Accounting in the Absence of Numbers

  • Vassili Joannidès de Lautour


This chapter rests upon Badiou’s Number Theory to question management accounting’s alleged mathematical roots and tools. It is shown that long-expressed academic concerns about the failure of financial reports to capture the performance of the entities they claim to portray have gained practical and political significance over years. Allegations were made not only that financial reports did not portray financial realities, but also that they actually contributed to the crisis. This chapter demonstrates that the accounting numbers contained in management accounting reports in their present form can never capture the economic activity they purport to portray, because they do not have the mathematical properties of numbers. This understanding of numbers highlights the significance of this for the future of management accounting.

Accounting standard setters identify faithful representation of economic phenomena as a key characteristic in the production of financial information (IFRS, 2010). However, critical accounting literature acknowledges the falsity of claims about “the representational accuracy of [accounting] numbers” (Robson, 1992), i.e. the failure of these numbers to represent the “real world” (Richard, 2014). There is general agreement that accounting numbers are socially constructed and therefore cannot have an objective and universal acceptance (McKernan, 2007; Miller, 1992), although they have calculative power (Hoskin & Macve, 1994; Miller & O’Leary, 1987; Palea, 2014). Relatedly, they are contestable and contested (Tinker, 2001). The deficiencies of accounting numbers result in representational failures (Robson, 1992; Sterling, 1988), enable entities to obscure unpleasant realities behind the numbers (Chwastiak & Lehman, 2008; Funnell, 1998) and conceal outright manipulation and fraud (Briloff, 2001; Lee, 2006).

Whilst researchers identify the shortcomings of the accounting numbers presented in financial reports (see, for example, Alexander & Archer, 2003; Bougen & Young, 2012; Robson, 1992), what is missing from the recent debate is a deep understanding of the ontology of accounting numbers and related foundational measurement principles (Stevens, 1946) that was evident in earlier work (see, for example, AAA, 1971a, 1971b, 1971c; Mattessich, 1964; Sterling, 1988). Much accounting research treats accounting figures as numbers on which mathematical operations can be performed, but never questions whether accounting numbers are in fact numbers. The ramifications of these deficiencies are highlighted in times of recurring economic and accounting crises, corporate collapses and regulatory responses, as epitomised by the Global Financial Crisis (GFC) of 2008–2009 and its aftermath (Joannidès & McKernan, 2015).

As accounting numbers assume the objectivity and rhetorical power of mathematics, their ontology needs to be informed with insights from mathematics theory. Yet, despite earlier attempts to define measurement scientifically (AAA, 1971a, 1971b, 1971c; Chambers, 1996; Mattessich, 1964, 1995a, 1995b, 2003), interpretive accounting researchers and accounting standard setters have moved away from normative, mathematical conceptions of measurement, calculations and accounting numbers to take a socially constructed user-centric view of how measurement methods are to be chosen (IFRS, 2010, 2013; Robson, 1992). These approaches neglect questions about the essence, meaning, procedures and material laws of measurement that produce the numbers that dominate all aspects of social life. In investigating those questions, we address a gap in accounting scholarship.

Since the early twentieth century, mathematics researchers have engaged in theorising numbers and developed what Modern Mathematics calls Number Theory (Frege, Dedekind, Cantor, Peano, Zermello, Neumann). We build on the synthesis of Number Theory offered by Badiou (2007a, 2007b, 2008, 2009a, 2009b) to address the twofold purpose of this paper. First, we enhance our understanding of the flaws of accounting numbers, as identified in the critical accounting literature (Cooper & Hopper, 1987, 1991, 2007). We show that what accounting uses as its raw material are not numbers but mere ciphers, which can never capture the behaviour, activity and performance they claim to portray. Consequently, the operations performed on these accounting numbers, being based on non-numbers, cannot offer mathematical authority. Second, we highlight the significance of this view of accounting numbers for the future of financial reporting, considering both what is included in the portrayal of an economic entity’s value and the way that value is measured and communicated.

In the conclusion of his book Number and Numbers, Alain Badiou (2008) denounces the reign of Number. This is consistent with the assumption that more and more accurate numbers are the ultimate goal of accounting. Putting everything and anything into numbers leads us eventually to question what Number is, stressing a paradox: “we live in the era of number’s despotism; thought yields to the law of denumerable multiplicities; and yet […] we have at our disposal no recent, active idea of what number is” (Badiou, 2008, p. 1). This is evident in accounting research which does not question the ontology of numbers, the measurement principles by which accounting numbers are derived, or their social implications. In contrast, alternative research identifies the “misleading clarity” of accounting numbers (DeMaria Harney, 2011), the governing power of numbers (Barney & Flesher, 1994; Potter, 2005), the way accounting numbers assist in dehumanisation and exploitation (Chwastiak & Lehman, 2008; Funnell, 1998) and the power of numbers to determine a reality on which people act (Hines, 1988; Rose, 1991).

Therefore, beyond the enhanced philosophical understanding of what number and calculations are, this paper contributes to knowledge by bringing mathematical thought and philosophy back into accounting research. In discussing the ontology of numbers and calculations and demonstrating the potency of mathematical theory for accounting research, we agree with Badiou’s (2007a, 2009a) provoking proposition that mathematics is the science of being, and initiate a discussion that has not been introduced to accounting scholarship to date. Our second contribution is to identify the accounting standard setting implications that flow from a heightened understanding of what accounting numbers are and are not. This is particularly relevant as the 2013 Review of the Conceptual Framework for Financial Reporting (IFRS, 2013) included an extensive section on Measurement, with the objective of contributing to “the faithful representation of relevant information” (IFRS, pp. 11, 106). This reinforces the fundamental importance of an understanding of the measurement processes by which accounting numbers are derived.

The next section of the paper briefly reviews the literature identifying number as an organising system with calculative power. Following this, the essence of Badiou’s Number Theory is presented and then applied to accounting. Based on this conception, we identify accounting numbers that are presented in financial reports as mere ciphers or representations of a number that cannot capture its matter or form. Furthermore, the more precise the accounting numbers are, the further removed they are from the wider social and political world of which they are a part, and the less they represent what they claim to portray. In the light of Number Theory, and using Badiou’s concept of worlds, we then explore the standard setting policy implications of this conception of accounting numbers. Concluding comments point to areas of future research based on the acknowledgment that “only when we grasp the ‘substance or reality behind our accounting numbers can we fully appreciate what accounting measures can do for us and what they cannot do” (Mattessich, 1995a, p. 50).

1 Towards the Ontology of Number?

Critical accounting scholars denounce the profusion of numbers and a trend to the ‘accountingisation’ of society (Kraus, 2012; Kurunmäki, 2004; Lapsley, 1998; Power & Laughlin, 1992). They acknowledge the social construction of accounting numbers and their contestability, highlighting three facets of the power of accounting numbers. Whilst they commonly agree on numbers’ oppressive power, some insist on their rhetorical power and others call their ethical potency into question.

1.1 The Oppressive Power of Accounting Numbers

Borrowing from the social sciences and humanities, accounting scholars have emphasised the appearance and evolutions of calculations which are used to justified decisions on economic grounds. This is first brought to light in the critical accounting literature in a review of André Gorz’s book Critique of economic reason (Power, 1992). Power (1992) critiques this book on the grounds it over-relies on the fundamentally flawed and simplistic assumptions of neoclassical economics and related calculations. Explicitly building on that critique, accounting research has traced the genealogy of calculations, arguing the history of appearance of four calculative technologies and their expansion from these four settings to the corporate world at large through the power of the discourses associated with them (Miller & Napier, 1993). These are the development of Discounted Cash Flows (DCF) calculations, the recording of costs, Economic Value Added (EVA) and standard costing.

Subsequent to these two critical accounting publications, accounting scholars have discussed the way discourses associated with calculations have so fashioned the self as a calculative self that its conduct and actions are now subordinated to those operations (Miller, 1992, 1997; Miller & Napier, 1993; Miller & O’Leary, 1987; Miller & Rose, 1990). By way of example, in some more specific settings, such as public sector hospitals, calculations transform medical staff into something they are not, i.e. requiring them to act as managers or accountants producing accounting numbers (Brunsson, Lapsley, & Miller, 1998; Kurunmäki & Miller, 2006; Miller, Kurunmäki, & O’Leary, 2008). In contexts with which accounting is not usually associated, such as prisons (Andrew, 2007) or churches (Joannidès, 2012), decisions are made and justified through reliance on accounting metrics of all sorts.

Following Miller and Rose’s (1990) idea that calculations govern life beyond economic relationships, the power relationships raised by calculations have been studied from a Foucauldian viewpoint (Vollmer, 2003). Research has demonstrated that the rise of calculations has contributed to the creation of institutions where people, especially minorities or indigenous people (Alawattage & Wickramasinghe, 2009a, 2009b; Wickramasinghe, Hopper, & Rathnasiri, 2004), find themselves dominated or oppressed by those who can add, subtract, multiply or divide (Alawattage, 2011; Hoskin & Macve, 1986, 1988; Jayasinghe & Wickramasinghe, 2007), In an extension of the calculative power of numbers, calculative operations have been shown to discipline the day-to-day conduct of people beyond economic transactions (Joannidès, 2012; Quattrone, 2004, 2009). In sum, these approaches portray accounting numbers as political objects (Townley, 1995).

1.2 The Rhetorical Power of Accounting Numbers

Number is commonly apprehended as the language of economics, business and organisational life. By determining what number is acceptable in certain situations, those who demand it create the social order, deciding what is right, what is wrong, what is worthy and what is not and consequently what deserves to be measured. As such, number has a performative capacity: it constructs the social and its values (Ezzamel, 2009; Robson, 1992, 1999). Number then becomes a manifestation of the right to produce knowledge and therefore has power to enrol others. To this end, “heroic efforts continue and the measurement of individual and organizational performance is always being imagined and re-imagined by politicians, policy makers and managers, irrespective of the availability of technologies and instruments” (Power, 2004, p. 768). Studies informed by Actor Network Theory have presented number as a non-human actor capable of creating the world by acting at a distance: contemporary organisations no longer need foremen and supervisors, since number suffices (Christensen, 2004; Quattrone & Hopper, 2001, 2005; Robson, 1992). Number sets the agenda, determines the parameters by which performance is judged and compels behaviour (Miller, 2008; Rose & Miller, 1992).

Conversely, we also know of the legitimising power of numbers, i.e. how producing one’s number enacts the social by providing the ultimate legitimation of conduct. Such a number can be what results from value creation for stockholders (Burchell, Clubb, & Hopwood, 1985), EVA (Miller & Napier, 1993) or other measures of value. Beyond mere economic matters, the legitimating role of number has been highlighted in the way an organisation chooses what to count and uses numerical representation to support its image or to strengthen its bargaining position with a third party (Agyemang & Lehman, 2013; Cho & Patten, 2013; Craig & Amernic, 2008).

These interpretations of the role of number have led to warnings against reducing accounting to the assumed objectivity, rationality and neutrality of the figures it produces (Broadbent, Gill, & Laughlin, 2008; Chua, 1996; Cowton, 1999; Power, 1992; Townley, 1995). In critical accounting research, it is well established that as a social practice, the making of number is the offshoot of discussions, compromises and struggles and therefore a number itself is neither objective nor neutral (McKernan, 2007; Miller, 1992). Such a contention has led to the emergence of a stream of thoughts focusing on the rhetorical nature of number: being part of a language, accounting numbers are inscriptions that follow scriptural and grammatical rules that accountants accept (Chua, 1995; Crowther & Hosking, 2005; Mouritsen, 2011; Mouritsen, Hansen, & Hansen, 2009; Quattrone, 2009; Robson, 1992). As such, number is presented as a powerful rhetorical device used to enrol a broad audience of devotees through its capability of rendering visible and memorisable what would otherwise be invisible (Quattrone, 2009). In an organisational context, accounting numbers give visibility to, and claim to represent, innovations (Alcouffe, Berland, & Levant, 2008; Mouritsen et al., 2009) or intangible assets (Power, 2001).

1.3 The Ethical Power of Accounting Numbers

A Lévinassian approach to accounting has reasoned that Number is the expression of how I perceive the Other as a mirror of who I am as an ontological self, therefore producing and reflecting a number that claims to represent value but also helps me to construct myself as a self by reflecting what I can see in the eye of the Other (MacIntosh, Shearer, & Riccaboni, 2009; Shearer, 2002). The number I produce is addressed to this Other who I deem capable of understanding it as I would. I discover myself as a human being through the process of producing a number directed at the Other, by which I become an accountable self.

This introspection about oneself, made possible by the production of a number, introduces a psychoanalytical dimension to number’s ontology and as evident in the quest for intelligent accountability and the limits of transparency or accountability. Producing a number is limited by my capability to reflect about myself and quantify all my actions (Joannidès, 2012; Messner, 2009; Roberts, 2009). Even if I were able to produce such a number, I would not have the guarantee that the Other would understand it in the same way I do.

Although the notion of these operations is sometimes addressed, their mathematical nature remains a mystery to us, leaving unanswered questions: what is Number; what is the point of adding, subtracting, dividing and multiplying and what does it mean; and what is the object of such operations? This is where Alain Badiou’s Number Theory will help us enhance our understanding of accounting’s core procedures in arriving at numbers and generally translating them into monetary terms.

2 Badiou’s Number Theory and Its Relevance to Accounting Research

Since the 1960s, Badiou’s (2007a, 2007b, 2008, 2009a, 2009b) philosophy has been driven by his desire to understand what Number is. Central to his argument is that we think we produce a true and objective Number because we are using mathematics but what we are doing has little to do with mathematics. Instead, we produce what he calls ciphers that at best selectively reflect the ideology of the time. As such, these ciphers are an expression of a phenomenon but not of the numenon.1 For Badiou, mathematics is inextricably linked with every aspect of being, transcending our usual understanding of its relevance or applicability (Badiou, 2007a). Badiou confronts us with the idea that mathematics orders the world, starting from language where the subject is defined as a (person) or one. That is, it is impossible to conceive of the world without mathematics. He demonstrates this by identifying four worlds (love, arts, science and politics) in which number is not usually envisaged as being relevant, and crucially identifies Number as the end point of the succession of sets and sub-sets that apply to all these worlds (Badiou, 2009a, 2009b). Staying focused on accounting, an area in which number is usually envisaged as being relevant, we extend his thought to the economic world which critical accounting research identifies as derived from (or a sub-set of) the world of politics (Miller, 1992; Palea, 2014; Rose & Miller, 1992). Under this purview, we explore the conceptual building blocks of Number, identifying its ontological qualifications and the distinction between its ontology and expression.

2.1 Ontological Qualifications of Number and Sets

It is commonly accepted that numbers are used to name (nominal), order (ordinals) or count (cardinals), with ordering occurring after numbers have already been defined and counted. For instance, nominals, e.g. the number assigned to a player on a football team, are not the concern of accounting. This is the belief Badiou (2008) is confronting, arguing that mathematical logic is exactly the opposite: a cardinal number is the end product of the four basic operations (addition, subtraction, multiplication and division) that order sets (Badiou, 2007b), from a single set that is an entire world (the largest set, whose limits are zero and infinity) (Badiou, 2008), to the most narrowly limited set (the smallest set) expressed as a single cardinal number. Thus, counterintuitively, a cardinal number is the extension of a series of ordinals, as the sets are ordered successively to the point where the upper and lower boundaries of the set coalesce, and a single cardinal number is identified: as a number is always the representation of an order and a place within that order, it cannot be considered in isolation from the world mathematics calls a set (Badiou, 2007a, pp. 53, 178–190; 2009a, p. 104).

Given that the limits of the set within its world, being infinity or zero, are beyond human understanding, the cardinal number so produced is also beyond human understanding, since it is an abstraction whose world or origin is at best implicit, and most likely lost (Badiou, 2008). Infinity being impossible to grasp for human understanding, it is itself bounded through multiple derivations, with the result that “the numbers that we manipulate are only a tiny deduction from the infinite profusion of Being in Number” (Badiou, 2008, p. 211). This poses an a priori unresolved contradiction: the smaller the sub-set is, the more intelligible its extractions appear but at the same time the further removed it is from the largest set of which it is a part, and consequently the less intelligible it really is (Badiou, 2007a, p. 131). The closer we come to the single cardinal number, the more removed we are from the larger set and hence our ability to understand the limitations of the single number as a descriptor of the larger set. Figure 1 portrays out interpretation of this concept for the four worlds Badiou (2009a) identifies.
Fig. 1

Worlds, sets and numbers

Belonging to the same set, two cardinals can be ordered (first, second, etc.) and compared (greater or smaller) but not if they were extracted from different sets (or worlds, as portrayed in Fig. 1. Thus, for example, length of relationship in years is an attempt to portray the quality of a relationship. It cannot be compared with temperature, which measures how hot something is. Based on this logic, there are two inconceivable responses. First, it would be inappropriate that the world of love (or arts, science or politics) could be captured in a single cardinal number. Hence, it would obviously be futile to rely on the number of years of a relationship to capture the world of love, of the age of a painting to portray art, of temperature to express science or of the number of votes to reflect the political world. These numbers would not be seen as representative of the entire world to which they belonged. Equally, it would be inconceivable that one accounting number could alone represent the entire value of an entity with its own unique characteristics.

Second, it would be inconceivable to perform operations across the cardinal numbers that were produced from these four worlds, i.e. to compare the single cardinal that purported to express the world of love with the single cardinal that expresses another world (arts, science or politics). If we apply this concept to accounting, we must acknowledge that to compare the values of disparate entities is fundamentally flawed, according to Badiou’s notion of sets. An accounting number therefore has no existence as a number, unless the actual set to which it belongs is known (Badiou, 2007a, pp. 64, 81–92; 2009a, p. 105). If this cardinal number happens to belong to a different set, it only exists within this one set and remains counted as nil in all other sets (Badiou, 2007b). This sheds light on fundamental problems in accounting’s use of numbers. Accounting does the inconceivable, by purporting to make entities comparable through the cardinal “numbers” it produces and expresses in monetary terms. This is evidenced in the IFRS project whose goal is to produce high-quality, comparable accounting information irrespective of differences contingency researchers identify between industry or sector, country or culture, age or size (Bhimani, Gosselin, & Ncube, 2005; Chenhall, 2003; Garengo & Bititci, 2007; Otley, 1980). Abstracted and disconnected from the world they claim to represent, these quantities are presented as concrete and are compared and ordered. For instance, the accounting number for total assets is the sum of tangible and intangible, current and non-current assets, as though these accounting numbers were numbers derived from the same set, which they are not. Furthermore, different measurements are applied to these various categories of assets, some measured according to fair value principles, and others using historical cost or alternate values (Bougen & Young, 2012; Ishikawa, 2005; Palea, 2014). In accounting, this summing of items from different sets is in conflict with Badiou’s notion of sets and represents a trade-off between the desired precision of a single accounting number and our understanding of what that number represents (Power, 2004).

2.2 Number or Cipher? Matter, Form and Residue

Badiou (2008) reasons that the properties of number (matter and form) must be clearly understood, since a cardinal is extracted as the end product of a succession of ordered sets with narrower and narrower limits. Matter is the largest set (the world) to which a number belongs, whilst Form is its position within this set: a number n is characterised by this pairing and can be expressed as n = [M(n), F(n)], where M is matter and F is Form. We can take as an example the numbering of section headings in this paper as 3.1, where 3 is the matter, i.e. Section 3 (Badiou’s Number Theory), and 3.1 is the form, i.e. first subsection in this section (set) (Numbers: sets and sub-sets). At the same time, this section is a lesser set belonging to the paper with P (for paper) as matter and 3 as form, i.e. its position within the set. There is thus a succession of ordered sets, from the largest to the smallest.

These larger properties of Number tend too often to be ignored or neglected so that the number produced is in fact not a number but rather what he describes as a cipher or residue. Badiou identifies this residue as Number’s third property, which claims to represent number, but does not. Thus, what we commonly think of as numbers are merely residues or ciphers “which serve to designate multiples fabricated” from a set (Badiou, 2008, p. 95). These three components of mathematics (matter, form and residue) are, to Badiou, mathematics as ontology, and therefore characterise the entire world. In accounting, what we understand as accounting numbers are, in Badiou’s terms, ciphers or residues, which can never portray the world to which they belong, as they cannot capture its matter and form.

Thus, the single cardinal numbers portrayed in Fig. 1, being the smallest intelligible sets, must be seen in the context of the matter and form from which they have been extracted. The more precise the number is, the smaller the set to which it belongs. Consequently, matter and form tend to be associated, not with the larger world but with the smallest set. If two numbers have the same form but different matters, they are from different sets, subject to different rules and cannot be compared or assembled by order of calculative operations (Badiou, 2008, p. 116). The existence of more than one cipher or residue for a supposedly similar matter is the manifestation of ideologies hiding behind purportedly scientific models and methods, so that having two representations of the same matter means that the model has failed to eventually capture it (Badiou, 2007b). As a result, the number produced is a cipher, a proxy disconnected from the world it purports to represent, privileging comparability over understandability and faithful representation.

This problem is evident in accounting research, for instance, when audit quality, which we cannot conceive of, is represented in monetary terms through audit fees (Bartlett, 1993; Pasewark, Shockley, & Wilkerson, 1995), or in cultural studies where Hofstede’s abstract dimensions are assigned numerical values (Alawattage, Hopper, & Wickramasinghe, 2007; Baskerville, 2003; Wickramasinghe & Hopper, 2005; Wickramasinghe et al., 2004). As accounting research has evolved over the last few decades, earlier discussions about the nature of measurement and its scientific basis (Chambers, 1996; Mattessich, 1964, 1995b) appear to have been neglected, with accounting numbers assumed to have the properties of numbers on which operations can be performed, and promoted as faithfully representing economic reality. Thus, the mathematical origins of measurement have been neglected in recent work on the Conceptual Framework for example (IFRS, 2013, 2014a, 2014b), stifling awareness of the limits of accounting numbers and of their calculative and governing power.

Badiou (2009a) argues that matter, form and residue, the three attributes of Number, apply in the same terms to the four worlds he has identified. Table 1 summarises this approach to the logics of Number and worlds, expanding Badiou’s conception into matter, form and residue. The respective matters of the four worlds identified by Badiou are the public sphere of Politics, the reality and aesthetic nature of the Arts, agape, philia, eros and storge as expressions of Love, and the nature and understanding of the physical world through Science. Their respective forms lie in the characteristics that depict them: political philosophies and ideologies, artistic expressions, declarations of love and scientific disciplines. The residue of Number is a cipher, and, similarly, the residue of the other worlds is a visible representation that captures neither their matter nor their form: political laws and regulations, artistic artefacts, symbols of love and scientific models, theorems and formulae.

An example illustrates this. From the Arts world, take two artistic artefacts. Both are painted between 1503 and 1519, both are oil on wood, both are of similar dimensions (77 cm × 53 cm), and both are portraits of a young woman, with a hilly, misty landscape in the background. The woman wears a dark silk robe, with a transparent black veil over her head and an enigmatic smile. In their form they are identical. However, in their matter they are entirely different, as one was painted by Leonardo da Vinci, and the other by his apprentice, Francesco Melzi. The painting by Leonardo was one of his latest works, an aesthetic masterpiece, whilst for Melzi it was a study painted after his master’s work. The two artefacts are therefore not two. They cannot be summed in the same collection or set as two paintings. They are both residues, with similar forms, but have a different matter, and hence are separate items in separate sets, disconnected from their matter and form. Each must therefore be counted as one.

This has direct applicability to what are presented as accounting numbers, which we propose are mere ciphers without matter and form. At present, it is acknowledged that “under existing requirements the amount presented as total net assets has little meaning because it is an aggregation of items measured using various different measurements” (IFRS Foundation, 2013, p. 108), but no consideration is given to the fact that in addition to this failing, the accounting numbers assigned to various assets fail to capture their matter and form. Hence, the claim that measuring all assets on the same basis would result in greater comparability is fundamentally flawed, as is the contention that the mode of measurement should depend on its relevance to financial report users (IFRS Foundation, 2013). Thus, accounting numbers, presented as intelligible numbers, are unintelligible because of their false inclusion in the same set. They are rendered even more unintelligible because they are far removed from the wider political world from which they are extracted.

The purpose of this paper is not comprehensively to devise Number Theory. Rather, we have applied Number Theory to address the first purpose of our paper, by demonstrating that accounting ‘numbers’ are merely ciphers which do not have the mathematical properties of numbers. We now address the second purpose of our paper, which is to highlight the significance of these mathematical insights for the future of measurement and numbers in financial reporting. In order to substantiate our argument, we focus on the political world which critical scholars recognise as the world in which accounting operates (Armstrong, 1987, 2006; Hopper & Armstrong, 1991; Tinker, 1980, 1988; Tinker, Merino, & Neimark, 1982).

3 Number Theory and the Possibilities of Accounting Numbers

Figure 2 expands Table 1 by providing a visual summary of our application of Badiou’s world of politics (as portrayed in Fig. 1) to apprehend accounting numbers. These ‘numbers’ represent the ultimate reduction of the world of politics through the successive reduction of sets and sub-sets comprising the economy, economic units and accounts. Each smaller sub-set is derived from the form of the larger set to which it belongs, but accounts are derived from the residue of the economic units’ sub-set (Fig. 3).
Fig. 2

Ontological worlds (adapted from Badiou, 2009a)

Fig. 3

Deriving accounts

Within the world of politics, the matter can be interpreted as the public sphere (Arendt, 1961). It is expressed through ideas, debates, ideologies and philosophies whose representation in society appears as laws, regulations and policies. Different forms in this world conceivably lead to different sub-sets such as political institutions, activism, education or the economy (Sen, 1990). For the purpose of this paper, we focus on the economy which allegedly has accounting as a natural offspring (Miller & O’Leary, 2007; Miller & Rose, 1990), and which Badiou (2009a) explicitly identifies as a sub-set of the political world. According to economists, the economy’s matter is the allocation of scarce resources, evident in the form of various economic units, which constitute a new sub-set. The economy is represented through a residue of expressions: wealth, happiness and welfare, for example (Allais, 1945, 1954a, 1954b, 1971; Arrow, 1971; Debreu, 1951, 1959, 1991; Elam & Arrow, 1993). The matter of economic units, a further sub-set, is the creation of groupings that produce, consume and exchange goods and services. They take the form of governments, organisations and households and are portrayed through various accounts (Williamson, 1979, 1985).

Extending Badiou’s concepts, we identify these accounts as a residue of the economic units’ sub-set, which constitutes a smaller sub-set again, with its own matter, form and residue. We interpret accounting’s matter as the portrayal of an economic entity’s value and the determination of what is included in that portrayal. Accounting’s form then becomes the measurement, portrayal and communication of that value through various modes. Whatever the mode is, it is always expressed through accounting numbers, which are merely the residue of numbers as they are conceived ontologically by Badiou (2008). In financial reports, these accounting numbers are invariably expressed in financial terms, which adds another layer of complexity to the measurement process. Ultimately, the elements of financial reporting (assets, liabilities, equity, income and expenses), expressed as accounting numbers, represent the utmost reduction of economic units, and therefore of the economic and, ultimately, the (political) world.

Not only are those accounting numbers totally disconnected from the world to which they belong, but, by claiming to be numbers, they close debate, thereby denying us the opportunity to reconnect these accounts to organisations and society (Armstrong, 1998, 2006; Carter & Tinker, 2006; Hopper & Armstrong, 1991; Tinker, 1980, 1988; Tinker et al., 1982). As the end product of “administrative and managerial proceduralism”, these accounting numbers convert “qualities into quanta” (Power, 2004, p. 771). This produces the conditions for misunderstanding, ignoring or misrepresenting the activities of economic units, since “critical data that cannot be readily quantified are marginalized and rendered invisible, and proxy measures end up representing the thing itself” (Power, 2004, p. 775). Enron is the perfect example of accounting numbers which not only failed to delineate the economic entity’s matter but actively portrayed a false picture. What was known in their reports was their alleged profit. Yet, as history proves, the form by which the entity’s value was presented, i.e. financial reports, provided no idea of how the company’s profit was generated, or of how its activities were organised. The accounting numbers, as residues, ignored the existence of numerous special purpose vehicles as well as the company’s core energy trading activities. However, with the elements of the accounts measured and presented as accounting numbers, they claimed accuracy and objectivity, yet obscured or concealed the “economic substance” of the company’s activities (Baker & Hayes, 2004).

What are the implications of Badiou’s Number Theory for accounting numbers and the measurement methods by which they are derived? Is it possible within current accounting frameworks to measure the economic activities of firms so that accounting numbers are reconnected to the world from which they are derived? Our insights from Badiou, the case of Enron and the GFC, make apparent at least two fundamental inadequacies of financial reporting and the current and proposed Conceptual Framework (IFRS, 2010, 2013): the restrictions on what is included in the determination of the value of the economic entity, and how those items are measured and portrayed.

Financial reporting is restricted to a consideration of the five elements, which means that other items of relevance that could more fully portray the performance of the entity are obscured or ignored, such as workplace health and safety (Coetzee & van Staden, 2011), human rights (Cooper, Coulson, & Taylor, 2011), gender equality (Anderson-Gough, Grey, & Robson, 2005), ethnic diversity (Hammond, Clayton, & Arnold, 2009, 2012), work/life balance (Johnson, Lowe, & Reckers, 2008) or the environment (Deegan & Blomquist, 2006). The Integrated Reporting project recognises the need to include items additional to traditional financial reports in order to provide a more complete picture of entities’ operations, particularly regarding sustainability issues (Adams, 2015). However, whether it will be effective in stimulating the production of reports that provide a greater degree of connection with an entity’s actual operations has been disputed (Flower, 2014).

The way the items selected to represent the entity (or world) are measured is crucial, as in financial reports all items are expressed in monetary terms. The recently proposed Conceptual Framework measurement model (IFRS Foundation, 2013) reinforces the financialisation of accounting standard setting (Müller, 2014), suggesting that all assets and liabilities should not be measured on the same basis, with the choice of measurement model depending on its relevance to financial report users rather than to a desire to measure items in a way that most fully portrays the operations and value of the entity. Further, and more fundamentally, whilst acknowledgement has been given to the impossibility of summing diverse items, as outlined above, the measurement models proposed do not address this deficiency, ignoring earlier research on the philosophical foundations of measurement (see, for example, AAA, 1971a, 1971b, 1971c; Mattessich, 1964, 1995b). In choosing to portray economic reality as single accounting numbers (e.g. profit, assets), the philosophical and scientific dimensions of numbers are ignored and distorted.

Because accounting numbers do not have the mathematical properties of numbers, they are disconnected from their origins. We advocate an acknowledgement by standard setters that this is the case and that subsequent measurement models therefore fail to capture an entity’s unique characteristics and value. Further, we suggest that within their financial statements, entities avoid standardised or “boilerplate” disclosures (Hoogevorst, 2013) and prepare alternative accounts to supplement traditional financial reports in order to more fully portray the economic realities behind their financial accounting numbers.

4 Conclusion

We live under the reign of number and are increasingly required to demonstrate accountability through numbers, which purportedly capture the value created for stockholders or society. However, we do not know what number is, and accounting literature has not explored this. Informed by Badiou’s (2007a, 2007b, 2008, 2009a, 2009b) Number Theory borrowed from mathematics, this paper fills this void, contributing to the critical accounting literature by demonstrating the potency of mathematical theory for accounting research and suggesting this has important implications for accounting standard setters and entities.

Badiou’s approach to number reveals that mathematics, far from being merely a set of techniques, embraces the world (including politics, love, arts and science). Accordingly, it is only through genuine mathematical, abstract thinking that accounting and its political world can be reconciled. Critical accounting research acknowledges the paucity and the misleading nature of accounting numbers. We provide an ontological justification of this opinion first by showing why they are correct: accounting numbers purport to have the power of numbers but are emphatically not. Second, by advocating unique situated and alternative accounts, we emphasise the social or political dimension of accounting numbers and attempt to connect them to the wider world to which they belong.

We open up three areas for further research. First, accounting research has not tapped into mathematical theory to any extent, although its abstraction can be very insightful for our discipline’s concerns. Therefore, beyond mere Number Theory, further research could discuss the algebra, arithmetic and geometrics of accounting. This is particularly important in the light of the Conceptual Framework project and proposals about measurement, with its implications for accounting standard setting. Second, this study is to date one of the first bringing Alain Badiou’s philosophy into accounting research. As this thinker has also addressed challenging issues in ethics (Badiou, 2001, 2003), research building on these works would further our understanding of the ethical dimensions of accountability. Third, this paper iterates the importance of moving from standardised reporting to the presentation of accounting numbers situated within unique accounts and stresses the need to reconnect accounts to the economic units, the economy and the political world in which they are prepared. As research to date on the subject is very much polarised around finance and CSR-related issues, knowledge needs to be advanced beyond these disputes. By attempting this, we can challenge “the reign of the unthought slavery of numericality” (Badiou, 2008, p. 213) in the form of accounting numbers masquerading as mathematical numbers.

Consistent with Badiou’s theory of number, “with rare exceptions accounting numerals do not represent phenomena, any phenomena … there are no phenomena that correspond to most of the numerals that appear on financial statements” (Mattessich, 1995a, p. 43). Further, it is only when we “grasp the ‘substance’ or reality behind our accounting numerals [that we can] fully appreciate what accounting measures can do for us and what they cannot do” (Mattessich, 1995a, p. 50). With the critique of financial reporting numbers that followed the GFC, and with accounting at a crossroads with its Conceptual Framework project, particularly in relation to measurement, it is important to address these issues not in a formulaic way, but in a thorough and fundamental way, if financial reporting is to build and maintain credibility.


  1. 1.

    The numenon/phenomenon distinction refers to Kant’s view of ontology. According to him, it is impossible to have full access to reality (numenon). At best, one can have a partial and fractional view (phenomenon).


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Authors and Affiliations

  1. 1.Grenoble École de ManagementGrenobleFrance

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