This is cassette 12, concerned with more connexions between late medieval and early modern thought. The first writer we will look at is George Berkeley, who criticised Locke's theory of abstract ideas and put forward his own theory of universality.

I have been surveying the spelling across a range of the manuscripts; my findings are given under “Profiles” at the end. The method I have used is to find the word by electronic search in my computer files, then find corresponding places in the MSS. If abbreviation conceals the spelling I search further. This method does not guarantee that the spelling I find at some place in a MS is used throughout the MS; indeed in some cases I have noticed (...) variations. All I claim is that at least sometimes the word is spelled that way in that MS. Because photocopy of some MSS is not available to me at present or is illegible, my survey of the MSS is not complete. (shrink)

The Cambridge History of Later Medieval Philosophy (CHOLMP) brings together in one volume an impressively large number (47) of short essays (averaging 18 pages) by an impressively large number (41) of able scholars. The final product, sad to report, is something less than impressive.

It is a commonplace in the historiography of medieval philosophy that theology represents philosophy's culmination in the later Middle Ages, and specifically, that it is in the work of theologians and theologically-trained Arts Masters that we find philosophy in its purest and most advanced form. By comparison, the philosophy produced by thinkers who worked exclusively or primarily in the Faculty of Arts is seen as inferior -- by which is usually meant that it is shallow, unsophisticated, immature, and driven (...) by disparate curricular and pedagogical concerns rather than by the more single-minded commitment to rationally articulate that sacred doctrine which, as Aquinas says, "extends [by virtue of its oneness] to things which belong to different philosophical sciences.". (shrink)

Descartes (1596-1650) is generally regarded as the first of the modern philosophers. Indeed, until about 50 years ago most philosophers would have said that Descartes was the first significant philosopher since Aristotle. Descartes himself does not draw attention to his sources--not to conceal them (that would have been pointless, because to his contemporaries the continuities of his thought with the books they had all been brought up on would have been obvious), but so as to avoid getting embroiled in learned (...) disputes about who had said what and what they had meant. Descartes wanted his readers to look at his arguments and judge them by using their own intelligence. He calls on his readers to empty their minds of prejudices, i.e. previous judgments, and take a fresh look. His writings had such an impact that philosophy after Descartes generally took his arguments and positions as a starting point or as a point of reference, and earlier writers were no longer read. (There was a social reason for this also: philosophical books were, after Descartes set the example, generally addressed in French or some other vernacular language to lay readers outside the universities, and most readers could not easily read the Latin authors Descartes had himself read when he was a student of the Jesuits.) So it came to be thought that Descartes had had no significant predecessors--that all of his ideas were original. Descartes was indeed an original thinker, but he used a good deal of medieval material. In this lecture I want to go through Descartes' chief work in philosophy, The Meditations , outlining the argument and drawing attention to the medieval material. (shrink)

With regard to the new directions in the Humanities, here I am going to consider and examine the approach of al-Farabi as a medieval thinker in introducing a new outlook to “language” in difference with the other views. Thereby, I will explore his challenges in the frame of “philosophical humanism” as a term given by Arkoun (1970) and Kraemer (1984) to the humanism of the Islamic philosophers and their circles, mainly in the tenth and eleventh centuries. Al-Farabi’s conception of (...) philosophical humanism, in which philosophy is thick and religion is thin, makes its agony with the other versions of humanism and also orthodox Islam. It means that his introduction of a humanistic understanding of language should be placed in such a multi-level contested environment. According to al-Farabi, language as a universal category has relation with reason that logic should function as its proper instrument. As a result, there is no specific privileged predetermined language, but the position of any language is shaped by its relation with human reason and formal logic that is something human-made. And such a conception means language in human terms. Key Terms: Al-Farabi; Language; Philosophical Humanism; Arabic: Greek . (shrink)

Usually thoughts are not in isolation but in varing degrees have interrelations with each other. With regard to this historical fact as a classist want to explore the reception of a few medieval Arabic texts and writers of Socrates available teachings about politics.

Perceptions of Medieval Manuscripts takes as its starting point an understanding that a medieval book is a whole object at every point of its long history. As such, medieval books can be studied most profitably in a holistic manner as objects-in-the-world. This means readers might profitably account for all aspects of the manuscript in their observations, from the main texts that dominate the codex to the marginal notes, glosses, names, and interventions made through time. This holistic approach (...) allows us to tell the story of the book's life from the moment of its production to its use, collection, breaking-up, and digitization--all aspects of what can be termed 'dynamic architextuality'. The ten chapters include detailed readings of texts that explain the processes of manuscript manufacture and writing, taking in invisible components of the book that show the joy and delight clearly felt by producers and consumers. Chapters investigate the filling of manuscripts' blank spaces, presenting some texts never examined before, and assessing how books were conceived and understood to function. Manuscripts' heft and solidness can be seen, too, in the depictions of miniature books in medieval illustrations. Early manuscripts thus become archives and witnesses to individual and collective memories, best read as 'relics of existence', as Maurice Merleau-Ponty describes things. As such, it is urgent that practices fragmenting the manuscript through book-breaking or digital display are understood in the context of the book's wholeness. Readers of this study will find chapters on multiple aspects of medieval bookness in the distant past, the present, and in the assurance of the future continuity of this most fascinating of cultural artefacts. (shrink)

“The expression ‘free logic’ is an abbreviation for the phrase ‘free of existence assumptions with respect to its terms, general and singular’.”1 Classical quantification theory is not a free logic in this sense, as its standard formulations commonly assume that every singular term in every model is assigned a referent, an element of the universe of discourse. Indeed, since singular terms include not only singular constants, but also variables2, standard quantification theory may be regarded as involving even the assumption of (...) the existence of the values of its variables, in accordance with Quine’s famous dictum: “to be is to be the value of a variable”. (shrink)

1 There have been several editions of Fridugisus’ letter. I have consulted those in Jaques-Paul Migne, Patrologiae cursus completus … series latina, 221 vols., (Paris: J.-P. Migne, 1844–1864), vol. 105, cols. 751–756; Francesco Corvino, “Il ‘De nihilo et tenebris’ di Fredegiso di Tours,” Rivista critica di storia della filosofia (1956), pp. 273–286; and the most recent and authoritative edition, in Concettina Gennaro, Fridugiso di Tours e il “De substantia nihili et tenebrarum”: Edizione critica e studio introduttivo, (“Pubblicazioni dell’istituto universitario di (...) magistero di Catania,” serie filosofica — saggi e monografie, no. 46; Padua: Casa editrice Dott. Antonio Milani, 1963). Fridugisus’ letter survives in four manuscripts. Nevertheless the text is corrupt in places, and all editors have had to suggest emendations here and there. For my translation I have followed Gennaro’s edition, but not always her interpretation. There is another translation, by Hermigild Dressler, in John F. Wippel and Allan Wolter, eds., Medieval Philosophy from St. Augustine to Nicholas of Cusa, (New York: The Free Press, 1969), pp. 104–108. Note that references to the Psalms in this translation are given according to the numbering in the Revised Standard Edition. (shrink)

The present volume completes the cataloguing of manuscripts. This impressive undertaking will be concluded with one further volume, which will contain addenda and extensive indexes to all the volumes. `a remarkable achievement of scholarship...The descriptions of the manuscripts are full and at the same time admirably concise...Any user of the work, whether his interests are palaeographical, iconographical, or textual, will be deeply grateful for the wealth of information contained in this volume'. Review of English Studies`will be invaluable not only for (...) reference but for the comprehensive and immensely precise assurance that it will give to scholars in every field of medieval studies that nothing relevant to their purposes now lurks in unrecorded concealment'. English Historical Review. (shrink)

The Works and Days is contained in far more manuscripts than the other Hesiodic poems. Altogether there are something over 260, as against seventyodd for the Theogony and sixty-odd for the Shield. Over a hundred of them are later than 1480, the approximate date of the earliest printed edition of the poem; but even when these are subtracted, a formidable number remains, many of which have never been investigated. The present century has seen more done in the way of cataloguing (...) them than the nineteenth, but less in the way of collating them. Since N. A. Livadaras published his list of Hesiod manuscripts in 1963, the disparity between what has been done and what might be done has become more apparent than ever before. (shrink)

Note: The Soka Gakkei (The Value Creating Society) is the largest lay Buddhist Organization in the world. They are one of 200 Buddhists sects in Japan that follow the medieval monk Nichiren’s exclusive focus on the Lotus Sutra . Daisaku Ikeda, scholar and..

Scholarship in Heideggerian philosophy can be broadly differentiated into three groups, which evolved in the European and Anglo-American discourses after WWII, namely, first a transcendental (idealist Kantian) approach; second, an Aristotelian approach; and third, a Christian approach to Heidegger’s analytic of Dasein and his fundamental ontology. All of these basic positions are a result of Heidegger’s philosophy on his way to Being and Time (1927) which he developed both in his broad ranging and fascinating lecture courses in Freiburg, where he (...) taught as Husserl’s assistant between 1917 and 1923, and in Marburg, where he taught between 1923 and 1927 (before he returned to Freiburg in 1928 as Husserl’s successor). Interestingly, the analytic reception of Heidegger focuses on Heidegger’s main work Being and Time, whereas the European and “Continental” discourse is oriented towards larger issues, which include philosophical anthropology, theology, hermeneutics, and the history of philosophy. McGrath’s study belongs to the theologically motivated studies on Heidegger’s phenomenology and ontology and thereby contributes to the recent renewed interest in Heidegger’s early philosophy, which arose after his early lecture courses were published in his Collected Works and after it became clear that Heidegger’s way to Being and Time (and his later thinking) not only was heavily influenced by Scholasticism, especially by Duns Scotus, but also by Augustine, Eckhart, and Luther, all of which took effect before Heidegger encountered Husserl’s phenomenology, Neo-Kantianism or Aristotle’s philosophy. The greatness of Being and Time is indeed a result of the ingenious transformation of all these sources into something new. (shrink)

Listed buildings, even if they are not top landmarks, are increasingly attracting visitors. People express interest in hidden gems in their neighborhood or along their travel itinerary, and in the history of the building they live in. All required data has been meticulously collected by the offices for historical monuments but is not flexibly accessible. In Bremen, the database of buildings (with location, map of the estate, construction history, architect, photos) is searchable and browsable online3, but that only helps users (...) who know how to use a rigidly structured database search form. Our beginning BauDenkMalNetz effort (“listed building web”) aims at a wider purpose: modeling the semantic structure of these data, starting in Bremen but open for other data, and exposing them via a semantic web interface with enhanced querying and presentation capabilities. Requirements beyond interactive browsing comprise auto-generation of customized printed guides (e. g. “Bauhaus villas in my neighborhood”), on-demand presentation on mobile devices (e. g. “medieval churches along my travel itinerary”), and serving linked data for usage by other services. (shrink)

There is a famous and important dictum reminiscent of the medieval age posited by Carl Jung in Alchemical Studies, the thirteenth volume of his collected works: in sterquiliniis invenitur—in filth it shall be found (35). Translated for modern society this might be better understood as “that which is most valuable will be found in the place you least want to look.” If there is one source in the corpus of popular culture that best typifies “the last place we would (...) want to look” for masculine values, it would be Mads Mikkelsen’s portrayal of Hannibal Lector, particularly Lector’s relationship with FBI profiler Will Graham during the first two seasons of the HBO series Hannibal. By stripping away the perverse horror of Lector’s actions toward Graham, and treating their relationship as an absolute value, I systematically explore the series’ portrayal of masculine nurturing in a way that reveals potentially praiseworthy facets relevant to modern masculinity. (shrink)

The manuscript tradition of the Theogony is not as good as that of the Erga, a poem which has always been more popular. The earliest complete manuscripts of the Theogony date only from the end of the thirteenth century, while those upon which the recensio must chiefly be based are of the fourteenth and fifteenth. The number of extant manuscripts, however, especially of the fifteenth century, is not inconsiderable, and knowledge of them has hitherto been far from complete. What is (...) known is known largely in consequence of the labours of Alois Rzach. Rzach collated many of the manuscripts, and tried, with some success, to establish the relationships between them. He published his conclusions in Wiener Studien xix, 15–70, and used them as the basis for his great edition of 1902. (shrink)

In the present chapter, the design of select margins of late medieval Old Norse manuscripts containing the Icelandic ‘Jónsbók’, ‘Kristinréttr Árna biskups’ and Norwegian ‘Landslǫg’ law codes is addressed. In particular, it discusses the size and fillings of margins in these codices and the relation to their modes of use by original clients and later owners. Although it is well-known that Scandinavian law manuscripts contain a large number of notes written by both original and later users, the particular use (...) of marginal spaces by original scribes and illuminators for glosses and other annotations and illuminations has scarcely been investigated to date. In my contribution, two distinctive features will be addressed: (1.) The different use of margins by Norwegian and Icelandic readers of the manuscripts, and (2.) the use of margins by illuminators surrounding the column(s) and incorporated initials. (shrink)

The “dragon” that graces the cover of this volume has a story that goes with it. In the summer of 1980, I was on the teaching staff of the Summer Institute on Medieval Philosophy held at Cornell University under the direction of Norman Kretzmann and the auspices of the Council for Philosophical Studies and the National Endowment for the Humanities. While I was giving a series of lectures there (lectures that contribute to this volume, as it turns out), I (...) went to my office one morning, and there under the door some anonymous wag from the Institute had slid the pen and ink drawing you see in the picture. It represents “Supposition” as a dragon, making a rude face at the viewer. The tail of the dragon is divided — not entirely accurately, as it turns out — into the various branches and subbranches of supposition. If the details are not altogether correct, the spirit is certainly understandable. (shrink)

Aristotle’s dialogue Protrepticus is not only his earliest work of ethics but also the root of all his subsequent investigations into ethics. Here we explore the various ways Aristotle retained in memory the contents of the Protrepticus and redeployed them in the Eudemian Ethics, including the common books. Since Aristotle himself does not explicitly acknowledge the foundational significance of the Protrepticus to his later works, our exploration must proceed on the basis of our knowledge of the earlier work, which can (...) then related to comparable passages in the treatises. But the Protrepticus is a lost work, unlike the EE and the EN, in the sense that no medieval manuscripts of it have survived. And so it first needs to be reconstructed on the basis of the streams of reception that deposited information in surviving works by later ancient authors. We begin in part 1 by reviewing the surviving evidence of the Protrepticus before presenting our wider reconstruction and conception of the work as a dialogue in part 2. In part 3, we discuss ideas and arguments in the reconstructed dialogue that are retained and redeployed in the Eudemian Ethics, focussing on the account of intellectual virtues in EE v and the introduction and methodological framework in EE i-ii.1. (shrink)

I am preparing an English translation of both the Tractatus longior and the Tractatus brevior of Walter Burley’s De puritate artis logicae for the “Yale Library of Medieval Philosophy.” My translation is based of course on the 1955 critical edition by Philotheus Boehner, the only reasonably reliable text available. Nevertheless, in preparing my translation, I have had several occasions to question or correct readings in Boehner’s edition. In some instances the corrections are merely obvious typographical errors, but in others (...) there was something more substantive at stake. The text of the Tractatus brevior is particularly problematic in places, since there are fewer extant manuscripts on which to base an edition. (shrink)

It has long been recognised that great art, whether visual art, literature or music, has a special capacity to “live on” – to endure – long after the moment of its creation. Thus, our world of art today includes, for example, ancient Mesopotamian sculpture, Shakespeare’s plays, and the music of medieval times. How does this capacity to endure operate? Or to ask that question another way: what does “endure” mean in the case of art? The Renaissance concluded that art (...) endures because it is timeless – impervious to change, “eternal”, “immortal” – and this solution, which was ratified without question by Enlightenment philosophers of art such as Hume and Kant, still lingers on in some quarters today. But developments since the nineteenth century have gravely weakened the credibility of the proposition that art is immortal, and the idea is now effectively dead. This leaves us with a major dilemma: if art is not impervious to change, how exactly does it endure? If the time-honoured solution of immortality is no longer viable, what alternative explanation can we find to replace it? -/- This paper explains why immortality is dead, describes our contemporary dilemma, and briefly canvasses a possible solution. (shrink)

Robert Gordon (Ph.D., Columbia) works primarily in philosophy of mind and cognitive science. For his Master's degree he specialized in Medieval and Renaissance philosophy, with a thesis on Nicholas of Cusa. His doctoral dissertation was in ethics and metaethics, on universalizability and analogy in moral arguments.

The four volumes of Neil Ker's Medieval Manuscripts in British Libraries were published by Oxford University Press between 1969 and 1992. They comprise a catalogue of about 3,000 manuscripts in Latin and Western European vernaculars in hitherto uncatalogued or inadequately catalogued institutional collections in the United Kingdom and form a major research tool for humanist scholars. The index volume, produced under the direction of A. G. Watson, a former pupil of Ker's and now his literary executor, and I. C. (...) Cunningham, formerly Keeper of Manuscripts in the National Library of Scotland, provides a variety of indexes, including authors/titles; owners; geographical origins and dates of manuscripts; vernacular manuscripts; Latin and vernacular incipits; manuscripts cited; repertories cited; and iconography. There are also lists of recent accessions to libraries and of manuscripts that have migrated from one institution to another. (shrink)

Comments on Roger Ariew’s “Descartes and Leibniz as Readers of Suarez," presented at Franscico Suarez, S.J.: Last Medieval or First Early Modern?, London, Ontario, University of Western Ontario, September 2008.

"Crooked people deceive themselves in order to deceive others; in this way the world comes to ruin." This quote from a medieval Confucianist expresses the ethical danger of self-deception. My paper examines the psychological proclivity for self-deception and argues that it lies behind much social and interpersonal injustice. I review Hitler's Mein Kampf, as a premiere example of such cognitive duplicity, and Socratic dialectic, as an example of the cognitive hygiene necessary to combat it. I conclude that a robust (...) educational program of Socratic-style critical thinking is crucial to the furtherance of a just society. (shrink)

The lectures presented here are the by-product of my teaching in Yale's Directed Studies program from 1991 through 1993 (hence the title, for want of a better). In fact, being what they are, lecture notes for an introductory philosophy course, they present rather elementary material. Yet, I flatter myself, they do not lack certain originality in the treatment of some of the basic questions of traditional metaphysics and epistemology. In any case, over the past couple of years they proved to (...) be quite useful in teaching my several other courses, especially in medieval philosophy. Thus, being too elementary for transforming them into scholarly papers, on the one hand, yet, containing what I think to be both philosophically interesting and pedagogically useful ideas, on the other, I decided to publish them here, in the Net's formally less stringent medium. Here they can easily be accessed by people who think what they need is a clear and simple discussion of the intriguing philosophical points themselves, rather than the meticulous and sometimes cumbersome scholarly discussions of the texts that raised them (a description which fits, at least, the majority of my students). Given these considerations (as well as the author's lack of time), the lectures are presented here basically unedited, in the form as they were actually delivered, without any notes or references (disregarding the occasionally inserted page numbers, serving as reminders for myself, referring to the texts we used in class). However, anyone who is interested in the more detailed scholarly discussion of some of the topics touched upon here may wish to check some of the papers listed on my.. (shrink)

This essay explores the discoved place in human noosphere called as "Cosmos-not-Here," encompassing the speculative realms of science fiction, religious eschatology, and theoretical astrophysics. The content of "Cosmos-not-Here" contrasts with the same of "Cosmos-Here," representing humanity's tangible explorations and mastery of the physical universe. The text delves into how the Cosmos-not-Here operates as a mental construct, offering humanity an imaginative escape into utopian visions and hypertextual narratives, while disregarding the constraints of established physical laws. -/- The discussion emphasizes humanity's innate (...) psychological drive, metaphorically expressed as "forward and upward," linking it to a sacred yearning for cosmic harmony and expansion. This drive manifests culturally in phenomena like Russian aspirations, illustrated by the "Gagarin Smile," and the global fascination with cosmic-themed speculative fiction, games, and spiritual constructs such as astrology. -/- The essay concludes by identifying a universal "Cosmic-We" ethos, characterized by a shared attraction to the cosmos as a concept of transcendence and infinite potential, reflecting humanity's enduring pursuit of meaning beyond the utilitarian confines of terrestrial existence. The analysis reveals the philosophical resonance of this semantic cluster with ancient and medieval cosmologies, suggesting its timeless significance in human thought. (shrink)

Abstract This paper explores Reiner Schürmann’s account of perigrinal ontology from the perspective of Meister Eckhart. What is so extraordinary about his work is its retrieval of nuances in Plato’s philosophy of mind. Professor Schürmann’s approach to Philosophy focused on a philosopher’s philosophy of mind. For example, his course titles, such as Augustine’s Philosophy, were listed and taught in Augustine’s Philosophy of Mind. The advantage of his approach can best be seen in his study of the Medieval Philosopher Meister (...) Eckhart. In this work, Professor Schürmann totalizes the relationship between the will and the intellect and unites the different categories of Platonic philosophy under the concept of perigrinal ontology. Instead of treating epistemology or aesthetics in isolation, they are examined as they relate to ontology. In Plato’s epistemology, the highest form of knowing is different; at its highest point, knowledge is a seeing. Meister Eckhart and the other Neoplatonic philosophers continued the argument that Plato initiated. This is not an instance of Gnosticism in that the successors of Plato in the Christian tradition are not introducing new material but are extending Plato’s philosophy. At the center of the controversies about Meister Eckhart’s alleged departure from Christian doctrine is the oneness with God. Here, Professor Schürmann acts like a good editor. He painstakingly draws out pertinent distinctions to demonstrate Meister Eckhart’s adherence to tradition. It is interesting in this light to consider what Saint Thomas Aquinas has said on some of these same issues. One can see, too, that Meister Eckhart is a good deal closer to Saint Thomas than is generally thought. Saint Thomas's writings are full of references to Neoplatonic philosophers, but he also actively engages with their ideas. Though exploring this is beyond this paper's scope, Saint Thomas’s commentary of the Christian Neoplatonist Pseudo Dionysius primarily supports this point. We also need to recall that the period in which all this unfolded was a period in history marked by the democratization of religion. More importantly, Meister Eckhart’s time was informed by the democratization of theology. Meister Eckhart’s writings and personal commitment to that project are noteworthy in this context. His decision to teach women in religious orders advanced theology, a historical breakthrough. There are some notable debates that Professor Schürmann addressed in this work. Perhaps chief among these is the overly close connection between the writings of Meister Eckhart and that of the late Heidegger. It had been suggested that Martin Heidegger’s interest in Zen Buddhism was thought to include that of Meister Eckhart. Waiting upon Being and detachment or releasement were similar in these three schools of thought. Professor Schürmann viewed this as a form of syncretism, the mashing up of ideas that seem similar but have important distinctions. For Professor Schürmann, the absolute absence of the faculty of the will in Meister Eckhart’s work distinguished him from these other philosophies. It is striking that Professor Schürmann repeatedly cites texts where Meister Eckhart sees the highest form of knowledge as purely a feature of the intellect. He even goes so far as to note that the will is almost absent from Meister Eckhart’s philosophy of mind. -/- . (shrink)

Después de la Reconquista, se tuvieron que traducir al latín muchos textos árabes en la España del siglo XII. La mayoría de los copistas necesitaban colaboradores para concluir el proceso, sin embargo, Johannes Hispalensis (Juan de Sevilla) conocía tanto la lengua árabe como el latín, por lo que podía trabajar solo. La duplicación de textos latinos se popularizó y divulgó rápidamente. Durante los siglos siguientes, los copistas medievales hicieron múltiples copias, y durante el proceso de reproducción cometieron muchos errores que (...) contribuyeron a la confusión entre la versión correcta del nombre del traductor y su identidad. Por consiguiente, Hispalensis apareció en copias posteriores de su trabajo con varios títulos añadidos, tales como ¿maestro¿ u ¿obispo¿, o unido a un colaborador. Los historiadores modernos aumentaron las complejidades creando un solo personaje de dos traductores distintos. En ocasiones, la propiedad de algunos de los manuscritos estaba basada únicamente en los nombres que aparecían en sus folios. Se hace aquí una tentativa de aclarar cuales son las traducciones de Johannes Hispalensis, trabajando solo, y aquéllas en que colaboró con otros. (shrink)

Empiricists are in general rather suspicious with respect to any kind of abstract entities like properties, classes, relations, numbers, propositions, etc. They usually feel much more in sympathy with nominalists than with realists (in the medieval sense). As far as possible they try to avoid any reference to abstract entities and to restrict themselves to what is sometimes called a nominalistic language, i.e., one not containing such references. However, within certain scientific contexts it seems hardly possible to avoid them. (...) In the case of mathematics some empiricists try to find a way out by treating the whole of mathematics as a mere calculus, a formal system for which no interpretation is given, or can be given. Accordingly, the mathematician is said to speak not about numbers, functions and infinite classes but merely about meaningless symbols and formulas manipulated according to given formal rules. In physics it is more difficult to shun the suspected entities because the language of physics serves for the communication of reports and predictions and hence cannot be taken as a mere calculus. A physicist who is suspicious of abstract entities may perhaps try to declare a certain part of the language of physics as uninterpreted and uninterpretable, that part which refers to real numbers as space-time coordinates or as values of physical magnitudes, to functions, limits, etc. More probably he will just speak about all these things like anybody else but with an uneasy conscience, like a man who in his everyday life does with qualms many things which are not in accord with the high moral principles he professes on Sundays. Recently the problem of abstract entities has arisen again in connection with semantics, the theory of meaning and truth. Some semanticists say that certain expressions designate certain entities, and among these designated entities they include not only concrete material things but also abstract entities e.g., properties as designated by predicates and propositions as designated.... (shrink)

Diagrams in medieval manuscripts of Greek mathematical and astronomical works can seem peculiar for a modern reader, given their persistent and widespread tendency to represent more geometric regularity than the argument requires and their usual visual inaccuracy in depicting the mathematical objects discussed in the text. Although most scholars believe that these tendencies go back to the original Greek authors, in a recent paper I argued that these odd features should not be attributed to Greek authors, but to transmission. (...) My main argument there is based on experiments made with university students who played the role of copyists. In this paper, I show that the vestiges of the changes caused by transmission are present in the very diagrams of the extant manuscripts. I analyze four diagrams taken from Aristarchus's On Sizes. (shrink)