Under the assumption that there exists an elementary embedding (henceforth abbreviated as and in particular under we prove a Coding Lemma for and find certain versions of it which are equivalent to strong regularity of cardinals below . We also prove that a stronger version of the Coding Lemma holds for a stationary set of ordinals below.

Sectio 1. Indices,--Sectio 2. Concordantia prima.

In Hsch. K 2238-2239 the paradosis of both the transmitted lemmata (καραισταί and καραιστής) is surely corrupt and has been corrected by Musurus respectively in κεραϊσταί (2238) and κεραϊστής (2239). However, Musurus’ corrections do not offer a good text since the lemmata do not agree with the following glosses. The aim of this article is to reconsider the correction κεράστης already suggested by Schmidt for K 2239, neglected by both the recent editions of Hesychius. On this basis, I (...) similarly propose to correct the preceding lemma 2238 in κεράσται. (shrink)

We prove the iteration lemmata, which are the key lemmata to show that extensions by Pmax variations satisfy absoluteness for Π2-statements in the structure 〈H , ∈, NSω 1, R 〉 for some set R of reals in L , for the following statements: The cofinality of the null ideal is ℵ1. There exists a good basis of the strong measure zero ideal.

A Papyrus commentary on Alcman published in 19571 brings us news of a poem in which Alcman “physiologized”. The lemmata and commentary together witness to a semi-philosophical cosmogony unlike any other hitherto known from Greece. The evidence is meagre, but it seems worth while to see what can be made of it; for it is perhaps possible to go a little farther than has so far been done.

Alexander of Aphrodisias's commentary (about AD 200) is the earliest extant commentary on Aristotle's Metaphysics, and it is the most valuable indirect witness to the Metaphysics text and its transmission. Mirjam Kotwick's study is a systematic investigation into the version of the Metaphysics that Alexander used when writing his commentary, and into the various ways his text, his commentary, and the texts transmitted through our manuscripts relate to one another. Through a careful analysis of lemmata, quotations, and Alexander's discussion (...) of Aristotle's argument Kotwick shows how to uncover and partly reconstruct a Metaphysics version from the second century AD. Kotwick then uses this version for improving the text that came down to us by the direct manuscript tradition and for finding solutions to some of the puzzles in this tradition. Through a side-by-side examination of Alexander's text, his interpretation of Aristotle's thought, and the directly transmitted versions of the Metaphysics, Kotwick reveals how Alexander's commentary may have influenced the text of our manuscripts at different stages of the transmission process. This study is the first book-length examination of a commentary as a witness to an ancient philosophical text. This blend of textual criticism and philosophical analysis both expands on existing methodologies in classical scholarship and develops new ones. (shrink)

It is well known that a degree-of-belief function P is coherent if and only if it satisfies the probability calculus. In this paper, we show that the notion of coherence can be extended to higher order probabilities such as P(P(h)=p)=q, and that a higher order degree-of-belief function P is coherent if and only if it satisfies the probability calculus plus the following axiom: P(h)=p iff P(P(h)=p)=1. Also, a number of lemmata which extend an incomplete probability function to a complete (...) one are established. (shrink)

Herbrand's Theorem, in the form of $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\exists } $$ -inversion lemmata for finitary and infinitary sequent calculi, is the crucial tool for the determination of the provably total function(al)s of a variety of theories. The theories are (second order extensions of) fragments of classical arithmetic; the classes of provably total functions include the elements of the Polynomial Hierarchy, the Grzegorczyk Hierarchy, and the extended Grzegorczyk Hierarchy $\mathfrak{E}^\alpha $ , α < ε0. A subsidiary aim of the paper is to (...) show that the proof theoretic methods used here are distinguished by technical elegance, conceptual clarity, and wide-ranging applicability. (shrink)

Part I examines various readings about which there persists editorial or other disagreement, Part II argues that six couplets are not from Ovid's hand. The lemmata give the reading of the Oxford Classical Text, followed by the rejected variants and any conjectures. ‘Goold’ = G. P. Goold, ‘Amatoria Critica’, HSCP 69, 1–107. ‘Geisler’ = H. J. Geisler, P. Ovidius Naso Rentedia Amoris mit Kommentar zu Vers 1–396. Normally only the principal manuscripts are cited individually.

Accompanied by a new translation of Aristotle's Nicomachean Ethics X, this volume presents a hybrid between a traditional commentary and a scholarly monograph. Aristotle's text is divided into one hundred lemmata which not only explore comprehensively the content and strength of each of these units of thought, but also emphasise their continuity, showing how the smaller units feed into the larger structure. The Commentary illuminates what Aristotle thinks in each lemma (and why), and also shows how he thinks. In (...) order to bring Aristotle alive as a thinker, it often explores several possible ways of reading the text to enable readers to make up their own mind about the best interpretation of a given passage. The relevant background in Plato's dialogues is discussed, and a substantial Introduction sets out the philosophical framework necessary for understanding Book X, the final and most arresting section of the Ethics. (shrink)

Das Handbuch bildet erstmals den empirischen und theoretischen Problembestand der deutschsprachigen Europasoziologie in seinem ganzen Facettenreichtum ab, benennt und diskutiert kontroverse und offene Probleme. Angelegt als Beitrage zum europasoziologischen state of the art werden die Lemmata zu den einschlagigen Sachproblemen dabei unter den Hauptstrangen "Institutionenbildung und Institutionenpolitik", "Territoriale Restrukturierung", "Sozialstruktur und Sozialpolitik", "Transnationale Verflechtungen" und "Gesellschaftstheoretische Perspektiven" versammelt. Das Handbuch stellt die jeweils zentralen Theorieansatze und Konzepte, die relevanten empirischen Befunde sowie die wichtigsten feldspezifischen Kontroversen konzise dar und diskutiert (...) mit Umsicht das Innovationspotenzial und die kunftigen Herausforderungen. Insbesondere aufgrund des Nachschlagecharakters bietet es damit auch fur Interessierte auaerhalb der Soziologie und fur wissenschaftliche Laien einen kompetenten und aktuellen Uberblick zugleich uber den Wissensfundus und den Diskussionsstand des Faches. (shrink)

In the Introduction to his Old English Glosses, published in 1900, the late Professor Napier asserted that Aldhelm glosses are to be found in the Corpus Glossary. He did not attempt any elaborate argument, but contented himself with giving a list of sixty-four instances in which the lemmata of the Corpus Glossary coincide entirely with words occurring in the text of the De Virginitate. Of these lemmata, twenty-three occur also in the Epinal and Erfurt Glossaries, and must therefore (...) have existed in the common archetype of the three collections. Napier's conclusion was that the compiler of the archetype had before him one Aldhelm glossary, and that the author of the Corpus Glossary, who rearranged the material of the archetype and made extensive additions, had among his sources another and an independent glossary. (shrink)

The volume contains, in addition to the final part of the Commentary, a critical text of the Parmenides through the first hypothesis, as it appears in the lemmata of the Latin Proclus, a new fragment of Speusippus, a new one-page summary of the Stoic-Peripatetic controversy over counterfactuals, and the marginalia of Cusanus on this final section of the Proclus in his Latin manuscript. There are, thus, primary sources in Hellenic, Hellenistic, Medieval and Renaissance philosophy appearing for the first time (...) in this modern volume. The continuity of the Platonic tradition could hardly be more dramatically emphasized. (shrink)

I myself became interested in textual work when I began checking the logical rigor of Plato’s Parmenides hypotheses. To my great surprise, the proof patterns were not simply valid, but as woodenly uniform and rigorous as Euclid’s Elements. Such rigor was exactly what a Neo-Platonist like Proclus would have expected, admired, and possibly imposed; it is not paralleled anywhere else in Plato. At that time, it was believed that the three primary manuscripts containing this dialogue—Oxford B, Venice T, and Vienna (...) W—came from a common archetype of a date as late as the fifth century, and that the only other records of the text of any extent—the lemmata in Proclus’ Commentary and the quoted passages in Damascius’ Problems—were, or at least could be, equally late. Only some evidence that the text as the ninth century manuscripts have it had been in this rigid form before the fifth century could finally settle the question of whether it was Plato’s own or that plus stringent re-styling. I thought that if there were traces of independent descent from some earlier archetype or archetypes, a dragnet technique applied to a collection of all the reported variant readings ought to catch them. (shrink)

This work is in two parts. The main aim of part 1 is a systematic examination of deductive, probabilistic, inductive and purely inductive dependence relations within the framework of Kolmogorov probability semantics. The main aim of part 2 is a systematic comparison of (in all) 20 different relations of probabilistic (in)dependence within the framework of Popper probability semantics (for Kolmogorov probability semantics does not allow such a comparison). Added to this comparison is an examination of (in all) 15 purely inductive (...) dependence relations. ————Part 1 leads in an axiomatic step-by-step development from the elementary classical truth value semantics of a sentential-logical language, called ‘L’, (chapter 1) to the elementary Kolmogorov probability semantics of L (chapter 2), which is then extended to four axiomatic semantical theories of dependence relations between the formulae of L. First the elementary Kolmogorov probability semantics of L is extended to a theory, called ‘Kdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 3). Then Kdd is extended to a theory, called ‘Kpd1’, of the degree to which formulae of L probabilistically depend on each other in regard to a given probability distribution on the set of all formulae of L (chapter 4). Kpd1, in its turn, gets extended to a theory, called ‘Kpd2’, of the relations of probabilistic dependence and independence, relativized to unary Kolmogorov probability functions defined on L (chapter 5). Then Kpd2 is extended to a theory, called ‘Kid’, of the relations of inductive dependence and inductive independence, again relativized to unary Kolmogorov probability functions defined on L (chapter 6). Finally, Kid is extended to a theory, called ‘Kpid’, of the relations of purely inductive positive and negative dependence, relativized to unary Kolmogorov probability functions defined on L (chapter 7). ——Chapter 1, which deals with the familiar notions of truth value functions, tautologies, consequence relations and relations of logical opposition, is naturally the shortest chapter of part 1.——In chapter 2, the elementary classical semantics of L is extended to the elementary Kolmogorov probability semantics of L, i.e. to an axiomatic theory of unary and of binary Kolmogorov probability functions defined on the set of formulae of L. Because of the elementary character of this theory, chapter 2 is also rather short.——Chapter 3 introduces the first theory on dependence relations, to wit: Kdd, the theory of deductive (in)dependence between formulae of L. I follow here the well-known idea of Popper and Miller, who have used it in a famous discussion on the nature of probabilistic support for their arguments that probabilistic support is deductive, not inductive. I develop Kdd in the form of about 100 theorems, making ample use of the fact that deductive independence is nothing but subcontrary opposition, and close with a remark on the fundamental difference between deductive and logical dependence—two relations the ideas of which are all too easily mixed up.——Chapters 4 and 5 deal extensively with the traditional ideas of probabilistic (in)dependence, applied to formulae rather than to events. As always, I proceed axiomatically in a step-by-step process under systematic viewpoints and obtain about 300 theorems in this way. In the formulation of the theorems, I took special care to state clearly and expressly so-called tacit assumptions, especially those concerning the probability values of the formulae said to be dependent on each other. These assumptions are usually missing in the literature, due either to economy of writing or to sloppiness of thinking. Presumably, both chapters contain little that is new, their value lying more in the systematic grouping and organic development of the theorems than in the newness of these.——In chapter 6, I extend the axiomatic theory about probabilistic (in)dependence which has been elaborated in chapter 5, to an axiomatic theory of inductive (in)dependence by requiring of the relation of inductive (in)dependence that it be probabilistic (in)dependence, but not also logical implication or logical opposition. I point out the differences between probabilistic and inductive (in)dependence by means of some 60 theorems and close my examination of inductive (in)dependence by considering its relationship to the notion of support in the philosophy of science.——Finally, in chapter 7, the last of part 1, I take the step from inductive dependence to what I call ‘purely inductive dependence’ by combining the idea of inductive dependence with that of deductive independence in a way which is suggested by writings of Popper and Miller. I arrive at two noteworthy theorems. Firstly, there is indeed no purely inductive support. But secondly, and perhaps amazingly, countersupport is purely inductive.————Whereas the probabilistic framework of part 1 of the present work is Kolmogorov probability semantics, the framework of part 2 is Popper probability semantics, which is not only worth examining as a fascinating alternative to orthodox Kolmogorov probability semantics, but also allows us to examine dependence relations more deeply, than Kolmogorov probability semantics does. Part 2 leads—again in an axiomatic step-by-step development—from the basic Popper probability semantics of L, called ‘Pb’, (chapter 8) via a probabilistic theory of logical attributes, called ‘Ps’, (chapter 9) to four axiomatic semantical theories of dependence relations between the formulae of L. First, Ps is extended to a theory, called ‘Pdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 10). Then Pdd is extended to a theory, called ‘Ppd’, of (in all) 20 relations of probabilistic (in)dependence, relativized to binary Popper probability functions defined on L (chapter 11). Ppd, in its turn, is extended to a theory, called ‘Pid’, of (in all) 10 relations of inductive dependence, again relativized to binary Popper probability functions defined on L (first part of chapter 12). Finally, Pid is extended to a theory, called ‘Ppid’, of (in all) 15 relations of purely inductive positive and negative dependence, relativized to binary Popper probability functions defined on L (second part of chapter 12).——Chapter 8, the first chapter of part 2 of the present work, is entirely preparatory. It introduces the axioms and about 180 theorems (150 of them together with their proofs) of basic Popper probability semantics in order to set this kind of semantics under way.——Then, in chapter 9, basic Popper probability semantics is extended to a probabilistic theory of logical properties of and relations between the formulae of L. Although I think that the way I did this extension is of some interest in itself, the main task of chapter 9 is again a preparatory one: to yield the indispensable lemmata (about 90 in number) for the theorems concerning probabilistic dependence relations in chapter 11 and concerning inductive dependence relations in chapter 12.——Chapter 10 brings the extension of Ps to the theory Pdd of deductive (in)dependence. Only half a dozen theorems are noted here for later use in the Pdd-extensions Ppd and Ppid. In view of the over 100 theorems already gained on this topic in the Kolmogorovian framework (cf. chapter 3), a similar extensive elaboration of Pdd would have been superfluous.——Chapter 11 is the most important one of part 2. It consists of a systematic comparison of 20 probabilistic (in)dependence concepts by means of about 230 theorems, obtained within the axiomatic theory Ppd, which is built up as an extension of Pdd. The main points of comparison were: differences in logical strength; reflexivity and symmetry; behaviour under the condition that the probability values of the formulae in question are extreme. It turned out that each of the examined concepts violates a strong and straightforward version of the intuitive requirement that probabilistic dependence should go with logical dependence. Whereas the corresponding chapter 5 in part 1 of the present work may not have led to new theorems, chapter 11 yields dozens of them in the process of comparison of concepts of dependence and independence which had—as far as I know—never before been treated in a single theoretical framework. With Popper probability semantics, this framework has become available, and here I have simply made full use of it.——In chapter 12, I extend the theory Ppd of probabilistic (in)dependence to the theories Pid and Ppid of inductive and purely inductive dependence, in a way very similar to that in which I have extended the theory Kpd2 to the theories Kid and Kpid in chapters 6 and 7. The first main result of Kpid (roughly: there is no purely inductive support) could be repeated for four of the five purely inductive positive dependence relations considered in chapter 12, whereas the second main result of Kpid (roughly: there is purely inductive countersupport ) could be repeated for each of the five examined purely inductive negative dependence relations. Chapter 12 closes with a brief recapitulation and critical discussion of the main results. (shrink)

Von Walchs Philosophischem Lexicon bis Zedlers Universal-Lexicon, von Diderots und D’Alemberts Encyclopédie bis zur Encyclopaedia Britannica: alle bedeutenden frühmodernen Wörterbücher und Enzyklopädien haben sich ziemlich viele Definitionen angeeignet, die der hugenottische Gelehrte Étienne Chauvin (1640 – 1725) in den beiden Ausgaben seines Lexicon philosophicum (1692 und 1713) bereits formuliert hatte. Chauvin verglich als erster die scholastische Tradition mit den Theorien der neuen Denker wie Descartes, Gassendi und deren Anhänger. Sein Werk befasst sich ausführlich mit der Naturphilosophie und beschreibt naturwissenschaftliche Instrumente (...) und Experimente. Erstaunlicherweise sind der komplexe Aufbau, die Quellen und die Nachwirkung von Chauvins Wörterbuch noch nie gründlich untersucht worden. Die vorliegende umfassende Studie über die Geschichte der philosophischen Terminologie und Ideen wirft ein helles Licht auf die „République des lettres“ zwischen dem Ende des 17. und dem Anfang des 18. Jahrhunderts. Sie behandelt Metaphysik, Logik, Ethik und anthropologische Themen sowie den Widerstreit zwischen alten und neuen Ansichten über die Natur. ---STIMMEN ZUM BUCH--- „Das Buch selbst bietet aber einen wichtigen Beitrag zur Aufklärungs- und Philosophie- bzw. Wissenschaftsgeschichte der Frühaufklärung sowie der Bildungsgeschichte Preußens. […] [Das Buch] bietet als solches auch aufschlußreiche Bausteine für das Projekt eines Vokabulars der europäischen Philosophien, dem man sich eben auch durch das Studium einschlägiger Lemmata alter Lexika nähern kann.“ (Till Kinzel, Informationsmittel (IFB), März 2017) From Walch’s Philosophisches Lexicon to Zedler’s Universal-Lexicon, from Diderot’s and D’Alembert’s Encyclopédie to the Encyclopaedia Britannica, all major early modern dictionaries and encyclopedias incorporate some of the definitions given by the Huguenot savant Étienne Chauvin (1640 - 1725) in the two editions of his Lexicon philosophicum (1692 and 1713). For the first time, Chauvin placed the scholastic tradition side by side with the theories of new thinkers like Descartes, Gassendi and their followers. His work covers natural philosophy extensively, describing scientific instruments and experiments. Surprisingly enough, the complex architecture of Chauvin’s dictionary, its sources, and its fortune have never been thoroughly investigated before. The present, broad study in the history of philosophical terminology and ideas casts light on the culture of the “République des lettres” between the end of the seventeenth and the beginning of the eighteenth century. It deals with metaphysics, logic, moral, and anthropological themes, and the clash between ancient and modern visions of nature. (shrink)

Most of the commentaries on Greek authors which circulated in the towns of Egypt during the late Ptolemaic and early Imperial periods ignored the critical and colometrical problems which had engaged the attention of the great Alexandrian grammarians. A few, however, based themselves on texts equipped with signs, included the signs in their lemmata and offered explanations. Such commentaries must be the source of the scattered references to signs in the older marginal scholia in Byzantine manuscripts of Homer, Hesiod, (...) Pindar and the Attic dramatists. The only Byzantine manuscript to transmit a pagan text still equipped with a large number and a variety of signs, namely cod. Venice, Bibl. Marc. gr. 454, is also the only one to transmit scholia with lemmata retaining prefixed signs. Just as texts and scholium-lemmata lost their signs in the course of transmission, so too did references to signs within scholia either disappear or become garbled. At best, a statement about the reasons for affixing a sign would turn into one about the content or style of the verse in question. The few mentions made of the great Alexandrians give no cause for thinking that we ever have a verbatim quotation of an πόμνημα written by one of them in order to explain his own signs. Time and again it is demonstrable that an explanation of a sign's presence against a particular verse goes back to some writer like Aristonicus. What survives of the ancient discussion of Latin literature is exiguous in comparison with the Greek material. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:American Journal of Philology 127.4 (2006) 607-611MuseSearchJournalsThis JournalContents[Access article in PDF]Reviewed byPaul Allen Miller University of South Carolina e-mail: [email protected] Habinek. The World of Roman Song: From Ritualized Speech to Social Order. Baltimore: Johns Hopkins University Press, 2005. x + 329 pp. Cloth, $52.It has become increasingly evident that the texts we study from ancient Rome are embedded objects, implicated in a rich field of symbolic systems and corporeal (...) practices. The image of the poem as an isolated aesthetic object has become untenable as the field has become dominated by concepts of intertextuality, performativity, social construction, and self-fashioning. The text in books like Tony Corbeill's Controlling Laughter (Princeton 1996) is less an object than an action. Thomas Habinek's The World of Roman Song represents an attempt to make good on the promise of these developments by rethinking the entirety of Roman literature as an embedded social process of "song," of marked speech, that stands at the origins of the Roman social order. Ritual hymns, funereal laudations, convivial play, and comedic performances become so many moments in the constitution of what it means to be Roman, even as conflicts between center and periphery, masculine and feminine, vir and cinaedus are both played out and resisted in the various genres that constitute the world of ritualized speech and its formal derivatives.Any such sweeping endeavor brings with it both a necessary boldness—asking us to rethink the history of Roman culture from a new perspective—and the danger of reductiveness. For the most part, these are dangers that Habinek manages skillfully to skirt through a combination of fine-grained philological analysis and a sophisticated, but never overbearing, theoretical apparatus. The World of Roman Song features close readings of the usage of words such as cano, carmen, dico, ludus, convivia, and sodalis, from their earliest attestations through their appearance in later imperial literature. It also deploys an intellectual armature that draws upon contemporary anthropology, Frankfurt-school Marxism, object-relations psychoanalysis, and the theories of Bourdieu, Bakhtin, and Bataille. Yet, as we shall see, the very methodology that makes this sweeping [End Page 607] and important survey possible—the examination not of texts but of lemmata to trace the memes of Roman self-constitution through formalized language—leads to certain unavoidable distortions. Complex textual systems become reduced to exemplary moments of embeddedness. This reduction is an enabling gesture that like any mode of analysis, however, ultimately produces its own limit.For this reader, the heart of the book is to be found in chapter 4, "Song and Play." Here Habinek traces the relation between three primary sets of terms: dico, dictum, and implicitly dictator, meaning to make an authoritative statement; cano, canto, and carmen, meaning to perform a song (carmen) of one's own (cano), or to repeat that of another (canto), so as to establish a relation between the singer and the constituted social, and ultimately cosmic, whole, via ritualized speech; and ludo, ludus, and lusus, referring to scripted or formalized movements of the body. Thus a poetic ludus, such as that described in Catullus 50 between the poet and Licinius Calvus, would refer not so much to the acts of song (carmina) to which the game of composition gave rise as to the formalized interchange and embodied practice of writing capping verses in different meters in a convivial setting. The previous chapter, "Song and Speech," had established the difference between loquor and dico, with the former referring to unmarked speech and the latter to the making of statements that the speaker asserts as authoritative and hence true. It is thus possible for the terms cano and dico to overlap and those of ludo and cano as well. Nevertheless, the ultimate dream of aristocratic Roman manhood (and, as any number of feminists would point out, of patriarchy as a whole) is for carmen—the ritualized speech that constitutes the community as a living unity—to assume the status of dictum, authoritative speech freed from the... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Commentary on Augustine City of God, Books 1–5 by Gillian ClarkJames J. O'DonnellCommentary on Augustine City of God, Books 1–5. By Gillian Clark. Oxford: Oxford University Press, 2021. Pp. xii + 281. ISBN: 978-0-19-887007-4.Pierre Bayard's masterful How to Talk about Books You Haven't Read offers soothing balm for readers in the daunting presence of Augustine's City of God. Weighing in at a third of a million words, Augustine's (...) magnum opus et arduum,1 offers a Moby-Dick and a half of verbiage spread out over twenty-two books. I make the claim, nervously and looking about for intelligent contradiction, that it is the longest work of sustained and coherent argument to survive from Greco-Roman antiquity. Other behemoths are compilations in the main of one kind or another, but this one has a structure and a linear direction and was tightly enough written that a theme opened in the second book with a promise of returning with later treatment is in fact picked up in the nineteenth book written perhaps a dozen years later.Those who really will read, or at least read in, Civ. benefit from all the help they can get. There are good translations (English alone in my lifetime by McCracken et al. in Loeb, Bettenson, Dyson, and Babcock) but none provides more than a minimalist annotation. Francophone readers have been better served since 1960 by the five volume edition with more ample annotation in the Bibliothèque Augustinienne of G. Bardy et al., and it is the standard point of entrance to serious study for scholars. That work has many strengths but the limitations of arising from a devout tradition of scholarship and of coming before the efflorescence in late antique and Augustinian studies through which we have lived.More help is now at hand in the form of the volume under review and its promise of more to come. Gillian Clark is known and admired among Augustinian scholars for many works, not least the earlier exercise in commentary of her Cambridge "green and yellow"2 edition of Confessions 1–4 (1995). The present work began as an ambitious multi-author collaborative project that proved unwieldy (see the present volume, pp. 31–32) and results in this first installment of [End Page 179] a series now in Clark's hands exclusively, drawing on her strengths as a classical historian specializing in late antiquity and patristics. Four additional volumes are anticipated, ideally on two-year intervals. The task requires multiple competences: at least, the history of the fourth and fifth centuries, the history and presence of ancient philosophy, the history of Christian reception and interpretation of scripture, and the reception of classical literature in late antiquity. It is a work that soars with no middle flight.As commentary on a behemoth, the commentary begins with the virtue of concision. At a rough calculation, commentary here runs at about half again the length of the text under review, producing volumes that can be usefully read alongside Augustine without swamping either Augustine or the reader in an ocean of erudition and detail. After an introduction that is as much to the whole work as to books 1–5, the book is organized strictly by lemmata to passages commented. The lemmata are all in Latin to facilitate use by readers of various editions and translations, with references given by book/chapter and page/line to the standard CCSL 1955 reprinting of the edition of Dombart-Kalb (itself originally a Teubner of 1928).3The focus of the annotation is on the work as historical artifact, well situated in both the moment and controversies of writing and in the apparatus of learning that Augustine brought to his work. Inevitably this includes welcome discussion of argument, rhetoric, and strategy (the very short discussion of how Augustine wrote on pp. 9–12 is remarkably insightful), but readers will welcome the lucid guidance offered to how the text made sense in Aug.'s own time, to what he was evidently reading as he wrote, and to the range of historical realia that make up his argument. Commentary on later... (shrink)

This translation and commentary is based on the Critical Text and Indices of Proclus: Commentary on the First Alcibiades of Plato, Amsterdam 1954, by L. G. Westerink. Index II has been of great help in the translation, and the commentary is much indebted to the critical apparatus. Dr. Westerink has also been kind enough to forward his views on the relatively few problems which the Greek text has presented. A further debt is owed to the review of Dr. Westerink's text (...) by Prof. E. R. Dodds in GNOMON 1955 p. 164-1, chiefly for some references and some emendations to the Greek text. W. R. M. Lamb's Loeb translation of Alcibiades I has helped considerably in construing the lemmata, which Signor Antonio Carlini has found to have been inserted by a later hand from a Plato MSS. of the W family. Evidence for this is their discrepancy with the text as read in the main body of the commentary (d. Studi Classici e Orientali, vol. x, Pisa 1961). On the personal side, the whole work has received the benefit of constant advice from Prof. A. H. Armstrong. It was he who first suggested the undertaking, and he has been kind enough to read through the translation and commentary, making many corrections and helpful suggestions. In particular lowe him the parallels with Plotinus and thanks for a Socratic patience in my more obtuse moments. (shrink)

Preferential structures are probably the best examined semantics for nonmonotonic and deontic logics; in a wider sense, they also provide semantical approaches to theory revision and update, and other fields where a preference relation between models is a natural approach. They have been widely used to differentiate the various systems of such logics, and their construction is one of the main subjects in the formal investigation of these logics. We introduce new techniques to construct preferential structures for completeness proofs. Since (...) our main interest is to provide general techniques, which can be applied in various situations and for various base logics (propositional and other), we take a purely algebraic approach, which can be translated into logics by easy lemmata. In particular, we give a clean construction via indexing by trees for transitive structures, this allows us to simplify the proofs of earlier work by the author, and to extend the results given there. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:A Historical Commentary on Arrian’s History of Alexander. Vol. II. Commentary on Books IV–VPhilip A. StadterBosworth, A. B. A Historical Commentary on Arrian’s History of Alexander. Vol. II. Commentary on Books IV–V. Oxford: Clarendon Press, 1995.In books 1–3, Arrian’s Alexander rushed from the Hellespont to Babylon, Susa, and Persepolis. In books IV and V the story changes: Alexander finds himself on the frontier, and beyond. No longer is (...) he confronting the enormous armies of the Persian king in set battles, but pushing beyond the frontiers of empire, seizing impregnable heights, and most important, struggling with his own Macedonians while defining himself.Bosworth, continuing his commentary after a fifteen-year interval, brings an exceptional background of historical, source critical, and literary studies. B. notes that his evaluation is “perhaps more sympathetic” than in his first volume, in part because the quality of the work “improves as it progresses” (v). The thoroughness [End Page 140] of the discussion (360 pages on the two books) is justified by the importance and complexity of the material. The reader is well served by an excellent subject index, a Greek index, ten maps, and four figures. An appendix on Nearchus suggests that that author may have reported much more than the journey from the Indus to the Persian Gulf found in the Indike, and may be a significant source for Arrian in the last four books of the Alexander history. Like the first volume, the commentary has Greek lemmata, translated only when there is a specific difficulty, but even Greekless readers can use it with the help of Brunt’s new Loeb text.Although the commentary deals frequently with textual questions, it focuses on elucidating the historical, geographical, stylistic, and interpretative problems of the text. B. ably notes the constant verbal reminiscences of Herodotus, Thucydides, and Xenophon, especially in the more elaborate passages, e.g., the speeches at the Hyphasis. Still more are undoubtedly to be found, such as the echo of Thucydides (1.110.1, 3.112.8, 87.87.6) in 5.27.6, ¹l¼goi ¨k poll©n. His elucidation of Arrian’s use of Megasthenes, Nearchus, and Eratosthenes in the digressions at the beginning of book 5 is a model of clarity and precision. Here as elsewhere he stresses Arrian’s purposeful blending of his sources: e.g., on 5.6.3–8: “It is an elaborately contrived passage, and the source material is carefully selected to fit the scheme of the argument. Arrian is not merely rewriting a passage of Eratosthenes.” Throughout, his comments on sources are precise and thoughtful.B.’s notes follow wherever the text leads, but he devotes special attention to the major focuses of Arrian’s attention: the great digression on Alexander’s orientalism, the murder of Cleitus, proskunesis, and the page’s conspiracy (4.7.4–14.4 5 45–101), the march to the Indus, with the siege of Massaga and the capture of Aornus (4.22.3–30.9 5 141–96), the series of digressions which begin book 5, (5.1.1–8.1 5 197–259), the battle on the Hydaspes against Porus (5.8.4–19.4 5 262–311), and the mutiny on the Hyphasis (5.24.8–29.5 5 337–60).Bosworth’s commentary on book 5 encompasses the multiple levels of the narrative: the reworking of Eratosthenes, Megasthenes, and Nearchus in the preliminary section; the topographical and tactical problems of the battle with Porus, and the rhetorical and stylistic subtleties of the debate at the Hyphasis. Throughout the book, Arrian shows Alexander going beyond his predecessors. By crossing the Indus he passes the limits of the Persian Empire. At Nysa he surpasses the mythical conquests of Dionysus (5.2.1). The digression on the Indus bridges recalls the bridges (and defeats) of Xerxes and Darius, as well as Roman imperial engineering (5.7.1–2). The crossing of the Hydaspes and great battle contrast with Cyrus’ disastrous battle with the Massagetae in Herodotus 1.204–14 (cf. 5.4.5). The description of the river systems of the Punjab (5.4.1–2) evokes Herodotus’ account... (shrink)

Logic is traditionally considered to be a purely syntactic discipline, at least in principle. However, prof. David Isles has shown that this ideal is not yet met in traditional logic. Semantic residue is present in the assumption that the domain of a variable should be fixed in advance of a derivation, and also in the notion that a numerical notation must refer to a number rather than be considered a mathematical object in and of itself. Based on his work, the (...) central question of this thesis is what kind of logic, if any, results from removing this semantic residue from traditional logic.We differ from traditional logic in two significant ways. The first is that the assumption that a numerical notation must refer to a number is denied. Numerical notations are considered as mathematical objects in their own right, related to each other by means of rewrite rules. The traditional notion of reference is then replaced by the notion of reduction (by means of the rewrite rules) to a normal form. Two numerical notations that reduce to the same normal form would traditionally be considered identical, as they would refer to the same number, and hence they would be interchangeable salva veritate. In the new system, called Buridan-Volpin (BV), the numerical notations themselves are the elements of the domains of variables, and two numerical notations that reduce to the same normal form need not be interchangeable salva veritate, except when they are syntactically identical (i.e., have the same Gödel number).The second is that we do away with the assumption that the domains of variables need to be fixed in advance of a derivation. Instead we focus on what is needed to guarantee preservation of truth in every step of a derivation. These conditions on the domains of the variables, accumulated in the course of a derivation, are combined in a reference grammar. Whereas traditionally a derivation is considered valid when the conclusion follows from the premisses by way of the derivation rules (and possibly axioms), in the BV system a derivation must meet the extra condition that no inconsistency occurs within the reference grammar. For if the reference grammar were to give rise to inconsistency (i.e., it would be impossible to assign domains to all the variables without breaking at least one of the conditions placed on them in the reference grammar), there is no longer a guarantee that truth has been preserved in every step of the derivation, and hence the truth of the conclusion is not guaranteed by the derivation.In Chapter 2 the BV system is introduced in some formal detail. Chapter 3 gives some examples of derivations, notably totality of addition, multiplication and exponentiation, as well as a lemma needed for the proof of Euclid’s Theorem. These examples, taken from prof. Isles’ First-Order Reasoning and Primitive Recursive Natural Number Notations, show that there is a real proof-theoretical difference between traditional logic and the BV system. Here we also find the first major point of departure between myself and prof. Isles, centered on the notion of inheritance of conditions in the reference grammar by way of lemmata. These different points of view are best illustrated in the sections on the totality of exponentiation and on Euclid’s Lemma: prof. Isles maintains that the proof of totality of exponentiation is not BV valid, while I maintain that it is. But I do agree with him that the traditional proof of Euclid’s Lemma is not BV valid. Chapter 6 also expands the arguments for my choice in this matter.Now that it has been shown that there is a difference between traditional logic and BV, the properties of BV need to be examined. In Chapter 4 we give a proof of Cut-elimination for BV minus induction and the subformula property for BV, which allows us to prove the consistency of BV minus induction. We also expand on the reasons for excluding induction. In Chapter 5 we consider in detail the proof of a finite analog to the Löwenheim–Skolem theorem given by prof. Isles in his article with the same title. He proves that under certain conditions it is always possible, given the existence of a (possibly uncountable) model for a derivation, to give a finite model for this derivation. The system he considers deviates from BV as considered in this thesis in two significant ways: it does not contain the induction rule and the domains contain numbers instead of numerical notations. We then go on to show that it is possible to extend the result to include induction, in the sense that the existence of a possibly uncountable model for a derivation guarantees the existence of a model that is at most countable. We also consider the complications that arise from taking numerical expressions instead of numbers as the elements of domains.Finally, in Chapter 6 we consider the philosophical consequences of the BV system, informed by the formal results from the previous chapters. In particular we discuss the relation between reduction and reference, the status of reference grammars, the notion of induction and its function within BV, and some brief considerations on the consequences of the BV system for the discussion regarding nominalism and realism with regard to mathematical objects. The object of the chapter is twofold. On the one hand applying the formal results to philosophical questions, on the other hand arguing that BV is not just a theoretically acceptable alternative to traditional logic, but is in fact deserving of further development and research into its properties. The latter will probably appeal most to those of a nominalist and/or finitist bent.Abstract prepared by Harrie de Swart and Sven Storms.E-mail:[email protected]:https://research.tilburguniversity.edu/files/6170 1294/Storms_The_Buridan_Volpin_04_05_2022.pdf. (shrink)

Der »Grundriss Heidegger« versteht sich als eine Einführung zu Martin Heideggers Leben und vor allem als Nachschlagewerk zu seinen Schriften. Diese haben (Stand Frühjahr 2012) einen Umfang von nahezu 27.000 Seiten, verteilt auf die bisher erschienenen 79 Bände der Gesamtausgabe, wozu noch zahlreiche Einzelveröffentlichungen und Briefbände kommen. Der erste Teil, Synopsis, ist der Versuch, über ein Denken umfassend zu orientieren, das sein Autor unter das Motto »Wege, nicht Werke« gestellt hat. In acht Hauptteilen (Sein, Welt und Sein, In-der-Welt-Sein, Kehre zum (...) Sein, Sein und Nichts, Ereignis und Sein, Bauen am Sein, Haus des Seins) soll die Einheit dieses Denkens sichtbar werden, die durchlaufend nummerierten Paragraphen folgen mit kleineren sachlich bedingten Abweichungen dem chronologischen Ablauf. Der zweite Teil, Lemmata, ist ein Heidegger-Lexikon mit 241 Stichworten von »Abendland« bis »Zwischen«. Um diesen Index in überschaubaren Grenzen zu halten, werden verwandte Stichworte gelegentlich in einem Artikel zusammengefasst; zudem ermöglicht eine Fülle von Verweisstellen eine weitergehende Orientierung. Den Stichworten folgen im Allgemeinen Angaben zur Sekundärliteratur. Der dritte Teil, Daten, umfasst drei Abschnitte: eine Übersicht über die wichtigsten Daten von Heideggers Leben und Wirken, Kurzbiographien wichtiger Personen aus Heideggers engerem Umfeld sowie Kurzbeschreibungen zu allen in den Bänden der Gesamtausgabe enthaltenen und einigen in dieser noch nicht erschienenen kleineren Schriften. Der vierte Teil, Appendices, enthält ein Abkürzungsverzeichnis, ein Verzeichnis aller im Buch zitierten Literatur, das Sachregister zum ersten Teil und das Inhaltsverzeichnis des Grundrisses. (shrink)

This article describes Syrianus' teachings on the One, as found in his testimonia on the Parmenides . In order to preserve the transcendence of the One, while still providing a fluid universe connected to the One, Syrianus shows how the nature of the One is seen in the structure of the Parmenides itself: the first hypothesis of the Parmenides outlines the primal God, while the intelligible universe is the subject of the second hypothesis, in so far as the intelligible universe (...) is a product of the One. Thus, whatever is negated of the One in the first hypothesis contains a positive analogue in the second hypothesis. With this description of the One in the Parmenides , Syrianus is able to create a complete, fluid universe. Readings of two lemmata, in particular, illuminate Syrianus' manner of interpreting the Parmenides to show how the One is both transcendent and connected to the universe. In his interpretations of Parmenides 137d and 138a, Syrianus shows how the One is partless with respect to itself, but contains parts with respect to the rest of the universe; and that the One is in itself and in another, again, with respect to itself and with respect to the rest of the universe. With his interpretation of the Parmenides , moreover, one can see how Syrianus differs from the interpretations of Porphyry and Iamblichus, and how he paves the way for Proclus' reading of the dialogue. (shrink)

The first genuine and comprehensive English-language handbook to the study of Kant's philosophy, containing sections on Kant's key works, the philosophical and historical contexts of his philosophy, essays on the reception and influence of the Kantian philosophy, a lexical A-Z list of lemmata addressing central themes and concepts of Kant's thought and an extensive English-language bibliography of secondary literature.

In this article I explain three puzzling features of Simplicius’ use of syllogistic reconstructions in his commentary on Aristotle’s Physics: (1) Why does he reconstruct Aristotle’s non-argumentative remarks? (2) Why does he identify the syllogistic figure of an argument but does not explicitly present its reconstruction? (3) Why in certain lemmata does he present several reconstructions of the same argument? Addressing these questions, I argue that these puzzling features are an expression of Simplicius’ assumption that formal reasoning underlies Aristotle’s (...) prose, hence they reflect his attempt to capture as faithfully as possible Aristotle’s actual mode of reasoning. I show further that, as a consequence of this seemingly descriptive use of syllogistic reconstructions, logic serves Simplicius not only as an expository and clarificatory tool of certain interpretations or philosophical views, but also motivates and shapes his exegetical stances and approach. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Otot ha-Shamayim: Samuel Ibn Tibbon’s Hebrew Version of Aristotle’s “Meteorology.” by AristotleSteven HarveyAristotle. Otot ha-Shamayim: Samuel Ibn Tibbon’s Hebrew Version of Aristotle’s “Meteorology.” Translated and edited by Resianne Fontaine. Leiden: E.J. Brill, 1995. Pp. lxxx + 268. Cloth, $108.50.This modest, seemingly unimportant, volume is in fact a surprisingly fascinating text that should be of interest to all historians of philosophy. Under the rather boring guise of an edition (...) and English translation of a medieval Hebrew translation of an early ninth-century Arabic translation of Aristotle’s Meteorology, this book is destined to be ignored by most historians of philosophy and even by those who have a special interest in Aristotle. This is a shame, and it is the goal of this brief review to alert the reader to the book’s value.The Hebrew translation of the Meteorology is, to be more precise, a creative translation of an inadequate Arabic version of the text, corrected, interpreted, and expanded on the basis of the commentaries of Alexander of Aphrodisias and Averroes, by a philosopher struggling to understand what was for him a seminal text of Aristotle’s. The philosopher-translator was Samuel Ibn Tibbon, best known for his faithful translation into Hebrew of Maimonides’s Guide of the Perplexed. What is immediately significant about the translation of the Meteorology, which was completed in 1210, is that it was the first text of Aristotle’s to be translated into Hebrew and, as far as is known, the first Hebrew translation of any philosophic or scientific work of a non-Jew. For the philosophically inclined Jew who did not know Arabic and who had struggled through Maimonides’s Guide without the benefit of translations, paraphrases, or even commentaries on Aristotle’s Physics and other prerequisite writings on natural science, the translation must have been an eagerly awaited and much welcome work. But why, of all things, the historian of philosophy will ask, the Meteorology? And however much appreciated the translation may have been in 1210, what possible use could an English translation of this patchwork Hebrew translation of a garbled and abridged Arabic translation of perhaps a Syriac translation of the Greek original or compendium of the Meteorology have for us today when we have a fine Greek edition of the text and modern translations from that edition?There were good reasons not to translate the Meteorology first. In contrast to most of Aristotle’s writings on natural science which existed in impressively reliable Arabic translations, the Meteorology existed in a poor and incomplete one. Ibn Tibbon comments in his Introduction to the translation that “errors and omissions” in the Arabic translation are evident from the context, from a comparison with Alexander’s commentary and the lemmata found therein, and from a comparison with other Aristotelian works that existed in trustworthy translations. The text could not simply be translated, [End Page 130] but needed to be reconstructed on the basis of a careful study of the commentaries of Alexander of Aphrodisias, Averroes, and the other commentaries that were available. Yet, even if the text had existed in a reliable translation, the tradition of text-study required that the sciences be studied in a proper order and this meant—as is clear from the opening words of the Meteorology—beginning the study of natural sciences with the Physics and turning to the Meteorology only after completing On the Heavens and On Generation and Corruption. Ibn Tibbon acknowledged this, and, in fact, interjected in his own name (27, 29) that “all the statements the philosopher has [made] thus far, are introductory remarks taken from earlier discussions in other books.... Someone who has not previously acquired knowledge and learning from his books that precede this one, will understand very little of this introduction.” Unfortunately for Ibn Tibbon’s reader, it would be forty years before any of those books or epitomes of them would be translated into Hebrew. Resianne Fontaine, in her wide-ranging and informative Introduction (xi–xii), brings support for A. Ravitzky’s suggestion that Ibn Tibbon’s decision to translate the Meteorology was motivated by his personal interest in the text... (shrink)

The Idea behind Tarski's Definition of Truth. In Tarski's presentations of his truth-definition, the steps of the construction are not sufficiently explained. It is not clear, on what general strategy the construction is based, what the fundamental ideas are, how some crucial steps work, and especially how the transition from the definition of satisfaction to the definition of truth should be understood. The paper shows that the account given in the model-theoretic literature, which is supported by Tarski's lemmata A (...) and B, is unsatisfactory, because Tarski's notion of truth can't be interpreted as ‘truth independent of the assignment of values to the variables’. Moreover, a satisfactory account of all the crucial steps is given. (shrink)

Die Arbeit an diesem wichtigsten Wörterbuch der gelehrt(er)en mittelalterlichen Gräzität schreitet erfreulich zügig voran: Mit dem vorliegenden Fasz. 4 (= Veröffentlichungen der Kommission für Byzantinistik, Bd. VI/4) ist bereits die erste Hälfte des Werkes abgeschlossen; er enthält auf 257 höchst inhaltsreichen Seiten den Rest des Zeta (1 Seite), die drei „kleinen“ Buchstaben Eta, Theta und Iota (13, 33 bzw. 28 S.) und auch schon das gesamte Kappa (182 S.); die Anzahl der Lemmata liegt bei eindrucksvollen 12.000.

In this paper, I have been able to demonstrate that the so-called Lexicon Theeteti is an apographon of Pal. gr. 173, a well known Plato's manuscript of Xth century. The codex Laurentianus 57,24, which contains the lexicon, previously dated to XIV/XV century, was also backdated to the first half of XIVth century.