In Chapter 2 we focus on problems concerning the structure of the world. This kind of structure is traditionally conceived as ontological, or categorial, structure. For Aristotle, who introduced the term, “categories,” or “things said” of a subject, are the most fundamental aspects of being, the ultimate classifications into which all objects, facts, processes, and events must ultimately fall. In the modern period, Kant argued that categories are grounded in the structure of human thought and provide the most general conditions under which we can conceptualize the world. For much of twentieth-century philosophy, categories and categorial structures were instead understood as aspects of language or languages. Many contemporary debates turn on the choice among these three models (sections 2.1 and 2.2). These debates are closely connected to others about the nature of logic (section 2.3). For early analytic philosophers such as Ludwig Wittgenstein and Rudolf Carnap, fundamental categories are aspects of “logical forms” or “conceptual frameworks” that structure the world as we know it by determining the structure of the language we use to describe it. Likewise, some continental philosophers, including Martin Heidegger and thinkers influenced by the structural linguist Ferdinand de Saussure, have held that particular languages impose categorial structures that vary dramatically over time and from culture to culture, while other philosophers of both traditions have challenged this idea. One guiding question in this debate is whether logic imposes a categorial framework on the world, and, if so, how (section 2.4).
A more specific problem in ontology is which categories are the most fundamental. Analytic and continental philosophers alike have considered the nature of things (section 2.5) and events (section 2.6). They have wondered what a thinking subject is, whether subjectivity is essentially gendered, and what self-reference involves (section 2.7). This last issue connects to more general questions about the nature of reference (section 2.8), which in turn connect to problems about the nature of modality and possible worlds (section 2.9). We conclude our discussion of ontology and logic by looking at debates about the nature of identity and difference, general concepts that cut across categorial structures, however the latter are interpreted (section 2.10).
In his brief treatise “Categories,” Aristotle introduces the term to philosophical discourse and gives the first inventory and description of the overall structure of categories, or types of things, events, and processes. Drawing on the etymology of the term in Greek, Aristotle understands categories as “things said” (and thus as types of language or linguistic terms), but also as general types into which objects, events, and properties fit, providing a kind of complete, high-level ‘inventory’ of the constituents of the world (Thomasson, 2013). Here he gives, as well, the first specific list of ten categories or “things said without any combination” (Aristotle, 1984: 4 [1b25–2a4]). The list is: substance, quantity, qualification, relative, where, when, being-in-a-position, having, doing, being-affected. In contemporary discussion, “categories” are sometimes identified as any conceptual types whatsoever, whereas in other discussions, they retain the significance of the highest or most general kinds or types under which anything falls, as in Aristotle's treatment.
In the Critique of Pure Reason, Kant complains that Aristotle's original structure of ten categories is lacking in motivation (Kant, 1998 [1781/1787]: A81/B107). Why should there be just ten categories, and why these particular ones? Arguing from a “transcendental idealist” perspective, Kant first maintains that two of Aristotle's categories – where and when – are not categories at all, since they pertain to spatio-temporal conditions of sensibility that are first needed to make any categorial determinations possible. Kant further holds that any possibility for spatiotemporal objects to exist objectively is in fact grounded in the constitutive forms or faculties of the cognizing subject. In particular, the structure of categories that determines the nature of real, objective things and their relations is grounded in the logical forms of possible judgments made by the “understanding,” the faculty of conceptual representation and judgment (Kant, 1998 [1781/1787]: A66–95/B92–128). For instance, the fact that spatiotemporal objects are able to affect one another causally is grounded in a particular form of relational judgment, the “hypothetical” (if-then) judgment. Accordingly, Kant derives four types of categories from the four logical aspects of the judgments we can make about objects. These types are: Quantity, Quality, Relation and Modality (with three further sub-divisions in each broad category). For Kant, the most general categories of the possible structures of objects are thus not intrinsic to things as they are in themselves, or to the world considered independently of the cognizing subject, since they are determined and formed by the logical aspects of judgments of which a cognizing subject is capable. Nevertheless, they remain essential aspects of the structure of any spatiotemporal object whatsoever.
Expanding and modifying this transcendental idealist approach to categories within his own phenomenological project, Husserl argues that phenomenologically accessible categories of meaning correlate to the possible types or “essences” of objects. Although these categories are accessible in phenomenological reflection, they are also thought of as determining the ontological structure of the world and the types of both sensory and non-sensory objects. For Husserl, essences are knowable by means of one of two kinds of intuition: categorial intuition (Husserl, 1977 [1901]; Husserl, 1969 [1929]) yields access to non-sensory categories corresponding to “syncategorematic” terms such as “on,” “not” and the predicative “is,” whereas eidetic intuition yields access to essences of objects and their perceptually experienceable properties (see section 1.1). These two types of intuition jointly yield access to abstract laws of essence that allow for the definition of the ideal categories of things (Husserl, 1977 [1901]: “Prolegomena” and Investigation VI). Through eidetic and categorial intuition it is possible to establish two kinds or levels of ontological categories: categories of formal ontology hold for any type of object (or objectivity) whatsoever, whereas categories of (various) regional ontologies establish the types of objects and situations treated by specific scientific disciplines and theories. For Husserl, ontological ideal categories are thus accessible in subjective phenomenological reflection but nevertheless determine the real structure of objects, events, and properties in the world.
In Being and Time, Heidegger suggests that the traditional understanding of the world in terms of categories of objects and their properties is itself the outcome of an over-emphasis on predicative judgment, and a privileging of what is actually only a certain way of being, that of the “present-at-hand” [Vorhanden] (Heidegger, 1962 [1927]: sections 15–17). Rather than focusing exclusively on objects that are “present-at-hand” before us and accessible to theoretical cognition, we should ground our understanding of the structure of objects in a broader and existentially deeper fundamental ontology that begins with the analysis of Dasein, the kind of being that we ourselves are. In this investigation, the traditional inquiry into the constitutive categories of objects is replaced with an inquiry into the “existentials” or structures of Dasein as, in each case, a living individual defined by its particular possibilities and the structure of care and temporality involved in this structure of possibilities.
A different approach is taken by early analytic philosophers who see the logical or grammatical structure of language as yielding fundamental categorial structures. Gottlob Frege investigated the logical structure of language in order to determine the structure of possible contents of thought. In line with this project, Frege drew a fundamental categorial distinction between objects and concepts as distinct logical types (Frege, 1997 [1892]). Objects are the referents of names, whereas concepts correspond to predicative and relational expressions. These expressions, such as “…is red” or “…is taller than…,” are not names, but rather refer to functions taking objects to truth-values. Both of these types of expressions (names as well as predicative or relational ones) are needed to form a declarative sentence that is either true or false. For example, a particular apple, A, may be said simply to exist, but the predicative expression “…is red” has no referent capable of such independent existence. Rather, we may think of the referent of the predicative expression as a function which takes particular individuals (such as the apple A) to truth-values (in this case, “True”). Given this, Frege argues that objects are capable of existing in themselves (or are “saturated”) whereas functions are fundamentally “unsaturated” in that they must be completed or “filled in” with one or more objects in order to yield a propositional sense and a truth-value.
For the early Wittgenstein, “logical form” is a general structure shared by language and the world, and responsible for the possibility that sentences correspond to actual or non-actual states of affairs (Wittgenstein, 2001 [1921]). For example, the sentence “Obama is president in 2012” corresponds to an actual state of affairs, and thus is true, whereas the sentence “McCain is president in 2012” corresponds only to a possible (not actual) state of affairs, and thus is false. In Wittgenstein's conception, the logical/categorial structure of any state of affairs is understood as a linkage of ultimately simple objects that shares the logical and combinatorial structure of the corresponding sentence; logical form thus “permeates the world” and makes both coherent facts and meaningful language possible.
In The Logical Syntax of Language, Carnap argued for a conventionalist doctrine of logical and categorial structure (Carnap, 1937). On this sort of view, as on Wittgenstein's, categorial structure is an aspect of language, but (quite at variance with Wittgenstein's view) here it is something we create by creating or instituting particular historical or formal languages. In particular, we can determine categories freely by stipulating constitutive rules for a language, and there can accordingly be no absolute answer to the question of which categories are the “right” ones independent of the language we are working in. In “Empiricism, Semantics, and Ontology,” Carnap further developed this argument, holding that questions about the categorial structure of objects can only be meaningfully addressed internally to a “language framework,” a stipulated or reconstructed set of rules for the usage and combination of a language's terms (Carnap, 1950). Such “internal questions” as whether there are numbers or universals are to be settled by reference to the rules of usage for the language framework in question. But outside particular language frameworks the general question of existence has no sense, and the question of which language framework or categorical structure to adopt is to be guided by merely pragmatic considerations. Others in the earlier stages of the analytic tradition (e.g. Ryle, 1949 and Strawson, 1959) argued that ordinary languages such as English (or ordinary language in general) already bear within themselves a structure of categories that can be reconstructed by philosophical analysis to demonstrate the categorial distinctions of things in the world, and that certain philosophical assumptions about the types of objects can be criticized on this basis as relying on errors about categories (more on this below).
In more recent analytic philosophy (since roughly the 1960s), many philosophers have returned to the “classical” idea that there is an objective, intrinsic categorial structure to the world, quite independently of the structure of subjectivity or language. The methodological idea underpinning this “return of ontology” is that philosophical ontology should be, at least, continuous with our best scientific theories, and that these theories themselves can identify, at least provisionally, the large-scale categories and types of objects and phenomena. In 1969, W. V. Quine argued in “Natural Kinds” that we can understand natural phenomena as falling into objective types or kinds determined by similarities in their natural properties, and that empirical science, as it progresses, can reveal the deep similarities that constitute actual natural kinds over against the superficial similarities that may appear at first. Relatedly, work by Kripke and Putnam on the reference and modality of “natural kind terms” has appeared to confirm the possibility of an ontology of natural kinds. For instance, Putnam (1975c) suggests that the term “water” refers to a specific natural kind of stuff, and that it bears this reference even before we know all the details of its actual material composition or chemical structure. Putnam further argues here for the position known as “externalism” about reference: what a speaker's words refer to is not necessarily determined wholly by factors internal to that speaker, but also by features of the environment. For instance, two speakers situated on different planets could use the same word, “water,” to refer to two different substances, actual H2O and some other substance, depending on which type of substance is locally prevalent, even if the two speakers are molecule-for-molecule identical to one another.
Along partly similar lines, Kripke (1980 [1971]) has argued that a natural kind term such as “tiger” refers to a particular type of object (here, a biological type of animal) and that this reference does not depend on any description or the state of our knowledge of the characteristic features of that type (rather, it's something like a placeholder for “whatever we discover the type to be”). In accordance with this conception of objective natural kinds as revealed by our best scientific theories, contemporary philosophers have argued for the possibility of a metaphysical ontology that determines, in a way continuous with empirical science, the concepts and categories that articulate the fundamental constituents and structure of the world and thus “carve nature at the joints” (see, e.g., Sider, 2011; Campbell, et al., 2011).
Other debates in contemporary ontology have concerned mereology, or the structure of parts and wholes of objects. In the Logical Investigations, Husserl developed a comprehensive phenomenological mereology of wholes, parts, and dependent and independent “moments,” which he used to theorize not only the structure of objects but also that of meanings and intentional acts of consciousness (Husserl, 1977 [1901]: Investigation 3). In 1940, Henry Leonard and Nelson Goodman developed a “calculus of individuals” which gives a comprehensive formal theory of the conditions under which particular individuals form other individuals (Leonard and Goodman, 1940). In recent discussions, some philosophers such as Peter van Inwagen and Peter Unger have argued for versions of mereological nihilism, the view that there are, strictly speaking, no such things as composite wholes (thus, e.g., strictly speaking there are no tables or chairs). David Lewis argues in Parts of Classes (Lewis, 1991) that the machinery of standard (ZF) set theory is sufficient to yield a complete mereological framework for parts and wholes on the assumption that parts are subsets. There are close connections to be drawn here to Alain Badiou's (Badiou, 2005 [1988]) claim that “mathematics is ontology” (again, in the sense of ZF set theory). Closely related debates concern the part-whole structure of objects over time and the conditions for the persistence (perdurance or endurance) of a particular entity or person (see section 2.5).
In the twentieth century, both analytic and continental philosophers have argued that our understanding of the types of objects and other entities in the world, as well as the structure of events and change, is imposed by a scheme, structure, or paradigm of concepts or linguistic terms. These schemes are often thought of as determined by, or closely linked to, the structure of particular languages, and are also often understood as closely linked to dominant practices and culturally specific ways of relating to the world. This view has some close connections to conventionalist views of categories and categorial structure within the framework of formal-logical analysis, such as Carnap's conventionalism (see section 2.1). However, those who think of conceptual schemes as determined by cultures or languages typically relate this view to existing natural languages and cultures rather than to formal or artificial languages such as the language frameworks envisaged by Carnap.
One root of the idea of variable conceptual schemes is in philosophically oriented anthropology and linguistics. The American linguists Benjamin Lee Whorf and Edward Sapir argued that the terms and concepts specific to one's language shape, in a determinate way, one's understanding and experience of reality, suggesting that speakers of different languages experience the world differently in important ways (Whorf, 1956). In the European structuralist tradition, much discussion of linguistic relativity and variable conceptual schemes originates in Ferdinand de Saussure's thesis of the “arbitrariness” or conventionality of the link between the signifier and what is signified in the sign (Saussure, 1959 [1916]). According to this thesis, the link between the specific signifier (e.g. the English word “tree”) and what is signified by it is arbitrary and variable from culture to culture; in other languages, for instance, the completely different word arbre or Baum is used for the same signified object. Later, the structuralist anthropologist Claude Lévi-Strauss (Lévi-Strauss, 1987 [1950]) argued for understanding cultures in terms of a variety of general “structures” of language and practice sharing certain general characteristics determined by the structural nature of language itself, but also showing specific differences in each individual case.
There are some questions and problems that can be raised for the view that variable historical languages determine significantly different structures of categories and of thought. One worry is that this kind of picture threatens to make ontology linguistically relative: there may seem to be no answer to questions about what there is, except relative to a particular language. But speakers of different languages nevertheless occupy one and the same world, so it seems there should be such general, language-independent answers. Relatedly, it is not clear that the kinds of divergences in the scope or range of single terms noted by Sapir and Whorf (or suggested by Saussure under the heading of the “arbitrariness” of the sign) actually cut very deep. English and French may have different terms for trees, but it is a simple matter to translate the English “tree” by the French “arbre,” and little, if anything, seems to be lost in translation (at least in this kind of case and in the context of everyday usage).
In The Order of Things, Michel Foucault argues that the fundamental categories of Western thought have shifted over time from one “episteme” to another (Foucault, 1970 [1966]). Like others influenced by structuralism, Foucault sees categories and concepts as determined by historically variable but total practical/discursive structures linked to particular cultural configurations at particular times. However, unlike earlier structuralists who situate these concepts within a framework of the “human sciences,” Foucault seeks to show how these dubious sciences operate as switch-points of power relations in institutional settings such as asylums and prisons (Foucault, 2006 [1961]; Foucault, 1979 [1975]). In The Archaeology of Knowledge, Foucault codified his methodological conception of “archaeology” as an inquiry into the “epistemic” (in his sense) conditions of statements, practices, institutions, and discursive entitlements (Foucault, 1994 [1969]; see section 2.7).
Jacques Derrida challenges Foucault's archaeological treatment of the institutions and practices surrounding madness in its classical and contemporary formations, for instance by posing the question of how and from what position it is possible to describe a history of madness, as Foucault attempts to do in his History of Madness (Foucault, 2006 [1961]; Derrida, 1978 [1963]). Relatedly, there are questions to be raised about the grounding of epistemes in what are characterized as ultimately “discursive” structures. Although Foucault gives “discursive” a broad sense, so that “statements” (énoncés) are distinguished from sentences and the structure of language as such is situated within the various institutions and aspects of practical behavior, it is not clear that we can or should see all the relevant aspects of power and the basis of institutions as discursive. In the later “genealogical” phase of his thought, Foucault corrects somewhat for these shortcomings by treating power and discourse (or “knowledge” in the sense of savoir) as equally basic factors, and by weakening his earlier sense of the monolithic and totalizing character of epistemes.
In Being and Time, Heidegger argues for a critical “destruction” of the ontology handed down from the Greeks on the basis of a more deeply penetrating interpretation of the question of the meaning of Being. Here, discourse or Rede is one of the basic phenomena in which the intelligibility of Dasein is articulated. In this sense, the world of Dasein is always already linguistically structured and this structure gives sense and articulation to the various structural categories of everyday life, including those that ontologically “precede” explicit ontological categories and types of entities as they are treated in science.
After the middle 1930s, Heidegger sees language as “the house of being” in the sense that historical languages provide the essential structure in which being and its meaning both appear and withdraw (Heidegger, 1993 [1947]; Heidegger, 1971 [1959]). Here, the history of Western culture is understood as embodying a series of different understandings of the “being of beings,” each determined by a specific conception of the “highest,” most real, or most determinative type of entity or phenomenon (such as the Idea of the Good, or God, or the subject). These specific conceptions of the being of beings are often described or announced in the work of philosophers (such as Plato, Descartes, or Kant) and make for determinative differences in our ways of understanding the world and ourselves. However, unlike other philosophers who suggest the historical relativity of ontological categories, Heidegger does not see these categories as simply determined by language or culture. Rather, the structure of categories along with the languages and cultures are ultimately determined by Being itself as it comes to presence, in various ways, in history.
According to analytic “ordinary language” philosophers such as Gilbert Ryle, categories are present in ordinary language in the sense that there are implicit or explicit rules or regularities that govern what sorts of combinations of terms make sense and which imply “absurdities” (Ryle, 1938; Ryle, 1949). Categories can be abstracted from the language by means of reflection on these possible and impossible combinations, and traditional philosophical pictures such as Descartes' mind-body dualism can be criticized as resting on illicit combinations or “category mistakes.” In a somewhat similar fashion, J. L. Austin suggests that there are general regularities or categories of linguistic performance that determine the conditions under which performatives (or linguistic acts that do or accomplish something as opposed to, or in addition to, merely saying something) are possible and successful (Austin, 1962).
There are various questions to be raised about the view that categories are present in the structure of ordinary languages. First, the view presupposes that languages are structured as systems of relatively well-defined rules of which we have at least implicit knowledge as ordinary speakers. The view that language is a calculus or system of rules, however, has been challenged, significantly, for instance, by the later Wittgenstein (Wittgenstein, 2009 [1953]). Second, Ryle's project of undertaking philosophical criticism by drawing distinctions between legitimate usage and absurdity appears to presuppose that the line between the two is always well-defined and is not historically variable, which is by no means obvious given the dynamic character of actual languages. Third, it seems possible that, in certain cases at least, the “category mistakes” committed by philosophers may in fact have at least a partial basis in ordinary language as it is actually (legitimately) used. For instance, it is by no means clear that ordinary usage does not already include at least some important aspects of the “Cartesian” picture of mind that Ryle denounces as a philosopher's category mistake (e.g. Wisdom, 1962 [1950]; Hampshire, 1970 [1950]).
Without disputing that categorial structure arises ultimately from language, Quine and Davidson hold that specific categorial structures can only be reconstructed from a particular language under translation (Quine, 1960; Davidson, 1977). Thus, there may be no “fact of the matter” about the “actual” categorial structure of a language, only various possible translations. Moreover, translation is itself indeterminate (even within a particular language) in the sense that there are various possible overall translations of a language each of which attributes to it a different overall ontological structure of fundamental categories. While Quine holds that this may lead to a significant degree of “ontological relativity” between various systematic translations of a language, Davidson emphasizes that translation must be governed by a “principle of charity” which leads us, in translating, to maximize the intelligibility (to us) of the language being translated.
In “On the Very Idea of a Conceptual Scheme,” Davidson argues against the claim that different languages or cultures may be seen as embodying distinct “conceptual schemes” that organize or capture the world (Davidson, 1973c). Davidson argues that, because our understanding of any language is dependent upon interpretation, the necessary structure involved in any interpretation also limits the extent of overall metaphysical and ontological difference that we can ascribe to speakers of an initially unfamiliar language. Since large-scale agreement on matters of ontology is thus a necessary presupposition for the possibility of interpretation, and since languages are plausibly inter-translatable, we cannot coherently suppose that we might interpret any language as embodying a conceptual scheme radically different from our own. Thus the “heady doctrine” of conceptual relativism is revealed as untenable. Nevertheless, if there is ultimately no sense to assuming that conceptual schemes might be different, there is also no sense in assuming them to be the same; thus the whole idea of a “conceptual scheme” is to be rejected.
In philosophy of science, an important debate has concerned the extent to which our general understanding of the world has changed in fundamentally important ways that are driven primarily by conceptual changes rather than simply by empirical results. In the 1930s, Gaston Bachelard argued that the transition from classical to contemporary (relativistic and quantum-mechanical) physics should be understood as a discontinuous “epistemological break” brought on by the inadequacy and exhaustion of the classical understanding of the world rather than as a continuous, progressive transition (Bachelard, 1984 [1934]). Similarly, Alexandre Koyré argued that the scientific revolution associated with Copernicus and Galileo arose primarily as a result of changes in the conceptual framework of thinking about the large-scale structure of the world – from an understanding of it as finite and closed to the early modern understanding, on which it is infinite and open – rather than simply as a result of empirical discoveries (Koyré, 1957).
Drawing on the picture of scientific change suggested by Koyré, Thomas Kuhn argues in The Structure of Scientific Revolutions that the history of disciplines such as physics and chemistry reveals a variety of successive and shifting “paradigms,” or organizing structures of concepts, methods, and key results, that make possible the work of “normal science” at any time, but also shift relatively suddenly in so-called “scientific revolutions” (Kuhn, 1962). The transition from an older to a newer paradigm is usually motivated by scientists' attention to “anomalies” or failures of the old paradigm, but can have as much to do with political and social factors bearing on the assumptions and conduct of scientists as it does with strictly empirical discovery. In the shift from an older to a newer paradigm, objects and phenomena that were thought to exist may be shown not to, and new objects and phenomena “come into existence” as a result of the new organizing structure of theory. In The Structure of Scientific Revolutions, Kuhn concludes that scientists working in different paradigms are in some sense “seeing different worlds” and that successive paradigms may be understood as incommensurable in the sense that there can be no neutral standpoint from which to evaluate which one is “better” or “closer to the facts.”
Kuhn's view of historical scientific change, and his claim in Structure that successive paradigms are or can be “incommensurable,” has led to many questions and challenges. Many have worried about the tendency of Kuhn's views to lead to relativism: if there is no neutral external standard by means of which to evaluate the success or failure of various paradigms in describing the world as it is, it may seem that scientific truth itself must be relativized to paradigms. Related to this, it is unclear how to make sense of Kuhn's bold claims in Structure that scientists working in different paradigms are, in a sense, living in “different worlds” and that in the shift to a new paradigm, new entities and objects can come into existence. Do these ontological claims make the ontology and the structure of the world as a whole dependent on how we happen to understand it at a particular time? Finally, Kuhn's picture suggests what has been called a “pessimistic induction” (Laudan, 1981) about the history of science: since, on Kuhn's picture, virtually every paradigm that has been held in the past has been shown to be (by the lights of our current conception) largely and foundationally false, there is no reason to suppose that our current best scientific understanding of the world will not be overturned (perhaps tomorrow) by the sudden advent of a new paradigm.
In The Differend, Jean-François Lyotard develops the implications of “incommensurability” in the sense of disputes for which there is no neutral standard or position from which they can be resolved (Lyotard, 1988). According to Lyotard, rules for the determination of validity and correctness can only be held to be in effect within a specific “language game” or “phrase regime” and it is unjustified to try to apply them across two or more such regimes. Lyotard suggests elsewhere that in contemporary, “postmodern” life, the grand organizing structures and narratives that formerly played the role of overarching conceptual schemes have tended to break down, leaving only local rules in place and leading to the prevalence of differends and incommensurabilities (Lyotard, 1984). Lyotard's conception of the “differend” thus generalizes the implications of (one interpretation of) what Kuhn calls “incommensurability” outside the scientific context per se. However, even if Lyotard is right about postmodernism and differends, it is not clear what we should do about real incommensurability in Lyotard's sense. When we encounter a differend between the claims or rules of two different language games or cultures, must we give up on any possibility of appealing to a universal standard of reason or justice in resolving disputes between them? If so, is it ever possible justly to adjudicate disputes between different cultures at all?
Many views and positions in twentieth-century philosophy are wholly or partially grounded in views about the structure and nature of logic. While the ultimate origin of the term “logic” lies with the Greek term logos, which has many significations including “word,” “statement,” “reason,” “account,” and “order,” among others, formal logic in the contemporary sense has its ultimate roots in Aristotle's definition of the syllogisms. These are formal schemas that capture a series of general argument forms independent of the specific objects or topics involved. Despite important advances in the medieval period in conceptions of intentionality and truth – advances closely linked to problems of logic – Kant held that these developments pertained primarily to psychology, or “applied” logic, and that pure (“general”) logic in his time had not advanced at all in the roughly two thousand years since Aristotle's conception (Kant, 1998 [1787]: Bviii). Kant's major contribution to logic was his development of the idea of a transcendental logic, the aim of which was to determine the a priori rules governing the subject's thought of an object in general. Kant divided his investigation into a logic of truth (“Transcendental Analytic”) and a logic of illusion (“Transcendental Dialectic”). This division reflected, and reinforced, Kant's fundamental distinctions between the faculties of understanding and reason, on the one hand, and between knowable phenomena and unknowable (but thinkable) noumena, on the other.
Philosophical dissatisfaction with these dichotomies led Hegel to rethink Kant's conception of transcendental logic. Instead of distinguishing an analytical logic of truth from a dialectical logic of illusion, Hegel represents logic in general as thoroughly dialectical insofar as it deals with “thought determinations” that are essentially partial and thus unstable when considered in abstraction from other thought determinations. Just as Hegelian logic blurs the Kantian distinction between an analysis of forms of understanding and the investigation of dialectical illusions of reason, so it assimilates the rules of general logic under a more encompassing conception of transcendental logic conceived as logic simpliciter. One of the main problems with Hegelian logic is figuring out what to make of its philosophical ambitions. Is Hegelian logic a form of metaphysics, as many of Hegel's earliest followers took it to be? Or is it just an investigation of the structures of human reason as these are embedded in linguistic forms, as many recent commentators have argued?
Despite its enormous prestige in Hegel's day, Hegel's logic was soon eclipsed by other approaches. For much of the rest of the nineteenth century, discussions and systems of logic often included considerations that we would today more likely call epistemological and psychological rather than strictly logical, including the attempt to give a general “theory of judgment” involving both psychological and formal aspects.
Through his work on clarifying the structure of mathematical proof, Gottlob Frege in Begriffsschrift created a system of formal logic capable of capturing and symbolizing the structures of existential and universal quantification (Frege, 1997 [1879]). Together with his new idea of treating concepts as functions, this represented a powerful and fruitful advance over Aristotle's syllogistic logic and it made possible a vast expansion in the power and scope of formal logic. On Frege's conception, in particular, the logical structure of sentences is not limited to the relationship between subject and predicate, but involves more complex and multiply differentiated aspects of predication and relation. Following Bernard Bolzano, Frege argued vehemently against the doctrine of psychologism in logic, which claims that the laws of logic describe psychological facts about how we, in fact, do think rather than rules governing how we should think. Frege's critique of psychologism about logic also supported his anti-psychologistic views about arithmetic and other branches of mathematics, which he believed could ultimately be reduced to logic (see section 1.7).
Partially following Frege's arguments, Husserl argued vehemently against psychologism in the “Prolegomena to Pure Logic” at the beginning of the Logical Investigations. (Husserl had previously given a theory of arithmetic apparently involving some psychologistic commitments in an earlier work, The Philosophy of Arithmetic.) For Husserl in the Logical Investigations, grounding a genuinely phenomenological theory of knowledge and reality requires that logic, as the structure of any possible theory as such, be developed as an ideal science prior to any phenomenological or empirical theory. Hearkening back to Leibniz's conception of logic as a mathesis universalis or universal calculus, Husserl develops the phenomenological conception of logical inquiry as the investigation of an ideal objective realm accessible to phenomenological insight in categorial intuition (see section 1.1). Logic, thus understood, articulates at a maximally general level the possible forms both of consciousness and of any objectivity as such.
In his early work, Heidegger follows Husserl in developing an anti-psychologistic and phenomenological treatment of logic as essential to the structure of intentionality and meaning. For Heidegger in the 1920s, the question of logic is primarily the question of the basis and possibility of truth. In Being and Time, he considers the structure of logic in terms of the question of the structure of the logos or assertoric sentence (one of the important historical senses of this multiply translatable term). Here, Heidegger reconsiders Aristotle's conception of the assertoric sentence, or logos apophantikos, and argues that the truth of assertions must be seen phenomenologically as grounded in a prior, pre-linguistic possibility of truth as unconcealment or disclosure (Heidegger, 1962 [1927]: section 44). For related reasons, Heidegger argues that the “traditional” logic of subject and predicate inaugurated by Aristotle and carried through the medievals, Kant, and Hegel, fails essentially to capture the underlying structure of truth as unconcealment, and suggests that contemporary systems of “formal” and symbolic logic exhibit similar failings. In later investigations, Heidegger interrogates the ultimate ontological basis of logical principles such as the principle of identity (“A = A”) (Heidegger, 2002 [1957]) and the principle of sufficient reason (first formulated by Leibniz) (Heidegger, 1991 [1956]), and he develops an original understanding of the structure of the logos itself as “gathering” (drawing on Heraclitus) (Heidegger, 1975 [1951]).
Many developments of analytic philosophy have complicated or added to Frege's original framework of quantificational logic with new logical systems and calculi. In the 1920s, intuitionist ideas about the structure of mathematics led to the development of intuitionist systems of logic, which allow the relaxation of the traditional law of the excluded middle for cases in which truth-value is as yet undetermined or indeterminable (see section 1.7). The 1950s and 1960s witnessed the influential development of modal logic, which handles the structure of possibility and necessity and has been seen as having important metaphysical and semantic implications. Today there are a bewildering variety of logical systems available to the formalizing philosopher, including deontic logics, non-monotonic logics, and inductive logics (just to mention a few types). Recent decades have witnessed a partial return of empiricist and psychologistic ideas about the basis of logic as well. On one view suggested by Quine and Putnam (e.g. Quine, 1951; Putnam, 1979), logical laws express what are essentially maximally general statements about the empirical world; these laws may be held with a great deal of confidence, but even they could be revised or abandoned in certain cases or for certain domains, for instance as a result of the discoveries of quantum mechanics. On other contemporary views, logic must accommodate the structure of actual thinking in empirically theorizing certain deviances or failures to attain “ideal rationality” that appear to characterize the actual behavior of real agents.
Some twentieth-century philosophers have held that the overall structure of the world and its objects is determined by logic. For instance, for the early Wittgenstein the world and language are structured in a unitary way by logical form. Logical form determines the possibilities for objects to combine into states of affairs and facts, and also the possibility for a sentence to have meaning by corresponding with respect to its logical form with an actual or possible state of affairs. Because logical forms are various and are “built into” objects as their possibilities of combination, however, there is no single list of possible “types” of objects or categories. Rather, there are innumerable different structures of the combination of objects into states of affairs and (on one interpretation of the Tractatus, at least) “universals” or predicables are themselves treatable as objects. According to the early Wittgenstein it is impossible even to think of or conceive an “illogical” state of affairs (Wittgenstein, 2001 [1921]: 3.03–3.032).
After his return to philosophical activity in 1929, however, Wittgenstein's conception of the determination of the categorial structure of the world changed in important respects. He no longer thought that simple sentences could be treated as simply logically independent of one another. As a consequence, although logical structures (in an extended sense) continue to determine the overall structure of what can be said about the world, Wittgenstein's middle-period conception of “logical grammar” allows that these structures are not simply derived from (Fregean) symbolic logic as such but may vary in important ways from one material region to another. Thus, the structure of judgments and possibilities of the relationship of objects depend in part on the specific “phenomenological” structure of specific domains and systems such as the system of colors or of measurements. In the Philosophical Investigations Wittgenstein appears to replace this conception of “logical grammar” with a fluid multiplicity of local “language-games” interrelated to each other in various different ways and essentially interlinked with non-linguistic objects, behavior, and elements of practice (Wittgenstein, 2009 [1953]).
In The Logical Structure of the World, Carnap argues that it is possible to understand the scientifically described world as having a unitary logical structure (Carnap, 1967 [1928]). This structure is assured by the procedure of “structuralizing” various domains in the progress of science. In “structuralizing,” we eliminate any essentially ostensive or demonstrative terms and any terms dependent on peculiarities of subjective experience, developing instead general concepts and categories with a deductive structure in terms of which we can give an objective, unified single description of the world. Nevertheless, the basis of this description remains phenomenalist and empiricist, since the most basic elements that are structured are thought to be “elementary experiences” or phenomena. This structuralist conception of the role of logic was influential also for Vienna Circle philosophers such as Moritz Schlick (Schlick, 1932) and Otto Neurath (Neurath, 1931).
There are various questions and problems that can be raised for this influential structuralist conception of the objectivity of scientific knowledge. First, it is not clear what we are actually discovering when we discover the “logical structure” of the world. On Carnap's conception, this structure is discovered by reflecting on the structure of scientific knowledge, but it is unclear why this should imply that it governs the world as such. Second, in Logical Structure Carnap already suggests that there are various “structural systems” of the world that one could discover, with different kinds of bases and overall forms. For example, one structural basis is phenomenal, but it is also possible to structuralize the world on a physicalist basis. If this is right, and the structure discovered in the structuralist project is not unique, why should we think that the world has a unique structure at all? Third, the structuralizing project that Carnap actually works out in detail in Logical Structure requires that all objects and phenomena be reduced to a single structural relation of “partial similarity” between total phenomenal experiences; but it is far from obvious that all scientifically comprehensible phenomena, including those of intersubjectivity, psychology, and sociology, can be reduced to this kind of basis. Fourth, it is not clear why a reconstruction of the (idealized) epistemological basis of our knowledge of the world should also yield an ontological or semantic understanding of its real structure. Fifth, for any structuralist project that identifies structuration with communicability there is a general question about the actual relationship of the structures to what they are seen as structures of – in particular, if the character of the individual basic elements (such as phenomenal experiences or data) in themselves is incommunicable (because unstructured), it is unclear how or even whether we can succeed in communicating about them by placing them within more general structures. Sixth, and finally, since the structuralizing project aims to eliminate any indexical or ostensive terms, it appears committed to denying the meaningfulness of such claims as “It is 3 o'clock now” and “I am N.N.” For later theories of reference and meaning in the analytic tradition, by contrast, sentences and devices of these types form an essential part of any reasonable account of the relationship between language and the world (for some critical discussion of some of these problems, see Friedman, 1999).
Within Husserl's phenomenology (Husserl, 1969 [1929]), logic is seen as determining the categorial structure of the world in two different ways. Formal logic, understood as explicating the “analytic” content of formal principles of general logic such as the principle of non-contradiction, establishes a general set of possible forms of judgment and categories of formal ontology that apply to all domains whatsoever. Transcendental logic, on the other hand, establishes the “material” content of “regional” ontologies and explicates general metaphysical and epistemological phenomena such as the structure of the world and of our knowledge of it. Neither kind of logic is primarily linguistic, for Husserl, but both rely on the possibilities of categorial and eidetic intuition to establish their main principles and results (see section 2.1).
One can raise various questions about Husserl's distinction between formal and transcendental logic. First, it is not clear how we should think of the “subject matter” of each kind of logic. If transcendental logic can be seen as establishing the constitutive structure of various specific material-ontological domains, what is the ultimate (logical or ontological) basis for the demarcation and differentiation of these regions from one another? If, on the other hand, formal logic establishes the “ideal laws” governing any possible objectivity as such, how should we understand the nature and existence of the “ideal realm” of legality that it appears to invoke? It is also not clear that a priori investigation, of which both formal and transcendental logic are types for Husserl, is in fact capable of determining the detailed structure of the world and its categories in advance of empirical investigation. In particular, it may (quite reasonably) be thought that we will necessarily have to do a great deal of empirical work before we are in a position to determine the general categories in which objects and phenomena actually fall. Relatedly, transcendental logic in Husserl's conception, though steadfastly avoiding psychologism, may tend in its analysis of the conditions for the possible givenness of objects to collapse into epistemology or the theory of knowledge rather than the theory of truth, and thus may seem not to be a chapter of “logic” at all, at least on some conceptions of it.
Some philosophers in the analytic tradition have argued that one's choice of a system of formal logic provides a basis for one of a variety of possible overall metaphysical conceptions of the world. For instance, Michael Dummett (Dummett, 1978 [1963]; Dummett, 1991) has argued that the choice of an intuitionist or a classical logic for a particular domain determines in important ways one's metaphysical view of objects and events of that domain as “realist” or “anti-realist” (see section 3.4).
In Being and Time and other works, Heidegger rejects the suggestion that logic (or categories drawn from logic) can establish the true structure of the world. Instead Heidegger holds that specific systems of logic are always based on (usually inexplicit) metaphysical presuppositions that are grounded ultimately in specific ways of understanding being (e.g., Heidegger, 1984 [1928]). Most generally, the Western tradition since Aristotle has assumed falsely that assertions are the primary locus of truth, and so has imposed a misleading metaphysical picture of the nature of beings. For example, Heidegger suggests, Aristotle's distinction between subject and predicate leads to a misleading picture of reality as structured into substances and properties.
In the 1929 lecture “What is Metaphysics?” Heidegger sought to describe the existentially important phenomenon of the experience of Angst, or anxiety, that arises when one faces up to “the nothing,” famously writing that in this experience “The nothing itself nothings” [Das Nichts selbst nichtet], and that as we interrogate this experience, “the idea of logic itself dissolves in a vortex of more originary questioning” (Heidegger, 1993 [1929]). In the essay “The Elimination of Metaphysics through the Logical Analysis of Language,” (Carnap, 1959 [1932]), Carnap singled out Heidegger's sentence about “the nothing” as representative of the tendency to create pseudo-problems by failing to comprehend the logical structure of language; in a logically structured language, Carnap argued, this sentence could not be expressed (since in such a language “nothing” has the meaning of “not anything.”) Recently, some philosophers (e.g. Friedman, 2000; Stone, 2006) have interpreted this debate in light of the philosophical (specifically, neo-Kantian) context that both Carnap and Heidegger shared. Others (e.g. Conant 2001) have brought out some of its ongoing implications for the analytic/continental divide.
In Logics of Worlds (Badiou, 2006), Alain Badiou has argued that a plurality of logical structures derived from mathematical category theory can be understood to determine the specific categorial structures and “phenomenology” of determinately structured “worlds.” These logical structures or “transcendentals” are generally non-classical logics which also determine the relative degrees of the intensity of appearance or “intensity of existence” of objects and phenomena within a particular world. The various non-classical logical calculi that yield “transcendentals” for specific worlds are themselves grounded in the broader mathematical framework of category theory, from which, as was demonstrated by mathematicians such as Lawvere, drawing on the earlier work of Grothendieck, particular logical calculi can be derived as special cases. Badiou argues that the specific logical/mathematical structure of an event, organized around what he calls a “truth procedure,” can under certain circumstances lead to a transformation of the categorial/transcendental logical structure of a world and thus its transfiguration into a new, differently structured one.
Badiou's conception of plural logics in Logics of Worlds thus reinvents the idea of a “transcendental” logic in a sense somewhat reminiscent of that of Kant, Husserl, and Heidegger, but emphasizes the absolute objectivity of the “greater Logic” thus conceived, as well as its independence from any category of the constitution or activity of the subject. Nevertheless, it is not completely clear how we should understand this logical “structuring” in each case of a specific world, if we don't understand it ultimately as a product of human decision or convention. In particular, it is somewhat obscure how we should understand the reality and force of a “transcendental” logic in maintaining the actual relations of existence and appearance typical of a world, if we do not consider this logic to be imposed by human decision or practice. Relatedly, despite the very detailed discussion of the formal-mathematical structures underlying worlds in Logics of Worlds, Badiou provides little explanation of what worlds actually are and how they are ultimately individuated. For Badiou, we are essentially capable of living in many worlds, which suggests that they resemble Husserlian “regions” (see section 2.1). But it remains somewhat unclear how we should think about the moments, or decisions, by means of which we inaugurate them, or move between them, and how to understand the possibility that determinations of “existence” in one world which we inhabit may not correspond to those in another.
One of the fundamental concepts of logic, whether Aristotelian, transcendental, or formal (in the post-Fregean sense), is the concept of an object or thing. Even ordinary language suggests that nothing can be more basic than a thing. This view is reflected in our use of words like “everything,” “something,” “anything,” and “nothing.” The debate between Heidegger and Carnap about the sense of “nothing” (see section 2.4) turned on whether the thought of nothing challenged our basic conceptions of logic and the world, as Heidegger argued, or whether it simply underscored the ineluctable character of the concept of a thing, as Carnap implied in maintaining that “nothing” could only mean “not any thing.”
For Aristotle, the most basic kinds of things are substances. Considered from a logical point of view, substances are subjects of predication – the things designated “S” in judgments or propositions of the form “S is P.” Considered from an ontological point of view, substances are bearers of attributes, including both intrinsic properties (essential and accidental) and relations. Since attributes depend upon their substantial bearers for their existence, they are less entitled than substances to the status of things. As Aristotle puts it, being is said primarily of substances and derivatively of everything else (Aristotle, 1984: 1623 [Metaphysics, 1028a]).
Aristotle divides substances into those that are sensible (or that can be sensed) and those that are supersensible (that cannot be sensed). Sensible substances have both essential properties and accidental properties. Essential properties belong to sensible substances for as long as the substances exist. Accidental properties are temporary states of the substance that may alter without destroying the underlying substance. Supersensible substances have only essential properties and persist through all times, or are outside time. Sensible substances, by contrast, persist for only a finite period of time. Included among sensible substances are both natural things, such as rocks, plants, and animals, and artifacts, such as statues. Sensible substances arise and perish, but for however long they exist they may be regarded as persisting.
Kant distinguishes things in themselves, about which we know nothing, from objects of possible experience. Objects of possible experience are spatiotemporal “appearances” that we subsume under categories (see section 2.1). These categories have logical significance (for instance, the category of substance is the concept of something that can be the subject, but not the predicate, of a categorical judgment) but since we have no intuitions of noumena we cannot apply them to things as they are in themselves. Their applicability to objects of sensible intuition is secured via “schemata” or pure “time-determinations” (Kant, 1998 [1781/1787]: A145/B184). Just as we cannot use the categories to determine things in themselves, so we cannot extend the spatiotemporal conditions of possible experience beyond the natural world of phenomena. The concept of a thing in itself remains irreducible for Kant, serving as a placeholder for unsolvable metaphysical problems (see section 1.1 on the negative conception of noumena, and section 3.1).
Frege abandoned the underlying predicative structure of subject-predicate logic, but he continued to give objects the central logical place of what is referred to by a name or “object term” (see section 2.1). Heidegger, similarly suspicious of the assumptions underlying subject-predicate logic, also suggests that the term “object” remains problematically correlative with the term “subject” – not only in the Aristotelian sense of a subject of predication, but also in the Cartesian or Kantian sense of a thinking subject. For this reason, Heidegger argues that the usage on which an “object” is exclusively what can be known or perceived by a “subject” should be overcome in the context of a post-subjectivist and post-representationalist conception of existence or Dasein.
One question about objects is what it means for them to persist over time. “Endurantists” holds that objects persist in the sense of remaining numerically identical throughout a period of time: for instance, the table in front of me remains one and the same object for as long as it exists. On this view, objects are “wholly present” at every moment of their duration. One problem for endurantists is the fact of so-called accidental change: we seem to be required to identify Socrates sitting with Socrates standing despite the seeming incompatibility of the property of sitting with the property of standing. An obvious response to this objection is to say that Socrates is not sitting and standing at the same time. But, as David Lewis points out, this forces the endurantist to transform the seemingly intrinsic properties of sitting and standing into relations between things, properties, and times: thus the sentence “Socrates sits” would not simply signify that Socrates possesses a monadic, or one-place, property; rather, it would signify that there is a relationship between Socrates, sitting, and a particular time or time span. To avoid this counterintuitive implication, Lewis advocates the perdurantist account, according to which physical things are not wholly present at every moment of their existence in time but rather are temporally extended wholes that are only partially present at each moment of their existence (Lewis, 1986: 202). On this view, things have temporal parts, just as they have spatial parts. Since a physical thing's past and future are no less actual than its present, there is no reason to privilege the part that happens to be present at any given time. On some versions of perdurantism, the very distinction between past, present, and future is treated as illusory or as reducible to quasi-spatial relations between point-like events. One difficulty with the perdurantist account is that it appears to do away with the useful Aristotelian distinction between essential and accidental properties. Perduring objects become the mereological sum of their temporal stages and thus lose their seemingly distinctive attribute of remaining fundamentally the same despite undergoing a change in accidental properties. Relatedly, perdurantists who level the distinction between past, present, and future do away with another useful Aristotelian notion, namely, that at every moment of their existence sensible substances have non-actualized potentialities.
An advantage of identifying objects with Aristotelian substances or Fregean referents of names is that it preserves our sense that a genuine thing has a holistic character. If we abandon the Aristotelian idea that things are individuated by substantial forms (e.g., a horse by the form of horse) it becomes open to us to adopt what David Lewis calls “the principle of absolutely unrestricted composition,” the idea that any “mereological sum,” however ontologically disparate its parts, constitutes an object or thing (for instance, part of the Statue of Liberty, my left food, and the number three) (Lewis, 1986: 212). Jonathan Schaffer rejects the admission of such “junk” into ontology. For Schaffer, the root of the problem lies in ontological pluralism, the idea that the parts of things are ontologically prior to the wholes they compose. Schaffer advocates a version of ontological monism, or the view that the cosmos as a whole is ontologically prior to its parts (Schaffer, 2010). A weakened version of ontological monism could accept the idea that wholes are prior to parts, while nevertheless allowing for a plurality of genuine as opposed to gerrymandered wholes. Finally, at the other extreme, mereological nihilists deny that there are any composite objects whatsoever (see section 2.1).
Another challenge to holism comes from ontologists who represent particular things as mere bundles of properties, a position once advocated by Bertrand Russell (1995 [1940]). Sometimes the properties in question are taken to be repeatable universals, other times as unrepeatable “tropes.” One problem with either version of the “bundle” theory is that it is unable by itself to indicate what exactly it is that does the bundling. In response to this difficulty, it is tempting to go in the other direction by identifying a thing with the underlying bearer of its properties. The problem this time is that it is difficult to say what distinguishes one otherwise undifferentiated bearer of properties from another. This problem can be addressed by ascribing to each thing the unique property of being just the bare particular bearer that it is – its so-called haecceity. An haecceity is an individual essence, conceived either as a unique cluster of properties (or tropes) (e.g., Chisholm, 2002 [1976]: 29) or, in this case, as just the bare property of being one particular thing and nothing else.
An alternative strategy would be to return to Aristotle's idea that to be a substance is not just to be a bearer of properties (with or without an haecceity) but to be a structured whole by virtue of possessing an essence. Different things with the same specific essence (an essence shared by all members of the same species or type) could be distinguished by their possession of individual essences, a concept that may be less obscure than that of bare haecceities insofar as it specifies the properties an individual must possess in order to be the individual that it is.
One problem for the Aristotelian model is that it seems to fit living things better than it does nonliving things. While this is itself not incontestable, it is plausible to think that an individual living organism has an essence by virtue of which its parts depend on the organization of the whole (cf. Kant, 2000 [1790]).1 In the case of nonliving things, however, it is less clear why or whether the parts should depend for their existence on the whole. If the parts of a thing do not depend on the thing as a whole, then it is not clear why the parts should not be regarded as independently existing entities that just happen to be yoked together. Likewise for the parts of those parts, and so on until we reach basic constituents of reality such as elementary particles. The risk here is that of failing to do justice to genuine wholes. The disintegration of things into parts is analogous to the reduction of things to bundles of properties or tropes. In each case, ontological “glue” of some sort appears to go missing, whether the items that need gluing are properties or parts. Drawing on the resources of dialetheist logic (or systems of logic that tolerate certain contradictions) Graham Priest has developed a conception of “gluons” – special entities that account for the unity of objects with multiple properties or parts. In response to the question as to whether gluons themselves are objects that exist over and above the objects they “glue” together, Priest suggests that one can say both yes and no (Priest, 2014: 56).
One way to block the inflationary view that any collection of parts or properties counts as an object or thing is to affirm that both living and nonliving things fall into natural kinds (see section 2.1), and that such kinds determine criteria of thinghood (just as they do criteria of identity). We could further allow that certain kinds of things have vague identity conditions. It may not be clear to us whether a particular lump of gold counts as the same thing after a few slivers of it have been shaved off, but we needn't let such ambiguous cases affect our overall conception of thinghood. Instead of blaming such ambiguity on the world we can blame it, as Lewis does, on the vagueness of language.2 To preserve the idea that temporal things are capable of enduring over time we need to be able to distinguish a thing's undergoing change from its coming into existence and passing out of existence. Essences and kinds may be able to do much of the requisite work here. A thing is said to persist through a change provided that its essential features remain the same and only its accidental features alter. A thing's accidental features alter when an event involving that thing takes place. Events of an entirely different sort take place when things themselves come into existence and pass out of existence. We may wonder though how sharp this distinction between two different kinds of events really is. Instead of distinguishing becomings from arisings and perishings, perhaps we would do better to reduce objects or things to events. Ordinarily we distinguish objects from events and processes, but some philosophers, such as Whitehead (Whitehead, 1929), have argued that things themselves are nothing but collections of events and/or processes. Others have made the converse argument that events can be reduced to relations between things, properties, and particular times. Is one of these reductionist proposals plausible? Or is the categorial distinction between things and events irreducible?
Questions about the nature of events are closely connected to questions about the nature of time. In an influential paper entitled “The Unreality of Time,” J. M. E. McTaggart argued that since no consistent account of events could be provided, time itself must be unreal (1908). In support of this counterintuitive idea McTaggart considered two different ways of thinking about time and temporal events. From one point of view, time is something that “flows” or “passes” from the future to the present to the past. From this point of view, events first have the property of being future, then the property of being present, and finally the property of being past. But, McTaggart argues, these are incompatible properties, for nothing can be future, present, and past simpliciter. The obvious response to this objection is to say that nothing can be future, present, and past at the same time, but then we have to say what we mean by “at the same time,” and McTaggart argues that this will lead to an infinite explanatory regress. So there is a problem with representing the series of events as successively future, present, and past. McTaggart calls this series of events the “A-series.”
To avoid this problem we could eliminate all reference to the A-series. Such an elimination would require us to reduce all tensed descriptions of events (e.g., “Tomorrow it will rain”) to tenseless descriptions (e.g., “On October 22, 2014 it rains”). We could then represent the structure of time and the events that occur in it as a space-like continuum in which events stand in (tenseless) relations of simultaneity and succession. McTaggart calls this the “B-series.” The problem with this picture is that by representing time as a space-like continuum it appears to eliminate time's “passage,” which appears to be an essential feature of our ordinary conception of time.
McTaggart's argument has given rise to an extensive debate between those who seek to repair the “A-series” model and those who defend some version of the “B-series” model. Those who defend the “B-series” model, such as David Lewis, sometimes treat time as (or as akin to) a “fourth dimension” of space, an idea in keeping with the physical representation of spacetime in the theory of general relativity. As Lewis develops it, the “B-series” model supports Lewis's “perdurantist” thesis that things have temporal parts (see section 2.5), and it enables him to identify events with properties of spatiotemporal regions (Lewis, 1986). Proponents of the “A-series” model point out that modern physical models of spacetime don't force us to accept the metaphysical “B-series” model (e.g., Prior, 1967; Zimmerman, 1996). Appealing to our strong intuition that time does pass, A-series theorists argue against the idea that things are spread out in time the way they're spread out in space. An object that is present at a moment in time is “wholly” present at that time; to persist it must endure and not simply perdure (see section 2.5). For “presentist” proponents of the A-series model, only present objects and events exist: those that we colloquially say “belong” to the future or past have no reality (i.e., no reality yet or no reality any longer). Insofar as we are situated in time, moreover, it seems that some tensed language is irreducible, notably those sentences in which temporal indexicals (such as “It is 3 o'clock now”) feature in a significant way. Proponents of the “new” B-series theory, such as J. J. C. Smart (1980), accept this but maintain nevertheless that the truth conditions for such statements can be expressed in tenseless language.
An alternative objection to the B-series model is that time appears to flow in such a way that the past and future are, to a certain degree, intermingled with the present. According to Henri Bergson, time and space have fundamentally different structures, the former being a “qualitative” multiplicity, the latter a “quantitative” multiplicity (Bergson, 2001 [1889]). Since our ordinary concepts of experience are pragmatically geared toward making sense of objects in space, it is difficult for us to articulate the nature of temporal duration. Inevitably, our language “spatializes” temporal relations – most obviously when we represent them in “B-series” terms, but also when we represent them in “A-series” terms. Only through a special kind of intuition can we apprehend the nature of duration and hence of temporal events. As soon as we try to conceive them they elude our perception and comprehension.
According to Davidson (Davidson, 1980) events are individuated by their causal powers: their distinctive capacities to bring about other events. Since causality is irreducible to things or objects, so are events. Individuating events on the basis of their causal powers yields a different inventory of events than the one we get by identifying events with exemplifications of properties at times, a view put forth by Jaegwon Kim (Kim, 1993). For Gilles Deleuze, by contrast, drawing on Bergson, events are intrinsically individuating occurrences (Deleuze, 1994 [1967]). An event can take place, for Deleuze, when an underlying structure undergoes a transformation or reaches a point of sudden transition. For example, when water is cooled to a certain point, it suddenly and discontinuously attains the crystalline structure of ice, thereby creating a particular (individual) block of ice. Since structures aren't themselves things, the conditions of such discontinuous change can't be ascribed to the properties of individual things alone, but they may result (as in this example) in a sudden transformation of an entire context or order of things. Deleuze distinguishes structures, which are “virtual” and non-actual but nevertheless real (and not illusory, imaginary, or merely abstract), from their actualizations in concrete objects. For example, the possibility of the formation of the block of ice is, for Deleuze, contained in the real, although “virtual,” underlying structure of the water molecules, rather than in anything merely potential or not fully actual before the event of freezing. Events mediate between the two levels of the virtual and the actual, for Deleuze, since an event is simultaneously a transformation of a virtual structure and an actual becoming of things. Events are thus omnipresent not because every becoming counts as an event, but because every becoming is grounded in such a structural transformation.
Central to Deleuze's ontology is the concept of repetition. What a presentist would characterize as the endurance of a thing Deleuze thinks of as the repetition of an actual occurrence. This view resembles Roderick Chisholm's suggestion that events can be thought of as repeatable universals rather than as property exemplifications or causes and effects (Chisholm, 1970). Chisholm's view differs from that of Deleuze, however, in that it represents repeatable events as universals. Deleuze's view seems to be closer to that of Derrida (Derrida, 1985 [1971]), for whom repetition is a function of iterability rather than of duplication. That an event is iterable, in Derrida's sense, means not simply that it is repeatable as the same, but that it is repeatable in an unlimited and essentially open variety of contexts, in each of which its significance or sense will be somewhat different. There is thus no way completely to predict or control the significance that the “same” event will have across the whole variety of its contexts of repetition, and this essential openness to difference must be considered an inherent aspect of the essential iterability of any event. This structural iterability of the event as such, for Derrida, is closely linked to the structurally necessary iterability of linguistic signs, for instance letters and words. Just as each word can be iterated in any number of different significant contexts and will have essentially different implications in each case, every event can be indefinitely iterated in an essentially unpredictable way. Thus, whereas repeatability multiplies an indivisible entity by giving it potentially many instantiations, iterability divides an entity by dispersing a singular instantiation among an indefinite plurality of manifestations or effects.
In Being and Event, Alain Badiou considers “events” in the special sense of occurrences that have the potential to transform the situations in which they take place, in any of the four domains of the “truth procedures” of politics, art, science, or love (Badiou, 2005 [1988]). As we have seen (section 1.7), Badiou identifies mathematics as captured by the axiomatization of ZF set theory with ontology, or the theory of being insofar as it can be described. For Badiou, the axioms of ZF set theory thus characterize the essentially regular domain of being; but an event (which introduces, by contrast, the possibility of transformative becoming) is a particular kind of set-theoretical structure that is actually prohibited from ontological existence in that it violates one of the axioms of ZF set theory, the axiom of foundation or regularity. This axiom implies that no set can be an element of itself. For Badiou, the event violates this axiom by designating or naming itself, or by including its own designation as an essential moment of its occurrence (think, for instance, of the way a revolution takes on a life of its own only when it is recognized and designated as such). The event's structure of self-membership or auto-designation allows what Badiou calls a “subject” (which can be an individual, but can also be a group or collective) to trace out faithfully the consequences of its having taken place for the surrounding context. In the most significant cases, this “fidelity” of the subject to the event will result in a radical structural change or transformation of this surrounding situation.
For Badiou, as we have just seen, a subject is defined by its fidelity to an event. This conception can be related to something other than an individual, psychological subject, but it is also meant to capture an essential feature of psychological subjectivity as it has been conceived by modern thinkers such as Descartes, Kant, and Lacan. Étienne Balibar has argued that the concept of a subject is fundamentally Kantian, but it is generally associated with Descartes's representation of the “cogito” (the “I think”) (Balibar, 1991 [1990]). In this Cartesian sense of the term, a subject is a “thinking thing” (res cogitans) whose essence is different in kind from that of a spatially extended thing. For Kant, by contrast, the fact that I necessarily represent myself as a seemingly simple, self-conscious thinking subject doesn't entitle me to conclude (though it gives rise to the illusion that I am entitled to conclude) that I am, metaphysically, a thing whose essence consists only in thinking (i.e., a soul). The illicit inference is based on a fallacy of equivocation, or what Kant calls a “paralogism” (Kant, 1998 [1781/1787]: A341–403/B399–432). All that I am entitled to say about my status as a thinking subject is that the simple (because empty) representation “I think” “must be able to accompany all of my [mental] representations” (Kant, 1998 [1781/1787]: B135). From this it follows that I can use the indexical term “I” to refer to whatever thing it is that grounds my capacity to think (or form representations), but since this ground lies beyond the bounds of possible experience, I cannot consider it as an object of cognition. In particular, I cannot know that what I am is a non-physical substance. Descartes' error, Kant concludes, consists in confusing the unknown ground of the activity of thinking with a supposed object of intellectual intuition. In “inner sense” I only encounter ever-changing mental states, and no stable, persisting appearance.
We can understand many conceptions of subjectivity, both positive and negative, in terms of the conceptions of agency they involve. According to Hume, what we take for the self (or what we find when we turn our attention inward) is nothing more than a “bundle” of diverse impressions and ideas, with no substantial “self” underlying them. On this account, there is thus no functional agent responsible for the act of bundling or the seeming unity of our experiences. Nietzsche echoes Hume's thought when he argues that we have no legitimate reason to ascribe the activity of thinking to a subject (Nietzsche, 2002 [1886]: 16–17); in a different context, Ryle similarly suggests that there is no distinctively mental volitional agent that can be separated from the overall physical acts and tendencies of a person (Ryle, 1949: esp. chs. 1 and 3). According to both philosophers, the idea that every intentional act involves a unitary and distinctively mental agent is in many ways a mere illusion fostered by the subject-predicate structure of language. Even the indexical “I” may be unable to pick out a persisting self. G. E. M. Anscombe (Anscombe, 1975) argues that even when we assume the existence of a self that persists over time, we cannot successfully refer to such an entity. Fixing self-reference requires an ability to track an object distinct from the self. The indexical “I” is thus neither a name nor a definite description; strictly speaking, “I” does not refer. Against this, David Kaplan (1977) has suggested that “I” and other indexical expressions (such as “now” and “here”) are devices of direct reference, capable of picking out or referring to a distinct individual in a context-dependent way.
For Kant, the representation “I think” is no more reducible to the flux of my lived experience (the object or objects of inner sense) than it is to physical objects in space (objects of outer sense). Nevertheless, the Kantian subject can be positively understood, to a certain extent at least, in terms of its functioning. The primary cognitive function of the Kantian subject is to make predicative judgments about objects of possible experience. Thus the Kantian subject is a predicating subject whose own structure can be understood in terms of the functional conditions for the activity of predication. For Kant, these conditions include not only our passive reception of affections from outside, but also our free agency in the active or “spontaneous” formation of articulated conceptual judgments. Similarly, for contemporary functionalists, although there may or may not be a distinctive kind of agency connected with the nature of subjectivity, minds are to be understood as systems whose primary function is to “process” representations in a manner roughly analogous to the way in which a computer processes data (see section 3.4).
Some recent philosophers of mind, including Lewis, Davidson, and Marcia Cavell, have considered the various ways in which people can be said to hold contradictory beliefs. If one subset of a person's beliefs conflicts with another, we may characterize her as having a divided mind. In the same way that one desire may be stronger than another, one belief may be held with a greater degree of conviction than another. In fact, the connection between beliefs and desires may run deeper than this analogy suggests, because beliefs can shape or determine desires, and vice versa. For instance, a strong desire may encourage us to ascribe greater or lesser weight than we should to whatever independent warrant we have for holding a particular proposition to be true. Most people are susceptible to this temptation of “wishful thinking” to one degree or another.
One of the aims of psychoanalysis is to explain how the repression of desires and beliefs can give rise to neurosis and other kinds of psychological pathologies. More broadly, psychoanalysis formulates the question of how the subject of such attitudes – the believing and desiring subject – comes to exist as a subject in the first place. Freud's account of ego formation addresses this question with a complex account of the influences and stages of the development of the ego in childhood, alongside the other two psychic “agencies” of the id and the superego. Jacques Lacan, combining Freudian insights with others drawn from structuralist linguistics, argues that there can be no speaking or predicating subject without a “subject of the unconscious” that is structured like a language. On this picture, the capacity for speech presupposes that the subject has “entered” language by identifying itself with a primordially repressed signifier. The functional exclusion of this signifier marks a structurally necessary “place” essential to the formation of any subjectivity, insofar as any subject understands herself as situated within a broader world of objects and meanings that pre-exists her and which she cannot completely control (what Lacan calls the ‘symbolic’ order). Lacan calls the presumed object of the subtracted signifier, whose absence from its “place” comes to organize the structure of the subject's unconscious, the “object small a” or “objet petit a.”
The result, according to Lacan, is a subject that is inherently “barred” or divided by this essential lack itself. Accordingly, he symbolizes this subject with a barred S ($). Slavoj Žižek has argued that the barred subject is equivalent to Kant's representation of the thinking subject as a “transcendental unity of apperception.” Just as, for Kant, the subject of apperception (the synthesizing “I think”) is cognitively divided from its metaphysical ground (what Descartes thought he could intellectually intuit as an immaterial substance), so for Lacan the barred subject is cut off from its unconscious. Lacan goes one step further than Kant, however, by suggesting that the unconscious itself thinks. Hence the Cartesian formula “I think, [therefore] I am” can be understood in either of two variant ways: either as “I think, therefore it is” or as “I am, therefore it thinks” (Žižek, 1993: 252n.26). The first version implies that the subject gains the capacity to think and speak at the cost of ceding its being to the unconscious, an uncanny “thing” within me for which I do not conceive myself as responsible. The second version implies that the subject gains its being at the cost of ceding the spontaneity and freedom of its thought to the unconscious. On either account, the subject is divided into conscious and unconscious components that cannot be superimposed.
Controversially, Lacan suggests that a primordial “choice” between being and thinking corresponds to a choice between “masculine” and “feminine” forms of subjectivity. Slavoj Žižek and Joan Copjec have developed this picture further by calling attention to a structural parallel between Lacan's “formulae of sexuation” and Kant's representation of the difference between mathematical and dynamical antinomies (Žižek, 1993; Copjec, 1994; for the formulae of sexuation, see Lacan, 1998 [1973]). In the Critique of Pure Reason Kant identifies four antinomies, or apparent contradictions, that arise when human reason seeks to represent the empirical world as a totality. Two of the antinomies are “mathematical” in that they concern the magnitude (finite vs. infinite) of the spatiotemporal world in the great and the small. The other two antinomies are “dynamical” in that they concern the dependence or independence of nature on ultimate metaphysical grounds (see section 3.5). According to Copjec and Žižek, the two sides of the mathematical antinomies together exhibit a logic of “non-all”: on the one hand, nothing escapes the whole; yet, on the other hand, the whole is somehow incomplete or “non-all.” Conversely, the dynamical antinomies exhibit a logic of the constitutive exception: on the one hand, nature is a closed totality; yet, on the other hand, there are “constitutive exceptions” at the noumenal level of reality (freedom and a necessary being). Analogously, Lacan takes feminine subjectivity to be inscribed in the symbolic order in a manner which makes it non-all, while the inscription of masculine subjectivity in the symbolic order gives rise to the symbolic fiction of constitutive exceptions such as the “big Other.”
Along similar lines, we might discern a comparable parallel between Lacan's two versions of the cogito and Kant's account of the split between transcendental apperception and empirical apperception (or inner sense). In transcendental apperception, the subject thinks but without appearing to itself as an object of thought. Conversely, in inner sense the subject appears to itself as an empirical object, but only as an effect of essentially hidden acts of thoughts. Once again, this non-coincidence of thought and being is reflected in the two fundamentally different ways in which Lacan reformulates the Cartesian cogito, according to Žižek: either I think where I am not, or I am where I do not think. To the extent that this distinction is supposed to constitute the difference between masculine and feminine forms of subjectivity, sexual difference would have to be understood neither as a biological fact, nor as a cultural construct, but as a quasi-transcendental phenomenon. One obvious problem with this account is how we should understand the terms “masculine” and “feminine” if they are not to be correlated with either the biological distinction between the sexes or with the cultural distinction between masculine and feminine genders. Critics of Lacan, such as Judith Butler (Butler, 1993), have objected that he and his followers conflate biological, cultural, and psychoanalytic points of view. By treating masculine and feminine subjectivity as quasi-transcendental structures, they overlook their historical genesis and contingency. For Butler herself, gender roles have a “performative” dimension that can be reinforced or undermined by how we respond to them.
Others have argued that psychoanalysis can be used to understand how ideology works. Lacan suggests that a child becomes a subject by undergoing processes of “imaginary” identification (identification with an object that is fundamentally alienating) and “symbolic” identification (identification with a signifier that marks its entry into language) (Lacan, 2006 [1966]: esp. ch. 30). The Marxist philosopher Louis Althusser interprets these processes as involving “ideological interpellation” (Althusser, 1971). To be ideologically interpellated is to respond to a call to assume a determinate “subject position” within the existing socio-economic relations of production. Various “ideological state apparatuses” play a role in this process, including not only the modern bourgeois family that was the original focus of Freud's inquiry but schools, media, and other pedagogical institutions. According to Althusser, the interpellated subject's way of thinking is determined “in the last instance” by economic factors. By subsuming the sexual dynamics of the Oedipus complex under economic mechanisms, he subordinates the Freudian/Lacanian theory of subject formation to a Marxist account of the process by which existing social relations of production reproduce themselves. Subjects are thus treated by Althusser primarily as ideological formations, occupying positions that are prepared in advance by the society's particular and necessarily distorted reflection of the real relations of production.
In Anti-Oedipus, Gilles Deleuze and Félix Guattari develop a somewhat different view (Deleuze and Guattari, 1983 [1972]). For Althusser, ideology is essentially representational: to be successfully interpellated is to learn to represent one's position in the symbolic order in a certain way. For Deleuze and Guattari, economic systems function by channeling “desiring-production” in a way that is, in the first instance, non-representational. In their view, the fundamental antagonism of capitalist society is not between the bourgeoisie and the proletariat, as it is for classical Marxists, but rather between Oedipalizing mechanisms that link desire to the formation and reproduction of capital and quasi-schizophrenic mechanisms that seek to liberate desiring-production.
Deleuze and Guattari's representation of desiring-production somewhat resembles Michel Foucault's representation of “power-knowledge.” For Deleuze and Guattari, subjects are secondary effects of desiring-production rather than ultimate sources of desire. Analogously, in some of his writings Foucault represents speaking subjects as effects of power-knowledge rather than as ultimate sources of acts of predication. For example, in the Archaeology of Knowledge he treats subjects as enunciative functions of discourses (Foucault, 1994 [1969]). The primary unit of a discourse is an individual statement. Statements carry with them determinate criteria for their utterance. A subject is someone who meets the relevant criteria. This view inverts the traditional conception of statements as expressions of a speaker's beliefs. Instead of granting primacy to the judging/believing/knowing subject, Foucault makes subjects depend upon what counts as knowledge within a particular discursive regime. In Discipline and Punish he emphasizes the role played by power in constituting human bodies as both subjects and objects of knowledge (Foucault, 1979 [1975]). Relatedly, in the first volume of the History of Sexuality he argues that the psychoanalytic theory of sexual repression, according to which our subjective identities are fundamentally sexual in character, is not the liberating discourse that Freud made it out to be but rather a manifestation of “biopower” (Foucault, 1978 [1976]). In the last two volumes of the History of Sexuality Foucault moderated this view somewhat, turning his attention to the history of practices of self-constitution (“care of the self”) from antiquity to the present (Foucault, 1985 [1984a] and 1986 [1984b]). In Plato's Apology, he argues, Socrates' fundamental injunction isn't “Know yourself” but “Take care of yourself,” yet over time the latter was eclipsed by the former (Foucault, 2005 [1981–2]: 5). Foucault seeks to explain how this transformation took place and to invent new forms of self-constitution. It is possible, he suggests, to embrace the injunction to care for one's self without accepting the narrowly hermeneutic task of explicating oneself, be it in a Platonic, Christian, or psychoanalytic sense.
In his earliest work, Alain Badiou, partially following Althusser, maintained that the category of the “subject” is primarily an ideological one and that the condition for genuine scientific knowledge is the exclusion of anything like a subject (Badiou, 2012 [1967]; Badiou, 2012 [1969]). By the middle of the 1970s, though, Badiou (2009 [1982]) had begun to think in Marxist and Maoist terms about the possible structure of a generally collective subject of political transformation: the sort of subject that Marxist philosophers such as Lukács (2000 [1923]) had earlier taken the proletariat to be. In the later Badiou's more developed conception of the subject of the event, the defining activity of an individual or collective subject consists in its faithful and transformative work, within a situation, to transform its structure in light of the event, working on language itself to render visible what was formerly only latent or invisible within that situational structure. Here, as indicated in section 2.6, the subject is understood neither as a subject of consciousness nor (any longer) as a merely ideological category. Instead, it is understood, in large part, through its capacity to transform the linguistic structure of possible designation and reference itself.
In the last decade of the nineteenth century, Gottlob Frege (Frege, 1997 [1892]) noted that judgments of identity give rise to difficult questions about language and reference. For instance, the judgment that “Hesperus is Phosphorus,” whereby we judge that the object we have called by the first term is the same thing as the one we have called by the second, can be informative even though it is obvious that for any A, “A = A.” This led Frege to distinguish between the sense of a singular term – the “mode of presentation” or the way it presents or picks out its object – and its referent, that object itself. Frege concluded that the work of names and other referring expressions could not be understood simply as a matter of their referring alone. Rather, it was necessary to distinguish their “sense,” or (as he sometimes calls it) their “mode of presentation,” from the object to which they refer (or which they present). For Frege, sense always determines reference, but not conversely: it is often possible for one and the same object of reference to be picked out through more than one sense.
According to Russell (Russell, 1911; Russell, 1988) we refer to things other than ourselves in one of two ways. The most direct way is to refer to things by their names. Names acquire their referential power by being directly assigned to objects when we are acquainted with those objects: i.e. when they stand directly before us or are in some sense directly present to us, for instance in a direct giving or intuition (see section 1.1). If we never get direct perceptual access to an object, we cannot name it in this way. Accordingly, most of the terms that we conventionally regard as names aren't really names at all – or rather, they aren't names for us. Whoever met Julius Caesar could have learned to use “Julius Caesar” as a genuine name.3 For everyone else, “Julius Caesar” is a hidden definite description – something along the lines of “the Roman general who was assassinated in the Capitol in 44 BCE and whom contemporaries called ‘Julius Caesar.’ ” This indicates the second way in which we refer to things – through definite descriptions. A definite description is an expression of the form “the such-and-such.” Provided it is well-formed, a definite description uniquely picks out one and only one object (see section 1.3).
According to what has been called the “new theory of reference” (now some 40-odd years old!), by contrast, Russell's theory of names is too restrictive. In order to use a name as a name, it is not necessary ever to have been acquainted with the object it names. Instead it suffices to stand in the right causal history to the named object. The name “Julius Caesar” first acquired its power to refer to Caesar by being causally linked to him in some appropriate way; for example, perhaps there was an initial act of baptism wherein Caesar's parents stood before him and gave him that name. But it has retained its status as a name by being passed down from speaker to speaker through further causal links. Today we succeed in using “Julius Caesar” to refer to Julius Caesar because we ourselves stand in the right accumulated causal relationships to the Roman general who was assassinated in the Capitol in 44 BCE. On this kind of view, then, something like “Julius Caesar” that functions as a name is not any kind of description; rather, it retains its ability to name the individual because of the causal history that connects us to the initial use of the name to pick out that very individual.
A crucial component of this theory, drawn in part from suggestions first made by Ruth Barcan Marcus (Marcus, 1961) and Saul Kripke (Kripke, 1980 [1971]), is that it makes no difference whether names are originally assigned to their referents as meaningless “tags” or as meaningful expressions. However the initial reference gets fixed, it is thereafter fixed in a “rigid” manner – it continues to refer to that particular individual. Names are thus understood as “rigid designators” – expressions that pick out the same referent, regardless of changes in the properties of that individual and across all possible worlds (where they pick out any referent at all). For example, the gangster whom we call “Baby Face Nelson” may have been given this nickname because he had chubby cheeks, but, if so, this baptismal fact is immaterial. We can now say, truthfully, that Baby Face Nelson need not have had chubby cheeks, or, for that matter, that he could just as well never have been called “Baby Face Nelson.” When we say such things, we nevertheless use the name “Baby Face Nelson” to pick out the unique individual that we do call “Baby Face Nelson” (or “Lester Joseph Gillis,” the gangster's given name).
Keith Donnellan (Donnellan, 1966) criticizes another feature of Russell's original theory. According to Donnellan, Russell not only mistook genuine names for abbreviated definite descriptions; he also failed to distinguish two kinds of definite descriptions: attributive and referential. An expression of the form “the such-and-such” can be taken to attribute to something the property of being the such-and-such. On the other hand, it can be taken to refer to the thing to which we attach the property of being the such-and-such. In the first case, we identify something by attributing to it the property of being the such-and-such; in the second, we pick something out from its surroundings by referring to it as the such-and-such. Russell focused primarily on the attributive aspect of definite descriptions and thereby reduced reference to denotation. Distinguishing reference from denotation enables Donnellan to show how we sometimes succeed in referring to an object despite the fact that the definite description we employ involves a misattribution. Kripke suggests, however, that it is unclear whether the pragmatic dimension of Donnellan's account is supposed to count as an objection to Russell's semantic analysis of definite descriptions (2013: 111). When someone succeeds in referring to someone else by calling her “the such-and-such” even though she isn't the such-and-such, the speaker's success doesn't necessarily change the meaning of the expression.
The distinction between semantics and pragmatics has been widely accepted, but some philosophers think it is too strict. Denotation may be different from reference, but even if this is so, we still need an account of how reference works. Otherwise we will end up begging the very question that the new theory of reference was designed to explain, namely, how language hooks up with objects with which we have no direct acquaintance. Moreover, even in the case of direct acquaintance we still need an account of how language and world hook up. When Julius Caesar was first called “Julius Caesar,” why – or rather how – did the name “take”? Just to say that it took because of conventions governing acts of baptism, or by appropriate causal relations between Caesar's parents and him, seems to beg the question. For this reason and related ones, others such as Gareth Evans (Evans and McDowell, 1982) have argued for returning to a partially Fregean conception of the relationship between sense and reference, while still maintaining in a broader context the suggestion that the possession of some thoughts requires the ability to track and identify their objects over time, and thus some aspect of the dependence of designation on the existence of the objects themselves.
Another answer, suggested by William Kneale (Kneale, 1962) is to say that “Julius Caesar” refers to Julius Caesar because it means something like “the name of Julius Caesar.” Kripke points out the circularity that this quasi-Russellian account entails – “Julius Caesar” ends up referring to Julius Caesar because “Julius Caesar” means “the name of Julius Caesar” – but Slavoj Žižek suggests that some such circularity may get at the heart of how we succeed in referring. Invoking the Lacanian concept of the objet petit a, Žižek argues that the only reasonable answer that can be given to the question “Why is ‘X’ the name of X?” is “Because ‘X’ is its name.” Prior to acquiring its name a thing bears no relationship whatsoever to its name. Once it acquires it, however, a kind of retrospective illusion is produced according to which there is something about the thing in question – its haecceity or objet petit a (see sections 2.5 and 2.7) – that makes it the bearer of its name. In the absence of its name, the thing can be referred to only by descriptions, but once it acquires a name it can be referred to in two different ways. It can be referred to de re – in a way that points directly to that object – as well as de dicto, or by description. The paradox is that it is only by acquiring its name that a thing acquires the very trait that makes it capable of bearing its name, for that trait is the property of being the bearer of that name. This is not to say that reference works by magic, but it is to say that our ability to refer to actual things – as opposed to being trapped in the “prison-house” of language – rests on a kind of dialectical illusion, one that is necessary to our communication about a shared world. Without the sustaining illusion that things possess their names as intrinsic properties, language would fall short of the world.
Antirealists such as Michael Dummett (Dummett, 1978 [1963]) and (for a time) Hilary Putnam (Putnam, 1981) draw a different conclusion (see section 3.4). Focusing less on names per se than on language in general, they argue that reference is always relative to a particular language (Dummett, 1978 [1963]; Putnam, 1981). Within a particular language we succeed in referring to the world, but only by the lights of our own language. Going even further than this, in other places (e.g. Putnam, 1988) Putnam draws on a model-theoretic argument to show that even within a particular language it is possible to reassign the reference of our terms in such a way as to make all true and false sentences come out respectively true and false under the new, perverse assignments. This shows that reference is “inscrutable” in a far more pervasive way than Quine had originally demonstrated in a more limited context (e.g., Quine, 1968; see also section 2.2). To defend a stricter reference relation, realists have invoked one or another privileged relation between terms and objects – such as a causal one, a privileged relation of reference to “natural” properties or objects, or so-called ‘reference magnetism’ – which does not seem to succumb to this kind of systematic reassignment or permutation (e.g., Lewis, 1984).
One kind of way we talk about things is to talk about their modal properties: that is, how they could have or might have been, even though they are not that way, or else why they necessarily are the way that they are. Talk about possible worlds originated with attempts to make sense of these kinds of counterfactuals and claims of necessity. Counterfactuals are expressions that say how things “might have been” even though they are not actually that way. To take a well-known example, we can say of a fragile vase that never actually breaks throughout its entire history that, nevertheless, it might have broken at some point in time. What exactly does this mean? One answer is that there is a possible world (or set of worlds) “in which” or “according to which” the vase does break at some point in time. Likewise, to take another popular example, to say that Hubert Humphrey might have won the presidential election in 1968 is to say that there are possible worlds “in which” or “according to which” Humphrey does win the election in 1968.
The general idea here is that a possible world is a temporally and spatially complete whole, some total way in which things might have been. David Lewis advocates “modal realism,” the view that all possible worlds are in some sense real, the actual world – the world in which we exist – being just one such possible world (Lewis, 1986). According to Lewis, the term “actual” should be treated as an indexical on a par with the temporal indexical “present”: it is only our perspective on our world that entitles us to call it actual. Every world counts as actual for its own members, but only for them.
According to modal realism, possible worlds are concrete entities composed of concrete parts (called “possibilia”). For every way in which possibilia can coexist there is some world in which duplicates of them do coexist. For example, the Humphrey of our world is a concrete possibilium that has the property of losing the presidential election in 1968. To say that Humphrey could have won the election is not to say that he himself wins it in other possible worlds, for like every other entity, Humphrey is “world-bound”: he belongs to our world and no other. What makes it true according to another world that he could have won the election here is that he has “counterparts” in other worlds that have the property of winning their elections. What make his counterparts count as his counterparts are relevant similarities in their respective intrinsic properties and external relations. What count as relevant similarities in one explanatory context might be irrelevant in another (Lewis, 1986).
Modal realism has many explanatory virtues. One (Lewis, 1973) is its ability to provide a counterfactual analysis of causality. According to Lewis, to say that Event C is the cause of Event E is to assert the counterfactual conditional that, had C not occurred, E would not have occurred. This can be taken to mean that in the nearest possible world in which a counterpart of C does not occur (or in some relevant set of nearby worlds in which counterparts of C do not occur), a counterpart of E does not occur (or counterparts of E do not occur). One of the challenges for this model is to deal with complications involving cases in which C is the cause of E in our world but in such a way that had C not occurred E would have occurred anyway (because of failsafe mechanisms, etc.). It is unclear whether a counterfactual analysis of causality can accommodate such counterexamples in a general way, but it might be enough for it to deal with them in a piecemeal way.
More potentially damaging to the cause of modal realism are arguments given by Kripke. In Naming and Necessity Kripke wryly observes that Humphrey probably “could not care less” if any of his counterparts win the election; what he cares about is the fact that he himself didn't win (but could have) (Kripke, 1980 [1971]: 45n.). If we are going to say, meaningfully, that Humphrey could have won the election, it should come out that there is a possible world in which Humphrey himself wins the election. Without committing himself to a full-blown metaphysics of possible worlds, Kripke argues that rigid designators (see section 2.8) provide us with sufficient means for tracking one and the same object across its alternative possibilities. The order of explanation does not consist in describing a world very much like ours and then asking if it contains within it a counterpart of Humphrey; the proper procedure is rather to stipulate that we wish to consider “worlds” (in some metaphysically neutral sense) in which the designated object has properties other than its actual properties. This is a matter of de re representation rather than de dicto representation (see section 2.8).
In response to Kripke, Lewis (1986) maintains that counterpart theory does allow for de re representation. By containing relevant counterparts of Humphrey that win their elections, other worlds represent Humphrey as winning. According to Lewis, moreover, it isn't as easy as Kripke seems to think to remain metaphysically neutral about possible worlds or to substitute “ersatz” worlds that substitute for genuine possible worlds. Lewis distinguishes three different types of “ersatzist programs”: linguistic, pictorial, and magical. Of these, he takes the linguistic to be the most promising. Linguistic ersatz worlds aren't really worlds at all; rather, they are sets of sentences (or each is a conjunction of sub-sentences). Each ersatz world purports to describe the (one and only) actual world, but only one of them describes it accurately. That ersatz world isn't itself the actual world; rather, the actual world is an actualization of it. The chief benefit of linguistic ersatzism is that it doesn't commit us to the reality of non-actual possibilia of any sort. All the non-actualized “worlds” and their “parts” are just the things there would be if the ersatz worlds described the actual world correctly. As for the ersatz worlds themselves, they are just sentences in some sort of actual language. Lewis discusses the “Lagadonian” model proposed by Carnap according to which names are particulars that name themselves and predicates are universals that apply to themselves (Lewis, 1986, 152; Carnap, 1947).
There are, however, several problems with this picture. One is that all of the sentences or sub-sentences that comprise a particular linguistic ersatz world have to be mutually consistent, and they have to be structured in such a way as to exhaustively inventory the objects it represents as existing. It is difficult if not impossible to meet both of these conditions without relying on “primitive” (i.e., unanalyzed) conceptions of modality – for “consistency” and “implicit representation” are both modal notions. Lewis explains modality in terms of possible worlds, but this option apparently isn't readily available to the linguistic ersatzer. Another problem has to do with “alien properties” – properties (whether universals or tropes) that aren't instantiated by anything in our world (and so don't belong to it) but which are instantiated in other possible worlds (Lewis, 1986: 142–65). The linguistic ersatzer seems to lack the linguistic resources to account for such possibilities.
“Pictorial” and “magical” ersatzism pose other difficulties, the former by representing worlds as pictorial models (but how?), the latter by abandoning a representational model but refusing to grant possibilia and possible worlds the same ontological status that the modal realist grants them (thereby lapsing, Lewis thinks, into a kind of obscurantism) (Lewis, 1986: 165–91). Lewis complains that some opponents of modal realism hedge their bets by refusing to choose among the major alternatives (Lewis, 1986: 141). In The Nature of Necessity Alvin Plantinga represents possible worlds not as concrete entities but as abstract entities (Plantinga, 1974). He rejects Lewis's “possibilism” (with its indexical analysis of “actual”) in favor of “actualism” (the idea that our world is the only world that actually obtains). Other worlds are non-obtaining, maximally complete states of affairs. Insofar as these non-obtaining worlds represent other possibilities for actual entities, it is those very entities themselves (and not counterparts of them) that are so represented. Hence the actualist's notion of “transworld identity.”
Kripke argues that an object's origin and initial material constitution are both essential to its identity: the only worlds in which it can meaningfully be said to exist are those in which it has the same origin and initial material constitution. Lewis is more lax about this requirement: the decision about whether or not to keep to it depends on our purposes in a particular explanatory context. In some contexts, Lewis observes, it is meaningful to consider worlds in which Kripke was brought by a stork rather than born to his parents. But there are limits to what can count as a counterpart; for instance, there aren't possible worlds in which Kripke is a poached egg.
For those who find modal realism itself too mysterious, it is tempting to argue that possible worlds are fictions, or that talk about possible worlds is just a convenient way of speaking about counterfactual situations. On these views, it is a mistake to invest modal operators – “It is possible that …,” “It is necessary that …” – with any ontological significance. For the sake of philosophical convenience we take “It is possible that p” to mean “There is a world in which p is true,” and we take “It is necessary that p” to mean “In every world p is true.” This gives us a model for interpreting statements in modal logic, but like all models it is ontologically neutral. In Modal Logic as Metaphysics, however, Timothy Williamson argues that modal logic is not ontologically neutral, at least no more so than empirical science. Williamson defends “necessitism,” or the view that “necessarily everything is necessarily something” (Williamson, 2013: 2): that is, any possible object existing in (or at) any possible world exists in (or at) all possible worlds.
Another question that arises is that of the temporal relationships, if any, between worlds. Lewis's worlds diverge from one another, but they don't branch off. One advantage of a branching model is that it links modality and temporality in a tighter way. To say that the future of our world is open is to say that there are distinct possible ways in which things in our world might go. As Lewis points out, however, the branching model actually closes off our sense of the openness of the future by allowing all “possible” futures to be actualized along distinct branches; what we don't know is not what will happen in the future but rather which branch of the fully determinate future we'll find ourselves on (though if we accept the doctrine of temporal parts, our present temporal parts will find themselves parts of mereological sums on all of the branches) (Lewis, 1986: 206–9).
Another way of thinking about modality is in terms of a teleological conception of the relationship between possibility and actuality. According to Aristotle, substances have inherent possibilities (“potentialities”) that they strive to actualize. Other philosophers, including Hegel and Marx, have suggested that human history has an overall teleological tendency – dynamical possibilities that may or may not be actualized. Adorno famously wrote that philosophy lives on because the opportunity to actualize it was missed (Adorno, 1983 [1966]: 3). What Adorno seems to mean by this is that the actual world has thus far failed to actualize inherently rational possibilities. Adorno is responding in this passage to Hegel's dictum that “What is rational is actual; and what is actual is rational” (Hegel, 1991 [1820]: 20). According to Adorno, the actual is irrational in the sense that it could – or rather should – have been more rational than it is. Something has prevented its inherently rational form from becoming actualized. As a result, we have ended up in a world that, in some sense, is less than fully actual (in the sense of being less actualized). Perhaps a branching model of possible worlds could do justice to Adorno's intuition. But Lewis gives us reason to think that a dialectical metaphysician might be better off with divergent worlds rather than with branching worlds.
In Plato's Sophist, two characters, Theaetetus and the Eleatic Stranger, associated with Parmenides, consider the question of the possibility of “non-being” – the possibility for “what is not” in some way to exist, or the possibility of speaking falsehood (saying “what is not”). Given that everything that exists is part of being, how is it possible for “what is not” somehow to appear? The interlocutors conclude that this is possible only if the “great type” Being can mix or combine with two other forms or types, identity and difference. Thus, for instance, in the false statement “Theaetetus flies,” difference combines with being to say something about Theaetetus which is different from every property that Theaetetus in fact has, thus producing the (false) claim that he is flying. Difference is thus at the very basis of the metaphysical distinction between being and non-being, as well as the logical distinction between the truth and falsehood of sentences.
As we have seen (section 2.8), Frege drew the distinction between sense and reference, at least in part, in order to explain the informativeness of judgments of identity. Nevertheless, Frege also held in The Foundations of Arithmetic (Frege, 1968 [1884]) that some such judgments – for instance judgments of the identity of numbers – can be grounded in judgments of equivalence with respect to some feature, for instance the equinumerosity of two groups. Because it is generally possible in a specific language to define a predicate that behaves like an identity predicate, but which may not capture identity in an “absolute” sense (Quine, 1961), philosophers have argued over whether there is an absolute, language-independent sense of identity, with some (e.g. Geach, 1980 [1962]) holding that there is no such sense and that we should accordingly abandon the claim that there are identities that are not dependent on language.
Against earlier philosophers such as J. J. C. Smart who had argued, in the context of the mind-body problem, that certain identities, such as that between electric discharge and lightning, might be contingent (Smart, 1959), Saul Kripke argued forcefully in Naming and Necessity that all actual identities are necessary and that a statement of identity involving two names (or other “rigid designators”; see section 2.8) is true in all possible worlds, even though such identities often cannot be known a priori (Kripke, 1980 [1971]). Further debates in the analytic tradition have concerned the status and structure of the identity of persons and objects over time. Generally, most analytic philosophers have understood difference primarily as non-identity, rather than understanding identity in terms of difference, as some ‘continental’ philosophers have (cf. Moore, 2012: Preface).
For instance, in Basic Problems of Phenomenology (Heidegger, 1982 [1927b]), Martin Heidegger defines the “ontological difference” as the difference between beings (or entities) and Being. Our everyday understanding of the world and most traditional philosophy exist in an indifference to this distinction, but it is crucial to understanding the nature of beings as such. Thus, in a sense, the ontological difference is the basic difference from which all identities ultimately arise. In the late lecture “The Principle of Identity” (Heidegger, 2002 [1957]), Heidegger considers the “law of identity,” A = A. According to Heidegger, this law captures the abstract formulation of a ‘sameness’ between being and thinking that was already suggested by Parmenides. To recover the ontological difference, and hence the possibility of thinking Being in itself, it is necessary to challenge this law of abstract identity and reconsider the fundamental possibility of specifying objects through concepts that yields it.
In Negative Dialectics (Adorno, 1983 [1966]), Theodor Adorno somewhat similarly criticized what he called “identity thinking” – a pervasive style of thought and action in which individuals are only understandable in terms of their identity as determined by their place within a broad, overarching and generalizing set of abstract categories. Adorno links “identity thinking” to the exchange form of capitalism and opposes it to a kind of dialectical thinking that allows differences to emerge and play out, up to the point of real antagonisms and divergences that cannot be assimilated to identities within a concept.
Other approaches to the relationship of difference and identity draw from the structuralist tradition and emphasize the way that difference is apparently primary in the constitution or phenomenon of linguistic meaning. In the Course in General Linguistics, Ferdinand de Saussure defined language as a “system of differences without positive terms,” claiming that, like units of money, linguistic units can only be defined uniquely in terms of their possibilities of exchange with other such unities and thus in terms of differences rather than identities (Saussure, 1959 [1916]). Structuralist and “post-structuralist” philosophers have emphasized the implications of this “differential” character of signification. For Jacques Lacan (e.g. Lacan, 1968 [1953]), the differential character of signification means that subjects are always caught up in a “signifying chain” without positive origin or a fixed destination. Similarly, Jacques Derrida (Derrida, 1982 [1968]) developed the neologism “différance” to express a movement of differing and deferring that is inherent to the play of language and signification. For Derrida, it is the play of différance that ultimately underlies any fixation of identity in concepts. By locating and interrogating binary oppositions that constitute general structures for philosophy, deconstruction elicits and demonstrates the movement of différance that is at their root and structurally inherent to the sign, as what is structurally capable of iteration in an unlimited variety of possible contexts (see sections 2.2 and 2.5).
In Difference and Repetition (Deleuze, 1994 [1967]), Gilles Deleuze develops this idea of a primary difference, drawing on structuralist premises, but as a fundamental category for a new kind of metaphysics rather than strictly as a linguistic or semantic phenomenon. In particular, Deleuze argues that all identities between instances of a concept or phenomenon in repetition must be thought of as produced through the more original operations of difference and differentiation. For Deleuze, all repetition is thus inherently differential, and the challenge for a metaphysics that thinks this primacy is to develop a concept of identity that shows how it is itself founded on this more original differential repetition. Similarly, difference itself is no longer to be thought primarily as conceptual or as an exterior imposition of the differentiating mind or subject, but rather as an inherent underlying character of the metaphysics of events, processes, and phenomena (see section 2.6). It is this underlying phenomenon of basic difference that allows for the definition of a “virtual” aspect or dimension of real things. This dimension, as entirely real, is to be distinguished from any realm of the merely “possible” as well as from the “transcendent,” but defines the wholly immanent space in which operations of differentiation and “differenciation” (the actualization of the virtual) occur in reality.