The final two Metaphysical Expositions argue that our original representation of space must be intuitive. I draw some surprising connections between Kant’s discussion and Leibniz’s account of the continuum. These connections indicate that the point of Kant’s analysis of <space> is to show that our original representation of space is infinitely complex in content. Since no discursive representation can be infinitely complex, our concept <space> cannot derive its content from discursive spontaneity. Its content must rather be given to the mind in order to be thought at all and thus originates in receptive intuition. Kant’s argument does not hinge on the singularity or holistic structure of space, as many hold, but on its infinite complexity and consequent givenness. I develop a novel account of the discursivity of conceptual representation that preserves the validity of Kant’s argument, defend Kant’s account of the infinity of space against prominent objections, and finally indicate how Kant’s argument entails the singularity of intuition (rather than presupposing it).

This essay introduces and explores David Tracy’s notion of ‘analogical imagination’ as something that prevents reason, theology, and social life from collapsing ‘into equivocation or else hopeless stupid conflict’. A capacious reflective reason, after Tracy, depends on imaginative habits and sensibilities that stay faithful to the discordant plurality and ambiguity of things while also acknowledging their analogies or ‘similarities-in-difference’. The essay argues that the continuing integrity and scope of Tracyean analogical imagination depends upon understanding that the negations that belong to apparently contrasting ‘dialectical imaginations’ reach ‘all the way down’ within analogical imagination itself. Aided by classic expressions of culture, furthermore, analogical imaginative possibility shades into contingent vision when organised by ‘focal meanings’ to fashion some global sense of the world. This is then brought into dialogue with Richard Kearney’s comparatively recent notion of ‘anatheism’, to help consideration of how Tracyean analogical imagination might maintain its imagination and ana- at the perilous point that it becomes also a matter of religious believing.

This introductory essay to the volume sets out the volume’s form and purpose, and then provides advance introduction of each of its component essays in turn. Since the volume comes together as a tightly organised and cumulative introduction to David Tracy, this essay forms its own concerted introduction to Tracy parallel to the performance of the book as a whole.

This essay begins with a close reading of Tracy’s recent programmatic formulations concerning: (1) the ‘strong fragments’ of culture that ‘shatter, fragment, negate any closed totality system’; and (2) those ‘most powerful fragments’ that ‘show themselves not as substances but as events and positively open to liminal Infinity’. If some cultural fragments are mere ‘period pieces’ without enduring truth or transformative power, and others are dangerously nostalgic, these fragments, Chase suggests, can act strongly when collaged into some ‘new form of witness against any false whole or claim to completeness’. T. S Eliot’s The Waste Land is an ambiguous example here. The pinnacle of the fragment for Tracy, however, is the ‘frag-event’ that opens towards the creative liminality of an invisible Infinity. ‘Marxist-Kabbalist’ Walter Benjamin is ‘the projective force’ behind Tracy’s forays into the fragment. The essay proposes the role of assemblage or collage for both fragmenting fragments and the Tracyean frag-event, stressing the role of edges and unexpected connections, and concluding by wondering how far Christian theology is really ready to think in such a manner of collage.

Thematically, formally and structurally, Wallace’s writing concerned itself with the infinite, from the antinomies of set theory and the obese Bombardini in The Broom of the System to the featureless horizon of Peoria in The Pale King, by way of the title of Infinite Jest and the brief and not wholly successful exploration of Cantorian mathematics in Everything and More, the idea of the infinite was never far from any of Wallace’s writing. Moreover, the structures of the writing continually reinscribe this obsession with infinity, with none of the novels conforming to a traditional boundaried structure and the collections of short fiction troubling the very concept of order in their use of pagination and enumeration. This chapter illuminates the importance of infinity to Wallace’s writing by exploring its formal and thematic development through his career, demonstrating that infinity worked as a conceptual counterpoint to solipsism, both an existential threat and a source of profound hope for the disassociated subject of contemporary culture.

Compares Cassirer and Heidegger's take on the human being's capacity to orient itself in the world in a meaningful way. Cassirer's theory of the functions of consciousness, the only meat to his functional conception of human subjectivity, is used to describe the diverse, cultural compasses by means of which the 'symbolic animal' navigates the human world (7.1). Heidegger's accounts of 'the they' and of owned ('authentic') existence in turn provide a theory of Dasein's capacity to orient itself within and towards its world (7.2). In view of their shared interest in orientation, I discern an important distinction for both Cassirer and Heidegger between an orienting and an oriented self. With regard to both, they ultimately disagree about the infinite (cultural) or finite (temporal) nature of the human being (7.3).

Cavendish displayed a lifelong fascination with one of the hardest of the “hard” problems, the nature of infinity. In an age which saw the birth of calculus as well as revolutionary developments in cosmology, a consistent theory of infinity was generally regarded as an illusory goal. Cavendish tackled this vexing scientific problem, which represented a radical departure from the cosmological and theological consensus of the 1660s; it anticipates a new worldview which emerged toward the end of the century, in which biblical revelation was eventually subordinated to empirical science, the Copernican hypothesis triumphed over rival theories, and the notion of a plurality of worlds became commonplace rather than shocking. From the playful speculations of the 1650s, Cavendish’s confident analysis of the nature of infinity had evolved into an essential ingredient in her prescient “theory of everything.”

In this chapter, the basic theory of sets is developed axiomaticallyin a paraconsistent logic. The two main goals are (1) to establish atoolkit for elementary mathematics, and (2) to prove the mainantinomies of naive set theory. The two goals come together inproving the Burali-Forti paradox for the theory of ordinals. Alongthe way, results are proved about the universal set, various formsof “empty” sets, Russell’s set, the axioms ofZFC, fixed points, Cantor’s theorem, and the possibility of awell-ordering theorem. The Routley set is introduced and studied asa particularly inconsistent object.

The entering into a gathering that discloses time and everything temporal and historical occurs through a submitting to determination by history rather than by turning away from it towards supposedly eternal ideals. Dante’s poem, even in its affirmation of theological transcendence, is remarkable for its showing of language in its emergence in and from historical realities. Dante’s thematization and dramatization of language and its component letters lends itself to suggesting a probe that scrutinizes the sense of language as such. Language speaks to him in the Heaven of Jove directly; it becomes not just an instrument or means, but also in itself immediately a revelation. Heidegger’s philosophy, similarly, culminated in an attunement to what language itself says, for “language speaks” (“die Sprache spricht”). It speaks in the connectedness and disclosedness of things in a world, their lying-together-before us, which is not produced by human activity or techné, but is discovered as unaccountably given. Hence also the astoundingly organized order of the letters that Dante sees spontaneously sparking – as if contingently – into recognizable and even portentous shapes. Language, deeply considered, is the imperative presence of the Other facing us with its ethical demands. The imperative here is justice – the ethical imperative vis-à-vis the Other. Like Levinas, Dante represents language – when it is displayed to him directly as divine revelation in the heaven of Jove – as a revelation of Justice. Levinas’s ethical injunction is already revealed to him in the form of a peremptory imperative: “Love justice.”

The Introduction presents the central questions and motivations of the book: why do Greek lists exist in such abundance, what are their purposes, and how do we trace their trajectory through and across the genres and text-types of the late archaic and Classical periods? How do literary and documentary texts intersect in this tradition? How, finally, does this widespread cultural phenomenon inform the post-Classical inventories and archival traditions we see in such abundance? As a grounding and point of departure, it provides a brief survey of lists and their manifestations in Greek literature and inscriptions. It turns then to definitions of lists, precursors to Greek alphabetic lists, and theoretical preliminaries, including: the connections of lists and literacy, orality, and numeracy, and lists’ relationship to memory, narrative, counting, and collecting.Finally, the Introduction establishes an original framework for the functions of Greek lists, to be explored and examined in the main body chapters of the book: Greek lists, I propose, serve to perform a spectrum of actions upon objects: they collect, count, control, display, distort, memorialize, and, finally, conjure them.