it allows a concept to change its reference over time without losing its identity. The possibility of reference-shift, however, raises the problem of misleading belief reports. S&T try to tackle the problem (...) by strengthening the sufficient condition for a truthful belief report. We will argue that, first, their solution fails, second, and more importantly, their diagnosis of the root of the problem is misguided, third, two initially appealing ways out of the problem fail, and fourth, the prospect of finding a solution to the problem within CO is dim. The view opens the Pandora’s box of reference-shift, in a wide range of cases, without providing the necessary semantic means to take care of them. (shrink)

Tuberculosis is caused by bacillus Mycobacterium tuberculosis. In this study, a mathematical model of tuberculosis is analyzed. The numerical behaviour of the considered model is analyzed including basic reproduction number and stability. We applied three numerical techniques to this model, i.e., nonstandard finite difference scheme, Runge–Kutta method of order 4, and forward Euler scheme. NSFD scheme preserves all the essential properties of the model. Acquired results corroborate that NSFD scheme converges for each step size. While the other two schemes failed (...) to preserve some properties of the model such as positivity and convergence. A graphical comparison presented in this study confirms the numerical stability of the NSFD technique shown here is maintained over a large area. (shrink)

Background The use of lengthy, detailed, and complex informed consent forms is of paramount concern in biomedical research as it may not truly promote the rights and interests of research participants. The extent of information in ICFs has been the subject of debates for decades; however, no clear guidance is given. Thus, the objective of this study was to determine the perspectives of research participants about the type and extent of information they need when they are invited to participate in (...) biomedical research. Methods This multi-center, cross-sectional, descriptive survey was conducted at 54 study sites in seven Asia-Pacific countries. A modified Likert-scale questionnaire was used to determine the importance of each element in the ICF among research participants of a biomedical study, with an anchored rating scale from 1 to 5. Results Of the 2484 questionnaires distributed, 2113 were returned. The majority of respondents considered most elements required in the ICF to be ‘moderately important’ to ‘very important’ for their decision making. Major foreseeable risk, direct benefit, and common adverse effects of the intervention were considered to be of most concerned elements in the ICF. Conclusions Research participants would like to be informed of the ICF elements required by ethical guidelines and regulations; however, the importance of each element varied, e.g., risk and benefit associated with research participants were considered to be more important than the general nature or technical details of research. Using a participant-oriented approach by providing more details of the participant-interested elements while avoiding unnecessarily lengthy details of other less important elements would enhance the quality of the ICF. (shrink)

Background:Emergency care providers are frequently faces with situations in which they have to make decisions quickly in stressful situations. They face barriers to ethical decision-making and recognizing and finding solutions to these barriers helps them to make ethical decision.Objectives:The purpose of this study was to identify barriers of ethical decision-making in Iranian Emergency Medical Service personnel.Methods:In this qualitative research, the participants (n = 15) were selected using the purposive sampling method, and the data were collected by deep and semi-structured interviews. (...) Finally, the data are analyzed using the content analysis approach.Ethical considerations:Permission to conduct the study was obtained from the Ethics Committee of the Shahid Beheshti University of Medical Sciences. The objectives of the study were explained to the participants and written consent was received from them. Also, participants were assured that necessary measures were taken to protect their anonymity and confidentiality.Findings:The results of the analysis are classified in five main categories. It encompasses the following areas: perception of situation, patient-related factors, input and output imbalance, uncoordinated health system, and paradoxes.Conclusion:Emergency Medical Service personnel make ethical decisions every day. It is important that prehospital personnel know how to manage those decisions properly so that clients’ moral rights are respected. Hence, by identifying the dimensions and obstacles of ethical decision-making in Emergency Medical Service personnel, it is possible to enhance the moral judgment and ethical accountability of the personnel and develop the strategies necessary for ethical decision-making in them. (shrink)

Bu çalışma, İslâm Eğitimi perspektifinden küresel vatandaşlık kavramıyla ilgili ilkeler ve uygulama alanlarını açıklığa kavuşturmayı hedeflemektedir. Ayrıca Kur’ân ayetleri ve hadislerde küresel vatandaşlığa yönelik değerleri destekleyen normları ve öğrenim çıktılarını belirlemeyi amaçlamaktadır. Burada küresel vatandaşlık kavramı, bilişsel, duygusal ve davranışsal hedef alanları çerçevesinde din eğitimi derslerindeki örnek uygulama ve uygun konularla birlikte ele alınmıştır. Kur’ân ayetleri ve hadisler doğrultusundaki İslâm inanç ve ahlak ilkeleri, insanların gerek kendi toplumları içinde ve gerekse diğer toplumlar ile olumlu ilişkiler kurmasını teşvik etmektedir. Bu teşvikler (...) hem yerel hem de evrensel özellikler taşımaktadır. Bu yönde karşılaşılan örnek olaylar aynı zamanda İslâm inancının ve ahlak değerlerinin evrenselliğini yaşanmış olaylarla da örtüşecek biçimde yansıtmaktadır. Bu ilkeler aynı zamanda İslâm'ın inanç, ahlak ve hukukla ilgili özel konularının bir bütünlük çerçevesinde ele alınmasını sağlamaktadır. Küresel vatandaşlık konuları öncelikle eğitim felsefesinin genel ve özel amaçları doğrultusunda müfredat çerçevesinde hedef kitleye evrensel bir değer olarak kazandırılmalıdır. Bu konu okullarda eğitsel ve kültürel faaliyetler ile de desteklenmelidir.Özet: Küresel vatandaşlık kavramı bütün dünyada giderek yaygınlık kazanan önemli kavramlar arasında yer almaktadır. İnsanların ortak kimliğinin yanı sıra özellikle göçmen ve mülteci hakları konusu eğitim alanında ön plana çıkmaktadır. Son yıllarda ise uluslararası sorunların çoğalmasıyla birlikte bu konu güncelliğini arttırarak önemini sürdürmektedir. Günümüz toplumlarında karşılıklı hoşgörünün korunması için yapılan çeşitli boyutlardaki farklı çalışmalara ek olarak bu konunun örgün eğitim müfredatlarına dahil edilmesi de gündemdedir.Din eğitimi, küresel vatandaşlık konularını kapsayan başlıca dersler arasında yer almaktadır. Bu nedenle küresel vatandaşlık kavramının din eğitimi açısından temellendirilmesinin yanı sıra din eğitimi müfredatında bilişsel ve davranışsal eğitim metotlarını vurgulamak zorunlu hale gelmiştir. Dolayısıyla bu çalışma, İslâmi eğitim perspektifinden küresel yaşama dönük eğitimin genel bir tasarımını oluşturmayı hedeflemektedir. Ayrıca dini kaynaklarda küresel vatandaşlığa yönelik değerleri destekleyen normları ve öğrenim çıktılarını belirlemeyi amaçlamaktadır.İslâm eğitimi, dini farklılıklara saygı duymayı desteklemektedir. Ancak bu, diğer dinlerin inançlarının onaylandığı anlamına gelmemektedir. Burada, inanç özgürlüğü kapsamına başka dinlerin öğrenilmesi girmemektedir. Bu nedenle, kişinin inancına vurgu ve diğer dinler hakkında takınılan tutum ile farklı din mensuplarına saygı arasında herhangi bir çelişki bulunmamaktadır. Bu durum, Müslümanlar arasındaki mezhep farklılıklarına yönelik takınılacak tutumun nasıl olması gerektiğini de gözler önüne sermektedir. İslâm dünyasında eğitim politikaları çerçevesinde, uluslararası bilgiye erişimi sağlayan ve aynı zamanda özel hayatın korunmasını, kültürel işbirliğini ve birlikte yaşama değerlerini gözeten standartlarda bir müfredat hazırlanabilir. Özellikle İslâm dünyasını, küreselleşmeyle birlikte çeşitli kültürel sorunlarla karşılaştığından dolayı küresel vatandaşlık konusunda bilgilendirilmeye ihtiyaç duyulmaktadır. Bu çerçevede, yabancılaşmaya karşı öze dönüş, az gelişmişlik karşısında kalkınma ve adalet ile çatışmalar karşısında işbirliği bu yöndeki faaliyetlerin doğal sonuçları olarak okunmalıdır. Küresel vatandaşlık kavramı çeşitli araştırmalarda çok yönlü bir biçimde ele alınıp incelenmiş bir konudur. Bütün bu araştırmalardaki temel konular şöyle sıralanabilir: Dünya barışı, toplumlar arası işbirliği ve dayanışma, bireylerin ahlaki sorumlulukları, insan hakları ve hak ihlalleri, çok kültürlülük, çevre sorunları, evrensel düşünce ve bilginin dolaşımı. Bu makalede yukarıda adı geçen kavram ve konular İslâm kaynakları açısından değerlendirilip eğitim müfredatlarına ilişkin öneriler sunulacaktır. İslâm, küresel vatandaşlığın ilkelerini, barış, işbirliği, ahlaki sorumluluk, insan hakları, kültürel çoğulculuk, çevreyi koruma, düşünce ve bilginin evrenselliği konularını desteklemektedir. Tarihte İslâm medeniyetinin farklı coğrafyalarda sunmuş bulunduğu zengin tecrübe bu ilkelere dönük önemli bir ilham kaynağı olarak göz önünde bulundurulmalıdır. Bu ilkeler, eğitim müfredatlarına dahil edilip çok zengin öğrenim çıktıları kazandırılabilir.Kur’ân ayetleri ve hadisler doğrultusundaki İslâm inanç ve ahlak ilkeleri, insanların gerek kendi toplumları içinde ve gerekse diğer toplumlar ile olumlu ilişkiler kurmasını teşvik etmektedir. Bu teşvikler hem yerel hem de evrensel özellikler taşımaktadır. Bu yönde karşılaşılan örnek olaylar aynı zamanda İslâm inancının ve ahlak değerlerinin evrenselliğini yaşanmış olaylarla da örtüşecek biçimde çok iyi yansıtmaktadır. Toplumlar arasındaki bu evrensel değerlerin uygulamasında yerel farklılıklar bulunmaktadır. Bu farklılıklar etnik, ideolojik ve siyasi sebeplerden kaynaklanabilmektedir. Buna rağmen İslâmi değerler Müslüman toplumların ortak noktaları belirlemeye devam etmektedir. Başka ülkelere çeşitli sebeplerle göç etmiş Müslümanlarda da aynı durum geçerliliğini korumaktadır. Eğitim, ulusal ve evrensel değerleri kazandırmada en etkili araç olma özelliğini taşımaktadır. Bu konuyla ilgili değerleri kazandırmada İslâm eğitimi derslerinin önemi ortaya çıkmaktadır. Aynı zamanda vatandaşlık bilgisi, din kültürü ve ahlak bilgisi derslerinin müfredatı da bu konuya katkı sağlamaktadır. Küreselleşme ve bilgi toplumu çağının şartları gereği, Müslüman toplumlar diğer toplumlarla olan ilişkilerinin sınırlarını belirlemeleri gerekmektedir. Yerellikten evrenselliğe geçişte karşılaşılan uyum zorlukları buna örnek olarak gösterilebilir. Coğrafi sınırların etkisinin giderek azalmasıyla birlikte artık vatandaşlık kavramı küresel hale gelmiş bulunmaktadır. İslâmın küresel vatandaşlığa bakış iki temel esasa dayanmaktadır. Bunlardan birincisi ortaklık ilkesi olup o da İslâm kültürünün diğer kültürlerle ilişkilerini geliştirmeye teşvik etmektedir. İkinci ise çok yönlülük taşıyan bütünsellik ilkesidir. Bu ilke benzerlikler ve farklılıklar arasında bir denge kurulmasına hizmet etmektedir. Bu ilkeler aynı zamanda İslâmın inanç, ahlak ve hukukla ilgili özel konularının bir bütünlük çerçevesinde ele alınmasını sağlamaktadır. Küresel vatandaşlığın getirdiklerinin yerel değerleri olumsuz yönde etkilememesi için gerekli önlemler alınmalıdır. Bunun için eğitim politikaları açısından bu konuların İslâm eğitimi dersleri müfredatı içinde yer alması ön görülmektedir. Bu müfredat toplum içindeki farklılıkları bir zenginlik olarak görüp kuşakları aynı potada eritmeyi sağlamalıdır. Aynı zamanda toplumlar arasındaki ilişkileri olumlu yönde geliştirmelidir.Küresel vatandaşlık konuları öncelikle eğitim felsefesinin genel ve özel amaçları doğrultusunda müfredat çerçevesinde hedef kitleye evrensel bir değer olarak kazandırılmalıdır. Bu konu aynı zamanda eğitsel ve kültürel faaliyetleri ile de desteklenmelidir. Bu konuda başarı sağlanabilmesi için eğitim planlayıcıları ve uygulayıcıları ortak hareket etmelidirler. Bu makalede küresel vatandaşlık kavramı, bilişsel, duygusal ve davranışsal hedef alanları çerçevesinde İslâm eğitimi derslerinde uygulaması bulunan örnek uygulama ve uygun konularla birlikte ele alınmıştır. Sonuç olarak küresel vatandaşlık değerlerine katkısı beklenen derslerin içerik analizlerinin gözden geçirilmesi ve öğrenim çıktılarının etkin biçimde izlenmesi önerilmektedir. (shrink)

Résumé L’histoire récente montre que les deuxièmes générations rencontrent aussi un problème d’intégration. Les immigrations post-coloniales sont maintenant mondialisées, et les quartiers dortoirs d’immigration sont devenus des places de commerce cosmopolites. L’espace public dans lequel se meut l’immigration s’est différencié. L’émigré devient l’immigré, la famille se regroupe. La nouvelle génération veut incarner la tradition et n’a plus peur de marquer l’espace public des signes ostentatoires d’une présence singulière.

Fix 2 < n < ω. Let CA n denote the class of cylindric algebras of dimension n, and let RCA n denote the variety of representable CA n ’s. Let L n denote first-order logic restricted to the first n variables. Roughly, CA n, an instance of Boolean algebras with operators, is the algebraic counterpart of the syntax of L n, namely, its proof theory, while RCA n algebraically and geometrically represents the Tarskian semantics of L n. Unlike Boolean (...) algebras having a Stone representation theorem, RCA n ⊊ CA n. Using combinatorial game theory, we show that the existence of certain finite relation algebras RA, which are algebras whose domain consists of binary relations, implies that the celebrated Henkin omitting types theorem fails in a very strong sense for L n. Using special cases of such finite RA ’s, we recover the classical nonfinite axiomatizability results of Monk, Maddux, and Biro on RCA n and we re-prove Hirsch and Hodkinson’s result that the class of completely representable CA n ’s is not first-order definable. We show that if T is an L n countable theory that admits elimination of quantifiers, λ is a cardinal < 2 ℵ 0, and F = 〈 Γ i : i < λ 〉 is a family of complete nonprincipal types, then F can be omitted in an ordinary countable model of T. (shrink)

RésuméSelon Avicenne, certains objets des mathématiques existent et d'autres non. Chaque objet mathématique existant est un attribut connotationnel non sensible d'un objet physique et peut être perçu par la faculté d'estimation. Les objets mathématiques non existants peuvent être représentés et perçus par la faculté d'imagination en séparant et en combinant des parties d'images d'objets mathématiques existants qui sont précédemment perçues par estimation. Dans tous les cas, même les objets mathématiques non existants doivent être considérés comme des propriétés d'entités matérielles. Ils (...) ne peuvent jamais être saisis comme des entités totalement immatérielles. Avicenne pense que nous ne pouvons saisir aucun concept mathématique à moins d'avoir au préalable des expériences perceptives spécifiques. Ce n'est que par l'opération non éliminable et irremplaçable des facultés d'estimation et d'imagination sur certaines données sensibles que nous pouvons saisir les concepts mathématiques. Cela montre qu'Avicenne approuve une sorte d'empirisme conceptuel sur les mathématiques. (shrink)

Eşʿarîliğin son aşamasını temsil eden Îcî’nin argümanları, ekoldeki geleneksel ve felsefî yaklaşımları yansıtmaktadır. Bu makale Îcî’nin Muʿtezile’nin ahlâkî realizmine karşı kullandığı temel argümanlarını sunmaktadır. Çalışmanın amacı Îcî’nin argümanlarını değiştirmeden sağlam bir şekilde sunmak, açıklamak, itirazları tartışmak ve sonunda güçlü ve zayıf yönlerini değerlendirmektir. Makalenin amacı Muʿtezile’nin argümanlarını açıklamak değildir; yine de Îcî’nin argümanlarını daha net anlamak için bazı açıklamalar yapmaktadır. Makalenin ilk kısmında Eşʿarîler ile Muʿtezile’nin ahlâk anlayışları arasında belirgin bir çizgi çizmektedir. Tartışma noktasını belirtip kelâmî argümanlar için zemin hazırlamaktadır. (...) Îcî’nin argümanları üç kısma ayrılmıştır. Birinci kısımda Îcî’nin Muʿtezile’nin ahlâkî temellerine şüphe düşürmek için insanın seçme özgürlüğünü ortadan kaldırmak için polemik argümanını sunmaktayız. Argümana karşı eleştirileri tartıştıktan sonra Îcî’nin insanın gücü ve seçme özgürlüğü konusundaki gerçek görüşünü ortaya koyuyoruz. İkinci kısım, intrinsik değerler görüşüne karşı üç argüman ihtiva etmektedir. İlk iki argüman Îcî tarafından benimsenmiş, üçüncüsü ise genel bir şekilde diğer Eşʿarîlere atfetmiştir. Bu iki argüman yalanı ve doğruyu söylemenin intrinsik etik değerleriyle ilgilenmektedir, üçüncüsü ise Eşʿarîlerin meşhur: “Bir araz başka bir araz üzerinde konamaz” deyişine dayanmaktadır. Makalenin son kısmı, Îcî’nin Muʿtezile'nin ahlâkî vecihler teorisine karşı argümanını tartışmaya ayrılmıştır. Îcî’nin argümanını tartışmadan önce teori ve taraftarları hakkında yeterli bir açıklama yapılmıştır. Ayrıca Îcî’nin ve Muʿtezile’nin ilâhî ahlâk anlayışına dair kısa bir giriş, argümanın içinde tartışılmaktadır. Adalet ve hikmet gibi bazı ilahî nitelikler Eşʿarî ve Muʿtezile’nin bakış açılarından ele alınmaktadır. Sonuç olarak makale, Îcî’nin Muʿtezile’nin ahlâkî realizmine karşı argümanlarını açık ve net bir şekilde ortaya koymakta, itirazları sunup değerlendirmekte ve argümanların güçlü ve zayıf yönlerini göstermektedir. Son olarak, Eşʿarîlerin Muʿtezile’ye karşı ahlâkî argümanlarını daha etkili bir şekilde anlamak için bir çözüm önermektedir. (shrink)

Fix \. Let \ denote first order logic restricted to the first n variables. Using the machinery of algebraic logic, positive and negative results on omitting types are obtained for \ and for infinitary variants and extensions of \.

Il s’agit d’essayer de penser un « entre-deux » entre les travaux novateurs de Gilbert Durand sur l’imaginaire et les conceptualisations sémiotiques de la signification. Bien que Durand semble rejeter toute forme d’« explication sémiologique » des images-symboles, sa conception de l’imaginaire est régie par une sémiosis et une rationalité spécifiques qui permettent d’entrevoir, même si l’intersection n’implique pas forcément la fusion, les contours d’un « entre-deux » entre son « archétypologie » et la sémiotique. This paper try to imagine (...) a “In-between” from the semiotic conceptualizations of the significance to the innovative work of Gilbert Durand on the imaginary. Although Durand seems to reject any form of “semiological explanation” of the image-symbols, his conception of imaginary is governed by a specific semiosis and rationality which make it possible to foresee, even if the intersection does not inevitably imply fusion, contours of a “In-between” between his “archetypology” and semiotics. (shrink)

Mu‘allâkâtların, tefsir, nahiv, sarf ve dil ilimlerindeki önemli rolünün yanı sıra Arap dili ve edebiyatı âleminde de yüksek ve önemli bir konumu bulunmaktadır. Cahiliye devri müfredatlarının pek çoğunu kapsamasından ötürü dil ve edebiyat erbabı ona önem atfetmiştir. Onlardan biri de, ‘Şerhü’l-Kasâ’idi’l-السبع’ adıyla el-Muâ‘llekât’a yaptığı şerhiyle Ebu Bekir Muhammed bin el-Kasım bin Beşar bin el-Anbari. Bu eserinde pek çok nahiv, zamirin aidiyeti, harflerin manası, zarf ile car ve mecrûrun bağlı olduğu yerin belirlenmesi, müfredatlarıni‘râbı, illetler arasındaki üstünlükler, kıyasa ve luğatta asıl olana, (...) kelimenin irabını belirlemede bazı seslerin etki nedenlerine, sarf, lügat, belağat, eleştiri vb. konulara değinmektedir. Bu itibarla bu araştırma, betimsel analitik yöntemini kullanarak et-Anbari’ninMu‘allâkât şerhindeki nahiv yöntemini, Arap nahiv ilminde iki önemli konu olan kıyas ve ta‘lîl ile ilgili duruşunu açıklayarak değerlendirmeyi hedeflemektedir. (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)

We study the Generalized Kurepa hypothesis introduced by Chang. We show that relative to the existence of an inaccessible cardinal the Gap-n-Kurepa hypothesis does not follow from the Gap-m-Kurepa hypothesis for m different from n. The use of an inaccessible is necessary for this result.

This paper aims to suggest a new approach to Plato’s theory of being in Republic V and Sophist based on the notion of difference and the being of a copy. To understand Plato’s ontology in these two dialogues we are going to suggest a theory we call Pollachos Esti; a name we took from Aristotle’s pollachos legetai both to remind the similarities of the two structures and to reach a consistent view of Plato’s ontology. Based on this theory, when Plato (...) says that something both is and is not, he is applying difference on being which is interpreted here as saying, borrowing Aristotle’s terminology, 'is is (esti) in different senses'. I hope this paper can show how Pollachos Esti can bring forth not only a new approach to Plato’s ontology in Sophist and Republic but also a different approach to being in general. -/- Keywords Plato; being; difference; image; pollachos esti; pollachos legetai 1. Being, Not-Being and Difference The three dialogues where the notion of "difference" attaches to the notion of being, namely Parmenides II, Sophist and Timaeus,and specifically the first two we try to discuss here. In these dialogues, Plato is going to achieve a new and revolutionary understanding of being which is not anymore based on the notion of "same" as it was before in Greek ontology. It was his discovery, I think, that the notion of being in the Greek ontology is attached to the notion of the "same" and it is because of this attachment that there have always been many problems understanding being especially after Parmenides. That being has always been relying on the "same" can be found out from the way most of the Presocratics understood it. It was based on such a relationship between being and "same" that a later Ionian, Heraclitus of Ephesus, rejected Being by rejecting its sameness: unable to be the same, being cannot be being anymore but becoming. Heraclitus’ criticism of his predecessors’ understanding of being was due to his discovery that what they call being is not the same but different in every moment. The relation of being and sameness reaches to its highest point in Parmenides. What Plato does in using the "difference" is nothing but the establishment of a creative relation between being and "difference". In this new relation, although he is in agreement with Heraclitus that being is not the same but different, he does not do it by use of becoming. He disagrees, on the other hand, with Parmenides that such a relation between being and difference leads to not being. At Parmenides 142b5-6 it is said that if One is, it is not possible for it to be without partaking (μετέχειν) of being (οὐσίας), which leads to the distinction of being and one: -/- So there would be also the being of the one (ἡ οὐσία του̑ ἑνὸς) which is not the same (ταὐτὸν) as the one. Otherwise, it wouldn’t be its being, nor the one would partake of it. (142b7-c1) -/- The fact that what is (ἔστι) signifies (σημαῖνον) is other (ἀλλο) than what One signifies (c4-5), is being taken as a reason for their distinction. The conclusion is that when we say 'one is', we speak of two different things, one partaking of the other (c5-7). Having repeated these arguments of the otherness of being and one at 143a-b, Parmenides says that the cause of this otherness can be neither Being nor One but "difference": -/- So if being is something different (ἕτερον) and one something different (ἕτερον), it is not by being one that the one is different from being nor by its being being that being is other than one, but they are different from each other (ἕτερα ἀλλήλων) by difference (τῷ ἑτερῳ) and otherness (ἄλλῳ). (143b3-6) -/- The fifth hypothesis, 'one is not' (160b5ff.) is also linked with the notion of difference. When we say about two things, largeness and smallness, that they are not, it is clear that we are talking about not being of different (ἕτερον) things (160c2-4). When it is said that something is not, besides the fact that there must be knowledge of that thing, we can say that it entails also its difference: 'difference in kind pertains to it in addition to knowledge' (160d8). Parmenides explains the reason as such: -/- For someone doesn’t speak of the difference in kind of the others when he says that the one is different from the others, but of that thing’s own difference in kind. (160e1-2) -/- Although the theory of being as "difference" is not fulfilled yet, an exact look at what occurs in Sophist can make us sure that this was the launching step for "difference" to get its deserved role in Plato’s ontology. The notion of the "difference" is not yet well-functioned in Parmenides because we can see that being is still attached to the same: -/- For that which is the same is being (ὄν γὰρ ἐστι τὸ ταὐτόν) (162d2-3). -/- The notion of difference in Sophist is the key element based on which a new understanding of being is presented and the problem of not being is somehow resolved. The friends of Forms, the Stranger says, are those who distinguish between being and becoming (248a7-8) and believe that we deal with the latter with our body and through perception while with the former, the real being (ὄντως οὐσίαν) with our soul and through reasoning (a10-11). Being is then bound with the "same" by adding: -/- You say that being always stays the same and in the same state (ἣν ἀεὶ κατὰ ταὐτὰ ὡσαύτως ἔχειν) but becoming varies from one time to another (δὲ ἄλλοτε ἄλλως). (248a12-13) -/- That the theory of the relation of being and capacity (247d8f., 248c4-5) matches more with becoming than with being (248c7-9) must be rejected because being is also the subject of knowledge which is kind of doing something (248d-e). It does, however, confirm that 'both that which changes and also change have to be admitted as existing things (ὄντα) (249b2-3). I believe that this is what Socrates would incline to do at Theaetetus 180e-181a, that is, putting a fight between two parties of Parmenidean being and Heraclitean becoming and then escaping. The solution is that becoming is itself a kind of being and we ought to accept what changes as being. This is what must be done by a philosopher, namely, to refuse both the claim that 'everything is at rest' and that 'being changes in every way' and beg, like a child, for both and say being (τὸὄν) is both the unchanging and that which changes (249c10-d4). This kind of begging for both is obviously under the attack of contradiction (249e-250b). For both and each of rest and change similarly are (250a11-12) but it cannot be said either that both of them change or both of them rest, being must be considered as a third thing both of the rest and change associate with (250b7-10). The conclusion is that 'being is not both change and rest but different (ἕτερον) from them instead' (c3-4). The notion of difference helps Plato to take being departed from both rest and change because it was their sophisticated relation with being that made the opposition of being and becoming. Plato is now trying to separate being from rest and, thus, from "same" by "difference". Such a crucial change is great enough to need a 'fearless' decision (256d5-6). The possibility of being of not being is resulted (d11-12) comes as the answer to the question 'so it’s clear that change is not being and also is being (ἡ κίνησις ὄντως οὐκ ὄν ἐστι καὶ ὄν) since it partakes in being?' (d8-9). It is then by the notion of difference that becoming is considered as that which both is and is not. This coincidence of being and not being about change is apparently similar to Socrates’ paradoxical statement at Republic 477a about what both is and is not. -/- Introduction The Republic 476-477 has always been a matter of controversy mainly about two interwoven points. The first problem is the meaning of being here; that whether what he has in mind is a veridical, existential or propositional sense of being. The second problem is his distinction between the objects of knowledge and opinion which seems to lead, some believe, to the Two Worlds (TW) theory. The crucial point in Republic is that what is considered between knowledge (ἐπιστήμης) and ignorance (α͗γνοιας), namely opinion, must have a different object that leads Socrates to draw the distinction of knowledge and opinion between their objects. The problem of understanding being in the fifth book of the Republic is that when it is said that the Form of F is F but a particular participating in F, both is and is not F, it sounds too bizarre and unacceptable. It cannot be imaginable how a thing can be existent and non-existent at the same time. At the first sight, the only solution seems to be the degrees of existence which is called by Annas (1981, 197) a 'childish fallacy' and a 'silly argument'. Kirwan (1974, 118) thinks that Republic V does not attribute 'any doctrine about existence' to Plato and Kahn (1966, 250) claims that the most fundamental value of einai when used alone (without predicate) is not "to exist" but "to be so", "to be the case" or "to be true". The problems of understanding being in Republic and Sophist besides the difficulties of the existential reading led scholars to the other senses of being, mostly related to the well-known Aristotelian distinctions between different senses of being. In the predicative reading, Annas, for example, refers this difference to the qualified and unqualified application. Whereas the Form of F is unqualifiedly F, a particular instance of F can be F only qualifiedly (1981, 221). Vlastos’ well-known substitution of 'degrees of reality' for 'degrees of being/existence' must be categorized as a predicative reading. Kahn thinks that the basic sense of being for Plato is 'something like propositional structure, involving both predication and truth claims, together with existence for the subject of predication' (2013, 96). Believing that the complete-incomplete distinction terminology is misleading about Plato, he thinks that semantic functions are only second-order uses of the verb and it is the predicative or incomplete function which is fundamental. Suggesting a veridical reading, Fine (2003, 70 ff) thinks that while both existential and predicative readings separate the objects of knowledge and belief, it is only her reading which does not force such separation of the objects and thus does not imply TW. Stokes (1998, 266) thinks that though Fine is right saying that Plato does not endorse TW in book V, she is wrong in rejecting existential in favor of the veridical reading. The reception of existential reading can be seen more obviously in Calvert who thinks, in agreement with Runciman, that 'it would be safer to say that Plato’s gradational ontology is probably not entirely free from degrees of existence' (1970, 46). At Sophist 254d-e Plato singles out five most important kinds (or Forms!?) in which the same (ταὐτὸν) and difference (θάτερον) are regarded besides being, rest and change. They are, therefore, neither the same nor the difference but share in both (b3). Being (τὸ ὄν) cannot be the same also because if they 'do not signify distinct things' both change and rest will have the same label when we say they are (255b11-c1). We have then four distinct kinds, being, change, rest and same, none of them is the other. The case of difference is more complicated. When the stranger wants to assess the relation of being and difference, he can say simply neither that they are distinct nor that they are not. He has to make an important distinction inside being to get able to draw the relation of being and difference: -/- But I think you'll admit that some of the things that are (τῶν ὄντων) are said (λέγεσθαι) by themselves (αὐτὰ καθ’ αὑτά) but some [are said] always referring to (πρὸς) other things (ἄλλα) (255b12-13) -/- The difference is always said referring to other things (τὸδέγ’ ἕτερον ἀεὶ πρὸς ἕτερον) (255d1). It pervades all kinds because each of them should be different from the others and is so due to the difference and not its own nature (253e3f.) After asserting that change is different from being and therefore both is and is not (256d), the difference is described as what makes all the other kinds not be, by making each different from being. Given that all of them are by being, this association of being and difference is the cause of their being and not-being at the same time, the issue that its version at RepublicV made all those controversies we discussed above: -/- So in the case of change and all the kinds, not being necessarily is (Ἔστιν ἄρα ἐξ ἀναγκης τὸ μὴ ὄν). Τhat’s because as applied to all of them, the nature of the difference (ἡ θατέρον φύσις) makes each of them not be by making it different from being. And we’re going to be right if we say that all of them are not in the same way. And conversely [we’re also going to be right if we say] that they are because they partake in being. (Sophist 256d11-e3) -/- Plato’s new construction of five distinct kinds and the role he gives to thedifference among them is aimed to resolve the old problem of understanding being which has always been annoying from the time of Heraclitus and Parmenides. Both the ontological status of becoming and that of not being were, in Plato’s mind, based on the absolute domination of the notion of the Same over being. Now, not only becoming is understandable as being but also not being which is not the contrary of being anymore but only different (ἕτερον) (257b3-4). Though I agree partly with Frede that the account of not being which is needed for false statements is more complicated than just saying, as Cropsey (1995, 101) says, that Plato is substituting 'X is not Y' with 'X is different from Y', I totally disagree with him that when we say X is not beautiful, Plato could not have thought that it is not a matter of its being different from beautiful because 'it would be different from beauty even if it were beautiful by participation in beauty' (1992, 411). Conversely, as we will discuss, it is exactly the relation of the beautiful thing, X, and the beautiful itself, in which X shares that is to be solved by the notion of not being as difference. Though it is beautiful because of sharing in beauty, X is not beautiful because it is different from beautiful itself. What the difference is to do is to show how something can both be and not be the same thing. The difference is what makes one thing both be and not be a certain other thing. This equips the difference with the ability to explain a certain thing’s not-being when it is. Thanks to the notion of difference, it is now possible to explain not only not being but also the simultaneous being and not being of a thing: 'What we call "not-beautiful" is the thing that ἕτερόν ἐστιν from nothing other than του̑ καλου̑ φύσεως' (257d10-11). The result is that not beautiful happens to be (συμβέβηκεν εἶναι) one single thing among kinds of beings (τι τῶν ὄντων τινὸς ἑνὸς γένους) and at the same time set over against one of the beings (πρός τι τῶν ὄντων αὖ πάλιν ἀντιτεθὲν) (257e2-4) and thus be something that happens to be not beautiful (εἶναί τις συμβαίνει τὸ μὴ καλόν); a being set over against being (ὄντος δὴ πρὸς ὄν ἀντίθεσις) (e6-7). Neither the beautiful is more a being (μα̑λλον ... ἐστι τῶν ὄντων) nor not beautiful less (e9-10) and thus both the contraries similarly are (ὁμοίως εἶναι) (258a1). This conclusion, it is emphasized again (a7-9), owes to θατέρου φύσις now turned out as being. Therefore, each of the many things that are of the nature of the difference and set over each other in being (τῆς τοῦ ὄντος πρὸς ἄλληλα ἀντικειμένων ἀντίθεσις) is being as being itself is being (αὐτοῦ τοῦὄν τοςοὐσία ἐστιν) and not less. They are different from, and not the contrary of, each other (a11-b3). This is exactly τὸμὴὄν, the subject of the inquiry (b6-7). Hence, not being has its own nature (b10) and is one εἶδοςamong the many things that are (b9-c3). Such far departing from Parmenides’ ontological principle is done on the basis of the nature of the difference. It was the discovery of such a notion that made the stranger brave enough to say that not being is each part of the nature of the difference that is set over against being (258d7-e3, cf. 260b7-8). That the relation of being and difference is difference is the key element of the new ontology. The difference is, only because of its sharing in being, but it is not that which it shares in but different from it (259a6-8). Not being is exactly based on this difference: ἕτερον δὲ τοῦ ὄντος ὄν ἔστι σαφέστατα ἐξ ἀνάγκης εἶναι μὴ ὄν (a8-b1). 2. Difference and the Being of a Copy We discussed above that the sense of being of particulars in Republic V made so many debates that whether being is there used in an existential sense or not. Particulars in Republic are regarded as images in the allegories of Line and Cave. The being of an image/copy makes, thus, the same problem. Plato’s analogy of original -copy for the relation of Forms and their particulars in Republic has obviously a different attitude to being. The main question is that what is the ontological status of a copy in respect of its original? Are there two kinds of being, 'real being' versus 'being' as Ketchum says (1980, 140) or only one kind? What is the difference of being in an original and its copy? Is it a matter of degrees of being or reality as some commentators have suggested? Is it a matter of being relational? By reducing the ontological issue to an epistemological one, Vlastos’ suggestion of degrees of reality in an article with the same name does neither, I think, pay attention to the problem nor resolve it. He agrees that Plato never speaks of "degrees" or "grades" of reality (1998, 219). What allows him to entitle it as such are some of Plato’s words in Republic as well as Plato’s words in some other dialogues (1998, 219). When Plato states that the Forms only can completely, purely or perfectly be real he means, Vlastos says, they are cognitively reliable (1998, 229); an obvious reduction of the issue to an epistemological one. He thinks that when in Republic we are being said that a particular’s being F is less pure than its Form, it is because it is not exclusively F, but it is and is not F and this being adulterated by contrary characters is the reason of our confused and uncertain understanding of it (1998, 222). Ketchum rightly criticizes Vlastos’ doctrine in its disparting from ontology thinking that 'to understand Plato’s talk of being as talk of reality is to obscure the close relation that exists between "being" and the verb "to be"' (1980, 213). He thinks, therefore, that οὐσία must be understοοd as being rather than reality, τὸὄν as "that which is" and not "that which is real" and … (ibid). His conclusion is that degrees of reality cannot interpret Plato correctly and we must accept degrees of being. Allen believes that a 'purely epistemic' reading of the passage in Republic is patently at odds with Plato’s text (1961, 325). He thinks that not only degrees of reality but also degrees of reality must be maintained (1998, 67). What Cooper suggests gets close to this paper’s solution: -/- Plato does not I think wish to suggest that existence is a matter of degree in the way in which being pleasant or painful is a matter of degree. Rather there are different grades of ontological status. (1986, 241) -/- A more ontological solution for the problem of understanding the being of a copy and its relation with the being of its original is suggested by the theory of copy as a relational entity. Based on this interpretation, 'the very being of a reflection is relational, wholly dependent upon what is other than itself: the original…' (Allen, 1998, 62). As relational entities, particulars have no independent ontological status; they are purely relational entities which derive their whole character and existence from Forms (ibid, 67). Although these relational entities are and have a kind of existence, we must also say that 'they do not have existence in the way that Forms, things which are fully real, do' (ibid). Allen (1961, 331) extends his theory to Phaedo where it is said that particulars are deficient (74d5-7, 75a2-3, 75b4-8), 'wish' to be like (74d10) or desire to be of its nature (75a2); an extension that, like F.C. white (1977, 200), I cannot admit. He correctly states that Plato did not start out with a doctrine of particulars as images and semblances but come to such a view after Phaedo, or perhaps after Republic V (1977, 202). Though we may not agree with him about Republic V, if we have to consider its last pages also, we must agree with him that not only the ontology of Phaedo but also that of Republic II-V (except the last pages of the latter book) are somehow different from (but at the same time appealing to) the ontology of original-copy which should exclusively assign to Sophist, Timaeus and RepublicVI-VII besides the last pages of book V. The answer to the problem of Plato’s sense of being in RepublicV can be reached only if we read Republic V based on and as following Sophist. We can find out his meaning of that which both is and is not only by the ontological status he assigns to a copy in Sophist. The kind of being of a copy in Sophist reveals as Plato’s key for the lock of the problem of not being. Let’s see how the ontological status of a copy is the critical point of Plato’s ontology. In the earlier pages of Sophist, we are still in the same situation about not being. To think that that which is not is is called a rash assumption (237a3-4) and Parmenides’ principle of the impossibility of being of not being is still at work (a8-9). At 237c1-4, the problem of "not being" is noticed in a new way which shows some kinds of a more realistic position to the problem of not being. Nevertheless, not being is still unthinkable, unsayable, unutterable and unformulable in speech (238c10). Soon after mentioning that it is difficult even to refuse not being (238d), the solution to the problem appears: the being of a copy (εἴδωλον) (239d). A copy is, says Theaetetus, something that is made referring to a true thing (πρὸς τἀληθινὸν) but still is 'another such thing (ἕτεροντοιου̑τον)' (240a8). Nevertheless, this 'another such thing' cannot be another such real or true thing. In answer to the question of the Stranger that if this 'another such thing' is the true thing (240a9), Theaetetus answers: οὐδαμῶς ἀληθινόν γε, ἀλλ’ ἐοικὸςμὲν (240b2). A copy’s being 'another such thing' does not mean another true thing but only a resemblance of it. Not only is not a copy another true thing besides the original, but it is the opposite of the true thing (b5) because only its original is the thing genuinely and being a copy is being the thing only untruly. The word ἐοικὸς is opposed to ὄντως ὄν in the next line (240b7): 'So you are saying that that which is like (ἐοικὸς) is not really that which is (οὐκ ὄντως [οὐκ] ὄν)'. But still a copy 'is in a way (ἔστι γε μήν πως)' (b9). While it is not really what it is its resemblance, it has its own being and reality because it really is a likeness (εἰκων ὄντως) (b11). The Stranger asks: -/- So it is not really what is (οὐκ ὄν ἄρα [οὐκ] ὄντως ἐστὶν) but it really is what we call a likeness (ὄντως ἣν λέγομεν εἰκόνα)? (b12-13) -/- This is Plato’s innovative ontological solution to the problem of not being. Theaetetus’ answer confirms this: 'Maybe that which is not is woven together with that which is' (c1-2). Therefore, a copy neither is what really is nor is not-being but only is what in a way is. Thanks to the ontological status of a copy, the third status intermediate between being and not being is brought forth. The essence of an image, in Kohnke’s words, does not consist 'solely in the negation of what is genuine and has real being' because otherwise 'it would be an ὄντως οὐκ ὄν,essentially and really a not being' (1957, 37). The characteristics of a copy can be summed up as folows: i) A copy is a copy by referring to a true thing (πρὸς τἀληθινὸν). ii) A copy is different from that of which it is a copy (ἕτερον). iii) A copy is not itself a true thing (ἀληθινόν) as that of which it is a copy but only that which is like it (ἐοικὸς). iv) It is not really that which really is (ὄντως ὄν) but only really a likeness (εἰκων ὄντως). The conclusion is that: v) A copy in a way (πως) is that means it both is and in not, the product of interweaving being with not being. This leads to the refutation of father Parmenides’ principle, accepting that 'that which is not somehow is (τό τε μὴ ὄν ὡς ἔστι)' and 'that which is, somehow is not (τό ὄν ὡς οὐκ ἔστι) (241d5-7). Besides copies and likenesses (εἰκόνων), we have also imitations (μιμημάτων) and appearances (φαντασμάτων) as the subjects of this new kind of being and thus false belief (241e3). In Timaeus, the world of becoming which cannot correctly be called and thus we have to call it "what is such" (τὸ τοιου̑τον) (49e5) or "what is altogether such" (τὸ διἀ παντὸς τοιου̑τον) (e6-7), consists solely of imitations (μιμημάτα) (50c5) which are identifiable only by the things that they are their imitations. The word τοιου̑τον which had been used to determine the situation of a copy in respect of its original, now becomes the definition of the world of becoming in which everything is an image of another thing, a Being, that stays always the same and is different and separated from its image. Cherniss, in my view rightly, draws attention to the very important point about the ontological status of an image that can at the same time be considered a criticism of the relational theory. What we are being said in Timaeus, he thinks,cannot be explained by saying that an image is not self-related and making its being relational. What is crucial about an image is that it 'stands for something, refers to something, means something and this meaning the image has not independently as its own but only in reference to something else apart from it' (1998, 296). This function finds its best explanation in the theory we are to suggest in the following. 3. πολλαχῶς ἔστι The best way to understand the ontological status of an image in Plato is to see first how his most clever pupil, Aristotle, resolved the same problem that Plato brought his theory of image for its sake. Aristotle’s theory of pollachos legetai is a brilliant and, at the same time, deviated version of Plato’s theory that is able, however, to help us read Plato in a better way. We discuss Aristotle’s theory to reach to a full understanding of Plato’s theory because it is, firstly, constructed in Aristotle in a more clear way and, secondly, it can also be taken as an evidence that our reading of Plato is legitimate. The phrase τὸ ὄν πολλαχῶς λέγεται, a so much repeated phrase in Aristotle’s works, is his resolution for some of the ontological problems of his predecessors all treating being as if it has only one sense. Aristotle is right in his criticism of the philosophical tradition specially Heraclitus, Parmenides and Plato since all did presuppose only one sense for being and his theory is, thus, a creative and revolutionary solution for many problems that all the past philosophers were stuck in. But it is at the same time somehow a borrowed theory. As we will discuss, both the structure of the doctrine and the problems it tries to resolve are the same as Plato’s doctrine (and even is comparable in its phraseology) though it is in Aristotle, as can be expected, a more clear and better structured doctrine. 1) Associated with the theory of pros hen and the theory of substance, the theory of several senses of being provides a structure which, I insist, is the best guide to understand Plato’s theory of Being in Sophist, Timeaus and Republic. a) Although the theory of pollachos legetai is not necessarily based on the theory of pros hen, they become tightly interdependent about being: -/- Being is said in many ways/senses (τὸ δὲ ὄν λέγεται μὲν πολλαχῶς) but by reference to one (πρὸς ἕν) [way/sense] and one kind of nature (μίαν τινὰ φύσιν). (Metaphysics 1003a33-34) -/- The doctrine of pros hen which is Aristotle’s initiative third alternative besides the homonymous and synonymous application of words, is primarily a linguistic theory that tries to provide a new theory to explain the different implementations of the same word. The pros hen implementation of being is to provide an alternative for the theory of the synonymous (in Plato: homonymous) implementation of being which says being is said in one sense (kath hen) (1060b 32-33). That both the pros hen and the kath hen implementation of a word has one thing (hen) as what is common, makes them in opposition to the homonymous implementation which does not consider anything in common. Whereas both pros hen and kath hen assume a common nature, with which all the implementations of the word have some kind of relation, their difference is that while kath hen takes all the implementations of the word as the same with the common nature, pros hen makes them different. Substance is called πρῶτον ὄν because it is said to be primarily: -/- For as is (τὸ ἔστιν) is predicated of all things, not however in the same way (οὐχ ὁμοίως) but of one sort of thing primarily and of others in a secondary way. So too τὸτί ἐστιν belongs simply (ἁπλῶς) to substance but in a limited sense (πῶς) to the others [other categories] (1030a21-23). -/- The word ἁπλῶς standing against κατὰ συμβεβηκός tries to make substance different from the accidents. When we are being said that τὸ ὄν πολλαχῶς λέγεται, it means that only the substance that is simply (ἁπλῶς) the ἕν, the common nature, τὸὄν. When we use the word 'being' about a substance, the being is said differently from when we use 'being' about an accident. The distinction between the substance and the other categories is a distinction between what simply is said to be and what only with reference to (pros) the substance is said to be. The doctrine of pros hen, changing kath hen to pros hen in respect of to on, makes a distinction that wants to show that while there is a kind of implementing the word being that is simply being, there is another kind which is called being only by reference to that which is simply being. In the doctrine of pros hen it is not so that all the things that are said to be are only by reference to a common one thing, but that while one thing is called being because it is that thing itself, the other things are called so without being that thing itself but only by referring to it. At the very beginning of book Γ, it is said that: -/- Being is said in many senses but all refer to one arche. Some things are said to be because they are substances, others because they are affections of substances, others because they are a process towards substances or destructions or privations or qualities of substances … (1003b5-9, cf. 1028a18-20) -/- Substance is what really is said to be and all other things that are said to be are said only in favor of it. This difference of substance from all other senses of being is what is, I believe, primarily aimed in Aristotle’s interrelated theories of pollachos legetai,pros hen and the theory of substance. b) The difference of the implementation of being in the case of substance and the accidents goes so deep that while substance is considered as the real being, the accidents are almost not being. An accident is a mere name (Metaphysics 1026b13-14) and is obviously akin to not being (b21). Aristotle adds that Plato was 'in a sense not wrong' saying that sophists deal with not being (τὸ μὴ ὄν) because the arguments of sophists are, above all, about the accidental (1026b13-16). At the beginning of book , he says about quality and quantity (which look to be more of a being than other accidents) that they are not existent (οὐδ̕ ὄντα ὡς εἰπεῖν) in an unqualified sense (ἁπλῶς) (1069a21-22). The two above-mentioned points, Aristotle’s (a) interwoven theories of pollachos legetai, pros hen and the theory of substance and (b) taking accidents almost as not being, comparedwith substance, brings forth a structure that I shall call Pollachos Legetai (with capital first letters). What is of the highest importance in this structure for me is the difference of substance from accidents and the kind of relation which is settled between them. There is a substance that without any qualification is said to be and the accidents that are said to be only by reference (pros) to it. Adding Aristotle’s point about accidents that they are nearly not being to this relation and difference, we can obviously see how much this structure is close to Plato’s original-copy ontology. We spoke of the relation of being and difference in Plato’s model and the way Plato construes the being of a copy. A copy is a copy only by referring to (pros) a model; it is different from (ἕτερον) that of which it is a copy; it is not itself a true thing as its model and not really that which is (ὄντως ὄν) but only is in a way (πῶς). If we behold the difference of substance and accident in the context of the theory of pollachos legetai and pros hen, we can observe its fundamental similarity with Plato’s original-copy theory in its structure. Allen draws attention to the fact that the relation between Forms and particulars in Plato’s original-copy model is 'something intermediate between univocity and full equivocity' (1998, 70, n. 24) and the same as what Aristotle calls it pros hen (ibid). What made us compare the two structures was not, of course, the complete similarity of two structures (we have to agree with many possible differences of the two theories) but exactly the specific relation between an original and its copy on the one hand, and a substance and its accident on the other hand. As substance and accident do not share a common character and the substance -accident model hints that they stand in a certain relation, there is no common character between the original and copy in Plato’s model as well. Furthermore, their similarity is not confined to their structure only; they are also aimed to solve the same problem. The central point of the theory is that all the predecessors took being in one sense and this was their weakness point. Besides the mentioned above passages about the relation of pollachos legetai and presocratics’, as well as Plato’s, ontology, the relation of the theory with the problem of not being is clear in several passages. In Metaphysics, it is said: 'Being is then said in many senses… It is for this reason that we say even of not being that it is not being' (1003b5-10). Discussing the accidental sense of being, Aristotle points that it is in the accidental way that we say, for example, that not-white is because that of which it is an accident is (1017a18-19, cf. 1069a22-24). We mentioned that he thought Plato was right saying that sophistic deals with not being because sophistic deals with accidental, which is somehow not being (1026b14-16). Plato turned sophistic not-being to what both is and is not and Aristotle to what accidentally is said to be. What helps Aristotle to resolve the problem of not being is his distinction between ἁπλῶς and κατὰ σθμβεβηκός. Aristotle’s "qua" (ᾕ) which is directly linked with his distinction between καθ’ αὑτο λέγεται and κατὰ συμβεβηκός λέγεται, is used to resolve the old problem of coming to be out of not being (Physics 191b4-10). He strictly asserts that his predecessors could not solve the problem because they failed to observe the distinction of "qua itself" from "qua another thing" (b10-13). He then continues: -/- We ourselves are in agreement with them in holding that nothing can be said simply (ἁπλως) to come from not being (μὴὄντος). But nevertheless we maintain that a thing may come to be from not being in an accidental way (κατὰ συμβεβηκός). For from privation which ὅ ἐστι καθ’ αὑτο μὴ ὄν, nothing can become. (Phy. 191b13-16, cf. b19-25) . (shrink)

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.

We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n ≤ w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin's axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey's omitting types theorem fails for Ln, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. Ln has been recently (and quite extensively) studied as a many-dimensional (...) modal logic. (shrink)

We give a new characterization of the class of completely representable cylindric algebras of dimension 2 #lt; n w via special neat embeddings. We prove an independence result connecting cylindric algebra to Martin''s axiom. Finally we apply our results to finite-variable first order logic showing that Henkin and Orey''s omitting types theorem fails for L n, the first order logic restricted to the first n variables when 2 #lt; n#lt;w. L n has been recently (and quite extensively) studied as a (...) many-dimensional modal logic. (shrink)

We give a novel application of algebraic logic to first order logic. A new, flexible construction is presented for representable but not completely representable atomic relation and cylindric algebras of dimension n (for finite n > 2) with the additional property that they are one-generated and the set of all n by n atomic matrices forms a cylindric basis. We use this construction to show that the classical Henkin-Orey omitting types theorem fails for the finite variable fragments of first order (...) logic as long as the number of variables available is > 2 and we have a binary relation symbol in our language. We also prove a stronger result to the effect that there is no finite upper bound for the extra variables needed in the witness formulas. This result further emphasizes the ongoing interplay between algebraic logic and first order logic. (shrink)

The paper argues that on three out of eight possible hypotheses about the EPR experiment we can construct novel and realistic decision problems on which (a) Causal Decision Theory and Evidential Decision Theory conflict (b) Causal Decision Theory and the EPR statistics conflict. We infer that anyone who fully accepts any of these three hypotheses has strong reasons to reject Causal Decision Theory. Finally, we extend the original construction to show that anyone who gives any of the three hypotheses any (...) non-zero credence has strong reasons to reject Causal Decision Theory. However, we concede that no version of the Many Worlds Interpretation (Vaidman, in Zalta, E.N. (ed.), Stanford Encyclopaedia of Philosophy 2014) gives rise to the conflicts that we point out. (shrink)

Let 1 n. We show that the class NrnCAβ of n-dimensional neat reducts of β-dimensional cylindric algebras is not closed under forming elementary subalgebras. This solves a long-standing open problem of Tarski and his co-authors Andréka, Henkin, Monk and Németi. The proof uses genuine model-theoretic arguments.