Fictions of Infinity

Levinasian Ethics in 21st-Century Novels

Martin Riedelsheimer

• Publisher: De Gruyter
• Year: 2020
• Print ISBN: 9783110712346
• eBook ISBN: 9783110712421
• Edition: 1
• Topic: Literature
• Subtopic: English Literary Criticism
• Index: Literature

This study traces the connection of infinity and Levinasian ethics in 21st-century fiction. It tackles the paradox of how infinity can be (re-)presented in the finite space between the covers of a book and finds an answer that combines conceptual metaphor theory with concepts from classical narratology and beyond, such as mise en abyme, textual circularity, intertextuality or omniscient narration. It argues that texts with such structures may be conceptualised as infinite via Lakoff and Núñez's Basic Metaphor of Infinity. The catachrestic transfer of infinity from structure to text means that the texts themselves are understood to be infinite. Taking its cue from the central role of the infinite in Emmanuel Levinas's ethics, the function of such 'fictions of infinity' turns out to be ethical: infinite textuality disrupts reading patterns and calls into question the reader's spontaneity to interpret. This hypothesis is put to the test in detailed readings of four 21st-century novels, David Mitchell's Cloud Atlas, Jeanette Winterson's The Stone Gods, Ian McEwan's Saturday and John Banville's The Infinities. This book thus combines ethical criticism with structural aesthetics to uncover ethical potential in fiction.

1 Introduction: Towards Infinity

Infinity is an elusive phenomenon. By its very nature it appears as too vast an idea to be fully understood. This is what has led to a fascination with the infinite pervading various academic disciplines, such as mathematics, physics, philosophy and theology, as well as the arts and literature – not to mention the ample exploitation of the buzzword ‘infinity’ in consumer culture and advertising, where it is used as a placeholder promising, more or less, that the sky is (not) the limit. In short, infinity is everywhere. The infinite, it would seem, captures the imagination precisely because it implies an inexhaustible ‘more’ beyond the here and now, beyond the finite constraints of our daily lives. Literature, of course, as all art, can be viewed as an exploration of what goes beyond the ordinary. In this widest possible sense, all fiction is itself then a gateway to infinity, if only because nothing, no content matter or perspective seems to be beyond the reach of fiction. David Winters in his essay collection Infinite Fictions takes this argument a step further and, quoting the American writer Gordon Lish, describes fiction as a “‘bounded infinity’ – an object which seems circumscribed on all sides, but which contains a limitless internal world” (Winters 2015: 2). As such a paradoxical container, any book spells out and opens up a world that “might exceed that outside it” (Winters 2015: 3). The pages of a book, this argument goes, contain more than the finite space between the covers may logically contain – and since storytelling conjures up concrete images this is not a result of extreme abstraction either. Fiction thus can store entities far larger than the physical space the text itself takes up.

In the following, I am focussing on a somewhat narrower understanding of ‘infinite fiction’ than suggested by Winters, namely on narrative fiction that thematises infinity. Although the infinite is not exclusively and perhaps not even primarily a mathematical concept, what Brian Rotman has to say about the presence of mathematics in literature equally holds true for any such thematisation of infinity in literature: it can occur at the content level of any fictional text, when a text is ‘about’ infinity – but it can “also, less obviously and more interestingly, enter and impinge on literature through its form” (Rotman 2011: 157). My interest in this study is above all in the latter, in fictional narratives that make the infinite an integral part of their aesthetic structure – not through the description of a large world or a possibly infinite universe, but through the thematisation, explicit or implicit, of infinity in the aesthetic form of the text so that ultimately the text itself appears to become infinite. The kind of text that achieves such a self-identification as infinite – and whose infinity is hence no longer “bounded” – is what I am calling in the following a ‘fiction of infinity’.

Beyond the questions of representation and of the aesthetics of the infinite such fictions of infinity must inevitably pose, by thematising infinity they are also invested in another property of the infinite: its tendency to challenge, and even overawe, our thought. Among the many attempts by various philosophers at approaching the infinite, my focus will be on the key role infinity takes in the work of Emmanuel Levinas, who can be considered one of the foremost thinkers in the field of ethics in the twentieth century and whose works have proved a crucial influence on the so-called ethical turn in literary theory (see e. g. Madison and Fairbairn 1999; Critchley 2002; Womack 2015). For Levinas, infinity is closely connected to the radically unknowable other and it is in the encounter with others that, because of their very otherness, an ethical demand is imposed on us. Alterity, and hence infinity, is therefore central to Levinasian ethics. If there is a connection between infinity and ethics that stems from the way in which we, as thinkers, readers or human beings in general, approach the infinite (or fail in this approach), then this should also be traceable when infinity becomes textual in fictions of infinity and so endow these texts with an ethical dimension.

It is thus the aim of this book to answer the question of how and why fictions of infinity become infinite, that is, to analyse the aesthetic properties that may endow a text with infinity as well as their function. My claim is (1) that certain aesthetic configurations of narrative texts have the capacity to endow texts with infinity; (2) that a central function of the infinite in such contemporary fictions of infinity is the breaking open of both ontological and epistemological certitude; and (3) that as a consequence these texts attain a forceful ethical dimension. I want to show that readers may understand texts as infinite entities due to a conceptual metaphor identified by George Lakoff and Rafael E. Núñez (2000), the Basic Metaphor of Infinity. Such infinite texts are necessarily paradoxical, both because their physical extensions remain finite and because an infinite text inevitably transcends itself, challenging established notions of understanding and interpretation. It is in this latter sense that fictions of infinity reveal their ethical potential in the context of Levinas’s ethics of alterity: in their textual self-transcendence they develop a disruptive potential and may thus function as ethical appeals to their readers. This will be illustrated in detailed readings of four novels I consider exemplary fictions of infinity: David Mitchell’s Cloud Atlas (2004), Jeanette Winterson’s The Stone Gods (2007), Ian McEwan’s Saturday (2005) and John Banville’s The Infinities[a] (2009). All four novels in their own different ways create infinite texts in which textual infinity is complexly coupled with an ethical forcefulness these texts attain.

1.1 Properties and History of the Infinite: A Brief Overview

Before turning to these examples of fictions of infinity, a brief overview of the history of the infinite in mathematics, theology, philosophy and the arts seems helpful to begin with, since such an overview makes it possible to trace some of the key properties of the infinite and ways in which these properties have preoccupied humankind over the past several millennia.¹ The two properties of infinity that will prove most important to my study of the ways in which infinity may appear as an aesthetic feature in literature and of what impact such fictions of infinity may have on readers are the following:

1. The infinite is beset by paradox and resists, or at least challenges, human understanding.
2. As a result, infinity likewise resists its own representation, at least where this representation is anything else but highly abstract.

It seems clear that these two properties (and certainly representation and understanding in general) are closely connected – for all practical purposes, when it comes to literature, an art form rooted in representation, they imply each other. As a consequence, both have influenced the ways in which infinity has been thought and talked about and both continue to influence the ways in which texts approach the infinite and, not least, in which we as readers approach such texts.

Attempting a definition of the infinite is in itself a difficult endeavour in the first place, since any definition is, as Wolfgang Schoberth observes, a demarcation and so imposes a boundary on the concept defined (2016: 85) – a definition of the infinite deprives it of infinity (the first and in many ways central of plenty of paradoxes of the infinite), or, conversely, the definite is also finite. There is, in this view, no meta-level at which infinity may be safely contained. Bernhard Waldenfels has described this as the ‘basic aporia’ of infinity: how is it possible to think infinity without rendering it finite?² Rather, infinity is fundamentally at odds with our – necessarily finite – experience of infinity, resulting in an antagonism between what we experience (the infinite) and how we experience it (Waldenfels 2012: 53).

It is little wonder, therefore, that most properties that are commonly associated with the infinite are themselves negative properties, characterised by the absence of boundaries. The infinite is endless, unbounded, or unlimited. Beyond this endlessness, the mathematician and writer Rudy Rucker names “indefiniteness and inconceivability” as key characteristics of infinity (1982: 1) and so adds two further defining aspects that are likewise marked by absence. Infinity, at least as far as an everyday understanding of the term goes, primarily is not. Indeed, in many languages, the morphology of the word for infinity implies a definition ex negativo of the concept behind it: that which encompasses all there is (and more) within the logic of language is understood as not that which is finite or bounded, the in-finite, l’in-fini, das Un-endliche, in-finitum, to a-peiron, etc. (see Hart 2011: 255).³ Since conceptualising the absence of a quality necessarily is less concrete than conceptualising its (physical) presence, this negative understanding of the infinite is already an abstraction of sorts and therefore indicates a difficulty with conceptualising infinity as a ‘thing’ – a problem that surfaces time and again in the history of thinking about the infinite.

It is curious that infinity should be so elusive to the grasp and so mired in negativity of expression although it is – quite literally – ubiquitous. Infinity surrounds us in many guises: There is the infinity of numbers in mathematics, where a largest countable number does not exist – in trying to count to infinity, “we run out of names before we run out of numbers” (Stewart 2017: 22). There is the infinity of time, eternity, as well as that of space (or the universe) – and the actual physical existence of both is open to debate. Conversely, there is infinity in divisibility, resulting in the infinitely small or infinitesimal. Blaise Pascal in one of the fragments in his Pensées even describes all of nature as “an infinite sphere, the centre of which is everywhere, the circumference nowhere” (1958: 16; II.72). This adds a spiritual or religious dimension to infinity, since Pascal takes this hypostasised infinity of nature to be a proof of God’s grandeur. Despite this omnipresence of the infinite, its exact nature does not become any clearer.

While this curious case of the elusiveness of the infinite is closely linked to the problem of its representation – as evidenced in the negative linguistic concepts for infinity – the reason for this elusiveness seems to be that infinity is associated with a number of self-contradictory and seemingly incongruous features that make it difficult to pin down a clearly delineated notion of infinity. On the one hand, the infinite is tied up with various logical paradoxes and challenges to understanding that have been discussed by mathematicians and philosophers alike.⁴ On the other hand, and more pertinent to fictions of infinity, as Ian Stewart stresses, “infinity is paradoxical” (2017: 1).⁵ There is a paradox at the heart of the infinite, then, and this paradox is engendered by our attempts to grasp the phenomenon. Writing about infinity, David Foster Wallace has pointed out that “[i]t is in areas like math and metaphysics that we encounter one of the average human mind’s weirdest attributes. This is the ability to conceive of things that we cannot, strictly speaking, conceive of” (2010: 22). Thinking something that cannot be measured means attempting to apply a framework of reason to something that exceeds this framework; it means to “think the unthinkable” (Clegg 2003) – this is the aporia of the infinite.⁶

It is this underlying aporia that perhaps best explains – and the notion that an aporia might explain something is just another paradox – the way in which humans have reacted to infinity. Rudolf Freiburg asserts that there is a “dialectics of fascination and fear” inherent in any encounter with the infinite – a fascination with the grandeur of the infinite and a fear at being dwarfed and rendered insignificant in comparison (2016: 7 – 8, my trans.; see also Waldenfels 2008: 4 – 8). In evidence of this claim, Freiburg quotes Pascal:

Car enfin qu’est-ce que l’homme dans la nature? Un néant à l’égard de l’infini, un tout à l’égard du néant, un milieu entre rien et tout. Infiniment éloigné de comprendre les extrêmes, la fin des choses et leur principe sont pour lui invinciblement cachés dans un secret impénétrable, également incapable de voir le néant d’où il est tiré, et l’infini où il est englouti. (Pascal 1976: 66; qtd. in Freiburg 2016: 7)⁷

Although the infinite is infinitely beyond human understanding, an “impenetrable secret”, Pascal writes, it ‘swallows up’ humans. This is why the infinite impacts on humans in this duplicitous way: like a secret or riddle that cannot be solved it provokes curiosity, interest or fascination; like the unknown often does, it may also provoke fear in the beholder.

These qualities of the infinite – the difficulty of representing it or defining it in any other way than ex negativo, its multi-faceted and inherently aporetic nature and the frequently ambivalent reaction to it – have all shaped the way infinity has been thought and spoken about, as the following short, and again necessarily eclectic, overview of the history of thinking infinity will show.

Most accounts of the history of the infinite begin with the Pre-Socratic philosophers of the seventh and sixth centuries BCE. Theirs is the first systematic, scientific approach to the infinite, but thinking about infinity goes further back and can be traced in myths from India and Iran of the second millennium BCE, which tell the story of a battle between the finite and the infinite (see Vilenkin 1995: 1 – 2). These myths in fact form the basis from which the Greek Pre-Socratic philosopher Anaximander’s notion of the apeiron, the ‘unbounded’, is derived (Vilenkin 1995: 2; for a thorough discussion of Anaximander’s apeiron see Gregory 2016: 85 – 102). As the chaotic, uncontrollable source of all being, “apeiron need not only mean infinitely large, but can also mean totally disordered, infinitely complex, subject to no finite determination” and as a result of this disorderly quality it was by later Greek thinkers mostly considered a “negative, even pejorative, word” (Rucker 1982: 3, 2). The reason is that in classical Greek thought – particularly for the Pythagoreans, who believed that the entire world could be described with proportions of whole numbers, but also for Plato – the finite and definite, in the sense of a “finite perfection” or “perfect unity” (Badiou 2011), was seen as a governing principle and associated with the good. The apeiron, of course, is almost the exact opposite of such rational order and as a consequence, where it interferes with rational determination and the commensurability of actions (e. g. when it leads into infinite regress), the infinite is considered ‘bad’, as opposed to (ethically) good finitude (see Waldenfels 2008: 5).⁸

This notion of a ‘bad’ infinity is also behind the most influential position on infinity in classical antiquity: Aristotle’s distinction in his Physics between ‘potential’ and ‘actual’ infinity shaped mathematical and philosophical thought on the infinite over the following centuries. Interestingly, for Aristotle, the question of infinity is one of (modes of) being and hence an ontological one.⁹ First he considers whether infinity can be an actual thing that may exist in nature and firmly rules out the existence of an infinite body in actuality (see 1961: 49 – 52; 204a8 – 206a8; for a summary of the argument, see Jori 2010: 17 – 23). However, he concedes that the infinite must exist in potentiality. In this potential sense it has “the kind of being which a day has […], the kind of being which does not belong to a concrete primary being that has come into being, but the kind of being which consists in continually coming to be and passing away, which is finite on each occasion, but which even so is different” (1961: 53; 206a 32 – 36). This potential infinity has then the character of a process that attains infinity ‘by implication’. The most accessible example of this potentiality of the infinite is the counting of integers: each integer is finite and there is no largest number, since in counting upwards a new, larger integer is created by simply adding one to any hitherto ‘largest’ integer. As a process, this could go on forever and hence the sequence of integers is infinite; yet it is also finite in every step – as soon as the process of counting stops, the result is a finite number, if possibly a very large one.¹⁰ As in the process of ‘adding one’, potential infinity thus depends on the possibility of always finding a next item, on a principal unendingness, and so is an early example of thinking the infinite ex negativo. Since this is the only kind of infinity whose existence Aristotle accepts, infinity then is perpetually deferred into a potentiality. Crucially, for Aristotle the potentiality of the infinite is itself different f...

Table of contents

• Title Page
• Copyright
• Contents
• List of Abbreviations
• 1 Introduction: Towards Infinity
• 2 Narrative Infinity: Aesthetics and Conceptualisation
• 3 Levinas and the Ethical Aporia of Infinity
• 4 Infinitely Encountering the Ineffable: David Mitchell’s Cloud Atlas
• 5 Infinitely Repeating: Jeanette Winterson’s The Stone Gods
• 6 Infinite Intertextuality: Encountering Alterity in Ian McEwan’s Saturday
• 7 Infinite Perspective: John Banville’s The Infinities
• 8 Coda: And Beyond?
• Index