This collection of original essays pays tribute to the man by exploring topics that have interested him through a long and productive career. Plato's mathematical imagery, his theory of perception, the role of engineering techne in the origin of Greek science, time and free will in Kant, Whitehead as teacher of teachers, mapping friendships, Kierkegaard and the necessity of forgery. These and other topics are given fresh treatments meant to stimulate further philosophical thinking in the spirit of Brumbaugh himself.

These essays examine a crucial premise of traditional readings of Plato's dialogues: that Plato's own philosophical dialogues can be read off the statements made in the dialogues by Socrates and other leading characters. The text argues that no character should be read as Plato's mouthpiece.

This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present. The Mathematical Imagination is available from the publisher on an open-access basis.

The first of two volumes collecting the published work of one of the greatest living ancient philosophers, M.F. Burnyeat.

Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.

Recently, in the past thirty years, there has been an upsurge in serious treatment of Platonic mythoi, which were once thought to be only literary decoration and/or the simplistic presentation of philosophic conclusions for the demos (dummies in effect). Nevertheless, the dominant tendency in the exegesis of Platonic mythoi still is to subordinate them to philosophic logos (reason) and not to recognize that such mythoi are philosophic in themselves in the broad sense of “the love of wisdom”. There is something conversional about Plato’s philosophic mythos, reformulating and superseding traditional Greek mythos and then charting the drama of the human soul from Socratic aporia, up and out of the cave, and into the beyond, the Idea of the Good. The late Professor Eric Voegelin understood this existential drama, and his exegesis of Platonic mythos, from engendering pathos to symbols, is revelatory to say the least. My understanding is that logos (reason) is a fundamental and necessary check on mythos, but logos and mythos are complementary via medias; neither are dispensable nor reducible, one to the other. Also crucial to my study of Platonic mythoi is the “analogy of being,” that Voegelin only touches on, but Erich Przywara explores and develops. The relationship between the human and the divine is analogical (likenesses but also significant unlikenesses), and Plato certainly explored the play of opposites and affinities covering the difficult philosophical problems of becoming and being and the temporal and the eternal. Most philosophic commentators on Plato ignore the suffusive presence of the divine in Plato’s love of wisdom. Perhaps only Platonic mythos at its best offers the philosophic imagination the vision of transcendence.