We use formal semantic analysis based on new constructions to study abstract realizability, introduced by Läuchli in 1970, and expose its algebraic content. We claim realizability so conceived generates semantics-based intuitive confidence that the Heyting Calculus is an appropriate system of deduction for constructive reasoning.Well-known semantic formalisms have been defined by Kripke and Beth, but these have no formal concepts corresponding to constructions, and shed little intuitive light on the meanings of formulae. In particular, the completeness proofs for these semantics (...) do not generate confidence in the sufficiency of the Heyting Calculus, since we have no reason to believe that every intuitively constructive truth is valid in the formal semantics.Läuchli has proved completeness for a realizability semantics with formal concepts analogous to constructions. We argue in some detail that, in spite of a certain inherent inexactness of the analogy, every intuitively constructive truth is valid in Läuchli semantics, and therefore the Heyting Calculus is powerful enough to prove all constructive truths. Our argument is based on the postulate that a uniformly constructible object must be communicable in spite of imprecision in our language, and that the permutations in Läuchli's semantics represent conceivable imprecision in a language, while allowing a certain amount of freedom in choosing the particular structure of the language.We give a detailed generalization of Läuchli's proof of completeness for the propositional part of the Heyting Calculus, in order to make explicit constructive and algebraic content.In our treatment, we establish several new results about Läuchli models. We show how to extend the sconing and gluing constructions familiar from Kripke and Frame semantics and Topos theory, to Läuchli models, and use them to give an algebraic approach to countermodel construction. In particular, the Läuchli arguments are given without the restriction to the integers, Z, as a group of permutations, which makes much of the coding scheme used in Läuchli's original paper transparent.We also make use of a new propositions-as-types syntax for the Heyting calculus, with limited nondeterminism, in which validity of formulae can be decided without loop-detection. (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)

There is an anomaly about the origins of Augustine’s great work of anti-pagan polemic and Christian apologetic that has not been accorded due weight in discussion of the development of the work’s idea in Augustine’s mind. The purpose of this brief note is to point out a hitherto unrecognized explanation for this anomaly, while leaving aside a full-scale development of the implications of this discovery.

There is an anomaly about the origins of Augustine’s great work of anti-pagan polemic and Christian apologetic that has not been accorded due weight in discussion of the development of the work’s idea in Augustine’s mind. The purpose of this brief note is to point out a hitherto unrecognized explanation for this anomaly, while leaving aside a full-scale development of the implications of this discovery.

James questions the validity of the very tentative statement made in the final sentence of our paper. Our claim concerned the proportion of twins in Britain in the 1990s that might have arisen through subfertility treatment and was linked to the suggestion that the natural twinning rate might still be in decline. If this were true, we, like James, would regard that prospect with concern.

The ramified legacy of Bernard Berenson’s writings within 20th century art historiography is both celebrated and maligned. In an effort to help reconcile this situation, this essay argues for the partial validity of Berenson’s peculiar version of art historical formalism by detailing its historical connections to the Pragmatist philosophy and psychology of William James and by analytically correlating Berenson’s arguments with recent work in aesthetics and the philosophy of perception. The essay examines the specific example of Berenson’s analysis of (...) Giotto’s paintings and leverages a Pragmatist interpretation of Berenson’s writings to frame Berenson’s known connections with other writers: including Adolf Hildebrand, Giovanni Morelli, and Walter Pater. In conclusion, the failure, potential, reception, and legacy of Berenson’s art historical scholarship are assessed in relation to Pragmatist ideas. Der vielfältige Einfluss von Bernard Berensons Schriften auf die Kunstgeschichte des 20. Jahrhunderts wird ebenso geschätzt wie verachtet. In dem Bestreben, diese Divergenzen zu berichtigen, versucht dieser Beitrag den Nachweis für die bedingte Gültigkeit von Berensons eigentümlicher Variante eines kunsthistorischen Formalismus zu erbringen, indem er einerseits seine historischen Verbindungen zur pragmatischen Philosophie und Psychologie von William James aufzeigt und indem er andererseits Berensons Argumentation ins Verhältnis zu aktuellen Debatten der wahrnehmungstheoretischen Ästhetik und Philosophie setzt. Am Beispiel von Berensons Interpretation der Gemälde Giottos führt dieser Essay eine pragmatische Analyse von Berensons Schriften durch und stellt diese ins Umfeld seiner Kontakte zu anderen Autoren: darunter Adolf Hildebrand, Giovanni Morelli und Walter Pater. Schließlich soll das Scheitern, das Potenzial, die Rezeption und das Erbe von Berensons kunsthistorischen Studien unter pragmatischen Gesichtspunkten bewertet werden. (shrink)

As contribution to a recent debate (James, 1998; Murphy etal., 1997, 1998) the proportion of twins following ovulation induction (OI) or assisted conception (AC) in 1994 in Oxfordshire and West Berkshire was estimated, and by extrapolation the natural twinning rate in England and Wales was judged to have maintained a plateau phase since the 1970s. Similar figures for 1995 and 1996 from the same study, and hence a more stable local estimate, are now provided. The proportions, as before, were (...) estimated from women's responses to a questionnaire within a case[hyphen]control study, with ascertainment from general practitioners' records or hospital case[hyphen]notes for non[hyphen]responders or for those excluded from the study originally. In 1994, 1995 and 1996 the proportion of twins following OI/AC was overall 27% (24%, 30% and 27% respectively). Restriction to the 87% locally resident made no difference. The national crude twinning rate for those years was overall 13·3 per 1000 maternities (12·8, 13·6 and 13·4 respectively). (shrink)

J. J. OʼDonnell is one those scholars whose learning is assumed rather than displayed. As a result, his brief approach to the long-terms effects of the computer revolution onreading and higher education feels like a bracing, sophisticated exchange of ideas. Like conversation, O'Donnellʼs thesis is not terribly unified or orderly. He often makessidetracks from his focus on high technology and literacy into explaining such interestingthings as how we choose our cultural ancestry instead of merely evolving out of it, the errors (...) of current education, and perhaps more than you ever wanted to know aboutother avatars of the word such as St. Jerome, St. Augustine, and Cassiodorus. Greatcover too. (shrink)

This is the first modern, annotated and scholarly edition of Jean-Baptiste Du Bos’ _Critical Reflections on Poetry and Painting_, one of the seminal works of modern aesthetics in any language.

This book presents a comprehensive, accessible survey of Western philosophy of music from Pythagoras to the present. Its narrative traces themes and schools through history, in a sequence of five chapters that survey the ancient, medieval, early modern, modern and contemporary periods. Its wide-ranging coverage includes medieval Islamic thinkers, Continental and analytic thinkers, and neglected female thinkers such as Vernon Lee (Violet Paget). All aspects of the philosophy of music are discussed, including music and the cosmos, music's value, music's relation (...) to the other arts, the problem of opera, the origins of musical genius, music's emotional impact, the moral effects of music, the ontology of musical works, and the relevance of music's historical context. The volume will be valuable for students and scholars in philosophy and musicology, and all who are interested in the ways in which philosophers throughout history have thought about music. (shrink)