Since William of Occam introduced his eponymous razor, there has been a distinct tendency towards ontological conservatism in philosophy. This is to say that there has been a consistent pressure to demonstrate the explanatory worth of our ontological commitments, so that we are discouraged from littering our map of the world with superfluous entities.
This perennial conservatism went largely unchallenged until Meinong’s controversial The Theory of Objects, which, as discussed above, insisted upon granting ontological status to every possible object of thought, including those that merely subsist because they do not genuinely exist (e.g., the present king of France, the largest prime number, the younger sister I never had, etc.).1 This challenge was motivated by the project of circumscribing the full range of possible intentional relations, a task that animated the Austrian school of philosophy that emerged out of Brentano’s work. However, this project was developed along divergent lines: metaphysically, by explicitly differentiating between existence and subsistence (Meinong and his successors), and phenomenologically, by explicitly bracketing questions of existence (Husserl and his successors).2 Let us call this the noetic challenge to ontological conservatism.
When the tendency toward ontological conservatism converged with the paradigm of explanatory reductionism in the twentieth century, a different response emerged, which refused to withhold existence from any entities whose features could in principle be derived from more fundamental entities (e.g., reducing economic systems to individual actors, reducing mental episodes to neurological states, reducing macroscopic objects to microscopic particles, etc.). Rather than being motivated by a particular explanatory problem such as intentionality, this response was motivated by more general concerns with explanation as such. However, these concerns were also developed along divergent lines: metaphysically, by developing a positive account of emergence in contrast to reduction (Deleuze and his allies), and methodologically, by diluting the relevant criteria of explanatory worth (Latour and his allies).3 Let us call this the anti-reductionist challenge to ontological conservatism.
More recently, a new generation of thinkers has synthesised these challenges in a way that no longer merely rejects the virtues of ontological conservatism, but actively articulates and espouses the virtues of ontological liberalism. This is to say that there has been growing pressure to reject the traditional worry about excessive ontological commitment in favour of a contemporary concern with comprehensive ontological commitment, so that we are encouraged to account for the full range of possible objects of thought, experience, and explanation. In drawing upon all of the above influences—uniting Husserl and Meinong in his account of representation,4 exploiting the homogeneity of Latour’s explanatory networks,5 and appealing to the spatio-temporal levels of DeLanda’s theory of emergence6—Harman is the paragon of this liberal synthesis. Although the banners of ‘flat ontology’ (Bhaskar and DeLanda) and ‘the democracy of objects’ (Latour) had already been raised before it, the banner of object-oriented ontology (OOO) raised by Harman and flown by others (Bryant, Bogost, and Morton) has proved to be a rallying point for those drawn to ontological liberalism, and its manifesto is contained in the opening lines of The Quadruple Object:
Instead of beginning with radical doubt, we start from naiveté. What philosophy shares with the lives of scientists, bankers, and animals is that all are concerned with objects. The exact meaning of “object” will be developed in what follows, and must include those entities that are neither physical nor even real. Along with diamonds, rope, and neutrons, objects may include armies, monsters, square circles, and leagues of real and fictitious nations. All such objects must be accounted for by ontology, not merely denounced or reduced to despicable nullities. Yet despite repeated claims by both friends and critics of my work, I have never held that all objects are “equally real.” For it is false that dragons have autonomous reality in the same manner as a telephone pole. My point is not that all objects are equally real, but that they are equally objects. It is only in a wider theory that accounts for the real and the unreal alike that pixies, nymphs, and utopias must be treated in the same terms as sailboats and atoms.7
This is the archetypical form of the demand for comprehensiveness that animates ontological liberalism. On the one hand, it deploys the favoured rhetorical device of anti-reductionism: extensive lists of objects ranging from the everyday to the extraordinary, which seem to collapse barriers between divergent explanatory registers simply by including diverse terms alongside one another.8 On the other, it invokes the vast noetic expanse of the Austrian school: menageries of fantasms and fictions whose lack of ‘reality’ is no good reason to ignore them. These are the two expressive strategies through which Harman endeavours to encapsulate the idea that ontology must account for ‘everything’.
Nevertheless, there is more to contemporary ontological liberalism than OOO. In particular, thinkers such as Tristan Garcia and Markus Gabriel have championed the demand for comprehensiveness in their own ways: the former systematically in his Form and Object, and the latter more sporadically under the heading of Transcendental Ontology.9 Garcia best captures the curious affect that seems to motivate this demand:
Our time is perhaps the time of an epidemic of things.
A kind of ‘thingly’ contamination of the present was brought about through the division of labour, the industrialisation of production, the processing of information, the specialisation of the knowledge of things, and above all the desubstantialisation of these things. In Western philosophical traditions, things were often ordered according to essences, substrata, qualities, predicates, quidditas and quodditas, being and beings. Precluding anything from being equally ‘something’, neither more nor less than any other thing, thus becomes a rather delicate task. We live in this world of things, where a cutting of acacia, a gene, a computer-generated image, a transplantable hand, a musical sample, a trademarked name, or a sexual service are comparable things. Some resist, considering themselves, thought, consciousness, sentient beings, personhood, or gods as exceptions to the flat system of interchangeable things. A waste of time and effort. For the more one excludes this or that from the world of things, the more and better one makes something of them, such that things have this terrifying structure: to subtract one of them is to add it in turn to the count.10
Moreover, in discussing his proximity with Harman, Garcia successfully pinpoints the crucial commitment underpinning the liberal synthesis:
Form and Object and Harman’s object-oriented ontology are thought-experiments on the “equality” of all things. Both see philosophy as having an imperative to combine knowledge and morality so that they cannot be separated. The role of philosophy is to understand what composes the world and the way to divide and order its elements on an equal plane by refusing to attribute any ontological privilege to anything in particular. It is therefore a question of grasping the equal ontological chance that every thing has, whether it is material, immaterial, possible, necessary, true, or false.11
In essence, what binds these new ontological liberals together is a commitment to some form of ontological egalitarianism: their demand to account for all things is fundamentally connected to the demand to account for them equally. This shows us that not only does the motivation for Harman’s metaphysics hang upon whether this conceptual connection can be made coherent, but so does the motivation for the liberal trend to which it belongs. If we are to analyse this connection then we must look deeper than Harman’s fairly superficial strategies for encapsulating ‘everything’ and the supposedly egalitarian notion of ‘thing’ (or ‘object’) that this implies.
The remainder of this chapter is devoted to this task. If we are to examine the notion of ontological commitment in more detail, it will first be necessary to clarify what we mean by ‘ontology’. This will provide the necessary historical background to explain Quine’s famous analysis of ontological commitment in ‘On What There Is’,12 which establishes the crucial link between ontological commitment and quantification, on the basis of which it will be possible to explain the logical connection between the problem of defining existence and the problem of unrestricted quantification. This will provide us with the necessary conceptual background to explain the final and in many ways most significant influence upon contemporary ontological liberalism: Alain Badiou’s set-theoretical approach to ontology in Being and Event. This detour into the logical role of ontological commitment will enable us to locate the precise point at which Harman’s ontological egalitarianism falls short of the noetic challenge to ontological conservatism. This will then be supplemented by a discussion of the explanatory role of ontological commitment that locates the corresponding point at which Harman’s egalitarianism falls short of the anti-reductionist challenge to conservatism. These fault lines within Harman’s project will then be traced back to a conceptual problem with his formulation of the metaphysics of ‘objects’, and a corresponding methodological problem with his formulation of the ‘metaphysics’ of objects. The chapter will close by addressing the wider conceptual problem with ontological liberalism, and how this emerges from the wider methodological problem regarding the relation between logic and metaphysics that has defined the last four sections.
Using the word ‘ontology’ in mixed philosophical company can prove challenging. The origin of the term lies in the scholastic division of metaphysics into its various sub-disciplines, in which ontology—as the science of beings qua beings—comprises metaphysica generalis, or the attempt to articulate the structure of beings as such, as opposed to cosmology, psychology, and theology—the sciences of natural beings, rational beings, and the highest being—which form the tripartite division of metaphysica specialis, or the attempt to circumscribe the structure of beings as a whole.13 However, gradually freed from these methodological shackles by the slow collapse of scholasticism, the sense of the term began to wander in divergent directions. As such, it is worth briefly tracing its wandering significance before delving into the discussion of ontological commitment, if only so as to avoid the various terminological confusions that are likely to arise. We will first explore the evolution of the term ‘ontology’ in the ‘Continental’ tradition, focusing upon Heidegger’s project of fundamental ontology and its influence, before examining the independent reintroduction of the term into ‘analytic’ discourse by Quine and its consequences.14 However, the discussion of each tradition will require a preparatory analysis of how the relevant problems emerge out of Kant and their divergent appropriations of his work. Overall, this will enable us to articulate the parallels between the two traditions and thereby clarify what is at stake in our discussion of ‘ontological commitment’.
In tracing the development of ‘ontology’ in the Continental tradition, it is useful to begin with the observation that the tradition is often delineated historically as well as geographically—as ‘Post-Kantian European philosophy’. Although this attests to the general importance of Kant’s thought within this tradition, it is essential to grasp the specific influence it has had upon the appropriation of scholastic ‘ontology’ and its subsequent development. Kant is very sensitive to the scholastic methodological framework in articulating his delimitation of the possibility of metaphysical knowledge in The Critique of Pure Reason: he dedicates the transcendental analytic and transcendental dialectic to the critical demarcation of the problems of metaphysica generalis and metaphysica generalis respectively. Although Kant initially presents the transcendental analytic and its account of the categories of pure understanding as replacing ‘ontology’, he subsequently adopts the term and treats the analytic as redefining its scope.15 Moreover, this redefinition is carried out as part of a wider engagement with the scholastic interpretation of the meaning of ‘metaphysics’, which no longer simply groups those works of Aristotle that come after his physics, but names the study of that which is beyond physics because it is beyond experience.16 Although Kant’s critical demarcation rejects the possibility of such transcendent knowledge of the Being of ‘things’ (Dinge) outside experience, insofar as it is disconnected from empirical (or immanent) knowledge of ‘objects’ (Objekte) as they appear within it, he nevertheless secures the possibility of transcendental knowledge of their conditions of possibility. In essence, this means that Kant redefines ontology as the study of objects as such (phenomena) as opposed to things as such (noumena). Notoriously, the distinction between phenomena and noumena that underwrites this move is attacked by subsequent German idealists (e.g., Hegel and Schelling), but we will refrain from discussing how this leads to the reincorporation of Kant’s ideas within more classical metaphysical projects.
Instead, we will turn to Husserl’s phenomenological transposition of the noetic challenge to ontological conservatism, because it marks the explicit dissociation of ‘ontology’ from ‘metaphysics’. For Husserl, formal ontology concerns itself with the eidetic structures of intentionality in much the way that formal logic does, differing only insofar as it addresses the objects rather than the contents of intentional relations; whereas regional ontology concerns itself with delimiting the various domains of possible intentional objects (e.g., physical, mathematical, historical, etc.).17 This distinction reconstitutes the scholastic division between the study of beings as such (formal ontology = metaphysica generalis) and as a whole (regional ontology = metaphysica specialis), while segregating them from ‘metaphysical’ questions regarding the existence and coexistence of these beings within the world. However, this methodological segregation is precisely what Heidegger takes issue with in his critique of Husserl, insofar as it amounts to systematically excluding a fundamental sense of ‘Being’ (Sein)—existence (Daß-sein)—from the formal ontological analysis of beings (Seienden) that is nevertheless foundational for this very analysis. In essence, although Husserl rejects Kant’s distinction between phenomena and noumena, he is only able to transpose ontology into phenomenology by presupposing a parallel distinction between reality and appearance (or Being [Sein] and seeming [Schein]) that he is thereby unable to thematise.18 Heidegger’s own fundamental ontology is concerned with overcoming this problem by completely thematising the Being of beings (das Sein des Seienden) on the basis of nothing but the pre-theoretical understanding of Being that we (Dasein) share in virtue of our ability to understand any beings whatsoever.
However, there is more to Heidegger’s project than compensating for Husserl’s lack of methodological self-consciousness in discussing ‘Being’, precisely because he sees this lack as endemic in the Western philosophical tradition, as exemplified by the scholastic appropriation of Aristotle’s ‘first philosophy’ (prote philosophia) under the name of ‘metaphysics’. Heidegger locates the original division and articulation of the study of beings as such and as a whole in Aristotle’s definition of first philosophy.19 Although Aristotle also defined first philosophy as theology, or that which concerns itself with the divine first cause, this characterisation is derivative, because the first cause (God—theos) is supposed to be that through which we think beings as such and as a whole. This division is the foundation of Heidegger’s whole critique of the metaphysical tradition, insofar as he holds that Aristotle never actually explained the underlying unity of the two halves of his definition of first philosophy, but merely posited an ad hoc theological principle to hold them together. Heidegger claims that the defining characteristics of the metaphysical tradition are all consequences of this move. The first consequence is the beginning of what he calls the forgetting of Being—the increasing lack of methodological self-consciousness that creeps into metaphysics over the course of its history (e.g., the Husserlian exclusion of existence from ontology). The second consequence is the birth of what he calls onto-theology—the systematic ignorance of what he calls the ontological difference, or the distinction between Being (the structure of beings as such and as a whole) and beings themselves (e.g., the scholastic account of beings as ens creatum in relation to God as ens increatum). The final consequence is the convergence of the previous two—the historical tendency to think Being (Sein) as substance (ousia).20 The tortured relationship between the terms ‘ontology’ and ‘metaphysics’ in the Continental tradition emerges out of the ways in which later thinkers appropriate and/or react to these insights.
It is a common assumption in Continental circles that Heidegger’s renewal of the question of Being in the face of its historical forgetting amounts to a decisive rejection of ‘metaphysics’ in favour of ‘ontology’. However, the truth is far more complicated. In Being and Time, Heidegger describes his project as ‘fundamental ontology’ not so as to distinguish it from ‘metaphysics’, but in order to emphasise its continuity with Husserl’s project of formal ontology.21 Although many of Heidegger’s criticisms of the metaphysical tradition can be found in this work, it does not identify the tradition’s problems with metaphysics as such. Moreover, there is a distinct period following Being and Time in which he presents his project as a renewal of metaphysics.22 It is only later on that he begins to view these problems as inherently metaphysical, and that the word ‘metaphysics’ takes on the pejorative sense it has in so much post-Heideggerian discourse; at the same time, the word ‘ontology’ also begins to disappear from his work, precisely as its continuity with Husserl’s project fades.23 Nevertheless, those who come after Heidegger tend to treat ‘metaphysics’ as inherently degenerate, and often treat ‘ontology’ as what the inquiry into Being (the structure of beings as such and as a whole) becomes once it has been divested of the baggage of the metaphysical tradition. Leaving the orthodox Heideggerians to one side for the moment, we can distinguish three distinct post-Heideggerian rejections of metaphysics according to the aspect of the concept of substance they hold responsible for its onto-theological legacy: presence (Derrida), unity (Badiou), or ground (Meillassoux).
Derrida focuses upon Heidegger’s reading of substance as presence (Anwesenheit)—according to which the essence of metaphysics is the privileging of the temporal present.24 It is on this basis that he introduces the supposedly pleonastic phrase ‘metaphysics of presence’ that is so common in orthodox discourse. This phrase signals a deeper affinity between the Heideggerian orthodoxy and its Derridean progeny, which consists in their mutual refusal to renew the project of ontology after ‘the end of metaphysics’: they concur in demanding a practical reorientation of our relation to the subject matter of metaphysics (the attitude of Gelassenheit, or the operation of deconstruction), rather than a theoretical resolution of its problems (which would lapse back into metaphysics); they merely differ on the question of whether this reorientation is capable of overcoming metaphysics (so as to pass over into a ‘second beginning’) or is condemned to remain within it (as an endless engagement with its ‘limits’).25 In each case, the re-orientation is prepared by subsuming Husserl’s unthematised distinction between reality and appearance within a more fundamental historical/temporal structure (Ereignis or différance) through which beings come to presence (clearing or presencing) within a structured horizon (Da-sein/world or arche-writing/text) in a manner that simultaneously erases and hints at its origins (withdrawal or trace); as such, the refusal is enacted by sublimating the opposition between Being and seeming, thereby denying any role to ‘ontology’ that could be separated from their pragmatically reoriented ‘phenomenology’ of historical/temporal coming-to-presence.
Badiou instead focuses upon the traditional link between substance and unity most clearly espoused by Aristotle (for whom substances are units to be counted) and Leibniz (for whom ‘that which is not one being is not a being’)—presenting the essence of metaphysics as this subordination of Being to the normative force of the one.26 Unlike Derrida and the later Heidegger, he uses this diagnosis to cleave ontology from metaphysics: he takes his axiomatic rejection of the one (or units) to imply the identity of ontology and mathematical set theory qua theory of pure multiplicity (or multiples without units); this does not so much foreclose ontology to philosophy as require a philosophical supplement (‘meta-ontology’) that can interpret the significance of its results.27 Badiou’s commitment to the identity of ontology and mathematics inaugurates this supplement—not only is it a philosophical rather than a mathematical thesis, but its intelligibility hinges upon a precise reformulation of the opposition between Being (as inconsistent multiplicity) and appearing (as consistent multiplicity) that Heidegger and Derrida sublimate.28 Badiou’s definition of Being’s appearance as its presentation in the form of countable units (or objects) is essentially a refinement of Husserl’s transposition of the noetic challenge: it cleanly separates phenomenology as the logic of appearance (or the formal/regional circumscription of the range of possible objects) from ontology as the mathematical presentation of presentation (or the subtraction of what is presented in every situation [inconsistent multiplicity] from its presentation [consistent multiplicity]).29 On the one hand, this makes phenomenology into a genuinely logical enterprise by unbinding it from any constraints imposed by ‘consciousness’ or ‘intuition’ and looking to category-theory for a formal analysis of the (transcendental) conditions governing the relations of self-identity that constitute regions of countable objects (or worlds).30 On the other hand, this overcomes the problems of phenomenological bracketing by confining existence to inconsistent multiplicity (Being) and positing an archimedean point—the empty set (Ø or the Void)—to which its existential import is indexed.31
Finally, Meillassoux focuses upon the conceptual link between substance and ground most clearly developed in Spinoza and Leibniz’s systematic extrapolations of the principle of sufficient reason (in terms of a single substance or infinite substances)—locating the essence of metaphysics in its search for an absolute ground (of existence and/or intelligibility) in the form of a necessary entity (paradigmatically, the God of onto-theology).32 Like Badiou, he uses his account of metaphysics to secure the possibility of a non-metaphysical ontology: he provides a proof of the necessity of contingency that simultaneously precludes all metaphysical absolutes (necessary entities) and provides a non-metaphysical absolute (the principle of factiality); not only does this restrict the scope of ontology from ‘what is’ to ‘what could be’—it also posits mathematics (the systematic extrapolation of the principle of noncontradiction) as that which thinks this pure contingency (as opposed to pure multiplicity) and philosophy as that which interprets its significance (the figures of factiality).33 This means that, although ontology is concerned with what necessarily exists (something), it is unconcerned with what actually exists (everything). The philosophical circumscription of the various regions of actuality (or worlds)—types of objects, their qualities, and the laws that govern them—is thus not a phenomenological analysis of appearance, but a speculative exploration of reality.34 That this speculative supplementation of ontology amounts to something like a return to metaphysica specialis can be seen from the three worlds Meillassoux takes to be extant—matter, life, and thought (cosmology/biology and psychology)—and the fourth world whose advent his speculative philosophy anticipates—justice (theology).35
What can we learn from this trajectory we have traced? To begin with, it is worth recognising the transition from Kant to Husserl as the crucial moment in the evolution of correlationism. Husserl’s formal ontology modifies metaphysica generalis in essentially the same manner as Kant’s transcendental analytic, replacing its concern with beings qua beings (understood as things in themselves) with objects qua objects (understood as the correlates of thought); but he opposes this to metaphysics rather than redefining it (replacing metaphysica specialis with regional ontology). This opposition is responsible not only for the split between ontology and metaphysics in the Continental tradition, but also for the emergence of correlationism as an anti-metaphysical stance. Husserl distances himself from Kant not so much by rejecting the distinction between phenomena and noumena (as the German idealists do), but by practically subsuming it within the phenomenological reduction: he extracts the phenomenal by repressing the noumenal. This repression is responsible not only for the Heideggerian critique of metaphysics that subsequently shapes the tradition, but also for the emergence of strong correlationism as an alternative to Kant’s weak correlationism.
In bracketing the existence of objects, Husserl’s phenomenological reduction suspends the epistemological limit that Kant placed upon the correlation between subject and object—the existence and noncontradictoriness of things in themselves—and thereby facilitates its reabsorption into the correlation. The historical/temporal sublimation of the phenomena/noumena distinction enacted by Heidegger and Derrida (through Ereignis/différance) should be seen as a radicalisation of this suspension, and their corresponding practical reorientation towards metaphysics (in Gelassenheit/deconstruction) as the resultant transmutation of Husserl’s methodology. There are other forms of strong correlationism, some of which have independent origins, but this Heideggero-Derridean form is without doubt the most influential in the Continental tradition.36 The mathematical reformulation of the Being/appearance distinction carried out by Badiou should be seen as breaking with this strong correlationism and returning to a form that is in many ways weaker than Kant’s: reinstituting the existence of the in-itself (as indexed to the Void) and thereby deducing ontological constraints upon the logic of appearance beyond mere noncontradiction (the meta-ontological analysis of the relation between set theory [ontology] and category theory [phenomenology]).37 This contrasts with the radicalisation of strong correlationism performed by Meillassoux, which should be seen as converting its practical suspension of the in-itself (de-absolutisation) back into theoretical knowledge of it (an absolute): demonstrating the absolute contingency of the in-itself and thereby deducing both its existence (as something rather than nothing) and its submission to non-contradiction (as the applicability of mathematics).
We are now in a position to show why the difference in usage between the terms ‘ontology’ and ‘metaphysics’ in the Continental tradition has progressively narrowed since Husserl first placed them in opposition. On the one hand, what constitutes ‘ontology’ in the tradition has gradually become more like the ‘metaphysics’ it was originally opposed to: the initial exclusion of existential questions from ontology (Husserl) gave way to a demand to thematise the notion of existence implicit in it (Heidegger), which in turn enabled the gradual reinclusion of these questions within a broader philosophical project (Badiou and Meillassoux). Meillassoux’s speculative philosophy exemplifies this trend, insofar as it treats ontology as the core of a larger speculative enterprise that has more than a passing resemblance to the programmeof scholastic metaphysics. On the other, this shift has been accompanied by the decline of the ‘end of metaphysics’ narrative that was dominant in twentieth-century Continental philosophy after Heidegger.38 Of course, metaphysics never entirely went away: there was always interest in self-avowed metaphysicians such as Hegel and Bergson, or in figures whose thought harboured an unexplored metaphysical dimension, such as Nietzsche and Bataille; but it wasn’t really until Deleuze’s self-avowed ‘metaphysics’ became popular in Anglo-American Continental philosophy that the term began to lose its pejorative edge.39 What one sees at the intersection of these two trends is an increasing pressure to place purportedly antimetaphysical figures such as Heidegger and Badiou and explicitly metaphysical figures such as Hegel and Deleuze into dialogue, and this results in the term ‘ontology’ being used as the lowest common denominator of their joint enterprise. However, this diplomatic usage elides the traditional difference between ontology as species (metaphysica generalis) and metaphysics as genus (also including metaphysica specialis). We can only hope that the increasing popularity of ‘metaphysics’ helps reverse this confusion by allowing ‘ontology’ to return to its more specific meaning.40
In tracing the development of ‘ontology’ in the analytic tradition we must return to a different part of Kant’s critique of metaphysics: his famous response to the ontological argument that God’s existence follows from his essence.41 This argument, which lies at the heart of both scholastic theology (e.g., Anselm) and early rationalist metaphysics (e.g., Descartes), essentially attempts to infer the actual existence of a possible entity (that it is, or its Daß-sein) from the properties that are predicated of it qua possibility (how it is, or its Sosein), or from those determinations that are internal to its concept. Kant’s negative thesis is that we can disqualify all such inferences on the basis that existence is not a real predicate: to predicate existence of something is not to add anything to it qua possibility, but merely to posit its actuality, and therefore existence is a determination that is external to its concept. Kant’s positive thesis is that positing the actuality of the thing is locating it within the intuitive bounds of experience, or situating it within the spatio-temporal realm of nature. The influence of these ideas upon the analytic tradition begins with Frege, who accepts the negative but rejects the positive dimension of Kant’s account of existence. Frege cashes out Kant’s negative thesis that existence is not a ‘real’ predicate by interpreting it not as a (first-order) predicate of objects but as a (second-order) predicate of concepts: to make a general existential claim is to say of some concept that it is instantiated (e.g., ‘horses exist’ is understood as ‘the concept <horse> has at least one instance’). Russell then refines this account by explaining singular existential claims in terms of his theory of definite descriptions (e.g., ‘my horse exists’ as ‘there is a unique instance of the concept <horse that belongs to me>’) and his associated descriptive theory of names (e.g., ‘Trojan exists’ as ‘there is a unique instance of the concept <horse that belongs to me, is black, is swift, is...etc.>’).42 However, although this does much to clarify the form of existential claims, it is not clear that it does much to clarify their content—the concept of instantiation is no less opaque than the concept of existence it is supposed to explain.43
In order to show how this relates to the evolution of ‘ontology’ in the analytic tradition, it is necessary to say something about the evolution of ‘metaphysics’. It is important to understand that neither Frege nor Russell were anti-metaphysical thinkers. Frege’s mathematical platonism, which treats mathematical objects and senses as existing independently of thought about them, is explicitly metaphysical, as is Russell’s logical atomism, which treats the propositions that provide the content of thoughts as actually composed by the individual objects and universals to which they refer.44 The rejection of ‘metaphysics’ in the analytic tradition begins with Wittgenstein’s Tractatus Logico-Philosophicus, and its appropriation by the logical positivists of the Vienna Circle. Though in many ways a development of Russell’s logical atomism, the Tractatus posed the first semantic challenge to metaphysics: it did not reject the possibility of knowing things in themselves, but the possibility of saying anything meaningful about them.45 This challenge was then developed and popularised by the Vienna Circle, who replaced Wittgenstein’s account of meaning as picturing with an account of meaning as verifiability, so that metaphysics is meaningless not because it cannot picture the structure of states of affairs, but because it cannot be empirically verified.46 Though this idea famously collapsed under its own weight—one cannot empirically verify the principle of verifiability—its sceptical inertia infused the tradition that coalesced after the breakup of the Vienna Circle and the resulting diaspora of logical positivism.47 Nevertheless, this inertia is consolidated and focused by Carnap in a gesture that parallels Husserl’s methodological suspension of the existence of things in themselves, determining the fate of ‘ontology’ in the analytic tradition much as Husserl did in the Continental tradition.48
In Carnap’s logical empiricism, the mere fact that existential claims share the same syntactic form (e.g., ‘horses exist’, ‘societies exist’, ‘transfinite cardinals exist’, etc.) does not mean that they share the same semantic content (e.g., horses, societies, and transfinite cardinals can ‘exist’ in different senses). He holds that existential questions are relative to the linguistic framework—or the set of rules governing the relevant terminology (e.g., the frameworks of biology, sociology, and mathematics)—in which they are posed. It thus makes sense to ask questions that are internal to a given framework (e.g., ‘is there a transfinite cardinal larger than the set of rational numbers but smaller than the set of real numbers?’ in a mathematical context), but not to ask questions that are external to a given framework (e.g., ‘do transfinite cardinals exist in the same way that horses exist?’); metaphysical questions about existence are thereby replaced with pragmatic questions about our choice of linguistic frameworks.49 Carnap is thus even more radical than Husserl: not only does he pragmatically suspend ‘metaphysical’ questions about the existence of things in themselves, he reduces anything like ‘formal ontology’ to syntactic analysis of language in general and anything like ‘regional ontology’ to the semantic analysis of specific theoretical languages. This reduction has had an important influence on the meaning of ‘ontology’ in the sciences, where it is used to talk about the typology of entities implicit in a given theoretical framework (e.g., anatomy, cosmology, economics, etc.).50 However, much as the meaning of ‘ontology’ in the Continental tradition is indexed to Heidegger’s critique of Husserl, so is its meaning in the analytic tradition indexed to Quine’s critique of Carnap.
It is important to emphasise just how much Quine agrees with Carnap’s views on metaphysics. Not only is he willing to accept Carnap’s choice of semantics as the terrain on which the battle over the possibility of metaphysics is fought; he is also willing to accept that most of the substantive claims made by all sides in the history of metaphysics are strictly meaningless. He also shares Carnap’s staunch commitment to the priority of natural science, which, as we shall see, ultimately leaves an untidy thread hanging from the account of ‘ontological commitment’ he provides. Where Quine demurs is simply on the question of the meaningfulness of univocal existential commitments.51 Quine thinks that there are good semantic reasons to think that there must be a single and privileged domain of objects in terms of which the meaning of ‘exists’ is to be understood, precisely because the external existential question par excellence—‘What is there?’—has an obvious and even trivial answer: ‘Everything’. It is important to see that this rejection of Carnap’s ontological pluralism functions by invoking the very connection between beings as such and beings as a whole from which metaphysics as a discipline originates.
This goes some way to explaining the unintended consequence of Quine’s critique: the gradual reconstruction of metaphysics within the analytic tradition on the foundation of ‘ontology’—no longer understood as the study of beings qua beings (‘What is a being?’), but as the study of beings as a whole (‘Which beings exist?’). Quine’s aim was deflationary: he aimed to defend Frege and Russell against the instantiation objection by showing that there simply is nothing more to be said about existence/instantiation than what is provided by the logical analysis of the syntax of existential claims. However, his influence was ultimately inflationary: not only did he enable analytic philosophers to argue for the (univocal) existence of naturalistically intractable entities—beginning with Quine’s own minimalistic commitment to the existence of numbers52 and leading to David Lewis’s extravagant commitment to the existence of fully formed possible worlds53—he inadvertently legitimated more substantial analyses of the semantics of existential claims (so called analytic ‘meta-ontology’)54 and with it a range of more classical metaphysical problems beyond the scope of ontology: the metaphysics of relations (e.g., Ladyman and Ross) modality (e.g., Lewis), universals (e.g., Armstrong)55 and beyond.56 This return to ‘metaphysics’ via ‘ontology’ curiously mirrors the progression of Continental philosophy in the twentieth century.
What remains is to try to synthesise the two stories just told, and to see how the notion of ontological commitment with which we began this chapter fits into the unified narrative. We have already seen that each tradition rejects ‘metaphysics’ only to revive some form of ‘ontology’, which then paves the way for its return; but we have not yet articulated the crucial difference between their uses of ‘ontology’ and thus precisely how their paths diverge before they converge once more. This crux is the concept of existence: Husserl and Carnap suspend it and Heidegger and Quine critique this suspension, but their attempts to explicitly thematise the concept develop in opposing directions. On the one hand, the tradition that follows Heidegger treats ‘ontology’ as the study of what existence is—or what it is to be a being—retaining the core theme of metaphysica generalis (e.g., fundamental ontology) and ultimately reconstructing the themes of metaphysica specialis on this basis (e.g., regional ontology). It is nevertheless resisted by an enduring correlationism that continues to reject unqualified existential claims until the work of Deleuze and Meillassoux. On the other hand, the tradition that follows Quine treats ‘ontology’ as the study of what exists—or which beings there are—retaining the core theme of metaphysica specialis (as applied ontology)57 and eventually regressing to the themes of metaphysica generalis on this basis (as meta-ontology). Quine’s introduction of the term ‘ontological commitment’ to designate the unqualified existential claims to which our theories commit us is thus opposed to the correlationist vision of ‘ontology’ that is still alive in parts of Continental philosophy. We shall now proceed to examine Quine’s account of ontological commitment and its importance for the debate between ontological conservatism and ontological liberalism.
In order to understand Quine’s account of ontological commitment it is necessary to explain how Frege and Russell’s idea that existence is a second-order predicate is formalised by contemporary logic. We have already explained how predicates are usually understood as mathematical functions (e.g., Fx) or open sentences (e.g., ‘…is red’), in which the variable must be given a determinate value (e.g., Fa) or the sentence must be completed with a singular term (e.g., ‘the apple is red’) in order to express a determinate proposition. We now have to introduce the notion of a quantifier, which is understood either as a mathematical function that takes predicates as arguments and returns truth-values (e.g., (∀x)(Fx) and (∃x)(Fx), read as ‘for all x, x is F’ and ‘for some x, x is F’, respectively), or as the main component of a quantified noun phrase that takes the place of a singular term in completing an open sentence (e.g., ‘not all…’ in ‘not all apples’, completing ‘not all apples are red’; ‘most…’ in ‘most integers’, completing ‘most integers aren’t primes’; or even ‘exactly four…’, in ‘exactly four planets’, completing ‘exactly four planets in the solar system are gaseous’).58 The obvious way to understand quantifiers is as devices for quantification, or for expressing the number of things in a given set that meets a certain criteria (e.g., ‘there are nine planets in the solar system’, ‘there are no unicorns on earth’, ‘every electron has a negative charge’, etc.). However, the best way to understand them is in terms of their role in binding the free variables of syntactically well formed formulas (e.g., the quantifier (∀…) binds the variable x in the formula Fx∧Gx to form the proposition (∀x)(Fx∧Gx)), or in progressively completing open sentences by closing the grammatical openings left for singular terms (e.g., the quantified noun phrase ‘most apples’ completing ‘…are green and sharp’ to form the grammatically complete sentence ‘most apples are green and sharp’).
This allows us to draw three overlapping distinctions between types of predicates. Firstly, we can make our earlier distinction between monadic and relational predicates more precise, as we can see that some predicates contain more than one free variable/grammatical opening (e.g., Fxy, or ‘…loves…’) which can be bound/closed by different quantifiers (e.g., (∀x)(∃y)(Fxy), or ‘everybody loves somebody’) even if they needn’t be (e.g., (∀x)(Fxx), or ‘everybody loves themselves’).59 Secondly, we can introduce the distinction between simple and complex predicates, or between predicates whose corresponding formulas/open sentences contain nothing but free variables/openings (e.g., Fx and Gxy, or ‘…is red’ and ‘…loves…’) and predicates whose corresponding formulas/sentences are composed out of simple predicates and logical operators (e.g., Fx ∧ Gx and ¬(Fxy ∧ Fyx), or ‘…is green and sharp’ and ‘…and… don’t love each other’). Finally, we can introduce the distinction between first-order and higher-order predicates, or between those predicates whose variables can only take objects as their values (e.g., Fx where x takes objects {a, b, c, …}) and those predicates whose variables can also take lower-order predicates as values (e.g., Kφ where φ takes first-order predicates {F, G, H, …}). This is the founding gesture of type theory, which distinguishes the types of values that free variables can have: either by being given a determinate value (e.g., a for x in Fx: Fa) or by being bound to a determinate range of values (e.g., {a, b, c, …} for x in Fx: (∀x)(Fx)). This enables the generation of a type hierarchy, beginning with a primary type of objects that are not functions (individuals) and a secondary type of functions whose arguments are of the primary type (first-order predicates) and then recursively enumerating new types of functions (higher-order predicates) whose arguments may be drawn from previously generated types.60 This means that we can treat an open sentence (e.g., ‘…has an arrity of 2’) as a second-order predicate if its grammatical openings can be closed with the name of a first-order predicate (e.g., ‘the relation ‘…loves…’ has an arrity of 2’) or some suitable nominalisation thereof (e.g., ‘love is a two-place relation’). We will return to the importance of type theory as a strategy for dealing with Russell’s paradox and other so-called impredicative definitions later.61
For now, it is important to explain why quantifiers are not higher-order predicates in the sense just defined, even though they are functions from predicates to truth-values. This is because quantifiers don’t specify variable types: the same quantifier (e.g., (∀…) and ‘most…’) can be used to bind free variables ranging over different types of values (e.g., (∀x)(Fx) and (∀φ)(Kφ), and ‘most mammals are quadrupeds’ and ‘most simple predicates are monadic’). It is for this reason that first-order logic contains quantifiers even though it excludes second-order predicates: first-order quantifiers take first-order predicates as their arguments by binding their first-order variables (x), not by containing additional second-order free variables (φ). The grammatical distinction between quantifiers (e.g., ‘most…’) and quantified noun phrases (e.g., ‘most mammals’ and ‘most simple predicates’) makes this separation between quantifiers and variable types clear, insofar as the noun (e.g., ‘dog’ and ‘simple predicate’) that gets added to a quantifier to create a quantified noun phrase is needed to specify the types of values the variable ranges over. This point is crucial for understanding Quine’s defence of Russell and Frege from the instantiation objection. This is because their idea that existence is a second-order predicate is often understood as meaning that it is equivalent to the existential quantifier (∃…), which appears to conflict with the definition of ‘second-order’ just provided.62 Quine’s defence of Frege and Russell exploits the difference between first-order existential quantifiers and second-order predicates in order to show that grasping the meaning of the former is quite a different matter from grasping the meaning of the latter, such that ‘…has an instance’ need not be defined in the same way as an ordinary second-order predicate. Although it is possible to use the existential quantifier to define existence predicates for both singular cases (i.e., Ex ≡ (∃y)(x = y), so that Ea≡(∃y)(φ = y) or ‘there is something identical with fido’) and general cases (i.e., Eφ≡(∃y)(φy), so that EF≡(∃y)(Fy) or ‘there is something that is a dog’), there is no more to understanding these predicates than understanding the syntactic role of the existential quantifier in binding the relevant first-order variables: ‘To be assumed as an entity is, purely and simply, to be reckoned as the value of a variable.’63
It is also important to explain why understanding the syntactic role of variable binding isn’t just a matter of understanding the existential quantifier, but quantification per se. We can show this simply by pointing out that the existential and universal quantifiers are interdefinable (i.e., (∃x)(Fx)≡¬(∃x)¬(Fx), which is to say ‘there is something that is a dog’ is equivalent to ‘not everything is not a dog’; and (∀x)(Fx)≡¬(∃x)¬(Fx), which is to say ‘everything is material’ is equivalent to ‘nothing isn’t material’). However, it is better shown by echoing Frege’s famous claim that ‘[a]ffirmation of existence is nothing but the denial of number nought’.64 This means that the existential quantifier is equivalent to the numerical quantifiers ‘more than zero…’ or ‘at least one…’ and as such demands nothing more than a practical grasp of counting. It is also important to explain that Quine adopts Russell’s anti-Meinongian solution to the problem of negative singular existential claims (e.g., ¬Ea, or ‘Pegasus does not exist’), namely, treating proper names (e.g., the constant a, or ‘Pegasus’) as covert definite descriptions (e.g., a unique descriptive predicate F, or ‘the winged horse of Perseus’), so as to remove reference to objects that don’t exist (e.g., Ea≡(∃x)(∀y)(Fx ∧ (Fy → x = y)) and ¬Ea≡¬(∃x)(Fx), or ‘there is one and only one winged horse of Perseus’ and ‘there is no winged horse of Perseus’). Once both of these points are recognised we can see that Quine essentially defends Frege and Russell’s explanation of existence in terms of instantiation by showing that there is nothing more to understanding instantiation than being able to count: if you know how to count individuals, then you know what it is for them to exist.
We have now explained the logical foundations of Quine’s account of ontological commitment, but there is still more to it than this. One way of bringing the remaining issues to light is by considering the claim that ‘two out of three little pigs lost their houses to the big bad wolf’.65 There is an obvious sense in which this claim is true, and in which it is the result of an accurate counting procedure. It would make sense to ask a child who had been told the story of the three little pigs ‘how many of them lost their houses?’ in order to test their counting ability, and to treat the above claim as a correct response. However, this implies the claim that ‘there are some little pigs that lost their houses to the big bad wolf’, which we are supposed to treat as synonymous with ‘there exist little pigs that lost their houses to the big bad wolf’, and this seems to ontologically commit us to the existence of some well-known fictional pigs. Quine thus has to methodologically differentiate ontological commitment from mere existential commitment if he is to avoid including fictional pigs in his ontology.
It is at this point that Quine invokes Occam. He claims that we are only ontologically committed to those entities that are explanatorily indispensable: meaning those entities that are within the range of the variables bound by the sentences composing our best scientific theories, once those theories have been translated so as to be as referentially frugal as possible.66 We are thus not ontologically committed to the existence of fictional pigs, even though we can count them, because counting them makes no contribution to the natural-scientific enterprise. However, Quine never properly thematises and justifies this restriction of ontological commitment to the natural sciences. Although he comprehensively articulates ontological conservatism from a naturalist perspective, he does not fully articulate this perspective, nor the reasons for adopting it. This uncritical naturalism is the untidy thread hanging from his account I alluded to earlier. To show why it is so unsatisfactory it is necessary to return to the initial gesture that Quine makes in his dispute with Carnap: invoking the conceptual connection between ‘what exists’ and ‘everything’, or the link between ontological commitment and unrestricted quantification.
To do this, it is necessary to explain what we mean by restricted quantification. On the standard interpretation of quantifiers, the bound variable ranges over a set of objects called the domain of quantification.67 This is naïvely understood as the set of everything that exists, or the unrestricted domain. To restrict this domain is to only allow the variable to range over some subset of the unrestricted domain (e.g., the set of dogs that exist). In practice, the vast majority of quantificational claims are restricted in some way, though these restrictions may be more or less explicit. For instance, when I say to my guests that ‘there is no beer’ I do not mean that all of the beer in the world has been consumed or otherwise eradicated; I am implicitly restricting my claim from the domain of everything to that of those things in my house (which is a subset of everything), or even that of things in my fridge (which is a subset of things in my house). This restriction can be made explicit by adding ‘…in my house’ or ‘…in my fridge’ to the original quantificational claim. Conversely, when I say ‘there is nothing in the fridge’ I am not denying that there are shelves, stains, oxygen molecules, and even light in there; I am implicitly restricting my claim to food (or perhaps just safely edible food). We have already seen how this sort of restriction gets made explicit, by combining the quantifier (e.g., ‘no…’) with a noun (e.g., ‘food’) to form a quantified noun phrase (e.g., ‘no food’) that specifies the range of the bound variable (e.g., ‘no food is in my fridge’). It is important to understand that quantifying with the noun ‘thing’ signals an absence of explicit restrictions, meaning that the associated quantifier (e.g., ‘no…’, ‘some…’, ‘every…’, etc.) is either implicitly restricted (e.g., ‘there is nothing in the fridge’) or explicitly unrestricted (e.g., ‘something exists’).
It is with regard to this question of unrestricted quantification that Quine’s ontological conservatism and contemporary ontological liberalism cross paths: both take themselves to be entitled to the seemingly unrestricted claim that ‘everything exists’, though they disagree about its significance. The problem is providing a precise interpretation of what either side means when they make this claim; though the crucial difference between them lies in what they mean by ‘everything’, this difference cannot easily be made explicit, because one is implicitly restricted and the other is implicitly unrestricted. On the one hand, although Quine takes ‘everything exists’ to be a trivial claim, insofar as he defines existence (qua instantiation) as belonging to the set of everything, he nevertheless wants to exclude some ‘things’ (e.g., fictional pigs, round squares, universals, etc.) from this set. This indicates that his account of ontological commitment depends upon an implicit restriction of ‘everything’ that he delegates to natural science. On the other hand, although ontological liberals take ‘everything exists’ to be a profound injunction, insofar as it indexes the ontological circumscription of the whole range of possible objects of thought in accordance with the noetic challenge to conservatism, they nevertheless experience difficulty defining ‘thing’ (or ‘object’) broadly enough to circumscribe ‘everything’ in the completely unrestricted sense. To appreciate this difficulty we must delve deeper into the logic of unrestricted quantification.
Although it might seem that quantifying without any restrictions would be the most simple form of quantification, its possibility is a highly controversial topic in philosophical logic. The most famous problems for unrestricted quantification are posed by the set-theoretical paradoxes formulated by Cantor and Russell.68 Cantor’s paradox shows that there cannot be a set of all sets (U) on pain of contradiction, because its cardinality (|U|) would have to both be lesser and greater than that of its power set (|℘U|): a power set—the set of all subsets of a given set—must always have a greater cardinality than its corresponding set (|U|<|℘U|), and a set must always have a cardinality greater than or equal to its subsets (|℘U| ≤ |U|).69 Russell’s paradox constructs another seemingly comprehensible set that cannot exist on pain of contradiction: the set of all sets that don’t contain themselves (W), which contains itself if it doesn’t contain itself (W∉W→W∈W), and doesn’t contain itself if it does (W∈W→W∉W). The general form of reasoning these paradoxes display rests upon impredicative definitions, or functions defined in such a way that they can take themselves as arguments (e.g., Fx where F(Fx) is syntactically well formed). This is the same sort of problematic self-reference that lies behind the liar paradox (e.g., ‘…is false’ where ‘this sentence is false’ is grammatical).70 Russell’s theory of types was formulated as a way of preventing such paradoxes of self-reference by hierarchically segregating functions into orders whose variables can only range over types in the orders beneath them.
One might object at this point that these paradoxes are concerned with sets and not ‘things’, and thus pose no problems for thinking about ‘every thing’ even if they cause problems for thinking about ‘every set’. We can respond to this by pointing out that sets are well-defined objects of mathematical thought, such that ontological liberalism ought to include whatever sets can be coherently specified within its comprehensive circumscription of what there is. However, if ‘everything’ should thus contain ‘every set’, then it seems that the set of everything (E) should include the set of all sets (U) as a subset (U ∈ E), and Cantor’s paradox precludes this. Similarly, for the set of objects that constitutes any given domain of quantification (D), one can exploit the reasoning of Russell’s paradox to construct a set that is not contained within it: the set of everything in D that doesn’t contain itself (RD = {x:x ∈ D ∧ x∉x}). This means that one can never define an absolutely unrestricted domain, because the very act of defining it enables one to construct an object that is not present within it, and thereby to define a more expansive domain that includes it (E'={x:x ∈ E, RE}).71 Once liberalism allows sets in, sets of things quickly get out of hand.
One might further object that the problem is not with sets qua objects, but with the attempt to circumscribe ‘everything’ by means of a determinate set of objects over which the bound variables of unrestricted quantifiers range. This objection is important, but we must be careful not to interpret it in a trivial manner: if one treats set theory as merely one mathematical formalism among others, so as to emphasise the sense in which it is concerned with a specific type of object (sets), rather than an attempt to formalise thinking about collections of objects as such, then one has merely stipulated one’s way out of the challenges it poses. One need not treat a given formalism as binding in order to see the significance of the problem that these paradoxes pose.72 They suggest that the capacity for self-reference (or the reflexivity of sense) is an internal obstacle to the circumscription of the totality of possible objects of thought demanded by the noetic challenge to ontological conservatism. Our ability to think about the very manner in which we think about objects (or to refer to senses) puts us in a position to generate an endlessly ramifying network of new objects of thought, the delimitation of which only offers further opportunities for ramifying beyond those limits.
The non-trivial form of the objection is that it is not merely the manner in which set theory articulates the idea of ‘everything’ as a determinate collection that is problematic, but the very notion that to think ‘everything’ is to think some determinate collection. However, it is possible to interpret the problematic feature of this notion either as reification or as de-absolutisation. So, one might hold that thinking ‘everything’ as a collection treats it as an additional object we are both obliged to include within itself (U∈U) and permitted to use in constructing further objects (e.g., ℘U and RU) that cannot be so included. This interpretation of the objection seems to be favoured by ontological liberalism, which on this basis follows Badiou in denying the existence of anything like the Whole that could be thought as such.73 However, one might instead hold that thinking ‘everything’ as one collection among others prevents us from grasping what differentiates it from all other such collections (e.g., ‘every dog’, ‘every number’, etc.)—its unique absoluteness. This interpretation of the objection is suggested by Kant’s positive account of existence: his distinction between the appearance of spatio-temporal objects within experience and the pure forms of space and time through which they appear amounts to a distinction between the specific contents and the general structure of ‘absolutely everything’ in relation to which objects qua objects are defined (ontology). Furthermore, this provides a way of demystifying the self-containment of ‘everything’: space and time appear within themselves insofar as they are coextensive with themselves. The spatio-temporal manifold need not appear as an object within a more expansive manifold.
This distinction between the structure and contents of ‘everything’ is taken up and articulated by the early Heidegger, who uses it to thematise the connection between beings as such and beings as a whole that simultaneously defines and escapes the metaphysical tradition. This is the significance of his discussion of ‘the Nothing’ (das Nichts) and its relation to what he calls the fundamental question of metaphysics: ‘Why is there something rather than nothing?’74 This discussion is famously ridiculed by Carnap, and taken to exemplify the way that seemingly profound but essentially vapid metaphysical theses can be derived from basic misunderstandings of the underlying logic of language.75 Explaining what Heidegger means and why Carnap’s criticism is wrong is a good way of getting a grip on the difference between the reification and de-absolutisation objections to set-theoretical approaches to ‘everything’ and their relation to the ontological difference.
To do this properly, it is necessary to frame the issue in terms of our discussion of quantificational restriction. Carrying on the earlier example: in a more philosophical mood I am entirely capable of asking the question ‘Why is there beer?’, and of making explicit its unrestricted scope (as opposed to ‘Why is there beer in the fridge?’) by saying ‘Why is there beer rather than none?’. This kind of construction has two effects. Firstly, it contrasts the state of affairs for which we are demanding a reason (the existence of beer) with an alternative state of affairs that is prima facie possible (the non-existence of beer). Used literally, all the ‘none’ does here is to pick out a state of affairs in which there is some number of beers (zero). We could ask very similar questions contrasting different states in which we varied this number (e.g., ‘Why are there two beers rather than three?’, ‘Why are there no beers rather than two?’, etc.). However, zero is the limit-case of the various possible states of affairs we can produce by varying the number of some kind of things. It is what we will call an empty state of affairs, or a nothing. We can contrast this limit-case with all non-empty states of affairs, i.e., those in which there are some of the kind of object in question. Secondly, it is an additional quirk of our language that this kind of contrast can be used to signal a lack of implicit restrictions on the quantifier (e.g., ‘…in my fridge’, ‘…in Saudi Arabia’, ‘…that I like’, etc.). When we combine these two features in the case of the fundamental question, we see that the qualification ‘…rather than nothing’ makes explicit a possible state of affairs (there is nothing) to which the actual state of affairs (there is something) is contrasted, and the fact that this is a unique limit-case (the limit-case of limit-cases). The quantifier is not explicitly restricted, nor is it supposed to be implicitly restricted—it is explicitly completely unrestricted. The qualification thus forces us to think the absolutely empty state of affairs, or the Nothing.
Carnap’s criticism of Heidegger works by treating his use of the singular term ‘the Nothing’ as naming a special metaphysical object, and thus as internally inconsistent insofar as it implies that there is something after all. This reification of ‘nothing’ directly parallels the reification of ‘everything’ which ontological liberalism by necessity opposes. It is clear from our above explanation of the Nothing that Heidegger rejects any such reification. This rejection is the foundation of Heidegger’s thesis that Being is Nothing: the fundamental question of metaphysics enables us to think the structure of ‘absolutely everything’ (beings as a whole) as distinct from its contents (beings) by identifying it with the structure of ‘absolutely nothing’ (the Nothing); this amounts to thinking Being as the unitary structure of beings as such and as a whole by understanding existence (beings as such) as the content of this structure (beings as a whole).76 Just as for Kant space and time do not appear as objects within themselves, so for Heidegger Being is not a being, but literally no-thing. This is the essential statement of the ontological difference between Being and beings that he takes to be elided by onto-theology.77
It is important to emphasise that Heidegger does not transcend the bounds of logic in drawing this connection between Being and Nothing, so much as slip the restraints of Carnap’s preferred logic. This is clear if we consider another controversy in the philosophy of logic that their debate skirts: the problem of empty domains. Classical logic and most forms of predicate logic cannot allow the domains over which their variables range to be empty. Relatively empty states of affairs (nothings) are perfectly acceptable (e.g., the cases where there is no beer, there are no unicorns, or there is nothing in the space between galaxies) insofar as they restrict the quantifier in some way, thus allowing there to be something in general despite there being nothing of a specific type or in a specific locale. But the absolutely empty state of affairs (the Nothing) is logically impermissible. The reason for this is that the truth conditions of the quantifiers are defined in terms of the way that the well formed formulas whose variables they bind are satisfied by objects in the domains they range over (e.g., (∀x)(Fx) is true iff every object in the domain {a, b, c, …} maps Fx to truth if taken as its value: Fa, Fb, Fc, …), and this makes even self-evident propositions false when the domain is empty (e.g., (∀x)(x=x) is false when there are no objects in the domain {}, or when the domain is Ø). This problem is rectified by free logics, which allow the introduction of non-referring singular terms (e.g., ‘the present king of France’, ‘Pegasus’, etc.).78 Although not all free logics can handle empty domains, the only logics that can (so called universally free or inclusive logics) are free in this sense. They do so by partially suspending Quine’s bond between quantification and existence: distinguishing between quantifiers that can range over existents (e.g., ‘there are no little pigs who lost their houses to the big bad wolf’ and ‘no unicorns have horns’), and those that can also take non-referring singular terms (e.g., ‘two out of three little pigs lost their houses to the big bad wolf’ and ‘all unicorns have horns’). This constitutes a distinction between the existential quantifier (∃…) and the particular quantifier (P…) by differentiating those uses of ‘some…’ that imply existence from those that don’t.
The crucial point is that, however the particular quantifier is defined (e.g., as taking both referring and non-referring singular terms, or as ranging over an outer domain that includes both existent and subsistent objects), the corresponding existential quantifier is defined by means of an inner domain that only contains existents: existence (beings as such) is understood as the content of this domain structure (beings as a whole).79 It is on this basis that the possibility of an empty inner domain can be thought consistently.
Lest this be seen as simply one more detour into irrelevant logical theory, let us explicitly articulate its significance for thinking about the ontological difference. Just as the set-theoretical paradoxes of self-reference trace an ontological obstacle internal to the project of noetic circumscription, so do free logic’s sundered quantifiers trace a noetic caesura internal to the project of ontological circumscription. This caesura is the manifestation of the ontological difference in thought: the singular difficulty of thinking beings as such and as a whole without thinking them in terms of some highest being (e.g., God) or some genus of beings (e.g. Ideas, subjects, etc.), or of thinking their structure (Being) as distinct from its content (beings). What this means is that, if we are to think beings comprehensively, then we must draw a distinction within thought between thinking about beings and thinking about Being. However, this distinction can be developed in two directions, depending on how one interprets the relation between noetic circumscription and ontological circumscription. Ontological conservatism is in a position to distinguish between beings and objects of thought because it does not identify noetic and ontological circumscription. This means that it can distinguish between thinking about beings qua objects and thinking about Being qua object, and thus does not need to radically dissociate the latter from the former. This is not to say that this is what ontological conservatism does in practice: Quine refuses to fully thematise thinking about Being, and defers to whatever implicit grasp the natural sciences have upon it in practice. Ontological liberalism is forced to identify beings and objects because it folds noetic into ontological circumscription. This means that it must radically dissociate thinking about beings qua objects from thinking about Being. This is the significance of the later Heidegger’s turn to poetry as a medium of thinking that escapes the objectifying power of literal discourse.80
We are now in a position to describe the ontological egalitarianism that binds ontological liberalism together: the connection between the demand to account for all things and the demand to account for them equally. The de-absolutisation objection to treating ‘everything’ as a determinate collection opens up the possibility of defining existence in terms of unrestricted quantification. This is because it identifies the whole to which the latter refers as a general structure whose specific content is provided by existents. In aiming to provide a comprehensive account of beings as such by comprehensively defining beings as a whole, it grasps the equality of things by way of the totality of things. However, this is not egalitarian enough for ontological liberalism, because it refuses to treat whatever objects we can think beyond the bounds of this totality as things in their own right. By contrast, the reification objection to treating ‘everything’ as a determinate collection suggests the converse possibility of defining unrestricted quantification in terms of existence by treating the latter as the general structure of the objects of thought. In aiming to provide a comprehensive account of beings as a whole by comprehensively defining beings as such, the objection grasps the totality of things by means of the equality of things. In essence, ontological egalitarianism dismisses any attempt to define the whole as reifying it, because it insists on treating whatever objects we can think beyond the bounds of any proposed totality as things in their own right. By denying existence to the Whole, the ontological egalitarian keeps their options perpetually open, enabling them to gesture towards ever larger samples of myriad and mythical entities. However, the role of these gestures is purely negative—they strip away predicates often illicitly attached to Being (e.g., not ‘spatio-temporality’ because we include non-locatable things, not ‘materiality’ because we include immaterial things, not ‘persistence’ because we include transitory things, etc.)—and there must be a corresponding positive account of Being. It is at this point that the need to radically dissociate thinking about Being from thinking about objects implied by the ontological difference becomes pressing. How are we supposed to think the equality of objects in a manner radically dissociated from thought about their differences? How are we to think their structure as radically alienated from their content? There are roughly two ways of approaching this question, but to understand them we must return to the logic of quantification one last time.
There is a further objection to the possibility of absolutely unrestricted quantification that is quite different from those based on the set-theoretic paradoxes: that it only makes sense to quantify over a domain that is sortally restricted.81 This is a special form of restriction using what are called sortal predicates, and although there is some disagreement over precisely what these are, it is commonly accepted that they are predicates that provide criteria of identification. For instance, the predicate ‘…is a natural number’ is defined in such a way that we have a clear criterion for whether two natural numbers are identical: if they are located at the same point in the succession of numbers, then they are the same number (e.g., if x is the successor of 2, then x = 3). The objection is then that it is impossible to count any kind of object without such a criterion of identity (e.g., it makes no sense to ask ‘how many instances of red are there in this street?’ unless one specifies that one is counting instances of red cars, red flashes of light, or red areas, etc.).82 In natural languages, sortal restriction is performed by the noun added to the quantifier in composing a complete quantified noun phrase (e.g., ‘cars’, ‘flashes of light’, or ‘areas’ in ‘there are some…that are red’), but not all such nouns correspond to sortal predicates (e.g., ‘food’ in ‘there is some food in my fridge’), because some do not specify a complete counting procedure. On the one hand, some nouns leave much of the counting procedure implicit (e.g., it might be easy to determine that we’ve got ‘some food’ rather than ‘none’, or ‘enough food’ rather than ‘not enough’, but this doesn’t mean that there are generic units of food that can be applied to both apples, oranges, and half-eaten tubs of yoghurt). On the other, some nouns correspond to rigorous counting procedures with conventional units (e.g., it is easy to determine that we’ve got ‘100ml of yoghurt’, and that this is comparable to ‘100ml of water’, but these generic units are conventional measurements of volume, not natural units of number).
The idea behind this objection is similar to the idea behind type theory: the variables bound by quantifiers must always correspond to a specific range of values, and there simply is no way to specify a range that includes every possible value that could be specified, not only because we use these specifications to produce new values that they don’t include, but because they correspond to a whole plethora of more or less determinate counting practices that can be indefinitely elaborated. This implies that the nouns ‘object’ and ‘thing’ that we use to signal an absence of explicit restrictions do not for all that signal an explicit absence of restrictions. They do not correspond to a sortal predicate that provides some special procedure for counting everything we could possibly think of. They are pseudo-sortals, and they must always be implicitly restricted by some genuine sortal.83 The consequence of this objection is that the sort of thinking that is made explicit by quantificational logic cannot possibly provide a positive account of the Being of objects. Ontological liberalism essentially embraces this consequence, albeit with variable levels of self-consciousness. The crucial point is that this provides it something to contrast its own form of thinking against, so as to clarify the methodological status of ontology. The difference between the two ways of approaching the methodological question lies in the way in which they contrast themselves with thinking that can be made explicit using quantifiers: Does ontology think something more than it, or something less?
This brings us to Badiou’s role in the emergence of ontological liberalism. Although Badiou’s work is not directly influential upon Harman in the same way as either the Austrian school or Latour, its influence upon Garcia, Gabriel, and Bogost84 is a synedoche of its influence upon the philosophical discourse as a whole, such that it indirectly enables the liberal paradigm of which Harman is the paragon. It is no secret that the primary motivation for Badiou’s philosophy is political. Even if politics is only one of philosophy’s four conditions (along with art, science, and love), it is clear that the principal contribution of Badiou’s meta-ontology is its account of the emergence of subjects as instances of truth-procedures initiated in fidelity to an Event (l’événement) that is ‘trans-Being’ or undecidable in the context of the situation in which it emerges (e.g., the French Revolution, Sophoclean tragedy, Cantorian set theory, an amorous encounter, etc.), and that this is specifically addressed to the problem of political agency.85 I raise this motivation not to make any critical comments about it or its consequences, but to explain Badiou’s affinity to the anti-reductionist challenge to ontological conservatism.86
We have already noted that Badiou follows Husserl in sublimating the noetic challenge in his study of the logic of appearance, transforming the task of circumscribing the full range of possible objects of thought into an exploration of the Logics of Worlds within which these objects appear. This is strictly different from ontology for him, but it remains close enough to the ontology of the liberal paradigm that one can see the affinity between them.87 However, one cannot appreciate Badiou’s proximity to anti-reductionism without seeing it as a result of his commitment to an account of political agency that is strictly irreducible to the economic, sociological, and biological dimensions upon which it is predicated. Though he is an avowed ‘materialist’ in the Marxist tradition, his rejection of the principle of sufficient reason in order to secure the trans-ontological supplement provided by the Event should indicate the extent of his anti-reductionism. His category-theoretical phenomenology should thus be seen as the noetic counterpart to this ontological anti-reductionism, providing a basis for the detailed circumscription of the political life-worlds within which political agency can emerge.
Given this, the most important thing to understand about Badiou’s philosophy is that he understands and embraces the sortal objection to unrestricted quantification more thoroughly than anyone. Badiou’s rejection of substance as unity is essentially a rejection of the idea that there are natural units: nothing is one until it is counted-as-one, or until it appears as an object within the quantificational domain specificied by a particular counting procedure. This explains his rejection of type theory, insofar as the hierarchy of types must always begin with a primitive type of natural units (objects) that can be unproblematically quantified over. It also explains why he retains Kant’s use of the term ‘object’ to designate what appears (units), as opposed to what is (multiples without units). However, this means that ontology cannot be the study of objects qua objects. As we have already explained, that is the province of phenomenology, or the study of the transcendental structures within which objects can appear as self-identical (i.e. worlds as domains of quantification). The province of ontology is the study of what is counted-as-one before it is unified by the count, or multiplicity qua multiplicity. This explains Badiou’s choice of Zermelo-Fraenkel (ZF) set theory over type theory, insofar as the former quantifies over sets without supposing that these sets must be composed by things that are not themselves sets. His meta-ontological identification of mathematics and ontology is more precisely the claim that ZF set theory is ontology.
It is important to understand why the thesis that mathematics is ontology cannot be articulated within the austere realm of mathematical inscription. For Badiou, mathematics does not think about objects—there strictly are no mathematical objects, but only a deductive practice that methodically (albeit sometimes brilliantly) extrapolates the consequences of an initial decision regarding axioms. However, it is this very austerity that enables mathematics to inscribe Being:
[B]eing qua [B]eing does not in any manner let itself be approached, but solely allows itself to be sutured in its void to the brutality of a deductive consistency without aura. Being does not diffuse itself in rhythm and image, it does not reign over metaphor, it is the null sovereign of inference.88
This is the essence of Badiou’s concept of subtractive ontology: mathematics can dissociate the structure of multiplicity (Being) from its apparent contents (objects) by quantifying over nothing but Nothing itself (Ø) and whatever multiplicities can be constructed out of it (i.e., {Ø}, {Ø, {Ø}}, {Ø, {Ø}, {Ø,{Ø}}}, etc.).89 Badiou fundamentally sunders Heidegger’s claim that Being is Nothing by refusing to identify the Nothing and the Whole qua Whole. In contrast to Heidegger’s claim that the Nothing qua Whole does not exist (the de-absolutisation objection), he claims that the Whole qua set of all sets does not exist (the reification objection), but that the Nothing qua Void exists as the sole index of existence (Ø as the name of Being). This scission marks his retreat from the strong correlationism of Husserl and Heidegger to one even weaker than that of Kant—a retreat that is simultaneously a consolidation and radicalisation of Kant’s own subtractive gesture: it converts the thing-in-itself as external limit of empirical knowledge into the Void as internal limit of mathematical knowledge.90
Badiou’s subtractive ontology uncovers the structure of beings qua beings by taking the objects that constitute the content of thought and stripping them of every possible predicate—and thereby even their objectivity—leaving nothing but multiplicities without unity. However, he refuses to explicitly define multiplicities as such, because this would be to treat ‘…is a set’ as one more sortal predicate by means of which to count objects. Badiou navigates the noetic caesura of ontological difference by implicitly defining sets (and thereby beings) in terms of the membership relation between them and their elements (…∈…): instead of stating what sets are, he demonstrates what set membership implies. This reveals an interesting parallel between Badiou and Quine: whereas Badiou implicitly defines beings as such by indexing them to the axioms of ZF set theory and the mathematical practice founded upon them, Quine implicitly defines beings as a whole by indexing them to the parsimonious syntactic reformulation of our theories about the world and the natural-scientific practice it is founded upon. Both take a subtractive approach that dissociates thought about Being from thought about objects by harnessing the power of formalism (ZF set theory/first-order quantificational logic) against positive definition, but they approach it from opposite directions (as such → as a whole/as a whole → as such). Both secure the implicitness of Being by deferring its content to a choice (between axioms/between explanations) that they delegate to another form of thought (mathematics/natural science), but they thereby foreclose the conditions under which that choice is made to philosophical reflection: whereas Badiou ignores issues regarding the semantics of quantifiers that determine the space of possible mathematical axioms,91 Quine ignores issues regarding the semantics of causal explanation that determine the space of possible scientific theories.92 However, despite this, their subtractive methodologies do effectively circumscribe what remains implicit in their meta-ontologies.93
We must now explain the alternative to subtraction, which takes thought about Being to access something more than thought about objects, rather than something less. Badiou provides an eloquent description of the way this alternative appears in Heidegger’s later work:
Heidegger still remains enslaved, even in the doctrine of the withdrawal and the un-veiling, to what I consider, for my part, to be the essence of metaphysics; that is, the figure of [B]eing as endowment and gift, as presence and opening, and the figure of ontology as the offering of a trajectory of proximity. I will call this type of ontology poetic; ontology haunted by the dissipation of Presence and the loss of origin […] For poetic ontology, which—like history—finds itself in an impasse of an excess of presence, one in which [B]eing conceals itself, it is necessary to substitute a mathematical ontology, in which dis-qualification and unpresentation are realised through writing.94
Although the later Heidegger no longer thinks that there can be an account of Being (Sein) outside of its particular historical manifestations (e.g., Physis, Logos, Hen, Idea, Energeia, Substantiality, Objectivity, Subjectivity, the Will, the Will to Power, the Will to Will, etc.) much as Badiou thinks that there is no objectivity outside of its manifestations within particular worlds, he nevertheless thinks that there can be an account of the singular structure (Seyn/Ereignis) through which these epochs come about. Heidegger’s poetic ontology aims to think this structure by means of the noetic supplement that poetry provides to literal discourse, as opposed to the noetic remainder that formalism subtracts from it.95 This is the poetic mirror image of Quine’s subtractive methodology: it aims to say what little can be said about beings (beings as such) by appealing to the unitary structure that withdraws behind every particular attempt to grasp them (beings as a whole) in a manner that can never become fully explicit.
We are now in a position to precisely articulate the proximity between Badiou and the ontological liberalism of which OOO is the exemplar. If Heidegger’s historical poeticism is the mirror image of Quine’s subtractive naturalism, then ontological liberalism is the shattered mirror reflecting jagged fragments of Badiou’s subtractive mathesis. Without the formal anchor provided by the deductive suture of the Void, the project of encapsulating ‘everything’ (beings as a whole) by means of a poetics of ‘objects’ (beings as such) fractures along metaphoric lines. The attempt to navigate the noetic caesura of ontological difference by transcending the expressive constraints of literal discourse inevitably turns to metaphor as its means of transcendence. We have seen this in the way in which Harman overcomes the gap between phenomenology and metaphysics not merely through the tactical use of metaphors to leap from phenomenological to metaphysical chains of reasoning and back again, but through the strategic use of metaphor in methodologically founding his metaphysics upon allusion. It is easy enough to see the tactical use of metaphor as a common theme in ontological liberalism, but it is important to see that this strategic move is what binds it together. The strategy is presented casually but revealingly by Ian Bogost in Alien Phenomenology:
In short, all things equally exist, yet they do not exist equally. The funeral pyre is not the same as the aardvark; the porceletta shell is not equivalent to the rugby ball. Not only is neither pair reducible to human encounter, but also neither is reducible to the other […] This maxim may seem like a tautology—or just a gag. It’s certainly not the sort of qualified, reasoned, hand-wrung ontological position that’s customary in philosophy. But such an extreme take is required for the curious garden of things to flower. Consider it a thought experiment, as all speculation must be: what if we shed all criteria whatsoever and simply hold that everything exists, even things that don’t?96
Here we see ontological liberalism in its most innocuous form: don’t worry that ‘everything exists’ is literally a tautology, because it is required for figurative goals (‘for the curious garden of things to flower’); don’t worry that it isn’t philosophically precise, because it is a speculative experiment in imprecision (‘everything exists, even things that don’t’). It is precisely insofar as it is bound together by a commitment to figuration (allusion) rather than formalism (subtraction) that ontological liberalism fractures itself: the strategic use of metaphor inevitably splinters into a multitude of metaphorical strategies.97 These strategies may borrow from, intersect, and overlap with one another, but, in the absence of formal devices for indexing and delimiting what is implicit in them (e.g., set theory or first-order logic) let alone making it explicit (i.e., in literal discourse), they are little more than an expressive patchwork of resonant metaphors held together by a common pool of rhetorical devices (e.g., ‘everything exists’, ‘the Whole does not exist’, and the increasingly bizarre lists of things that flank them).
We can see this complicity between metaphor and rhetoric in Harman’s version of the reification objection, which rejects the existence of the Whole qua holism by strategically alluding to the reality of multiplicity by means of its appearance. This strategy is realised less by a litany of expressive tactics than by the expression of tactical litanies—the deeper truth about objects to which metaphysics refers is secured by referencing and rhetorically ramifying the superficial diaspora of non-metaphysical sense: pupils and Popeye; muons and moods; the holy spirit and flatulence; Zimbabwe and lambda functions; misogyny and melanomas; klingons and car crashes; lists of lovers and lovers of lists; spells and spookiness; Being, time and Being and Time; the Big Mac™ and the empty set (Ø); The Big Bang and The Homosexual Agenda; Proustian experiences and Cthulhu; the best of all possible worlds and the perfect sandwich; boredom and Boris Johnson’s famous haircut; Microsoft and Minesweeper; Bruno Latour and Latour litanies; true contradictions and false tautologies; evil and Elvis; something that cannot be referred to in this list and everything else that can; Gödel’s famous theorems and his infamous paranoiac fantasies; qualia and quiche; whatever I am currently alluding to and the sublime excess over our collective imagination thereby invoked; transfinite sets and the slow, creeping, horrific, but nevertheless inevitable and in truth almost Lovecraftian realisation that none of us understand the implications of their usefulness in mathematical practice; ambiguity and aubergines; lists of (lists of (lists of […])) and the uncomfortable reflexivity of this phrase; the dawning realisation that litanies such as this one are at best rhetorically grandiose and at worst cognitive anaesthetics with performative pretensions, and the corresponding hope that they will fade from the pages of history like an exhausted simile.98
Nevertheless, it is important to acknowledge that, while this alliance of strategic metaphor and tactical rhetoric is insufficient, there is always more to ontological liberalism than mere metaphor and rhetoric. If there were no explicit metaphysical supplement, then there could be no useful metaphysical debate between it and other such positions, much as there can be no such debate with the later Heidegger’s anti-metaphysical position. The problem is that its explicit metaphysics is always in conflict with the implicit metaphorics it is founded upon. The demand for a positive concept of ‘object’ sufficient to encapsulate an expressive allusion to ‘everything’ requires that we curtail the expressive power of this metaphorics to allude to objects that don’t fit the concept. The conflict between metaphysics and metaphorics can only ever resolve itself in the form of a representational blockage.
In Harman’s work, the principal site of this conflict is the temporal underpinnings of his renewed concept of substance. This conflict and the resulting temporal blockage is perfectly articulated by Tristan Garcia in contrasting his own work with Harman’s OOP:
Time is a tribunal deciding between a theory that treats everything as equal objects, but transforms these objects into purely formal things, and a theory that treats its objects as objects, but excludes some things and transforms them into secondary objects.
I choose a path that leads me to treat no-matter-what as a thing and to explode the spatio-temporal constraints in order to define a formal system […] But there is a price to pay. My thing hardly has anything to do with objects of common sense or at least the objects that ‘object-oriented ontologies’ would like to account for. No-matter-what being something, my thing is too formal: each instance of something, each event, and each part of each thing are so many things. And in this way, my thing slips through my fingers. My world is populated not only with football teams, words, ghosts, falsities, golden mountains, and square circles, but also and above all parts of ghost fingers, parts of parts, and parts of these parts at any time t, and in the following moment, and the hundred moments before, and ten seconds before that […] On the other hand, Harman chooses to remain at the level of objects and not to break with the common sense notion of objects, that is, spatio-temporal identifiable and re-identifiable entities. In this way, his objects are more concrete, more easily discernible. The price to pay for his ontology is that it presupposes time and space as specific constraints, internal to the object […] He borrows from the classical model of substantiality and endows it with an innovative meaning. Internally, his model is strengthened by space and time. But in this way, he gives up considering many things like full-fledged objects.99
Despite the fact that we can think the temporal parts of objects (e.g., a person as infant and as adult) as distinct from the temporally enduring objects they compose (e.g., the person who was once an infant and is now an adult), Harman refuses to count them as distinct objects. Although he diverges from classical substance theorists by insisting that fleeting occurrences and events (e.g., a birth, a death, a gamma ray burst, etc.) can be thought as substances in their own right, he nevertheless refuses to allow the division of substances into discrete temporal events. In essence, Harman diverges from Badiou, Garcia, and Gabriel by refusing to take the noetic challenge to its extreme—his unthematised dependence upon deep time curtails the representational dimension of his ontological egalitarianism.
This temporal blockage is peculiar to Harman (and OOO to a lesser extent),100 yet the self-limiting character of the alliance between metaphysics and metaphorics makes similar blockages in other strands of ontological liberalism inevitable. Subtractive ontology may leave too much unsaid, but allusive ontology tries to say too much—to say the unsayable—and becomes tangled in its own ambitions. It is a cautionary example of the importance of recognising the difference between meaningfulness and the experience of meaningfulness, or between genuine profundity and the affect of edification. Badiou provides the best account of the dangers of confusing philosophical insight and poetic allusion:
Now, to abandon the rational mathematical paradigm is fatal for philosophy, which then turns into a failed poem. And to return to objectivity is fatal for the poem, which then turns into didactic poetry, a poetry lost in philosophy […] Let us struggle then, partitioned, split, unreconciled. Let us struggle for the flash of conflict, we philosophers, always torn between the mathematical norm of literal transparency and the poetic norm of singularity and presence. Let us struggle then, but having recognized the common task, which is to think what is unthinkable, to say what is impossible to say. Or, to adopt Mallarmé’s imperative, which I believe is common to philosophy and poetry: ‘There, wherever it may be, deny the unsayable—it lies.’101
We need not follow Badiou in his attempt to mathematically trace the edges of the unsayable to agree that philosophy cannot but lose itself in the attempt to transgress these limits: the methodological foundation of allusive ontology is built on the shifting sands of insincerity.
What lesson should we learn from all this? I think that we must realise that ontology—both in the sense of defining ontological commitment in general (meta-ontology) and that of articulating our specific ontological commitments (applied ontology)—has an important representational function, and that this function should be understood in terms of its epistemological role in our practices of explanation. This is the essential truth revealed by the way ‘ontology’ is approached by both natural and informational science: there is a practical need to organise the systems of reference through which we index and identify both the explanandum of our theories and their explanans.102 There is a connection here with type theory, which is an attempt to formally circumscribe mathematical reference by means of a system of variable types, but is sometimes misunderstood as an attempt to formally circumscribe reference as such. This is a misunderstanding because, although there is a primitive type of non-mathematical objects, it does not distinguish between non-mathematical types. We can see that the interface between the explanatory tools that mathematics provides and the non-mathematical domains in which they are applied is provided by the more or less implicit counting procedures corresponding to interconnected systems of predicates: including sortal predicates (e.g., [dog → mammal → animal], [flathead → screwdriver → tool], [network interface → daemon → program], etc.) and quasi-sortal predicates (e.g., [electron → lepton → fermion],103 [gouda → cheese → food], [water → liquid → volume], etc.). This reveals a similar insight underlying Husserl’s phenomenological sublimation and Badiou’s subsequent category-theoretical reorientation of the noetic challenge to ontological conservatism. Though their respective suppression and suturing of existence obviates anything like a global set of ontological commitments (metaphysica specialis), their attempts to internally delimit the phenomeno-logical structure of different domains of objects (regions/worlds) should be seen as performing the crucial epistemological role of organising reference within the areas of theory and practice that correspond to those domains (e.g., computer science, sociology, and anatomy, along with database design, social organising, and forensics). Moreover, Badiou sees this precisely as a matter of articulating the logical regimes of counting procedures within which objects can appear as units. In essence, they aim to facilitate intra-disciplinary organisation, even if they thereby preclude inter-disciplinary organisation.
How exactly does the appeal to metaphor undermine this representational function? It is best to approach this question from the opposite direction, and explain how metaphors can contribute to the systematisation of reference within given domains.104 This means saying something about how metaphors enable semantic grafting between sortal and quasi-sortal predicates, without getting too deep into the corresponding semantics of singular terms.105 This might best be described as referential transport, or the transposition of counting procedures and the referential infrastructure they implement from one system of predicates to another. For example, by describing musical genres as ‘families’ we can begin to describe their subgenres and the artists that compose them in terms of ‘lineages’, and to refer to them on this basis (e.g., ‘the father of free jazz’, ‘the children of blues and rock music’, etc.) and even to anticipate their as yet nonexistent ‘progeny’ (e.g., ‘the descendants of the union of progressive rock and contemporary folk music’). The metaphors underlying referential transport can be transformed into analogies in the same manner as other metaphors, by precisely delimiting the relations between objects that are transposed from one domain to another (e.g., ‘…is father of…’, ‘…descends from the union of … and …’, etc.). These analogies can even become systems of predicates in their own right, potentially constituting relatively autonomous domains of objects. For example, the metaphor of corporate personhood has developed from a suggestive way to look at group enterprises through multiple iterations of analogical pruning into a constitutive legal framework for individuating corporations and managing their rights and responsibilities.
Alternatively, relevant metaphors can remain inchoate, providing a reservoir of conceptual resources for organising and extending our referential capabilities within a given domain: for example, Wilfrid Sellars’s famous metaphor of ‘the space of reasons’, which licenses more or less open-ended transport from the geometric/topological domain to the logical/discursive domain (e.g., ‘concepts in the same neighbourhood as...’, ‘the inferential maps one needs to navigate...’, etc.). It is this ability of inchoate metaphors to perpetually extend the range of possible objects we can refer to by licensing new referential transports that undermines the representational function of any ontology founded upon them—the dissemination of sense prevents the organisation of reference. However, this problem with metaphors reveals a deeper problem with the noetic challenge to ontological conservatism: the egalitarian drive to ontologically encapsulate every possible object of thought is incompatible with the epistemological demand to ontologically organise thought by articulating a fixed referential framework. One necessitates ontological expansion while the other necessitates ontological contraction. This tension can only be kept at bay by binding the epistemological demand within the domains themselves, refining and reorganising their internal referential systems, while freeing the egalitarian drive to roam between domains, generating new and stranger modes of reference. This differs from Husserl and Badiou’s patchwork of regions and worlds only insofar as its insistence on reality over appearance (metaphysica specialis over phenomeno-logic) requires that thought’s referential profligacy is metaphysically significant.
It is this space between domains of objects, and the hierarchical and transversal explanatory connections it enables between them (e.g., reducing the domain of chemistry to the domain of physics, or explaining changes in artistic domains through interactions between economic, sociological, and psychological domains), with which the anti-reductionist challenge to ontological conservatism is concerned. This is because reductionism as an ontological schema is essentially a representational paradigm for organising reference globally (between domains), rather than locally (within domains). The challenge to reductionism must thus be formulated at this global level (as being concerned with ‘everything’). This enables us to explain the difference between the methodological (Latour) and metaphysical (Deleuze) forms of anti-reductionism outlined at the beginning of this chapter.
However, the names I have given to these two strands might seem counterintuitive, so it is important to explain why I have chosen them. The reason for this counter-intuitive character is that Harman’s engagement with Latour consists in treating his methodology (ANT) as a metaphysics (OOO). This engagement has been a dialogue, and Latour has in many ways embraced Harman’s reframing of explicitly methodological issues as implicitly metaphysical ones.106 However, this reframing is only possible on the basis of something like a shared commitment to the noetic challenge to ontological conservatism. This is to say that methodological issues regarding the organisation of explanatorily transversal reference are converted into metaphysical ones by treating the senses that determine these references as entities in their own right (e.g., sensual objects, fictions, theories, etc.). This solves the relevant methodological issues by subsuming sense within ontology, rather than using ontology as a means to organise reference. The former strategy (Latour/ANT/OOO) is merely methodological because it disarticulates the functional role of ontology in mediating between explanation and representation; whereas the latter strategy (Deleuze/Delanda/emergentism) is properly metaphysical because it proposes a genuine alternative to the ontological schema of reduction—namely, emergence—and thereby provides an alternative global representational paradigm.107
To understand this contrast between Latourian methodological anti-reductionism and metaphysical emergentism we must return to Latour’s anthropological bracketing of differences between epistemic activities, because his account of transversal explanation is fundamentally motivated by his own work in the anthropology of science.108 It is because Latour has a specific interest in representing science as a domain of objects (e.g., experiments, theories, paradigms, etc, qua explanandum) to be explained in terms of its relations to other domains of objects (e.g., experimental equipment, the referents of theories, the sociological environment of paradigms, etc., qua explanans) that he ends up disarticulating the general relation between explanation and representation encoded by ontology. This disarticulation can be seen most clearly in his theory of circulating reference, which he introduces by describing a device that scientific researchers use for storing, organising, and comparing soil samples:
[T]he pedocomparator will help us grasp the practical difference between abstract and concrete, sign and furniture. With its handle, its wooden frame, its padding, and its cardboard, the pedocomparator belongs to “things.” but in the regularity of its cubes, their disposition in columns and rows, their discrete character, and the possibility of freely substituting one column for another, the pedocomparator belongs to “signs.” Or rather, it is through the cunning invention of this hybrid that the world of things may become a sign […].
Notice that, at every stage, each element belongs to matter by its origin and form by its destination; it is abstracted from a too-concrete domain before it becomes, at the next stage, too concrete again. We never detect the rupture between things and signs, and we never face the imposition of arbitrary and discrete signs on shapeless and continuous matter. We see only an unbroken series of well nested elements, each of which plays the role of sign for the previous one and of thing for the succeeding one.109
Here Latour turns an empirical practice of referential organisation into an object that is itself to be examined empirically. He thereby aims to understand the practical basis of referential organisation internal to the sciences (e.g., the counting procedures implicit within the relevant systems of predicates as used by a given discipline) by treating reference as the operation of a sequence of increasingly rarified signs—understood as naturalistically tractable representational vehicles or referents—embedded within our explanatory practices.110 However, by explaining the process through which signs are abstracted from the things they refer to as the production of new concrete things in their own right, he essentially suspends the gesture of abstraction, by refusing to understand these signs qua signs—as bearers of representational contents or senses.
We are now in a position to see that the concept of translation is essentially a metaphysical generalisation of Latour’s concept of circulating reference that makes explicit the epistemological and metaphysical homogeneity hiding within it. This generalisation proceeds in two steps: reflexively subsuming itself by referentially expanding its anthropological focus from specific practices of representation to representation in general, before de-anthropocentrising itself by unilaterally cancelling the difference between its own specifically referential chains and chains of causal interaction in general. This radicalises the initial anthropological bracketing of the difference between epistemic practices into an anthropomorphic reduction of the difference between explanatory connections and causal connections, homogenising its own activity of explanation with what it aims to explain. It is harder to find a methodology more diametrically opposed to Husserl’s phenomenological reduction, not just because Latour refuses to bracket the existence of things, but because he actively projects his understanding of himself onto their existence. This flight from anthropocentrism into anthropomorphism is the essence of Latour’s amodernism, or his elision of the divide between culture and nature (or norms and causes).111
However, in collapsing this divide, he has equally collapsed the distinction between sense and reference. This is no longer the local collapse with which we began, in which he permits himself to incorporate scientists’ means of reference alongside their referents within his models of scientific practice, but a global collapse, which makes concepts interchangeable with their objects—making them nodes in representational networks of explanatory connections that are indiscernible from the real networks of causal interactions they supposedly represent. Latour essentially inverts the relationship between explanation and representation (putting the epistemological cart before the metaphysical horse): he solves the problem of transversality not by providing an alternative ontological schema for organising representation of causal interactions between disparate domains, but by ensuring us that they can interact because we can refer to them. Ray Brassier describes the metaphorical underpinnings of this move in the most eloquent terms:
In dismissing the epistemological obligation to explain what meaning is and how it relates to things that are not meanings, Latour, like all postmodernists—his own protestations to the contrary notwithstanding—reduces everything to meaning, since the difference between ‘words’ and ‘things’ turns out to be no more than a functional difference subsumed by the concept of ‘actant’—that is to say, it is a merely nominal difference encompassed by the metaphysical function now ascribed to the metaphor ‘actant’. Since for Latour the latter encompasses everything from hydroelectric powerplants to toothfairies, it follows that every possible difference between powerplants and fairies—i.e. differences in the mechanisms through which they affect and are affected by other entities, whether those mechanisms are currently conceivable or not—is supposed to be unproblematically accounted for by this single conceptual metaphor.112
The metaphysical homogeneity of networks is deeper than we previously realised. Not only does the concept of ‘actant’ elide the ontological difference between individuals and general kinds (e.g., between Joliot and neutrons), but it does so by eliding the difference between general kinds and the concepts that refer to them (e.g., between neutrons and the concept <neutron>). However, although Harman effectively exploits Latour’s conflation of individuality and generality, and otherwise praises his willingness to incorporate fictions, phantasms, and other senses in his explanatory networks, he does not follow Latourian anti-reductionism in conflating sense and reference—his corresponding metaphysical distinction between sensual and real curtails his ontological egalitarianism from the explanatory direction.113
What alternative does metaphysical emergentism provide to this referential catastrophe? It can obviously account for hierarchical explanation insofar as it provides a complementary ontological schema for reduction between domains, but how does it account for the transversal explanations that motivate Latour’s anti-reductionism? There is no single answer to this question, but Deleuze and DeLanda’s metaphysics provide an illustrative example. As we noted in the last chapter: ‘it is no easy matter to outline how every variable characteristic of every physical system in the universe could in principle be incorporated as dimensions of a single continuum which would thereby informationally encode the complete actual state of those systems along with their virtual tendencies, let alone how this continuum can still be divided into discrete chunks corresponding to individual systems and their specific tendencies.’114 However, this is precisely what Deleuze and DeLanda aim to do: to articulate a global representational paradigm capable of situating every entity within this continuum (as individualising loci of pre-individual variables), and to thereby enable the explanation of every causal interaction between those entities (as actual trajectories across virtual surfaces), including transversal interactions between those traditionally confined within the quantificational domains of disparate disciplines.115
Deleuze’s account of the plane of immanence is an exquisite formulation of the de-absolutisation objection to the Whole—an attempt to reimagine Spinoza’s Substance through the lens of the ontological difference—aiming to re-articulate universals as dimensions of qualitative and quantitative variation within a dynamically unfolding informational surface.116 DeLanda’s notion of flat ontology is a radical experiment in ontological univocity—an attempt to universalise dynamic systems theory through population theory—aiming to reconceive individuals as intensive indices within a unitary causal-mereological nexus of reciprocally constraining processes, in which populations of populations evolve and effervesce out of one another and their interwoven environments across a manifold of spatio-temporal scales.117 In essence, although they work in opposing directions (universal → individual and individual → universal), they both aim to understand beings as such (the univocity of Being)118 through beings as a whole (the plane of immanence) in the same manner as Quine.
Nevertheless, they diverge from Quine in refusing his subtractive suturing of the Whole to the referential systems implicit in the supposedly unified enterprise of natural science, but aim to intervene in this enterprise by explicating and revising these referential systems. It is for this reason that their anti-reductionism is properly metaphysical: it adopts an active role in the global organisation of scientific representation.119 Yet this is the same reason that their anti-reductionism should not be opposed to ontological conservatism: in adopting this role it reaffirms the explanatory value of parsimony, rejecting only the twisted form of parsimony popularised by the propagandists of metaphysical reductionism. It is clear that everything has a place within Deleuze and DeLanda’s worlds except those things that don’t (‘everything exists’ is trivial), and that these placeless things are placeless not because they are strictly unthinkable, but because they are explanatorily irrelevant (precisely, ‘some things don’t exist insofar as they give us no reason to suppose they do’). Although ontological liberalism might appear to be an alliance between the noetic and anti-reductionist challenges to ontological conservatism, this alliance is more fragile than it seems. Metaphysical anti-reductionism is less an attack upon ontological conservatism in general than upon the specific form allied to metaphysical reductionism in the twentieth century. Once ontological conservatism abandons reductionism, it can make its peace with emergentism.
It is now time to consolidate our understanding of Harman’s OOP and attempt a serious answer to the question with which this chapter (and perhaps this whole book) is concerned: What are objects? However, our dissection of ontological liberalism has revealed that answering this question is far from simple, principally because it must be prefaced by a more subtle question: What does ‘object’ mean? The popularisation of this term, as a (pseudo-sortal) alternative to ‘thing’ (Ding, res, entity, being, etc.) emerged directly from Kant’s development of the Cartesian opposition between the ‘subject’ and ‘object’ poles of the noetic relation. This noetic connotation of the term was retained in its appropriation by the Austrian school and the Husserlian phenomenology that developed out of it—both of which aimed first and foremost to circumscribe all possible noetic foci (intentional objects). It was later openly resisted by the numerous critiques of the subject-object relation that emerged from Heidegger’s critique of this Cartesian tradition—all of which invariably seek to free ‘things’ from the theoretical/practical constraints imposed upon them by the thinking/acting subject.120 That Harman’s demand to return to the objects themselves positions itself to inherit both of these traditions is thus somewhat peculiar, but it is clear that his distinction between sensual and real is supposed to bind these seemingly conflicting enterprises together, by granting each their own half of the concept <object>. However, this feeds back into our initial question, as it is unclear whether this binding is a mere terminological trick, or a genuine conceptual synthesis.
Harman’s divergences from the noetic and anti-reductionist challenges to ontological conservatism frame this issue on either side: he curtails the representational dimension of ontological liberalism by refusing to extend the term ‘object’ to absolutely everything we can think about (i.e., not all noetic foci are sensual objects); and he curtails the explanatory dimension of ontological liberalism by refusing to treat every ‘object’ as a legitimate explanans (i.e., some sensual objects don’t have corresponding real objects). This means that the term ‘object’ has a positive content that excludes some things we can think about (e.g., non-enduring time-slices of objects), although it isn’t clear how this positive content is shared by both real and sensual objects (e.g., whether sensual objects and real objects endure in the same sense). It is thus absolutely crucial to make explicit what is common to both types of ‘objects’, because it is this generic notion of ‘object’ that Harman appeals to in differentiating himself from his opponents:
Some of these objects are physical, others not; some are real, others not real in the least. But all are unified objects, even if confined to that portion of the world called the mind. Objects are units that both display and conceal a multitude of traits. But whereas the naive standpoint of this book makes no initial claim as to which of these objects is real or unreal, the labor of the intellect is usually taken to be critical rather than naive. Instead of accepting this inflated menagerie of entities, critical thinking debunks objects and denies their autonomy. They are dismissed as figments of the mind, or as mere aggregates built of smaller physical pieces. Yet the stance of this book is not critical, but sincere. I will not reduce some object to the greater glory of others, but will describe instead how objects relate to their own visible and invisible qualities, to each other, and to our own minds—all in a single metaphysics.121
Whether they are underminers who downwardly reduce objects to something more fundamental (e.g., physical systems, atoms and void, or formless Apeiron), overminers who upwardly reduce objects to something less tangible (e.g., sensations, textual effects, or bundles of qualities), or both simultaneously (e.g., by means of an epistemologically Janus-faced ‘materialism’), Harman thinks philosophers have not been sincere in their theoretical dealings with objects.122 They have overlooked the middle ground (or ‘mezzanine level’) of the universe in their rush to theorise their favoured fundament.123
Yet one cannot sincerely demand that they return their attentions to objects without being willing to explain what one means by ‘object’, and, for all his protestations to the contrary, Harman remains surprisingly elusive on this point. Of course, this elusiveness goes hand-in-hand with his allusiveness. However, as we have seen, the confluence of metaphysics and metaphorics in allusive ontology is, if anything, a breeding ground for philosophical insincerity. Our aim should thus be to extract as much precision from Harman’s allusions as possible, so as to reconstruct his determinate commitments, or what he sincerely believes. The locus of this precision—the metaphysical innovation hinted at in the above passage—is almost certainly the fourfold schema; yet it is also in this titular quadruplicity that the elusiveness of the ‘object’ is most clearly manifest: does the schema confront us with a single genus of objects that are genuinely quadruple (sensual/real and object/quality), or two distinct species of objects (sensual/real) that are merely double (object/quality)?
Seemingly subverting its title, The Quadruple Object only ever explicitly describes ‘objects’ as belonging to mutually exclusive species (sensual objects or real objects); yet it constantly invokes the allusion embedded therein by implicitly suggesting that ‘objects’ somehow unite the two sides: ‘I will not reduce some object to the greater glory of others, but will describe instead how objects relate to their own visible and invisible qualities’124 (‘objects’ with both sensual and real qualities). The allusion is concentrated in the categorial connections that span the two sides of the schema: the sensual object is in tension with its own real qualities (eidos), the real object is in tension with its own sensual qualities (space), and sensual qualities radiate from their real counterparts (duplicity), while the sensual object is encountered by a potentially distinct real object (sincerity). In the first three categories (eidos, space, duplicity) the implicit unity of ‘objects’ is encoded in the hypostatized referential relation between the sensual object (qua sense) and the real object (qua reference).125 On the one hand, the referential relation between a specific sensual object and a specific real object is what enables the counterpart relation between their specific qualities. On the other hand, this specificity is itself hypostatized in the form of the ‘it’ to which both sensual and real qualities can belong. But it is telling that the final category (sincerity) does not address this unity at all, but displaces the concern with the reference relation between sensual object (qua sense) and real object (qua reference) with a diametric concern for the referring relation between sensual object (qua sense) and real object (qua referrer). This forces the unity to which the fourfold schema alludes to remain implicit, by occupying the only schematic location where it could be made explicit. This leaves us hovering between the species interpretation explicit in the fourfold schema and the genus interpretation implicit in its categorial allusions.
Although this tension between implicit and explicit is intricately woven into both the form and the content of the fourfold schema in The Quadruple Object, it is already present in an inchoate form in Tool-Being. We can even trace its genesis to a specific passage:
To say that every entity is both tool and broken tool is to say that every entity is half physically real and half merely relational. No entity can be assigned unequivocally to one side of the equation or the other. But this implies something more than we have seen so far. It is not only the case that every entity has a deeper essence—rather, every essence has a deeper essence as well. This will be simpler if we revert to our own earlier terminology: not only does an object have tool-being, but this tool-being in turn has its own tool-being […]
The preceding paragraph has a rather strange implication. The initial argument of this book was that Vorhandenheit and Zuhandenheit are not two distinct classes of entity, but two modes of being that belong to every entity. But we have now pushed Heidegger’s insight far enough that the situation has reversed into its opposite. In a sense, it has now turned out that the hammer in use and the hammer in its tool-being are not simply two sides of the same coin, but two different coins altogether. In an unexpected sense, presence-at-hand and readiness-to-hand turn out to be two distinct beings.126
This passage provides us with three insights into the genesis of Harman’s system. The first insight is that the ‘objects’ which unify the two halves of the fourfold are descended from the reading of Heidegger with which his metaphysics begins, which insisted upon treating the ready-to-hand (substance) and the present-at-hand (relation) as two aspects of the same object, rather than two types of distinct objects. The second insight is that, in clawing its way out of the belly of this reading, his metaphysics transitions from the aspect view to the type view, even if it never entirely cuts the cord between them that its allusions to unity depend upon. The final insight is that the catalyst for this transition is the collision between his Husserlo-Meinongian account of representation and the reflexivity of sense—the realisation that in referring to the object-for-us and the object-in-itself independently from one another, he has converted them into distinct objects that must themselves be sundered between the for-us and the in-itself (i.e., the for-us-in-itself, the for-us-for-us, the in-itself-in-itself, and the in-itself-for-us).
It is this final insight that concerns us, because this newly discovered reflexivity heralds a runaway recursive doubling of every ‘object’ through which even the referents of metaphysical thought (i.e., sensual objects and real objects) perpetually evade us, escaping across fractal senses (i.e., [sensual [sensual [sensual […]]]] or [[[[…] for us] for us] for us]). It thus seems as if the reflexive transubstantiation of aspects into types should make metaphysical knowledge of these types impossible in the same way that the initial distinction between aspects made knowledge of ‘objects’ impossible. This would mean the total and utter collapse of Harman’s metaphysical edifice. He briefly addresses this worry in a different section of the previous passage:
Will this lead to an “infinite regress” of tool-beings? For now, we can simply call it an “indefinite regress”, and move on to other problems that arise from the emerging concept of substance.127
It is first worth pointing out that the substitution of ‘indefinite’ for ‘infinite’ is, at best, a clarification of what makes the regress problematic, and, at worst, a mere terminological sleight of hand designed to dismiss the severity of this problem. It is next worth pointing out that the tacit promise to return to this regress after addressing other problems is never actually fulfilled. Although Guerrilla Metaphysics stumbles through the same conceptual terrain at various points, it fails to reformulate the problem, let alone solve it.128 The type view is simply restated in The Quadruple Object, as a seemingly stable axis harbouring no hidden regress. This blocks the recursive doubling of objects into sense/reference branches in a manner parallel to the temporal blockage upon the division of objects into time-slices, but it also erases the genesis of the type view. This erasure is responsible for both its allusiveness—by securing its continued indiscernibility from the aspect view—and its elusiveness—by concealing the continued absence of a distinct justification for it.
Ultimately, the seemingly diagrammatic precision of the fourfold schema is nothing but an alibi for a more insidious conceptual vagueness.129 Its neat numerological derivation of ontographic categories conceals the intractable obscurity of the elementary metaphysical categories they are founded upon: object, quality, and relation. We have progressively traced the pathologies of Harman’s deployment of these categories across the three preceding sections, but having contextualised his concern with ‘objects’ and shown how this concern is embedded in his mature categorial schema, we are now in a position to integrate those insights into a comprehensive epidemiology of obfuscation.
Harman can never give the concept <object> a determinate positive content qua genus to which sensual and real objects belong as species, because our grasp of the latter is still tethered to understanding them as aspects of a unified ‘object’. Conversely, he can never give the concept a determinate positive content qua universal of which these unified objects are instances, because the allusion to them which the fourfold schema encodes cannot be made explicit without contradicting its axial division of ‘objects’ into mutually exclusive types. This conflict within the concept is the ultimate consequence of the hypostatization of reference explained in chapter 3,1, ‘Sense and Sensuality’. The catastrophic contradictions of Harman’s representationalism are only contained by the representational blockage allusively encoded in the fourfold diagram, which disguises the choice between the de-reification of sense—refusing the ontological distinction between the object-for-us and the object-in-itself—and its fractal proliferation—allowing the recursive branching of objects-[...]-for-us that is seemingly indistinguishable from anti-metaphysical correlationism. As ever, only the invocation of allusion as an oblique mode of reference immune to the ontological bifurcation of sense and reference is sufficient to cut the gordian knot this choice presents us with: we avoid contradiction by thinking in a manner that is supposedly beyond such logical niceties.
The resultant vacuousness of the concept <object> is positively virulent, infecting and evacuating the concept <quality> of its determinate content by means of their opposition within the second axis of the fourfold schema. The orthogonal opposition between real and sensual precludes understanding <quality> as a genus to which both sensual and real qualities belong in much the same way it precludes understanding <object> as a genus. However, in this case it is a consequence of the hypostatization of predication (as explained in chapter 3.2, ‘Qualities and Qualia’, above). Harman severs the representational connection between reference and predication and thereby establishes the duplicitous relationship between the qualities of the object-for-us and the object-in-itself that absolutely segregates them. This segregation prevents us from abstracting anything common to them that is not already supplied by Harman’s implicit account of the predicative dimension of representation. Harman’s qualitative haecceitism is less an attempt to fill this conceptual void than its recognition qua void: the ‘vacuous actuality’ of real qualities is simply the projection of the sheer thisness of sensory qualities onto their representational counterparts, constrained by a duplicitous filter that permits no commonality beyond mere thisness. It is thus hardly surprising that Harman complements this explicit recognition of vacuousness with an implicit allusion to mereology, because he has nothing else with which to shore up the axial distinction between the referential thisness of objects and the predicative thisness of qualities.
Nevertheless, it is the concept <relation> that incorporates the most fascinating paradox. As explained above (chapter 3.3, ‘What are Relations Anyway?’), the very possibility of categorially circumscribing the various possible ‘relations’ that can obtain within Harman’s world (confrontation, theory, allure, and causation)—by means of the ‘tensions’ between the four poles of the schema (time, eidos, space, and essence) as their ‘fission’ (confrontation-time and theory-eidos) and ‘fusion’ (allure-space and causation-essence)—is dependent upon not counting these tensions (nor the junctions and radiations) as the relations between poles that they so obviously are (SO–SQ, SO–RQ, RO–SQ, and RO–RQ). Distilling the paradox: the concept <relation> is used to restrict itself in a way that would preclude this very use. Once more, Harman’s only way to navigate paradox is by harnessing the power of metaphor to evade inconvenient reflexivity: the sense in which tensions are relations must be a metaphorical appropriation of the sense in which their fusions and fissions are relations. This evasion turns in a metaphorical circle that is not so much vicious as it is absurd: a metaphor that is parasitic upon the very concept it is constructed to define. Nevertheless, as absurd as this is, it is not the most egregious obfuscation diagrammatically embedded in the fourfold, an honour which belongs to the category of sincerity.130 Not only does sincerity occupy the only place in the schema in which its underlying unity could be articulated (SO-RO), but in doing so it equally suppresses the crucial factor that distinguishes the ‘surface relations’ of confrontation and theory from the ‘deep relations’ of allure and causation—namely, the referential connection between the sensual object and real object that enables us to vicariously encounter the latter through the former.
All of these considerations bring us back to the Husserlo-Meingonian account of representation from which Harman’s metaphysics unfurls, and the primitive relation between the object-for-us and the object-in-itself that defines it. We have already said much about this account, both in trying to wrest it from its lair, hidden deep between the lines of Harman’s texts, and in trying to dissect it, unveiling its limited explanatory skeleton; we have even situated it within a broader lineage of noetic challenges to ontological conservatism; but we have yet to really consider what motivates these challengers to ground representation in metaphysics. The best way of bringing out this motivation is to consider the case of fictional objects, such as Eldorado, Popeye, or the three little pigs. It is even better to return to the sort of claims about fictional objects that proved problematic for Quine (e.g., ‘Eldorado has a golden king’, ‘Popeye has a girlfriend’, and ‘two out of three little pigs lost their houses to the big bad wolf’). Intuitively, these claims seem to be true, but they cannot be interpreted as true unless we take them to quantify over fictional objects, and this seems to suggest that these fictional objects exist. However, and just as intuitively, these fictional objects don’t seem to exist in the same way as non-fictional objects such as London, Boris Johnson, or the 650 elected members of the House of Commons. Of course, just as there are ontological conservatives who deny the former intuition (e.g., Quine), there are ontological liberals who deny the latter (e.g., Gabriel), but there are others who try to affirm them both (e.g., Meinong). Meinong aims to synthesise them by means of a distinction between modes of Being—some things do not exist but merely subsist—whereas Harman holds that everything exists, but that everything is not therefore real. For Harman, the difference between Popeye and Boris Johnson is not that, as generic ‘objects’, they have different modes of Being, but rather that, as encountered sensual objects, only one of them conceals a corresponding real object.
It is a useful exercise to consider whether there is another way to synthesise these intuitions, or an alternative to both Meinong and Harman’s Husserlo-Meinongian hybrid. Consider the following suggestion: what if we agree that it is true that ‘Popeye has a girlfriend’ and thus that there is some sense of ‘existence’ in which it is true that ‘Olive Oyl exists’, but that nevertheless there is a univocal sense in which ‘Olive Oyl doesn’t really exist’. This is precisely the sort of talk that free logic formalises, by enabling us to introduce non-referring terms that we can nevertheless use in quantification.131 On this view, what ‘really exists’ is what lies within the inner quantificational domain (the Whole)—the content (beings) corresponding to its structure (Being/Nothing). But how does this differ from Harman’s view? Surely, they both agree that ‘Popeye has a girlfriend’ and that ‘Olive Oyl isn’t real’? The crucial difference is that this view—my view—denies the need to provide a metaphysical explanation for how we can think about Olive Oyl even if she isn’t real. This non-metaphysical approach to fictions is not for that matter anti-metaphysical: it simply maintains that metaphysics begins and ends with reality, and that we can happily think and talk about unreal things that lie entirely beyond its scope. In endorsing this view I am an unabashed ontological conservative, albeit one who is more drawn to Deleuze’s metaphysical emergentism than to Quine’s subtractive naturalism.
How can we resolve the conflict between my non-metaphysical approach to fictions and Harman’s object-oriented metaphysics? I think it is worth drawing some inspiration from Hegel’s account of Sense-Certainty: ‘But language, as we see, is the more truthful; in it we ourselves directly refute what we mean to say’.132 That is, we should aim to explicitly articulate the motivation for Harman’s approach, and see if this very attempt leads to its refutation. This means capturing what it is about the non-metaphysical approach that Harman would find so inadequate. Harman might insist that ‘Olive Oyl exists!’, to which I would respond with qualified agreement. He would then try to leverage my qualification into a disagreement, claiming that ‘But you don’t think she really exists!’, to which I would most certainly agree, and add ‘But surely, neither do you?’ At this point, Harman would want to say something like ‘I mean that Olive Oyl really exists qua sensual object even if she doesn’t really exist qua real object!’ This is the point at which language is more truthful—the natural way to counter my ‘really’ qualification is to posit a different sense of ‘really’, but this sense must split apart from the sense in which real objects are ‘real’, so that we distinguish between ‘really unreal’ objects and ‘really real’ ones. However, it is crucial to understand that this bifurcation of ‘reality’ is nothing but the other fork of the recursive sense/reference branching engendered by the reflexive application of Harman’s account of representation. In the attempt to talk about the object-for-us-in-itself, our metaphysical referent escapes us along the edge of a ramifying pathway: object-for-us-[[[...]]-in-itself]in-itself]-in-itself or really-[really-[really-[...]]]-unreal. Harman would no doubt insist that his allusive escapology secures the possibility of metaphysics against the trivial reflexive gymnastics of literal thought, but this can never compensate for the fact that he cannot say what he sincerely believes, even if he can allude to it. What are objects? If you ask Graham Harman, expect a gesture, not an answer.
1. A. Meinong, The Theory of Objects, tr. I. Levi, D.B. Terrell, R.M. Chisholm, in R.M. Chisholm (ed.), Realism and the Background of Phenomenology (New York: The Free Press, 1960), 76–117, <http://www.hist-analytic.com/Meinongobjects.pdf>.
2. With regard to Meinong and his successors, we have explained the motivations of his theory and their effect upon Harman’s metaphysics in more depth in the ‘Sense and Sensuality’ chapter (chapter 3.1). With regard to Husserl and his successors, it is important to note that Heidegger differs from much of the rest of the phenomenological tradition in attempting to use the bracketing provided by the phenomenological method to methodologically ground metaphysics. See my The Question of Being for further details.
3. With regard to Deleuze, the important reference is his and Guattari’s A Thousand Plateaus, tr. B. Massumi (Minneapolis: Minnesota University Press, 1983); his allies include figures such as Manuel DeLanda, Isabelle Stengers, and the proponents of complexity theory (cf. Ian Stewart and Jack Cohen, The Collapse of Chaos: Discovering Simplicity in a Complex World [London: Penguin, 1994]). With regard to Latour, the crucial reference is his ‘Irreductions’ (second part of The Pasteurization of France [Cambridge, MA: Harvard University Press, 1993]); his allies include figures such as Michel Serres, Jane Bennett, and the adherents of actor network theory (ANT) who draw upon him.
4. Chapter 3.1.
5. Chapter 3.3, subsection 2.
6. This aspect of DeLanda’s influence on Harman is not something we have addressed in any depth. It is evident from his discussion of DeLanda’s multi-layered ‘flat ontology’ (Towards Speculative Realism, 178–82) and his subsequent adoption of this term (albeit with a slightly modified meaning, cf. ‘Response to Garcia’, Parrhesia 16 [2013], 27). This expands upon the concept of ‘levels’ that he had already drawn from Alphonso Lingis’s work (Guerrilla Metaphysics, chapter 5).
7. The Quadruple Object, 5.
8. This device has been dubbed the ‘Latour litany’ by Ian Bogost.
9. T. Garcia, Form and Object : A Treatise on Things, tr. M. A. Ohm and J. Cogburn (Edinburgh: Edinburgh University Press, 2014); M. Gabriel, Transcendental Ontology: Essays in German Idealism (London: Bloomsbury, 2013).
10. Garcia, Form and Object, i.
11. T. Garcia, ‘Crossing Ways of Thinking: On Graham Harman’s System and My Own’, tr. J. Cogburn and M. Ohm, in Parrhesia 16 (2013), 15.
12. W. V. O. Quine, ‘On What There Is’, in From a Logical Point of View (New York: Harper, 1953).
13. It is important to note that the scholastic division between metaphysica generalis and metaphysica specialis is older than the term ‘ontology’, which was only introduced in the seventeenth century (cf. A. Baumgarten, Metaphysics, tr. C. D. Fugate and J. Hymers [London and New York: Bloomsbury, 2013]; H. Caygill, A Kant Dictionary [Oxford: Blackwell, 1995], 307–8).
14. I shall have more to say about the historical and sociological dimensions of the split between the ‘analytic’ and ‘Continental’ traditions of Western philosophy below (chapters 3.5 and 4.1).
15. Caygill, A Kant Dictionary, 307–8.
16. Heidegger traces this shift in the meaning of the term in Fundamental Concepts of Metaphysics (§§11–14).
17. Husserl, Ideas I, §§148–149.
18. Heidegger discusses this distinction in detail in Introduction to Metaphysics (103–22).
19. Fundamental Concepts of Metaphysics, 33. Heidegger also shows the way in which these two different inquiries emerge out of a single concern with physis, which is interpreted as both beings as such and beings as a whole. This develops into Heidegger’s later analyses of physis as the initial form that Being takes at the beginning of the history of metaphysics. Cf. Introduction to Metaphysics, 14–19; Contributions to Philosophy (From Enowning), tr. P. Emad and K. Maly (Bloomington, IN: Indiana University Press, 2000), part III; and ‘The Onto-Theo-Logical Constitution of Metaphysics’, in Identity and Difference, tr. J. Stambaugh (Chicago: University of Chicago Press, 42–74: 66).
20. Cf. Introduction to Metaphysics.
21. The project of fundamental ontology is sometimes read as identical with the inquiry into the Being of Dasein. In Being and Time, Heidegger seems to deny this, explicitly stating that: ‘The analytic of Dasein […] is to prepare the way for the problematic of fundamental ontology—the question of the meaning of Being in general.’ (Being and Time, 227) However, in Basic Problems of Phenomenology he states: ‘We therefore call the preparatory ontological analytic of the Dasein fundamental ontology […] It can only be preparatory because it aims to establish the foundation for a radical ontology.’ (224) It thus appears that what Heidegger means by ‘fundamental ontology’ shifts between these two works. I choose to use the term as it is used in Being and Time, where it names the project of grounding regional ontology by attempting to provide a concept of Being in general.
22. Cf. Heidegger, Fundamental Concepts of Metaphysics, Introduction to Metaphysics, ‘What is Metaphysics’, in W. McNeill (ed.), Pathmarks (Cambridge: Cambridge University Press, 1998), and Metaphysical Foundations of Logic (Bloomington, IN: Indianapolis University Press, 1984)
23. The last substantive and indicatively minimal engagement with ontology is to be found in ‘The End of Philosophy and the Task of Thinking’ (in Basic Writings, ed. D. F. Krell [London: Routledge Classics, 1993]).
24. J. Derrida, ‘Ousia and Gramme’, in Margins of Philosophy (Chicago: University of Chicago Press, 1982), 29–68.
25. Cf. Heidegger, ‘On the Essence of Truth’, in Pathmarks, 126–7; Basic Questions of Phenomenology, §§31–3 ; Contributions to Philosophy, §85, §87, §91; Derrida, ‘Ousia and Gramme’, 63–7.
26. A. Badiou, ‘The Question of Being Today’, in Theoretical Writings, ed., tr. R. Brassier and A. Toscano (London: Continuum, 2006).
27. A. Badiou, Being and Event, tr. O. Feltham (London: Continuum, 2005), 9–16.
28. Ibid., Meditation I.
29. Badiou, ‘Being and Appearance’, in Theoretical Writings.
30. A. Badiou, Logics of Worlds, tr. A. Toscano (London: Continuum, 2009).
31. Badiou, Being and Event, Meditation IV.
32. Meillassoux, After Finitude, 32–4 and 125–6.
33. ‘Speculative Realism’ in Collapse vol. 3, 393; After Finitude, chapter 6; P. Wolfendale, ‘The Necessity of Contingency’, in P. Gratton, P. J. Ennis (eds), The Meillassoux Dictionary (Edinburgh: Edinburgh University Press, 2014).
34. This is not to say that there are not important connections between Meillassoux’s treatment of the distinction between possibility and actuality and the distinction between reality and appearance (or Being and seeming) that is implicit in Husserl, problematised by Heidegger and Derrida, and explicitly reformulated by Badiou. Importantly, the way that Meillassoux uses the emergence of worlds from one another ex nihilo to underwrite the distinction between primary and secondary qualities (cf. After Finitude, chapter 1; Philosophy in the Making, appendix B) can be seen as grounding his account of appearance in his account of actuality.
35. Philosophy in the Making, appendix D.
36. Meillassoux explicitly acknowledges Wittgenstein as the founding figure of strong correlationism in analytic philosophy (After Finitude, 41–51), whose Tractatus Logico Philosophicus is undoubtedly inspired by Kant’s correlationism. However, he also draws a useful distinction between universalist and anti-universalist strains of strong correlationism, which differ on whether there is a universal structure of correlation (e.g., language, consciousness, etc.). Husserl, the early Wittgenstein, the early Heidegger, and perhaps Habermas exemplify the former strain, and the later Wittgenstein, the later Heidegger, Derrida, and the loose agglomeration of thinkers who self-identify as ‘postmodernists’ exemplify the latter.
37. Cf. Badiou, ‘Kant’s Subtractive Ontology’ in Theoretical Writings.
38. Although it is in decline (or remission) it is far from dead, and has in fact been radicalised into a more general ‘end of philosophy’ narrative by François Laruelle, whose non-philosophy aims to axiomatically extend philosophical practice in much the way that Heidegger and Derrida aimed to pragmatically reorient it (cf. F. Laruelle, Principles of Non-Philosophy, tr. A. P. Smith [London and New York: Bloomsbury, 2013]; F. Laruelle, From Decision to Heresy, tr. M. Abreu et al. [Falmouth and New York: Urbanomic and Sequence Press, 2012]).
39. It is important to note that Deleuze is sensitive to Heidegger’s critique of the metaphysical tradition: he acknowledges the problems of onto-theology and incorporates the idea of ontological difference into his work (cf. Difference and Repetition, 77–9); he simply rejects Heidegger’s identification of onto-theology and metaphysics; and on that basis continues to draw upon the tradition (e.g., Spinoza and Leibniz).
40. It is worth noting that Badiou has warmed to the term ‘metaphysics’ over time, precisely because it provides a better index of the relation between his project (‘meta-ontology’) and that of figures such as Deleuze (‘Political Perversion and Democracy’, talk given at the European Graduate School 08/12/2004: <https://www.youtube.com/watch?v=AcKdPzB3gYQ>).
41. Kant, Critique of Pure Reason, B620–30, B660–70.
42. See chapter 3.1, subsection 2 for a more thorough description of Russell’s theory of descriptions and the controversy over its extension into a theory of proper names.
43. Frege is more perspicuous than Russell in this regard. He rejects Kant’s positive thesis because he is concerned to provide an account of the existence of numbers, which are abstract objects and therefore non-spatio-temporal. He derives the existence of abstract objects from concrete ones by means of an operation of abstraction (e.g., [abstract] orientations must exist because the relation ‘…is parallel to…’ holds between [concrete] lines, such that ‘the orientation of x’ is identical to ‘the orientation of y’ iff x is parallel to y). This does not provide a complete alternative to Kant’s positive account, but it does present an important conceptual link between existence and criteria of identity (cf. Brandom, Making It Explicit, chapter 7).
44. B. Russell, ‘On Propositions: What They Are and How They Mean’, Proceedings of the Aristotelian Society, Supplementary Volumes, vol. 2, Problems of Science and Philosophy (1919), 1-43.
45. This is the origin of strong correlationism in the analytic tradition. See note 36, above.
46. M. Schlick, ‘Meaning and Verification’, Philosophical Review 45:4 (1936): 339–69.
47. The influence of this diaspora is why the analytic tradition is sometimes referred to as ‘Anglo-Austrian’ as much as ‘Anglo-American’.
48. R. Carnap, ‘Empiricism, Semantics, and Ontology’ in Revue Internationale de Philosophie 4 (1950), 20–40.
49. See H. Price, ‘Metaphysics After Carnap: The Ghost Who Walks?’ and M. Eklund, ‘Carnap and Ontological Pluralism’, in D. Chalmers, D. Manley and R. Wasserman (eds), Metametaphysics (Oxford: Clarendon Press, 2009), 320–46 and 150–56.
50. The explicit cultivation of such ‘ontologies’ is most popular in computer science and biomedical science. For a useful discussion of the terminology see Werner Ceusters, ‘Biomedical Ontologies: Toward Sound Debate’, <http://www.referent-tracking.com/RTU/sendfile/?file=CeustersCommentaryOnMaojoLongVersion.pdf>.
51. Quine, ‘On What There Is’.
52. See Quine, The Roots of Reference (La Salle, IL: Open Court, 1973), part III.
53. See D. Lewis, On the Plurality of Worlds (Oxford: Wiley-Blackwell, 2001).
54. The Metametaphysics collection (see chapter 3.4, n. 49, above) is an excellent survey of contemporary work in this field. Kit Fine’s essay (‘The Question of Ontology’, 157–77) provides the best example of the sort of substantial analysis that Quine himself rejects.
55. See D. M. Armstrong, Universals: An Opinionated Introduction (Boulder, CO: Westview Press, 1989).
56. Of course, there are figures in the analytic tradition who entirely ignore the Viennese rejection of metaphysics (e.g., substance theorists such as E.J. Lowe and David Wiggins), and there are others who stick with Carnap against Quine (e.g., neo-Carnapians such as Eli Hirsch and Huw Price).
57. This term is introduced by Dale Jacquette in his book Ontology (Montreal: McGill-Queen’s University Press, 2002) and is contrasted to ‘pure ontology’ which covers both Heideggerian fundamental ontology and analytic meta-ontology.
58. The standard account of quantifiers is called the objectual interpretation (cf. J. Barwise and J. Etchemendy, Language Proof and Logic [Stanford, CA: CSLI Publications, 1999], part II), because it treats variables as ranging directly over sets of objects. This is contrasted with the substitutional interpretation, in which variables ranges over sets of singular terms that purportedly refer to objects, rather than the objects themselves (cf. Making It Explicit, chapters 6–7; M. Lance, ‘Quantification, Substitution, and Conceptual Content’, Nous 30:4 [December 1996], 481–507; and J. Tomberlin, ‘Objectual or Substitutional’, Philosophical Issues vol. 8 [1997], 151–67). It is also sometimes contrasted with the interpretation of the quantifiers provided by free logic, which standardly uses two domains: an inner domain of existing objects and an outer domain of either non-existing objects or the singular terms that refer to them (cf. K. Lambert, ‘The Philosophical Foundations of Free Logic’, in Free Logic: Selected Essays [Cambridge: Cambridge University Press, 2003]). However, as Lance shows, it’s possible to reconstruct objectual quantification in substitutional terms (using substitution-inferential semantics as opposed to model-theoretic representational semantics), and as Tomberlin shows, Brandom’s own way of doing this is essentially a variant of free logic. This shows that there are more complex interactions between the different interpretations of the quantifier than a simple threefold distinction might indicate. Nevertheless, I will remain neutral on these issues until specified otherwise.
59. See chapter 3.3.
60. There are a number of complexities involved in the formulation of type theories that I have deliberately glossed over in the above presentation (e.g., the distinction between type and order necessitated by the ramification of types once relational predicates are considered, and the successor theories proposed by Church and others). For a detailed historical overview of these issues, beginning with Frege’s hierarchy of concepts and its development in Russell and Whitehead’s hierarchy of propositional functions, see W. Kneale, Development of Logic (Oxford: Clarendon Press, 1962), 652–72; and C. Chihara, Ontology and the Vicious Circle Principle (Ithaca: Cornell University Press, 1973).
61. In explaining type theory as the classic solution to these paradoxes, I am not thereby advocating the idea that it is the definitive solution. There has been much useful work done that tries to get beyond this approach (cf. Ø. Linnebo. ‘Plurals, Predicates, and Paradox: Towards a Type-Free Account’, <http://semantics.univ-paris1.fr/pdf/ppp-description.pdf>; J.-Y. Girard ‘Locus Solum: From the Rules of Logic to the Logic of Rules’, <http://iml.univ-mrs.fr/~girard/0.ps.gz>).
62. This conflict arises from the terminological differences between Frege’s hierarchy of concepts (which quantifiers are internal to) and Russell’s hierarchy of propositional functions (which quantifiers are external to).
63. Quine, ‘On What There Is’, 13.
64. G. Frege, The Foundations of Arithmetic, tr. J. L. Austin (Oxford: Blackwell, 1950), 65.
65. No relation. See Chapter 2, n.2, above
66. For a comprehensive overview of just how referentially frugal Quine thinks we can be, see The Roots of Reference. It is worth pointing out that Quine rejects higher-order logic in favour of set theory, meaning that he is committed to the numbers and sets ranged over by the first-order variables of mathematical discourse as much as the concrete individuals ranged over by the first-order variables of empirical discourse (x), but is not committed to the existence of anything ranged over by supposedly second-order variables (φ) such as concepts, properties, etc.
67. This is the objectual interpretation mentioned in chapter 4.2, n.58.
68. For a slightly less brief summary of these paradoxes, consult Glenn W. Erickson and John A. Fossa’s Dictionary of Paradoxes (Lanham, MY: University Press of America, 1998). For a thorough exposition cf. Kneale, The Development of Logic, and Chihara, On the Vicious Circle Principle.
69. Cantor’s paradox has become popular in recent Continental philosophy because of the work of Badiou. It has been appropriated by various other thinkers (e.g., Meillassoux, Slavoj Žižek, Adrian Johnston) as evidence for the non-existence of the Whole. However, unlike Badiou, they tend not to explain how we are to deduce the nonexistence of a totality of entities as such from a claim about the totality of sets.
70. Cf. Kneale, The Development of Logic.
71. For a detailed exploration of this move and its potential pitfalls, see K. Fine, ‘Relatively Unrestricted Quantification’ in A. Rayo and G. Uzquiano (eds), Absolute Generality (Oxford: Oxford University Press, 2006).
72. Whether one chooses to work within the confines of some form of type theory, a system that allows for a distinction between sets and classes such as Quine’s New Foundations, or a typeless system such as ‘pure’ Zermelo-Fraenkel set theory, one has been forced to navigate the noetic obstacles thrown up by the possibility of self-reference.
73. Markus Gabriel provides the clearest formulation of this objection and the liberal response to it, explicitly defending the idea that the totality of what exists is the only thing which does not exist (‘The Meaning of “Existence” and the Contingency of Sense’, in Speculations vol. IV [2013], <http://www.speculations-journal.org/storage/Gabriel_Meaning%20of%20Existence_Speculations_IV.pdf>).
74. Heidegger ‘What is Metaphysics?’ in Basic Writings; and Introduction to Metaphysics.
75. R. Carnap, ‘The Elimination of Metaphysics Through Logical Analysis of Language’, in S. Sarkar (ed.), Logical Empiricism at its Peak: Schlick, Carnap, and Neurath (New York: Garland, 1996), 10–31.
76. Heidegger, Introduction to Metaphysics, 2–3.
77. It is worth pointing out that the early Heidegger’s project was essentially to provide an account of this structure within which beings appear as content (the worldhood of the world) in terms of the primordial temporality (Temporalität) involved in Dasein’s projection of a world. For a more thorough discussion of this project and its failure, consult chapters 4 and 5 of my The Question of Being.
78. See chapter 4.2, n.58.
79. The definition of existence predicates proceeds exactly as we discussed earlier (e.g., Ex ≡ (∃y)(x=y).The only difference is that Russell’s theory of descriptions is not needed to parse its application to non-referring singular terms (e.g., Ea ≡ (∃y)(a=y)).
y)(a = y)).
80. Cf. M. Heidegger, Poetry, Language, Thought, tr. A. Hofstadter (New York: HarperCollins, 1981). It is worth pointing out that this puts the later Heidegger in the unique position of endorsing the de-absolutisation objection to the idea that beings as a whole can be grasped as a determinate collection (as opposed to the reification objection endorsed by most ontological liberals) while nevertheless refusing the conservative move of decoupling noetic circumscription from ontological circumscription. However, this is best understood as the result of a more thorough annihilation of the distinction between the noetic and the ontological performed by the notion of Ereignis.
81. This is the view adopted by Brandom in Making It Explicit (chapters 6–7).
82. The same idea is approached from the opposite direction by Peter Geach, who famously claims that there is no absolute identity, only identity relative to a sortal predicate (‘Identity’, Review of Metaphysics 21 [1967], 3–12.)
83. Brandom, Making It Explicit, 437–8.
84. Cf. I. Bogost, Unit Operations: An Approach to Videogame Criticism (Cambridge, MA: MIT Press, 2006).
85. See P. Hallward, Badiou: A Subject to Truth (Minneapolis, MN: University of Minnesota Press, 2003).
86. I owe this point to Ray Brassier.
87. It is that part of Badiou’s work that could be legitimately described as ‘object-oriented’.
88. Badiou, Being and Event, 10.
89. This is the consequence of Zermelo’s axiom schema of separation, which limits the scope of the operation of abstraction through which sets are constructed to sets that already exist, combined with the axiom of the Void which stipulates the existence of the empty set as a fixed point from which other sets can be constructed (Being and Event, §3 and §5).
90. Cf. Badiou, ‘Kant’s Subtractive Ontology’, in Theoretical Writings; and the introduction to Being and Event. This might be seen as Badiou’s mathematical synthesis of Kant and Lacan, insofar as he has always identified the Void with the Lacanian Real, or thought’s constitutive impossibility.
91. It is important to understand that axiomatics has been gradually superseded by semantics in the history of mathematical logic, insofar as the latter represents an attempt to map the use of the relevant terms (e.g., connectives, quantifiers, modal operators, etc.) onto other mathematical structures (e.g., models, proof structures, strategies, etc.) that explain the range of choices between axioms encoding their inferential behaviour (e.g., mapping modal operators to sets of possible worlds so as to explain axiom choice [K, S4, S5, etc.] in terms of the algebraic properties of the accessibility relation between worlds). Understood in this way, axiomatic set theory represents the last bastion of axiomatics against semantics, which should ultimately replace it with a complete semantics of quantifiers (incorporating plural and predicate quantifiers). The main reason this is often overlooked is that the dominant semantic paradigm for analysing other forms of logical vocabulary (model theory) is founded upon axiomatic set theory, so that the standard semantics of generalised quantifiers turns in a tiny explanatory circle.
92. See my Essay on Transcendental Realism.
93. It is curious that this word is entirely appropriate to both Quine and Badiou here.
94. Badiou, Being and Event, 9–10.
95. The term ‘poetic ontology’ conflicts with my earlier characterisation of Heidegger as rejecting ‘ontology’ in describing his later project, but I think the term is useful enough to adopt as long as this conflict is borne in mind.
96. I. Bogost, Alien Phenomenology, or What it's Like to Be a Thing (Minneapolis: Minnesota University Press, 2012), 11.
97. Once again, Markus Gabriel presents perhaps the clearest example of this logic at work, even if he does not articulate it himself (cf. Transcendental Ontology, ‘Introduction’; and ‘The Meaning of “Existence” and the Metaphysics of Sense’). His transcendental ontology rejects the possibility of providing a general formalisation of the ‘fields of sense’ within which ‘objects’ are defined as appearing, because it accounts for metaphors as specific fields of sense that resist such formalisation. It is then reduced to using formalism as a metaphor, which conveniently allows Gabriel to pick and choose between those features he takes to allude to important metaphysical truths (e.g., Cantor’s and Russell’s paradoxes) and those that he can dismiss as mere precision for precision’s sake (e.g., the need for a precise equivalent of the axiom of extensionality for fields of sense, if they are to analogically inherit these extensional paradoxes).
98. To this list I add, for the sake of Benedict Singleton, ‘your mum’.
99. Garcia, ‘Crossing Ways of Thinking’, 9–10. It is worth noting that Harman concurs with this analysis of the difference between his and Garcia’s work (‘Tristan Garcia and the Thing-in-itself’, in Parrhesia 16 [2013]).
100. It is certainly present in Levi Bryant’s processual fork of OOO in The Democracy of Objects (Ann Arbor, MI: Open Humanities Press, 2011), but Bryant’s subsequent reversion to a more classical materialism (under the heading of ‘machine-oriented ontology’ or MOO) seems to abandon the noetic challenge to ontological conservatism in favour of a more Deleuzian anti-reductionism, which would suggest that he has abandoned the radical ontological egalitarianism characteristic of the rest of OOO.
101. Badiou, ‘Language, Thought, Poetry’ in Theoretical Writings, 233–41.
103. These predicates are quasi-sortal for the reasons pointed out by Ladyman and Ross: they permit the counting of particles but not their absolute individuation (see Every Thing Must Go, §§3.1–3.2).
104. This amounts to giving something like an account of how metaphors compose ‘fields of sense’ in Gabriel’s terms (see chapter 3.4, n.97).
105. For my earlier explanation of the concept of semantic grafting, see chapter 3.1, subsection IV. For a more detailed discussion of the semantics of singular terms, see Brandom (Making It Explicit, chapters. 6 and 7).
106. Cf. The Prince and the Wolf (Winchester: Zero Books, 2011) and An Inquiry into Modes of Existence (Cambridge, MA: Harvard University Press, 2013).
107. See Stewart and Cohen, The Collapse of Chaos for a thorough discussion of what this alternative paradigm involves, especially their notions of simplexity and complicity.
108. See chapter 3.3, subsection II.
109. B. Latour, Pandora's Hope (Cambridge MA: Harvard University Press, 1999), 47–56.
110. See chapter 3.2, subsection I for a discussion of the distinction between the vehicles and contents of representation. It is also worth noting that this is not entirely dissimilar from Kripke’s causal theory of reference (chapter 2.2, subsection III).
111. Cf. B. Latour, We Have Never Been Modern (Cambridge, MA: Harvard University Press, 1993).
112. Brassier, ‘Concepts and Objects’, 52.
113. See chapter 3.1.
115. The classic statement of this transversality is contained in Deleuze and Guattari’s A Thousand Plateaus (chapter 3).
116. Cf. Deleuze and Guattari, A Thousand Plateaus, chapters 3 and 10; What is Philosophy, tr. G. Burchell and H. Tomlinson (London: Verso, 1994), chapter 2. See my ‘Ariadne’s Thread: Temporality, Modality and Individuation in Deleuze’s Metaphysics’ for a detailed discussion of this point. It is also worth pointing out that Deleuze’s emergentism is often misinterpreted along the lines of Latour’s catastropic anti-reductionism by means of a failure to distinguish between ‘the’ plane of immanence and ‘a’ plane of immanence, and the ‘Ideas’ composing the former from the ‘concepts’ composing the latter.
117. Cf. DeLanda, Intensive Science and Virtual Philosophy, chapter 4; A New Philosophy of Society (London and New York: Bloomsbury Academic, 2006). This term has unfortunately become somewhat of an etymological car crash after its appropriation by OOO. As Harman himself points out (Towards Speculative Realism, 180) it was initially used by Roy Bhaskar but with an opposing sense to DeLanda’s usage. However, whereas DeLanda quite explicitly uses it to withhold existence from certain entities (i.e., universals such as ‘Lionhood’), the proponents of OOO use it to mean the rejection of all such gestures (cf. Bogost, Alien Phenomenology, 11–19).
118. Cf. Deleuze, Difference and Repetition, 377–378.
119. Cf. Deleuze, ‘I Feel I am a Pure Metaphysician’ in Collapse vol. 3.
120. Not to mention the parallel critiques of the ‘objectification’ of subjects.
121. The Quadruple Object, 7.
122. Ibid., chapter 1.
123. Cf. ‘I am also of the opinion that materialism must be destroyed’.
124. The Quadruple Object, 7 , my emphasis.
125. See chapter 1.2, above.
126. Tool-Being, 258–9.
127. Tool-Being, 259.
128. This stumbling takes two forms: (a) Harman’s fleeting dalliance with ‘elements’, which does little but blur the lines between qualities and objects, and (b) his disastrous attempt to defuse the distinction between an object and its essence, which results in a complete collapse of the distinction between objects and their qualities (see chapter 3.2, subsection II).
130. That the most obfuscatory category within Harman’s schema is called ‘sincerity’ is an irony that is not lost on me. I will have more to say about Harman’s invocation of the virtue of sincerity in chapter 3.6.
131. See chapter 3.4, subsection II.
132. G.W.F. Hegel, Phenomenology of Spirit, tr. A. V. Miller (Oxford: Oxford University Press, 1977), §97.