This paper attempts to quantify the development of the key monetary values and changes in monetary trust that occurred during Roman times under ever-increasing prices. To track those developments, the paper introduces a minimal-parameter model that builds on available numismatic data relating to the Roman landmark coinages and on papyrological findings. The modelling produces a series of graphs which clearly signal the occurrence of a later crisis of confidence. It is argued that the monetary measures typically taken by (...) the Roman authorities actually fostered a crisis of confidence, and even made it inevitable. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Coinage in the Roman Economy, 300 b.c. to a.d. 700Leah JohnsonKenneth W. Harl. Coinage in the Roman Economy, 300 b.c. to a.d. 700. Baltimore: The Johns Hopkins University Press, 1996. x 1 533 pp. 31 plates. Cloth, $49.95.In Coinage in the Roman Economy Kenneth Harl proposes to examine “how the Romans minted and used coined money—its role in payrolls, tax collection, trade and daily transactions—over (...) the course of a millennium, 300 b.c. to a.d. 700” (1). Most previous works on Roman coins have tended to treat them as objects worthy of study in and of themselves and not as evidence for understanding the social and economic policies of the Roman world. (R. Duncan-Jones’s Money and Government in the Roman Empire [Oxford 1994], a survey of the use of coins in the first three centuries of the Roman empire, is a notable exception to this rule.) The expansiveness of Harl’s welcome new treatment allows the reader access to virtually all of the significant stages and changes in the development of Roman coinage and their effects on the economy of the ancient Roman world and supplies knowledge crucial to a comprehensive understanding of how the Roman economy functioned, and, ultimately, why the empire was successful.Surprisingly enough, it was necessary for Harl to address many long-standing objections to the significance of coinage in the Roman economy before engaging in his survey. The significance of coins in Roman fiscal policy has been discounted on the basis of their limited numbers and availability by M. I. Finley (The Ancient Economy 166). According to Finley, since the Romans struck coinage only intermittently, coins could not have played a major role in determining Roman fiscal policy. Others who now acknowledge that a great number of Roman coins were put into circulation, object that coinage could not have played an important role in the “underdeveloped” agrarian-based society of Rome. Still others, admitting the significance of coins in commerce in the Roman world, have argued that their use in trade was only incidental. In other words, the Roman government did not mint coins to stimulate trade, but simply to pay for expenses such as military and administrative payrolls or building contracts.In chapter 1, “Coins, the Money of the Roman Economy,” Harl counters Finley’s objections by arguing that since Finley’s work, many statistical studies have estimated the enormous outputs of coins that the Romans could mint on short notice if necessary. So in periods when there was a shortage of coins, the Romans could in fact very quickly pump more money into the economy. Harl argues that the supposed absence of coins in rural areas of the Roman world is simply due to the limitations of archaeology in that not all of the town centers and marketplaces in rural areas of the Roman world have been excavated. Furthermore, although he acknowledges the centrality of land in the Roman economy, he also points out the importance of seaborne trade to it. He next admits that coins were primarily issued by the state for government payrolls or payments [End Page 139] to contractors, but nonetheless he stresses that the degree of importance which Roman coinage had in commerce was equal to that which it possessed in government fiscal policies. Thus, although the use of coinage was fiscal in origin, its contribution to commercial growth was increasingly important as the empire expanded.Harl then provides a summary of the methods by which the Roman government manipulated the coinage in periods of inflation or emergency, or when the currency simply needed to be replenished due to deterioration of the metal content. In such instances, the Romans generally didn’t melt down and restrike worn coins but instead either lowered the tariff of the old coins against new coins which were issued or simply minted debased new coins with a precious metal content equal to that of the old coins in circulation. Harl concludes his first chapter with a survey of the various types of numismatic research currently being employed in the area of Roman coinage—metrological analyses, die and hoard studies... (shrink)

Joseph Eckhel was the most influential numismatic scholar of the Enlightenment. Eckhel’s key contribution was the creation of the ‘system’ named after him: a novel arrangement of ancient Greek and Roman coins that was swiftly adopted in major international collections and publications and largely still stands today. This article presents and discusses a previously unknown manuscript in Latin written by Eckhel in 1775, the Animadversiones in methodum, secundum quam nunc digestum est Museum numismaticum Magni Ducis (‘Observations on the Method (...) according to which the Coin Collection of the Grand Duke is Now Arranged’). This new source is the earliest attested methodological text by Eckhel. It sheds light on a crucial phase in the development of his system for the first time and demonstrates how Eckhel shaped his ideas while ordering the coin collection of Grand Duke Peter Leopold in Florence in 1773, together with Raimondo Cocchi. (shrink)

This volume - the first project of its kind in the field - collates c. 1200 biographical entries on Greek sophists and rhetors who flourished in the Roman Empire from the first to the seventh century AD. Ancient Greek sophists, the masters of speech and teachers of rhetoric, constituted one of the most important and interesting intellectual circles of the ancient world. The prosopography provides comprehensive information on sophists and their activities, using abundant and varied source material such as (...) literary texts (including those of the rhetors themselves) and papyrological, epigraphic, and numismatic evidence. Each entry provides data (where available) on sources in which the person is attested, biographical details, career, and rhetorical activity. This book constitutes a basis and a tool for subsequent in-depth studies on the Greek Sophistic movement, as well as a useful reference book for students and all those interested in the culture of the ancient world. (shrink)

In this paper, I want to focus on a specific set of numismatic images of Alexander the Great, which has received less attention than comparable ones: the depictions on the Late Roman medallions known as contorniates. First, in two introductory sections, I connect the tradition of Alexander's numismatic imagery with the contorniates and present the general characteristics of these medallions. Next, I offer a detailed analysis of the different depictions of Alexander on contorniates. Thirdly, I briefly summarise the discussion (...) of the functions of the contorniates and, on this basis, question the interpretations of them as pagan symbols and amulets proposed by Alföldi and Mittag. Finally, based on the critique of these interpretations, I argue that the Alexander contorniates reflect an interest in the historical figure of the great conqueror and the quasi-fictional hero of the Alexander Romance. If this Alexander was a symbol, it was of Greco-Roman patriotism and the empire's ability to prevail over its barbarian enemies. (shrink)

Name der Zeitschrift: Journal of Ancient History Jahrgang: 4 Heft: 2 Seiten: 191-239.

In 1903 the German art historian Karl Giehlow argued that a 1514 treatise on Greek numismatics, written by the Augsburg humanist Conrad Peutinger and addressed to the Holy Roman Emperor Maximilian I, shed new light on Albrecht Dürer’s mysterious engraving Melencolia I. Since the treatise has never been published, the question has never been investigated. This article presents a transcription, commentary and translation of the treatise for the first time in any language. It also situates Peutinger’s work within (...) the history of scholarship on Greek antiquity and the history of German Renaissance art. The central concern of Peutinger’s treatise turns out to be a precocious and unexpected one: neither the exploits of the ancient hero whom the coin in question depicts, nor the possible lineage of the Habsburg emperor back to Hercules, but the material history of religion on an island in the Hellenistic Aegean. The article describes the leaps and misunderstandings that led Peutinger to endow his object, an everyday piece of ancient currency, with artistic significance and a sacred aura. PaceGiehlow, it is not the Melencolia I that is illuminated by the text, but artworks produced locally: the Prayer Book of Maximilian and the classical and sacred craftsmanship of an Augsburg goldsmith. The interpretation of Greek artworks did not just influence the art of a Christian city: Christian art, on the evening of the Reformation, coloured the interpretation of Greece. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Maternal Megalomania: Julia Domna and the Imperial Politics of Motherhood by Julie LangfordLien FoubertJulie Langford. Maternal Megalomania: Julia Domna and the Imperial Politics of Motherhood. Baltimore, Md.: Johns Hopkins University Press, 2013. xiv + 203 pp. 20 black-and-white figs. Cloth, $55.It is now well-established that, through various media, imperial propaganda was aimed at different groups in Roman society. Ever since Jaś Elsner’s influential publication (Art and the (...) Roman Viewer: The Transformation of Art from the Pagan World to Christianity [Cambridge 1995]), scholars have also widely acknowledged that one should always reckon with the role of “the viewer” when studying processes of communication. Yet it remains difficult to find ways of measuring viewers’ responses to imperial messages, in particular when it concerns imperial [End Page 678] women, for whom we have far less evidence than for the male protagonists of Roman imperial history. Julie Langford’s study of the representation of Julia Domna and the way in which her image as a mother was perceived by the military, the Populus Romanus, and the Senate is, therefore, a much needed scholarly enterprise. By choosing this approach, the author builds on the model of the Principate as an “acceptance system,” first introduced by Egon Flaig in 1992 (Den Kaiser herausfordern: die Usurpation im römischen Reich [Frankfurt]), although this influence remains implicit as Flaig’s text is not mentioned in the introduction nor is it included in the bibliography. In this monograph, which is explicitly not intended as a biography in search of the “real” Julia Domna, Langford aims at examining the ideological negotiations that took place between image-makers.In chapter 1 (“Not Your Momma. Problematizing Julia Domna as the Mater Castrorum”), the author sets out to examine the relationship between the military and Julia Domna by means of a study of ideological discourses on the presence of women in a military context up to the time of Septimius Severus, the conferral of the title Mater Castrorum on Faustina Minor and Julia Domna, and the reactions to the latter by different groups within the army (one should also consult M.A. Speidel’s “Faustina—mater castrorum. Ein Beitrag zur Religionsgeschichte,” Tyche 27 [2012]: 127–52, which probably appeared too late for the author to take into account). She concludes that, contrary to what is often assumed, the title of “Mother of the Camps” was not granted to tighten or emphasize the connection between empresses and the army, but was instead aimed at the people of Rome and the provinces. For by creating the image of a familial connection between the soldiers and the imperial house, and thus implying that the military would support and protect their imperial “mother,” her husband, and her sons, the inhabitants of the Roman Empire would be discouraged from starting an uprising. The arguments that are put forward by the author are twofold. On the one hand, inscriptions, coins, and literary sources indicate that the military did not constitute a well-defined target of imperial propaganda with regard to Julia Domna’s military representations. For instance, less than 6 percent of the dedications to the empress studied by the author were set up by soldiers. In addition, although the Roman mint produced coins that advertised the empress’ title of Mater Castrorum from 196 onwards, this practice was not extended to the eastern traveling mints, which are often assumed to have been fundamental for the distribution of salaries or donations and, consequently, would have been a logical starting point for spreading ideological messages. On the other hand, the author pays attention to the poor reputation of Julia Domna within the army, focusing above all on the figures of Plautianus and Julius Crispus (38–44), and sees this as an indication of the initial reluctance of the soldiers to associate the empress with anything connected to the military sphere, including the acknowledgment of Julia Domna as “their mother.” The first argument in particular is convincing, since—even though the author admits that much remains unproven with regard to the role of eastern mints—the combination of epigraphic and numismatic source material shows that messages sent out by the imperial administration... (shrink)

Located astride the shipping routes linking southern Asia Minor with the coasts of Syria and Palestine and Egypt, the island of Cyprus has always been regarded as a stepping stone of the cultural and economic communications interconnecting different areas of the eastern half of the Mediterranean. Politically this role has been first enhanced during the Hellenistic, Roman and then in the early medieval period when in the seventh century Cyprus acquired an important role as military Byzantine stronghold. Economically, the (...) significance of Cyprus in the passage from the late antiquity to the early middle ages benefitted from its essential role as hub along the eastern tax-spine through which Egypt fed Constantinople and along the long-distance trade-routes based upon the sea-movement of luxury goods. This multifunctional role of Cyprus as a bridge between different regions of the eastern Mediterranean can be further assessed through the analysis of the numismatic material. Here, indeed, the study of the coins and coinage yielded by the archaeological excavations in urban centres like Salamis-Constantia, Paphos-Saranda Kolones, and Kourion should be paired with both the reassessment of the publication of the old Cypriot hoards and stray finds and the recent studies on the so-called Arab-Byzantine coinage found both in Cyprus and in the closer Syria-Palestine region. The examination of this material allows to develop a different interpretative scheme than the one traditionally adopted to interpret the fate of Cyprus after the Muslim raids and the occupation of Syria and Palestine. Cyprus and its cities were still frequented in the passage from late antiquity to the early middle ages, preserving a variable but still traceable degree of monetary economy including Byzantine emissions and Arab specimens, inferring the maintenance of political, commercial and cultural relations between the Byzantine Empire and the Umayyad Caliphate. (shrink)

La présente contribution se propose de réfléchir, à partir de l’exemple péloponnésien, au rôle joué par les références mythiques dans la représentation qu’élaborent d’elles-mêmes les cités grecques d’époque impériale romaine. Sans que soit négligé l’apport de l’archéologie, de la numismatique ou du texte de Pausanias, l’enquête s’appuie essentiellement sur les inscriptions honorifiques qui, même si elles s’inscrivent dans un cérémonial de la célébration publique, peuvent être considérées comme discours officiels, traces documentaires de la conscience de soi des cités. Dans le (...) jeu complexe des influences romanisantes et de la continuité hellénique, la question sera aussi posée de la portée spécifique que prennent les références mythiques et, pour mon propos, spécialement les figures héroïques doriennes, dans la définition des axes grec et romain de l’identité civique. Myth and civic identity in the Roman Peloponnese. In the present article, I explore how far mythical references are involved in the way the Peloponnesian cities define themselves during the Roman imperial age. Archaeological remains and numismatical material will be taken in account, but also Pausanias’ Description of Greece and mainly epigraphic texts, especially honorific inscriptions, which, despite their rhetorical phraseology, provide evidence of great interest for the study of self-definition in the cities of Roman Greece. Through a study of the relationship between Greek and Latin components of civic identity, I will try to make a reasonable assessment of the primacy of Dorian heroic characters, as revealed particularly throughout the Spartan epigraphic material, and I will ask whether this is to be understood as the expression of a distinct sense of Dorian self-consciousness. (shrink)

Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics.

This paper restores the historical context of Milindapaha. The text is unique, because it is one of the very few documents of Ancient India, in which one of the authors is considered a Greek as a participant in the dialog. To reconstruct the context of the book, the basic archeological data about the Indo-Greek Kingdom, including epigraphics, are summed up, as well as there are analyzed some references to the kingdom given in the Mahāvaṃsa, the earliest chronicle of Sri Lanka. (...) These mentions in the Mahāvaṃsa are matched with the numismatics of Ceylon. From this analysis it is concluded that the document of Milindapaha was most likely created in Gāndhārī in the interval from the beginning of the 1st century B.C. to the end of the 1st century A.D., i.e. during the period of the domination of the syncretic culture of the North of India, combining Buddhism with certain elements of Hellenism. The treatise of Milindapaha was then preserved in Sri Lanka's tradition by continuing good political contacts with the Roman Empire after 400 A.D., that is, after the collapse of the Kushan and the Western Kshatrapas, the last dynasties that had previously preserved elements of Hellenism in the Indian subcontinent. The philosophical meaning of the treatise is then considered and it is concluded that in the text we can find direct references to the proto-Nyāya with the requirement to verify premises by examples. But the logical teaching of Milindapaha is far more archaic than the teaching of Nyāyasūtra, because only two sources of true knowledge are implicitly used: paccakkha and anumāna, and instead of the two verification methods called udāhārana and upamā, only one verification method called opamma is offered. (shrink)

Introduction The starting point for our reflections upon the musical work will be the unsystematized convictions that we encounter in daily life in our communion with musical works before we succumb to one particular theory or another.

A primary issue in the field of business and society over the past 25 years has been the relationship between corporate social performance and corporate financial performance. Recently, Griffin and Mahon (1997) presented a table categorizing studies that have investigated this relationship. Motivated by concerns with this table, as well as a desire to account for progress in research in this area, the authors reconstructed it. The authors present a portrait of this relationship that is (a) substantially different from that (...) shown in the Griffin and Mahon table and (b) more consistent with the latest research on the topic. (shrink)

"Vom Erkennen des literarischen Kunstwerks" ist zuerst (poln. 1937) als erkenntnistheoretisches - und geringfügig populäreres - Pendant zur ontologischen Theorie "Das literarische Kunstwerk" (1931) angelegt. In der deutschen Fassung (Erstpublikation 1968) wird es zum gedankenreichen literaturphilosophischen Alterswerk. Wie schon "Der Streit um die Existenz der Welt" (Erstpublikation 1947/48), so ist auch "Vom Erkennen" als Antwort auf Krieg, Völkermord und Totalitarismen zu lesen, im Sinne des Beharrens auf den Fundamenten der humanen Existenz. Dem "Ende der Ontologie" setzt Roman Ingarden (1893-1970) (...) den Nachweis der Notwendigkeit ontologischer Reflexion bei der Ergründung erkenntnistheoretischer Sachverhalte entgegen (vgl. die 'ästhetische Konkretisation'), der am Wert verzweifelten Nachkriegsliteratur die Erörterung der Werte, Wertqualitäten und ihrer möglichen Synthesen im konkretisierten literarischen Kunstwerk. Gegenüber "Das literarische Kunstwerk" arbeitet er neu die quasi-zeitliche Dimension des literarischen Kunstwerks aus, 'entdeckt' die künstlerischen Funktionen der Unbestimmtheit, bezieht die Lyrik und das Gattungswesen der Literatur ein und analysiert die verschiedenen Erkenntnisziele und -zugänge zum literarischen Kunstwerk. Dem Liebhaber vermittelt das Buch eine Begründung des legitimen Entzückens am ästhetischen Gegenstand, dem Literaturwissenschaftler eine Grundlegung seiner analytischen und funktionellen Erkenntnisoperationen. Ein ausführliches analytisches Inhaltsverzeichnis, ein davon abgeleitetes System von Kolumnentiteln sowie ein Personenverzeichnis erleichtern in dieser neuen Ausgabe die Arbeit mit diesem Buch. (shrink)

English Summary: Marcus Aurelius was Roman Emperor and the last important ancient stoic philosopher. His Meditations are one of the most widely read and known ancient works. Thus, research on this emperor has spread across an almost unprecedented number of scientific disciplines. This volume, which originated at the first conference on Marcus Aurelius, held in Cologne in 2009, reunites publishes recent research in history, archaeology, philosophy, philology, numismatics, rhetoric, legal studies, and literature. German text. German Description: Marc Aurel (...) war romischer Kaiser und der letzte bedeutende stoische Philosoph in der Antike. Seine Selbstbetrachtungen sind eines der meistgelesenen und uber die Fachwelt hinaus bekannten antiken Schriftstucke. Er ist daher wie kaum eine andere antike Figur Gegenstand eines so grossen Spektrums von Forschungsdiziplinen. Im vorliegenden Sammelband, der auf der ersten Tagung zu Marc Aurel (2009 in Koln) basiert, werden aktuelle Forschungsbeitrage aus den Fachern Geschichtswissenschaft, Archaologie, Philosophie, Philologie, Numismatik, Rhetorik, Rechtsgeschichte und Literaturwissenschaft vereint. (shrink)

This study examines whether corporate social responsibility performance is associated with corporate tax avoidance. Employing a matched sample of 434 firm-year observations from the Kinder, Lydenberg, and Domini database over the period 2003–2009, our logit regression results show that the higher the level of CSR performance of a firm, the lower the likelihood of tax avoidance. Our results indicate that more socially responsible firms are likely to display less tax avoidance. Finally, the results from our additional analysis show that the (...) CSR categories community relations and diversity represent particularly important elements of CSR performance that reduce tax avoidance. (shrink)

Roman Frigg and James Nguyen present a detailed statement and defense of the fiction view of scientific models, according to which they are akin to the characters and places of literary fiction. They argue that while some of the criticisms this view has attracted raise legitimate points, others are myths. In this chapter, they first identify and then rebut the following seven myths: that the fiction view regards products of science as falsehoods; that the fiction view holds that models (...) are data-free; that the fiction view is antithetical to representation; that the fiction view trivializes epistemology; that the fiction view cannot account for the use of mathematics in the modeling; that the fiction view misconstrues the function of models in the scientific process; and that the fiction view stands on the wrong side of politics. As a result, they conclude that the fiction view of models, suitably understood, remains a viable position. (shrink)

The paper is devoted to the discussion of some philosophical and historical problems connected with the theorem on the undefinability of the notion of truth. In particular the problem of the priority of proving this theorem will be considered. It is claimed that Tarski obtained this theorem independently though he made clear his indebtedness to Gödel’s methods. On the other hand, Gödel was aware of the formal undefinability of truth in 1931, but he did not publish this result. Reasons for (...) that are also considered. (shrink)

This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section (...) of the research project _Logical Systems and Algorithms for Automatic Testing of Reasoning,_ 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia??l??ystok Branch of the University of Warsaw, and supported by the Ministry of Education 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE ) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration. (shrink)

This long-awaited translation of Das literarische Kunstwerk makes available for the first time in English Roman Ingarden's influential study. Though it is inter-disciplinary in scope, situated as it is on the borderlines of ontology and logic, philosophy of literature and theory of language, Ingarden's work has a deliberately narrow focus: the literary work, its structure and mode of existence. The Literary Word of Art establishes the groundwork for a philosophy of literature, i.e., an ontology in terms of which the (...) basic general structure of all lliterary works can be determined. This "essential anatomy" makes basic tools and concepts available for rigorous and subtle aesthetic analysis. (shrink)

Notwithstanding the opportunities it provides, the implementation of some measures of the EU Common Agricultural Policy (EU CAP), including agri-environment-climate measures (AECMs), also generates threats. The study identifies an extremely disturbing process that can be referred to as “internal neo-colonialism”, which has been driven by the technocratic agrarian policy of the EU and transformations in Poland at the turn of the twenty-first century. The associated disadvantageous practices mainly affect areas under threat of marginalisation and peripheralisation, including Poland with its post-Socialist (...) heritage, which has shaped the attitudes and behaviour of society and has consolidated linkages between politics and business. In order to retrace such activities, the study analyses EU funds granted in support of farmers implementing AECMs, with a focus on analysing the place of residence of the “farmer” and the location of the farm. As the research shows, the attractiveness of CAP support causes Polish agriculture and Poland’s countryside, including its natural and financial resources, to be drained by so-called “suitcase farmers”, i.e. people/entities not tied to the place where the agricultural activity is pursued, many of whom live in cities. One common practice is to take over land located in legally protected areas noted for their high quality of natural environment. Not only does the practice of land grabbing strengthen the social exclusion of rural communities and the peripheralisation and pauperisation of these areas, but it also hinders discussion about environmental justice and the ecological integrity of rural areas. (shrink)

This long-awaited translation of Das literarische Kunstwerk makes available for the first time in English Roman Ingarden's influential study. Though it is inter-disciplinary in scope, situated as it is on the borderlines of ontology and logic, philosophy of literature and theory of language, Ingarden's work has a deliberately narrow focus: the literary work, its structure and mode of existence. The Literary Work of Art establishes the groundwork for a philosophy of literature, i.e., an ontology in terms of which the (...) basic general structure of all literary works can be determined. This "essential anatomy" makes basic tools and concepts available for rigorous and subtle aesthetic analysis. (shrink)

As a remedy for the bad computational behaviour of first-order temporal logic (FOTL), it has recently been proposed to restrict the application of temporal operators to formulas with at most one free variable thereby obtaining so-called monodic fragments of FOTL. In this paper, we are concerned with constructing tableau algorithms for monodic fragments based on decidable fragments of first-order logic like the two-variable fragment or the guarded fragment. We present a general framework that shows how existing decision procedures for first-order (...) fragments can be used for constructing a tableau algorithm for the corresponding monodic fragment of FOTL. Some example instantiations of the framework are presented. (shrink)

Primary object of interest of mathematicians can be identified as a „mathematical matter”, the concept analogous to „physical matter” or „biological matter”. The „mathematical matter” is the soil upon which mathematics grows. One can distinguish three levels of it: some abstract but not necessarily clear conceptions, operational notions (like number) but not necessarily openly defined, theories not necessarily axiomatic. The „mathematical matter” originates in the abstract reflection upon events and forms in time and space. Its important elements are notions formed (...) mostly in the process of idealization and/or abstraction. Once formed, notions usually evolve being, e.g., simplified or complexified. Mathematics is a mirror of the world, most abstract and therefore fundamental. Although it is a free activity of human mind, mathematics reflects some deep ideas (beauty, simplicity etc.) while most interesting notions come up in tension fields between pairs of poles: the notion of a function can be seen as a bridge connecting variability and immutability, while that of a limit – connecting finiteness and infinity. A fusion of freedom and internal restrictions leads to mathematics which is simple, beautiful and effective. (shrink)

OBJECTIVE PREDICATION The author claims that there are two kinds of predicates that are used to describe cognitive states of mind like beliefs or perception. Using some of them, one can describe the cognitive states of mind directly, whereas using some others, one can describe these states in comparison with one’s own. For example, one can say that a person has a belief or one can say that that person’s belief is according to his own beliefs. In the latter situation, (...) he uses the predicate “to know”. The conditions that Peter uses correctly the sentence “John knows that p” are as follows: (1) Peter believes that John believes that p; (2) Peter believes that p; (3) Peter believes that the reasons for which John believes that p have a good justification. In a similar way one can ascribe to somebody a visual impression of an object x or to compare that person’s impressions with his own cognitive states. In the latter situation one uses the predicate “to see” (to perceive). The conditions that Peter uses correctly the sentence “John can see x” are the following: (I) Peter believes that John has visual impression of object x; (II) Peter believes that object x exists; (III) Peter believes that this that John has visual impression of object x is according to the laws of vision. When one uses predicates that describe cognitive states of mind of a person (possession of beliefs or sensory impressions), one speaks subjectively, whereas when one speaks objectively, he uses predicates that allow him to compare cognitive states of mind of a person with his own. Keywords: PREDICATION, BELIEFS, PERCEPTION. (shrink)

It is argued that some elusive “entropic” characteristics of chemical bonds, e.g., bond multiplicities (orders), which connect the bonded atoms in molecules, can be probed using quantities and techniques of Information Theory (IT). This complementary perspective increases our insight and understanding of the molecular electronic structure. The specific IT tools for detecting effects of chemical bonds and predicting their entropic multiplicities in molecules are summarized. Alternative information densities, including measures of the local entropy deficiency or its displacement relative to the (...) system atomic promolecule, and the nonadditive Fisher information in the atomic orbital resolution(called contragradience) are used to diagnose the bonding patterns in illustrative diatomic and polyatomic molecules. The elements of the orbital communication theory of the chemical bond are briefly summarized and illustrated for the simplest case of the two-orbital model. The information-cascade perspective also suggests a novel, indirect mechanism of the orbital interactions in molecular systems, through “bridges” (orbital intermediates), in addition to the familiar direct chemical bonds realized through “space”, as a result of the orbital constructive interference in the subspace of the occupied molecular orbitals. Some implications of these two sources of chemical bonds in propellanes, π-electron systems and polymers are examined. The current–density concept associated with the wave-function phase is introduced and the relevant phase-continuity equation is discussed. For the first time, the quantum generalizations of the classical measures of the information content, functionals of the probability distribution alone, are introduced to distinguish systems with the same electron density, but differing in their current(phase) composition. The corresponding information/entropy sources are identified in the associated continuity equations. (shrink)

In the paper n -valued paraconsistent matrices are defined by an adaptation of the well-known Łukasiewicz’s matrices. An appropriate set of axioms is presented and the 3-valued case is examined.