Act 4, scene 1 of Shakespeare's A Midsummer Night's Dream opens with the amorous dialogue between Titania and her newly beloved Nick Bottom. In a show of immoderate attention to one of the "hempen home-spuns,"1 Titania's affectionate imperatives add to the scene's dramatic irony: "Come, sit thee down upon this flow'ry bed / While I thy amiable cheeks do coy, / And stick musk-roses in thy sleek smooth head, / And kiss thy fair large ears, my gentle joy". Titania's pursuit (...) of Bottom is so excessive that the love scene becomes sadly comical: not only has the queen of the fairy world been tricked into falling in love with one of the "rude mechanicals" but he is one whose head, as we know, has... (shrink)

Giovanni Sambin has recently introduced the notion of an overlap algebra in order to give a constructive counterpart to a complete Boolean algebra. We propose a new notion of regular open subset within the framework of intuitionistic, predicative topology and we use it to give a representation theorem for overlap algebras. In particular we show that there exists a duality between the category of set-based overlap algebras and a particular category of topologies in which all open subsets are regular.

We study some connections between two kinds of emph{overlap} relations: that of point-free geometries in the sense of Grzegorczyk, Whitehead and Clarke, and that recently introduced by Sambin within his constructive approach to topology. The main thesis of this paper is that the overlap relation in the latter sense is a necessary tool for a constructive and intuitionistic development of point-free geometry.

We construct a Galois connection between closure and interior operators on a given set. All arguments are intuitionistically valid. Our construction is an intuitionistic version of the classical correspondence between closure and interior operators via complement.

A positive topology is a set equipped with two particular relations between elements and subsets of that set: a convergent cover relation and a positivity relation. A set equipped with a convergent cover relation is a predicative counterpart of a locale, where the given set plays the role of a set of generators, typically a base, and the cover encodes the relations between generators. A positivity relation enriches the structure of a locale; among other things, it is a tool to (...) study some particular subobjects, namely the overt weakly closed sublocales. We relate the category of locales to that of positive topologies and we show that the former is a reflective subcategory of the latter. We then generalize such a result to the category of suplattices, which we present by means of cover relations. Finally, we show that the category of positive topologies also generalizes that of formal topologies, that is, overt locales. (shrink)

This paper provides a constructive topological semantics for non-deducibility of a first order intuitionistic formula. Formal topology theory, in particular the recently introduced notion of a binary positivity predicate, and co-induction are two needful tools.

We characterize the category of Sambin’s positive topologies as the result of the Grothendieck construction applied to a doctrine over the category Loc of locales. We then construct an adjunction between the category of positive topologies and that of topological spaces Top, and show that the well-known adjunction between Top and Loc factors through the constructed adjunction.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Eucharistic Form of God: Trinity, Incarnation, and Sacrament in the Theology of Hans Urs von Balthasar by Jonathan Martin CirauloNicholas J. HealyThe Eucharistic Form of God: Trinity, Incarnation, and Sacrament in the Theology of Hans Urs von Balthasar. By Jonathan Martin Ciraulo. Notre Dame, Ind.: University of Notre Dame Press, 2022. Pp. xiii + 297. $50.00 (hardcover). ISBN: 978-0-268-20223-1.In Fides et Ratio 93, under the heading (...) “current tasks for theology,” John Paul II writes:The chief purpose of theology is to provide an understanding of Revelation and the content of faith. The very heart of theological enquiry will thus be the contemplation of the mystery of the Triune God. The approach to this mystery begins with reflection upon the mystery of the Incarnation of the Son of God: his coming as man, his going to his Passion and Death.... From this vantage-point, the prime commitment of theology is seen to be the understanding of God’s kenosis, a grand and mysterious truth for the human mind, which finds it inconceivable that suffering and death can express a love which gives itself and seeks nothing in return. In this light, a careful analysis of texts emerges as a basic and urgent need: first the texts of Scripture, and then those which express the Church’s living Tradition. On this score, some problems have emerged in recent times, problems which are only partially new; and a coherent solution to them will not be found without philosophy’s contribution.These words about the mystery of Jesus Christ’s life and death as a revelation of the Triune God—and about the emergence of new difficulties and questions—underscore the importance of a dialogue between St. Thomas Aquinas and the great twentieth-century theologian Hans Urs von Balthasar. As two recent books written from a Thomistic perspective have shown (Aidan Nicholas, Balthasar for Thomists [San Francisco: Ignatius Press, 2020]); [End Page 715] Matthew Levering, The Achievement of Hans Urs von Balthasar [Washington, D.C.: The Catholic University of America Press, 2019]), Balthasar’s profound indebtedness to the metaphysics of Aquinas provides a solid foundation for dialogue. And yet a number of difficulties remain. What is the relationship between the so-called real distinction of esse and essence and the hypostatic union of two natures in the person of the Son? How and in what sense does the paschal mystery of Jesus’s death and Resurrection presuppose and express the mystery of the Father’s eternal generation of the Son? In the words of Joseph Ratzinger, “in the pierced heart of the Crucified, God’s own heart is opened up—here we see who God is and what he is like” (Spirit of the Liturgy [San Francisco: Ignatius Press, 2000], 48). How does the mystery of Christ’s Eucharist reveal the heart of God?This last question about the Eucharist and the nature of God is explored in depth in Jonathan Martin Ciraulo’s monograph, The Eucharistic Form of God: Hans Urs von Balthasar’s Sacramental Theology. Despite the expansive title, the primary aim of this book is fairly straightforward: to present Balthasar’s theology of the Eucharist and to show the significance of his thought for contemporary sacramental theology. Anyone who seeks to offer a systematic account of Balthasar’s theology of the Eucharist is confronted with at least two basic obstacles or challenges. First, his reflections on the Eucharist are scattered throughout (and often hidden within) an immense and complex corpus of writings. Second, the most distinctive feature of Balthasar’s theology of the Eucharist is the inseparability of his sacramental theology from his speculative account of the central mysteries of the Christian faith—Trinity, Incarnation, Cross and Resurrection, Church, and eschaton.The Eucharistic Form of God represents a thoughtful, well-written, and original response to this twofold challenge. Regarding the first point: Ciraulo demonstrates an intimate familiarity with the whole of Balthasar’s corpus. He draws together Balthasar’s early writings on German literature, his monographs on Origen, Gregory of Nyssa, and Maximus the Confessor, his engagement with Karl Barth, his interpretation of twentieth-century French Catholic literature... (shrink)

In Distributed Like Bread: Hans Urs von Balthasar Speaks to Seminarians, Jonathan Ciraulo engages with the theological insights of Hans Urs von Balthasar, especially as they pertain to the priesthood and seminary formation. This work not only introduces readers to Balthasar's complex and nuanced understanding of the priestly vocation but also serves as a guide for those discerning or living out this calling. Through a detailed examination of Balthasar’s life and writings, Ciraulo uncovers the profound notion that the (...) priesthood is a mission, one in which God elects individuals to become instruments of divine grace despite and within their human limitations. (shrink)