Cardinal Bessarion (1408–1472), in the second chapter of the first book of his influential work In calumniatorem Platonis, attempted to reply to Georgios Trapezuntios’ (1396–1474) criticism against Plato in the Comparatio Philosophorum Platonis et Aristotelis. Bessarion investigates why the Athenian philosopher maintained, in several dialogues, that the sacred truths should not be communicated to the general public and argued in favor of the value of oral transmission of knowledge, largely based on his theory about the cognitive processes. Recently, Fr. (...) Bessarion Kouotsis has argued that Cardinal Bessarion’s reasoning draws primarily on the “Disciplina Arcani”, i.e., the rule of secrecy, which was an established practice of the Early Christian Church, aimed at protecting and preserving the core elements of the religion from outsiders. While I find Kouotsis’ approach interesting and thought-provoking—for instance, the idea that Bessarion’s argumentation was likely influenced by Eastern Christian views on the rule of secrecy—I intend, first of all, to discuss why Bessarion did not explicitly mention it. Moreover, I would like to argue that Bessarion’s good knowledge of the long Platonic tradition and Eastern mysticism, encompassing both pagan and Christian elements, should also be considered a significant source. Furthermore, I would like to question Kouotsis’ implicit argument that Bessarion’s views were dominated by his training in Orthodox theology and discuss the possibility that Pletho’s (1355–1454) teaching was the obvious influence for Bessarion’s defense of secrecy. After all, we should bear in mind that Anastos has already pointed out Pletho’s reverence for the rule of secrecy. Finally, I would like to support that Bessarion, in the specific text, focused predominantly on the epistemological and cognitive aspects of oral teaching, resorting to the rule of secrecy only to enhance his views. (shrink)

This article presents an approach to the semantics of non-distributive propositional logics that is based on a lattice representation theorem that delivers a canonical extension of the lattice. Our approach supports both a plain Kripke-style semantics and, by restriction, a general frame semantics. Unlike the framework of generalized Kripke frames, the semantic approach presented in this article is suitable for modeling applied logics, as it respects the intended interpretation of the logical operators. This is made possible by restricting admissible interpretations.

The contribution of this paper lies with providing a systematically specified and intuitive interpretation pattern and delineating a class of relational structures and models providing a natural interpretation of logical operators on an underlying propositional calculus of Positive Lattice Logic and subsequently proving a generic completeness theorem for the related class of logics, sometimes collectively referred to as Generalized Galois Logics.

Part I of this paper is developed in the tradition of Stone-type dualities, where we present a new topological representation for general lattices (influenced by and abstracting over both Goldblatt's [17] and Urquhart's [46]), identifying them as the lattices of stable compact-opens of their dual Stone spaces (stability refering to a closure operator on subsets). The representation is functorial and is extended to a full duality.In part II, we consider lattice-ordered algebras (lattices with additional operators), extending the Jónsson and Tarski (...) representation results [30] for Boolean algebras with Operators. Our work can be seen as developing, and indeed completing, Dunn's project of gaggle theory [13, 14]. We consider general lattices (rather than Boolean algebras), with a broad class of operators, which we dubb normal, and which includes the Jónsson-Tarski additive operators. Representation of l-algebras is extended to full duality. (shrink)

We present an algebraic theory of structured objects based on and generalizing Aczel's theory of form systems. Notions of identity of structured objects and of transformations of systems of such objects are discussed. A generalization of Aczel's representation theorem is proven.

A systematic approach to the algebraic and Kripke semantics for logics with restricted structural rules, notably for logics on an underlying non-distributive lattice, is developed. We provide a new topological representation theorem for general lattices, using the filter space X. Our representation involves a galois connection on subsets of X, hence a closure operator $\Gamma$, and the image of the representation map is characterized as the collection of $\Gamma$-stable, compact-open subsets of the filter space . The original lattice ${\cal L}$ (...) is thus imbedded in the complete lattice of stable sets. The representation is shown to be functorial and is extended to a Stone-type duality. ;In the presence of additional operators, the extension problem is addressed in terms of what we call adjoint completions of normal operators. An operator f on a lattice L is normal if f: $L\sp{} \times \cdots \times L\sp{} \to L\sp{}$ is a monotone map, where each $L\sp{}$, $i \in n$ + 1, is either L or $L\sp{op}$ and f sends finite joins of $L\sp{}$ to joins in $L\sp{}$. Every familiar operator, such as $\circ$ , + , $\gets, \to, \neg, \square$ O is normal. By a uniform argument we show that normal operators $f\sb{i}$ on L extend to operators $F\sb{i}$ on $\Gamma X$ that distribute over arbitrary joins or meets and that \sb{i\in I})$ is a universal such extension. ;We also raise and resolve the question of representability of operators on stable sets by relations. We give an extensive number of examples of representation of specific operators and provide explicit constructions of canonical Kripke frames, based on our extension arguments, for a number of logical systems, notably for Intuitionistic and Classical Linear Logics, or Non-commutative Linear Logic and of fragments thereof. (shrink)

In an article dating back in 1992, Kosta Došen initiated a project of modal translations in substructural logics, aiming at generalising the well-known Gödel–McKinsey–Tarski translation of intuitionistic logic into S4. Došen's translation worked well for (variants of) BCI and stronger systems (BCW, BCK), but not for systems below BCI. Dropping structural rules results in logic systems without distribution. In this article, we show, via translation, that every substructural (indeed, every non-distributive) logic is a fragment of a corresponding sorted, residuated (multi) (...) modal logic. At the conceptual and philosophical level, the translation provides a classical interpretation of the meaning of the logical operators of various non-distributive propositional calculi. Technically, it allows for an effortless transfer of results, such as compactness and the Löwenheim-Skolem property and it opens up new directions for deducing properties of substructural logic systems by establishing appropriate transfer theorems. (shrink)

Michael Apostolis (c. 1422–1478),¹ the Greek scholar and prolific author of the fifteenth century, studied in Constantinople under John Argyropoulos (1395/1405–1487)² and taught at Katholikon Museion (Xenon). After the fall of Constantinople, Apostolis shared his time between Crete, Constantinople and Venice, where he improved his Latin. He became Bessarion’s (1408–1472) protégé only briefly, because the latter did not like the polemic overtone of his treatises and came quickly to dismiss his views on the preponderance of Platonic over Aristotelian philosophy. After (...) losing Bessarion’s favor Apostolis returned to Crete, where he worked as a copyist. In addition he established a school.³ In several letters sent to his friends and colleagues he complained about his poverty and the difficulties he faced.⁴ Apostolis appreciated the Platonic philosophical tradition, particularly the philosophy of Georgios Gemistos Pletho (c. 1360–1454). Apostolis’ religious views seemed to be influenced by Pletho’s polytheism, despite his claim that he was nothing but Christian, namely a supporter of the Union of Orthodox and Catholic Church.⁵ Apostolis took part in the dispute between Platonists and Aristotelians that embroiled also the Greek speaking philosophical community throughout the fifteenth century.⁶ Apostolis wrote in favor of Plato with enthusiasm and in a polemic tone. Specifically, he confronted Theodoros Gaza⁷ (1398–1475), a well-known scholar, translator and author of the treatise Adversus Plethonem pro Aristotele,⁸ who was also Bessarion’s protégé. In his Ad Theodori Gazae pro Aristotele de substantia adversus Plethonem obiectiones⁹, Apostolis turned to Bessarion in order to gain his favor and support. (shrink)

This article addresses and resolves some issues of relational, Kripke-style, semantics for the logics of bounded lattice expansions with operators of well-defined distribution types, focusing on the case where the underlying lattice is not assumed to be distributive. It therefore falls within the scope of the theory of Generalized Galois Logics, introduced by Dunn, and it contributes to its extension. We introduce order-dual relational semantics and present a semantic analysis and completeness theorems for non-distributive lattice logic with n -ary additive (...) or multiplicative operators, with negation operators modally interpreted as impossibility and unnecessity, as well as with implication connectives. Order-dual relational semantics shares with the generalized Kripke frames, or the bi-approximation semantics approach, the use of both a satisfaction and a co-satisfaction relation, but it also responds to the recently voiced concerns of Craig, Haviar and Conradie about the relative non-intuitiveness of the 2-sorted semantics of the aforementioned approaches. In this article, we provide a standard interpretation of modalities and natural interpretations of both negation and implication, despite the absence of distribution. Thereby, our results contribute in creating the necessary background for research in non-distributive logics with modalities variously interpreted as dynamic, temporal etc, by analogy to the classical case. (shrink)

We present dualities for implicative and residuated lattices. In combination with our recent article on a discrete duality for lattices with unary modal operators, the present article contributes in filling in a gap in the development of Orłowska and Rewitzky’s research program of discrete dualities, which seemed to have stumbled on the case of non-distributive lattices with operators. We discuss dualities via truth, which are essential in relating the non-distributive logic of two-sorted frames with their sorted, residuated modal logic, as (...) well as full Stone duality for residuated lattices. Our results have immediate applications to the semantics of related substructural logical calculi. (shrink)

Although the two worlds, Arabic and Byzantine, were in proximity for many centuries, the influence of Arabic philosophy on the Byzantine intellectual tradition has not been studied thoroughly. Recent studies have substantiated the influence of the Arabic and Persian thought over Byzantine science. However, in the field of philosophy, research is still at an early stage and the impact of Arabic thought on Byzantine and vice versa has not been examined widely and in depth. Direct references to philosophers in the (...) Islamic world are rare and, apart from occasional studies, there is not an organised, in-depth account of the influence the Arabic philosophy exercised on Byzantine scholars. The present study is a wider, complete, and renewed presentation of the initial conclusions of my research, which aims to bring out and evaluate the perception of Arabic philosophy by the Byzantine intelligentsia during the 14th and 15th centuries. As exemplary cases Ι have chosen Georgios Gemistos Pletho (c.1360-1454) and Georgios Scholarios (c.1400-1472), whose rivalry defined Byzantine philosophy of the 15th century to a considerable degree. (shrink)

Cet ouvrage se propose de confronter les problématiques relatives à la falsafa et à la religion islamique dans leur approche du corps. Le corps a toujours été marginalisé au profit de la notion de l'âme. Pendant que les penseurs ont été intéressés par l'étude de l'âme, le corps a toujours été leur point de départ. Son statut éthique et ontologique doit être réexaminé en refusant de se limiter aux dualismes classiques corps/âme ou matérialisme/spiritualisme qui masquent par leur dimension formelle ou (...) réductrice l'enjeu politique et existentiel de la question ainsi que ses implications théoriques et pratiques. Deux grandes perspectives apparaissent dans le développement de la falsafa lorsqu'elle problématise la question du corps. La première porte sur le fondement psychologique du lien existant entre l'âme et le corps et ses conséquences quant à la détermination de leur valeur réciproque. La deuxième est métaphysique et s'inscrit dans une visée eschatologique impliquant une conception de l'au-delà et du jugement dernier. Comment penser le corps d'un point de vue philosophique pour qu'il ne soit pas incompatible avec l'islam? Pour répondre à cette question, nous étudions les textes fondateurs de la falsafa spécialement ceux de Al-F r b, Ibn S n, Al-Ghaz l et Mull Sadr tout en les comparant aux textes coraniques. Georgio Rahal enseigne l'islamologie, l'histoire médiévale de l'islam, l'arabe littéraire et la philosophie arabe à l'Institut Catholique de Toulouse. (shrink)

ABSTRACTCorrespondence and Shalqvist theories for Modal Logics rely on the simple observation that a relational structure is at the same time the basis for a model of modal logic and for a model of first-order logic with a binary predicate for the accessibility relation. If the underlying set of the frame is split into two components,, and, then frames are at the same time the basis for models of non-distributive lattice logic and of two-sorted, residuated modal logic. This suggests that (...) a reduction of the first to the latter may be possible, encoding Positive Lattice Logic as a fragment of Two-Sorted, Residuated Modal Logic. The reduction is analogous to the well-known Gödel-McKinsey-Tarski translation of Intuitionistic Logic into the S4 system of normal modal logic. In this article, we carry out this reduction in detail and we derive some properties of PLL from corresponding properties of First-Order Logic. The reduction we present is extendible to the case of lattices with operators, making use of recent results by this author on the relational representation of normal lattice expansions. (shrink)

Durch die Veröffentlichung des vorliegenden Bandes wird ein Desideratum der Briefliteratur verwirklicht, auf welches bereits S. Lampros im Jahr 1915 hingewiesen hat. Es handelt sich um ein alphabetisches Verzeichnis der Anfänge aller in griechischer Sprache geschriebener Briefe aus dem Zeitraum von etwa 300 n.Chr. bis ca. 1500, das über 15.000 Briefexordia von etwa 260 spätgriechischen und byzantinischen Briefschreibern umfaßt und sich auf die jeweils neuesten Editionen von Briefsammlungen stützt, wobei an die 890 Eintragungen von unedierten Briefen stammen. Treffliche Emendationen werden (...) bei den aufgenommenen Exordia berücksichtigt sowie auch wichtige Handschriftenvarianten, die evtl. die Autorenhand wiederzugeben beanspruchen. Briefanfänge, die ein Zitat darstellen, werden durch Kursivschrift gekennzeichnet, darunter auch viele, die nicht von den Herausgebern selbst, sondern erst vom Autor des vorliegenden Bandes erkannt worden sind. Bei welchem Wort das zu aufnehmende Exordium unterbrochen werden muss, ist eine delikate Sache, die im Verzeichnis in der Weise geregelt wird, dass der Eintrag nach Möglichkeit eine Sinneinheit bildet, weswegen auch die aufgenommenen Exordia von unterschiedlicher Länge sind. Urkundenschreiben werden in der Regel nicht berücksichtigt, in Fällen jedoch, in welchen sie sich von Briefen nicht einwandfrei unterscheiden lassen, sind sie in das Verzeichnis aufgenommen worden. (shrink)

El presente artículo tiene por objetivo analizar desde un punto de vista ontológico los retos económicos y existenciales que Europa afronta durante los últimos años, a consecuencia de la crisis económica y de la masiva oleada de refugiados derivada de los conflictos en el mundo Árabe. Cimentando nuestra argumentación en la interpretación de Martin Heidegger del ser humano como δεινόν, asombroso, tratamos de demostrar que el núcleo ontológico de la situación turbulenta que actualmente vivimos puede hallarse en el evento de (...) la ausencia de hogar, en tanto que carencia de una morada propia en Europa. Por último, presentamos la política e ideológicamente convulsa matriz del esquema político europeo moderno, a fin de subrayar la relevancia de redefinir, por una parte, el significado de familiaridad y coexistencia para nosotros, los europeos, y, por otra, Europa en tanto que totalidad.The aim of this article is to analyse from an ontological point of view the challenges, economic and existential, that Europe has been facing the last years as a result of the economic crisis and the incoming human waves of the refugees as a result of the conflicts in the Arab world. Namely, founding our argumentation on the interpretation of the human being as δεινόν, uncanny, made by Martin Heidegger we would like to show that the ontological core of the turbulent situation we are currently living in can be found in the concept of homelessness as the lack of our abode in Europe. Finally, presenting the political and ideologically intense matrix of the modern European political scene we aim at highlighting the importance of redefining what homeliness and cobelonging mean to us, Europeans and Europe as a whole. (shrink)

There is a widespread practice of spelling the forms κεχρώσμεθα in Euripides' Medea 497 and ϕώζειν in Strattis, fr. 9 K.–A. with the long diphthong omega–iota, that is, κεχρώισμεθα or κεχρῴσμεθα and ϕώιζειν or ϕῴζειν. These spellings are not correct from the etymological point of view, but are recommended by ancient grammarians. In this note I identify the foundation on which these recommendations rest, and provide an assessment of its philological solidness.

"A valuable book... it very nicely relates Aristotle's views about exactness to more general ethical and epistemological themes in Aristotle."--Charles M. Young, The Claremont Graduate School "A valuable book... it very nicely relates Aristotle's views about exactness to more general ethical and epistemological themes in Aristotle."--Charles M. Young, The Claremont Graduate School.

_The Blackwell Companion to Aristotle_ provides in-depth studies of the main themes of Aristotle's thought, from art to zoology. The most comprehensive single volume survey of the life and work of Aristotle Comprised of 40 newly commissioned essays from leading experts Coves the full range of Aristotle's work, from his 'theoretical' inquiries into metaphysics, physics, psychology, and biology, to the practical and productive "sciences" such as ethics, politics, rhetoric, and art.

Many Buddhist rulers attained the cultic status of divinity as buddhas or celestial bodhisattvas and were expected to exercise their power in accord with Buddhist principles. The bodhisatta is depicted as perfecting both the virtues of kingship and the virtues of renunciation, thus preparing the way for his supreme enlightenment in which the two strands of sovereignty and renunciation “receive their final synthesis and fulfilment”. Politics was realistically seen as an unavoidable exercise of power that can and ought to be (...) used to promote righteousness, while the philosophical interpretation of Buddhist doctrines reflects the pragmatic nature of Buddhist ethics, which, unlike the deontological and absolutist ethical traditions, allows for the expression of multiple and variant attitudes towards the state and the role of religion in shaping and being shaped by social and political conditions. (shrink)

Plotinus’ thesis of the relationship between the One and Nous (Intellect) is central to his thought. In dealing with this relationship, he concentrates far more on what makes the One and Nous alike than on what makes them different. This is because by preference he envisages the One as the ‘causal principle () of everything’, in what might be termed a ‘top‐down’ model of metaphysics in which first cause (the One) leads downwards to second cause (Nous). Plotinus is obliged to (...) present the distinction between the One and Nous as relative, not as absolute, precisely because he wants to show that Nous is firmly grounded in the One. The One differs from Nous to no more than the degree, and in no more than the manner, that are necessary for there to be created a Nous which is as like as possible to the One Itself. (shrink)

ABSTRACT The article revisits the history of the ‘Eastern Question’ and its impact in late Victorian England through the lens of the British scholar Arthur J. Evans. Evans is best known for his archaeological discoveries in the island of Crete in the beginning of the twentieth century. His journalistic and archaeological ventures in the Balkans in the 1870s and 1880s have received scant attention. The article recovers Evans’ activities which straddled humanitarianism, political activism, archaeology, anthropology/ethnography and journalism. Although Evans was (...) not a systematic thinker on international affairs, his writings typified the liberal internationalist ambivalences on the ‘plight’ of eastern christians in southeastern Europe and the Balkans. The article argues that his thought fused two interrelated temporal frames: the deep anthropological and archaeological time of ancient civilizations and the modern framework of nationalist politics. These different horizons guided his understanding of the world of international affairs and underpinned the key role he played in debates on the Bosnian and Albanian questions. (shrink)

Georgios Mantzarides; Globalization and Universality: Chimera and Truth, Christian bioethics: Non-Ecumenical Studies in Medical Morality, Volume 8, Issue 2, 1 J.

Heidegger’s reading of Plato is variable and multifaceted, giving way to different and, at times, opposing interpretations of Plato’s work. To give an example that is relevant to the following pape...

The Contribution of Byzantine Scholars to Renaissance Aristotelianism It is widely known that the Byzantine scholars who fled to Italy during the fifteenth century contributed to Renaissance philosophy. They brought with them manuscripts and produced editions and translations of Greek philosophical texts. Despite the common view that their works were seminal for the development of Renaissance Platonism, a closer examination of the texts and their activity proves that they were mainly interested in Aristotelian philosophy. The vast majority of them did (...) not support Renaissance Platonism. On the contrary they defended both the Scholastic and Byzantine Aristotelianism. I argue that their stance was not the outcome of dogmatic reasons; in other words, a projection of the heated debate between Hesychasm and Thomism in late Byzantium. Rather, they realized that the Latin philosophical community actually ignored the rich commentary tradition of Late Antiquity, which had reinterpreted the Aristotelian corpus. As a result they offered to the Latin audience a different Aristotle, capable of overcoming the predominant Scholastic one, which was heavily attached to Averroism. (shrink)

This volume constitutes an attempt at bringing together philosophies of time—or more precisely, philosophies on time and, in a concomitant way, history—emerging from Christianity’s and Islam’s intellectual histories. Starting from the Neoplatonic heritage and the voice of classical philosophy, the volume enters the Byzantine and Arabic intellectual worlds up to Ibn Al-Arabi’s times. A conscious choice in this volume is not to engage with, perhaps, the most prominent figures of Christian and Arabic philosophy, i.e., Augustine on the one hand and (...) Avicenna/Ibn Sina on the other, precisely because these have attracted so much attention due to their prominence in their respective traditions—and beyond. In a certain way, Maximus the Confessor and Ibn Al-Arabi—together with Al-Fārābi—emerge as alternative representatives of their two traditions in this volume, offering two axes for this endeavor. The synthesis of those approaches on time and history, their comparison rather than their mere co-existence, is left to the reader’s critical inquiry and philosophical investigation. (shrink)

This chapter contains sections titled: Early Years in Stageira First Athenian Period Period of Travels Second Period in Athens Last Year in Chalcis, Euboia Notes Bibliography.

This chapter contains sections titled: Introduction Aristotle's Presuppositions and Demonstration Induction (epagôgê) and Comprehension or Intuition (nous) Collecting Facts and Finding Causes Dialectic and its Uses Notes Bibliography.

This chapter contains sections titled: Catalogues and Editions of Aristotle's Works Chronology of Aristotle's Works The Development of Aristotle's Thought Notes Bibliography.

This paper inquires into the inability ofsubjects in English to topicalise. Treatingtopicalisation as a specific case of d-linking,it asks: why don’t subjects topicalise inEnglish? And why cannot they be d-linkedthrough further movement? It concludes thatthe property of [aboutness] of subjects is anunderspecified instance of a more compositederivative effect realised as [topic]. Giventhe ability of objects in English to be readilyd-linked through extraction in CP, theanalysis takes a detailed look at the structuraldifferences between subjects and objects. Itconcludes that d-linking of an (...) argument iscontingent upon the derivational memory ofits prior inclusion within vP that has yielded itsdenotational set-membership. Treating EPPas an A’-operation that embeds one instance ofthe subject-chain into discourse, the inabilityof subjects to topicalise is explained as an “online”denotational dependency on discourse,which lacks the systemic memory of thesubject’s embedding. In turn, their immobilityis treated as a modular dependency betweenthe two subject copies, mediated through Texcluding the one instance of the chain. (shrink)