Dr. Cyril Bailey and Dr. C. M. Bowra have most recently analysed Virgil's method of using the expressions of Lucretius and Ennius respectively, and Mile A.-M. Guillemin has lately added significant considerations to Father F.-X. M. J. Roiron's long examination of Virgil's method of using again his own former expressions. Since then other work has been done with the purpose of clarifying the less rational part of Virgil's self-repetition; it might be called complementary to the well-known researches of Mr. John (...) Sparrow. With such a purpose I have tried to suggest how Virgil reached the strange phrase in the first Eclogue, rapidum Cretae, or cretae, Oaxen, by a not unparalleled confusion of the names of several different rivers and at least one town. (shrink)

For about a hundred years there has been an intermittent but sometimes vigorous debate1 on the question whether Quintus Smyrnaeus and Tryphiodorus directly used the Second Aeneid as a source for their epic descriptions “of the capture and destruction of Troy. Heyne thought that they did not; but towards the end of the nineteenth century it appeared more likely that they did. Heinze opposed the general belief: but it was reaffirmed for Quintus by Paschal and Becker4 and for Tryphiodorus by (...) Dr. E. Cesareo on internal evidence. Meanwhile Professor Samuel E. Bassett had concluded that Quintus was not after all dependent on Vergil: and still more recently Dr. J. W. Mackail, reviewing Cesareo's monograph, has maintained with emphasis that the Aeneid is certainly not the source of the late epic. Accordingly the controversy cannot even now be considered closed. (shrink)

For about a hundred years there has been an intermittent but sometimes vigorous debate1 on the question whether Quintus Smyrnaeus and Tryphiodorus directly used the Second Aeneid as a source for their epic descriptions “of the capture and destruction of Troy. Heyne thought that they did not; but towards the end of the nineteenth century it appeared more likely that they did. Heinze opposed the general belief: but it was reaffirmed for Quintus by Paschal and Becker4 and for Tryphiodorus by (...) Dr. E. Cesareo on internal evidence. Meanwhile Professor Samuel E. Bassett had concluded that Quintus was not after all dependent on Vergil: and still more recently Dr. J. W. Mackail, reviewing Cesareo's monograph, has maintained with emphasis that the Aeneid is certainly not the source of the late epic. Accordingly the controversy cannot even now be considered closed. (shrink)

It is sufficiently probable that quantitative scansion in Latin, imposed on a language in which accentuation by stress was alone significant originally, not only gave way to the earlier principle in the decline of Latin literature, but scarcely tended to suppress it at any time in common speech and in familiar writing. It is also probable therefore that even in literature dominated by quantity stress-accentuation was not obliterated altogether. In fact the incidences of it, in Vergilian verse at least, seemed (...) so characteristic that in late Antiquity the Vergilian stress-rhythms were apparently copied without any knowledge of the prosody of the hexameter. In modern expositions, the variety of Vergil's rhythms is generally referred, not only to scansion, but also to stress-accentuation: and it has recently been shown that lines in which stress and metrical ictus predominantly coincide are different in quality and expressiveness from lines in which they do not. Since however no general explanation or definition of this difference in quality seemed to have been offered, I lately attempted a simple theory which would account for the different aesthetic values of lines of these two classes, and which would define, if possible, what these different values are. (shrink)

It is sufficiently probable that quantitative scansion in Latin, imposed on a language in which accentuation by stress was alone significant originally, not only gave way to the earlier principle in the decline of Latin literature, but scarcely tended to suppress it at any time in common speech and in familiar writing. It is also probable therefore that even in literature dominated by quantity stress-accentuation was not obliterated altogether. In fact the incidences of it, in Vergilian verse at least, seemed (...) so characteristic that in late Antiquity the Vergilian stress-rhythms were apparently copied without any knowledge of the prosody of the hexameter. In modern expositions, the variety of Vergil's rhythms is generally referred, not only to scansion, but also to stress-accentuation: and it has recently been shown that lines in which stress and metrical ictus predominantly coincide are different in quality and expressiveness from lines in which they do not. Since however no general explanation or definition of this difference in quality seemed to have been offered, I lately attempted a simple theory which would account for the different aesthetic values of lines of these two classes, and which would define, if possible, what these different values are. (shrink)

Computable structures of Scott rank ${\omega_1^{CK}}$ are an important boundary case for structural complexity. While every countable structure is determined, up to isomorphism, by a sentence of ${\mathcal{L}_{\omega_1 \omega}}$ , this sentence may not be computable. We give examples, in several familiar classes of structures, of computable structures with Scott rank ${\omega_1^{CK}}$ whose computable infinitary theories are each ${\aleph_0}$ -categorical. General conditions are given, covering many known methods for constructing computable structures with Scott rank ${\omega_1^{CK}}$ , which guarantee that the (...) resulting structure is a model of an ${\aleph_0}$ -categorical computable infinitary theory. (shrink)

This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega _{1}^{\mathit{CK}}}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}$ , the class $K_{\omega _{1}^{\mathit{CK}}+1}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}+1$ , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete $\Sigma _{1}^{1},\,I(K_{\omega _{1}^{\mathit{CK}}})$ is m-complete $\Pi _{2}^{0}$ relative to Kleen's O, and $I(K_{\omega _{1}^{\mathit{CK}}+1})$ is m-complete $\Sigma _{2}^{0}$ relative to O.

Assume ZF + AD +V=L and letκ< Θ be an uncountable cardinal. We show thatκis Jónsson, and that if cof = ω thenκis Rowbottom. We also establish some other partition properties.

In [8], the third author defined a reducibility$\le _w^{\rm{*}}$that lets us compare the computing power of structures of any cardinality. In [6], the first two authors showed that the ordered field of reals${\cal R}$lies strictly above certain related structures. In the present paper, we show that$\left \equiv _w^{\rm{*}}{\cal R}$. More generally, for the weak-looking structure${\cal R}$ℚconsisting of the real numbers with just the ordering and constants naming the rationals, allo-minimal expansions of${\cal R}$ℚare equivalent to${\cal R}$. Using this, we show that (...) for any analytic functionf,$\left \equiv _w^{\rm{*}}{\cal R}$. $is noto-minimal.). (shrink)

This Festschrift in Professor Kristeller’s honor consists of contributions by scholars who have had some connection with Columbia University, his "intellectual home in the United States for three decades." It also includes a Tabula Gratulatoria listing many other friends from the United States and Europe. The editor’s opening essay provides an interesting and informative account of this scholar’s academic career, and should be read together with the complete annotated bibliography of his publications through 1974. The latter lists 149 "major publications" (...) and 220 "minor publications." Kristeller’s contributions to the history of Renaissance philosophy are well known to historians of philosophy, and deservedly so. Here reference should be made to his groundbreaking studies on Marsilio Ficino and Pomponazzi, and on others such as Pico della Mirandola and Petrarch, as well as on Renaissance Platonism, Aristotelianism in the Renaissance, Thomism in the Renaissance, Paduan Averroism, and Alexandrism. But he has also contributed greatly to the fields of medieval and Renaissance history, and especially to our understanding of Renaissance humanism, Renaissance music, and Renaissance art. He is universally recognized as one of the world’s foremost authorities on manuscript research, as is witnessed, for example, by the cooperative project, Catalogus Translationum et Commentariorum, which he founded, and by his Iter ltalicum. In all of these enterprises he has set an enviable example for other scholars by the exacting standards and the breadth of his expertise. It is only fitting, then, that the many essays in this Festschrift should reflect the breadth and depth of the scholarship so evident in the man to whom they are dedicated. Limitations of space will only permit us to list them here, with a few remarks reserved for those of more special interest to philosophers and historians of philosophy: Eugene F. Rice, Jr., "The De magia naturali of Jacques Lefèvre d’Etaples" ; Donald R. Kelley, "Louis Le Caron Philosophe", on Le Caron’s effort to bring together jurisprudence and classical, especially Platonic, philosophy; Richard H. Popkin, "The Pre-Adamite Theory in the Renaissance", with fascinating material about theories concerning men before Adam in La Peyrère and widely scattered earlier sources; Richard Lemay, "The Fly against the Elephant: Flandinus against Pomponazzi on Fate", on an unedited attack by an Augustinian Bishop against Pomponazzi’s espousal of the Stoic doctrine of fate; Martin Pine, "Pietro Pomponazzi and the Medieval Tradition of God’s Foreknowledge", on Pomponazzi’s solution to the problem of divine foreknowledge and human freedom inlight of his familiarity with earlier discussions by Boethius, Aquinas, Scotus, and Ockham; F. Edward Cranz, "Editions of the Latin Aristotle Accompanied by the Commentaries of Averroes", helpful to all who wish to consult late fifteenth- and sixteenth-century versions of the Latin Aristotle and especially the Latin Averroes; Josef Soudek, "A Fifteenth-Century Humanistic Bestseller: The Manuscript Diffusion of Leonardo Bruni’s Annotated Latin Version of the Aristotelian Economics" ; Edward P. Mahoney, "Nicoletto Vernia on the Soul and Immortality", which details a radical shift on Vernia’s part from an earlier Averroistic reading of Aristotle; Joan Kelly-Gadol, "Tommaso Campanella: The Agony of Political Theory in the Counter-Reformation", which attempts to account for some of the shifts and inconsistencies in Campanella’s political writings by placing them within the troubled personal and political circumstances of his life; Charles Trinkaus, "Protagoras in the Renaissance: An Exploration" ; Maristella de Panizza Lorch, "Voluptas, molle quoddam et non invidiosum nomen: Lorenzo Valla’s Defense of voluptas in the Preface to his De voluptate" ; Neal W. Gilbert, "Richard de Bury and the ‘Quires of Yesterday’s Sophisms"’, with much interesting material on the medieval tradition of sophismata, especially at Oxford; Malcolm Brown, "A Pre-Aristotelian Mathematician on Deductive Order" ; John H. Randall, Jr., "Paduan Aristotelianism Reconsidered", on evidence for influence of the Italian Aristotelian tradition on Galileo; William F. Edwards, "Niccoló Leoniceno and the Origins of Humanist Discussion of Method" ; C. Doris Hellman, "A Poem on the Occasion of the Nova of 1572" ; Edward Rosen, "Kepler’s Mastery of Greek" ; W. T. H. Jackson, "The Politics of a Poet: The Archipoeta as Revealed by his Imagery" ; John Charles Nelson, "Love and Sex in the Decameron" ; George B. Parks, "Pico della Mirandola in Tudor Translation" ; Richard Harrier, "Invention in Tudor Literature: Historical Perspectives" ; Helene Wieruszowski, "Jacob Burckhardt and Vespasiano da Bisticci " ; Morimichi Watanabe, "Gregor Heimburg and Early Humanism in Germany" ; Raymond de Roover, "Cardinal Cajetan on ‘Cambium’ or Exchange Dealings" ; and a series of text editions with introductions including Julius Kirshner, "Conscience and Public Finance: A Questio disputata of John of Legnano on the Public Debt of Genoa" ; John Mundy, "The Origins of the College of Saint-Raymond at the University of Toulouse" ; Charles B. Schmitt, "Girolamo Borro’s Multae sunt nostrarum ignorantionum causae " ; Guido Kisch, "An Unpublished Consiliumof Johannes Sichardus" ; Patricia H. Labalme, "The Last Will of a Venetian Patrician " ; Felix Gilbert, "The Last Will of a Venetian Grand Chancellor" ; Herbert S. Matsen, "Giovanni Garzoni to Alessandro Achillini : An Unpublished Letter and Defense" ; Theodore E. James, "A Fragment of An Exposition of the First Letter of Seneca to Lucilius Attributed to Peter of Mantua". The editor, his collaborators, and the contributors are all to be commended for the high quality of this volume.—J.F.W. (shrink)