I What is modal actualism?

The term ‘modal actualism’ was used by Kit Fine to characterize the metaphysical orientation of his former teacher, the New Zealand logician and philosopher, Arthur Prior (Fine Reference Fine2005: 133). The modal actualist, according to Fine, is committed to both ‘actualism’ and ‘modalism’.

‘Actualism’ might seem to be a name for an attitude towards reality that is little more than what passes for common sense: reality is, as Prior put it, just the world that ‘we indicate by waving our arms about in a vague way and calling it “this” world’ (Prior and Fine Reference Prior and Fine1977: 92). In short, the actualist is dismissive of things conceived as belonging to some transcendent ‘beyond’, Plato’s realm of ‘ideas’, Meinong’s realm of an ‘Aussersein’ of non-existing (in the sense of non-actual) objects, and Lewis’s realm of alternate possible worlds, to provide just three examples. But with metaphysics things are rarely so simple, and here the qualifier ‘modal’ signals a problem for any such simple, commonsensical actualism, since common sense also seems to be committed to the reality of modal notions, for example, to the reality of possible alternatives to the way the world actually is—ways the world might have been. The modalist is committed to the ineliminability and irreducibility of such modal talk.

Classically, such a ‘this-worldly’ actualist approach is indeed often associated with the philosophy of Aristotle, and given the relevance of modal notions for Aristotle’s essentialism, it is not surprising that here a return to Aristotle has proved popular for some opponents of Lewis’s approach to modality (e.g., Plantinga Reference Plantinga1974; Fine Reference Fine1994). For Hegel, however, Aristotle’s essentialist metaphysics could not accommodate the features of thought that typify the modern world, and some think such a limitation was reflected in his conception of modality. In this sense, Hegel’s approach is closer to certain non-Aristotelian contemporary actualists.

From his Lectures on the History of Philosophy (LHP II; Redding Reference Redding2017)Footnote ² it is clear that Hegel was favourably disposed towards the actualist dimensions of classical Greek thought and of Aristotle’s philosophy in particular. He was, however, equally critical of Aristotle’s limitations: his philosophy, and the life-form in which it was based, had lacked the resources to properly accommodate the type of free rational ‘subjectivity’ to which that life-form had given birth. Thus, while recognizable in the philosophical practice of Socrates, this element of free subjectivity was also the feature of Socrates’s practice that had brought him into conflict with his society. The further development of this feature of human existence would rely on social changes that would only come about after the collapse of the classical world, and that would ultimately issue in the modern world. In turn, this ‘modern’ form of subjectivity brought with it new conceptions of the possible (Hartmann Reference Hartmann2013).

From a modern perspective, Aristotle seems to have been only partially successful in accounting for the modal notions that were otherwise central to his metaphysics. For example, it is sometimes claimed that Aristotle had tended to collapse what we separate as modal and temporal considerations (e.g., Hintikka Reference Hinkikka1973) or that his ontological distinction of potentiality (dynamis) and actuality (energeia) was made problematic by the need to keep it internal to the actual (Bechler Reference Bechler1995). In contrast, the modern modalist wants to accommodate the reality of non-actualized possibilities in a more specific way—this counting particularly within moral philosophy, for example, where the reality of an agent having been able to have acted otherwise seems presupposed by their being held accountable for their actions. Here, indeed, we might think that Russell’s concerns about the limitations of Aristotle’s subject-predicate logic are apt, as it would seem that the logical resources for the development of modern notions of possibility lay elsewhere—in particular, in the logical tradition leading from the Stoics to Medieval nominalism and to Leibniz (Bobzien Reference Bobzien2003).

Although still ultimately working within the constraints of Aristotle’s syllogistic ‘term-logical’ system, Leibniz developed the propositional forms of logic originally conceived by the Stoics, and with this, the idea of applying the notions of necessity and possibility to the contents of what is said (‘de dicto’ modality) rather than the things or substances (‘de re’ modality) characteristic of Aristotle. When possibility is so conceived, the range of actual truths will be conceived as a subset of possible ones, because actually p implies possibly p, but not vice versa. From here, it is a short step to the idea of the ‘actual world’ being taken as one of an encompassing array of ‘possible worlds’, as found in Leibniz, revived by Kripke, and taken literally by Lewis. It is in the context of such a Leibniz-Lewisian ‘possibilism’ that opposed ‘actualist’ attitudes emerged, and it is in this context that I want to examine Hegel. While rarely, if ever, considered in these debates, Hegel, I suggest, might be seen as advancing a novel, coherent and plausible actualist position, one reflected in his analysis of the structure of predication as found in his account of judgement.

It is not difficult to make a general case from Hegel’s Logic for the type of actualist interpretation of Hegel found in Findlay.Footnote ³ For example, in the Encyclopaedia Logic (EL: §6), Hegel describes actuality (Wirklichkeit) as the content (Inhalt) of philosophy, while in the Objective Logic, making up the first two books of the Science of Logic, the category or thought-determination Actuality is the final category in a series that starts with Being (SL: bk. 2, sect. 3).Footnote ⁴ Very broadly, if we think of metaphysics as, in Aristotle’s terms, the investigation of ‘being qua being’, and if for Hegel Actuality is to be conceived as the cognitively mature ultimate successor category to the problematic category of Being (Sein)—what Being in truth turns out to be—then metaphysics will surely have what is actual as its object or content.

Moreover, an examination of his category of Actuality also reveals Hegel as a modalist. Hegel’s categories are ‘thought-determinations’ (Denkbestimmungen), which suggests that we should, at least initially, understand their relations intensionally. As with the previous categories treated, that of Actuality is made determinate only by standing opposed to an array of contrary notions: Possibility, Necessity and Contingency. But, as it is Actuality itself, rather than any of those contraries, that is the terminating and most comprehensive category, then it must be that those contraries are somehow to be thought of as contained in Actuality. Hegel makes this explicit in the Encyclopaedia Logic, when he notes that ‘the notion of possibility appears initially to be the richer and more comprehensive determination, and actuality, in contrast, as the poorer and more restricted one. But in fact, actuality is what is more comprehensive … it contains possibility within itself as an abstract moment’ (EL: §143A). But here a word of caution is necessary: when it is said that ‘intensionally’ the category Actuality contains that of Possibility within it, this should not be taken as leaving open the idea that ‘in reality’, the situation might be otherwise—for example, that metaphysically the relation between possibility and actuality could be as it is conceived by David Lewis, for example. Hegel’s attitude to ‘thought’, the most rational of the cognitive faculties, is generally realistic in the way that Greek philosophy was. We should be confident in the assumption that it is thought, rather than some other attitude—immediate un-reflected-upon perception, for example—that gives us the truth here. If, from the perspective of thought (i.e., from philosophy), we come to the conclusion that possibility is properly understood as internal to actuality, then that is how we should take things to be. However, as we will see below, we only learn to appreciate how thought determinations bear on the world and ‘acquire’ content when we come to Hegel’s account of judgement in the Subjective Logic, where what could be described as a concept’s ‘extension’ comes to acquire an ineliminable role in the determination of that concept. Together, these considerations will bear on the claim that Hegel is a modal actualist, and to enable this case to be filled out, I will detour through Findlay’s path to contemporary actualism via his study of Meinong.

II Findlay’s path towards a modal-actualist interpretation of Hegel

Arthur Prior’s modal actualism is bound up with, and appears to have grown out of, his work on the logic of tensed sentences (‘tense logic’) in the 1950s and 1960s (Prior Reference Prior1957, Reference Prior1967) and which formed part of the renewal of modal logics around that time. Prior acknowledged the crucial role of his former teacher, Findlay, in the development of his own approach, referring to Findlay as ‘in a sense, the founding father of modern tense-logic’ (Prior Reference Prior1967: 1) on the basis of a paper Findlay had written about time (Findlay Reference Findlay1941). Given the significance of Prior’s work, it is surprising that Findlay is rarely, and his own philosophical background is effectively never, discussed in this context.

In relation to his actualist reading of Hegel, I suggest that Findlay’s earlier work on modal issues is crucial, and here a few biographical notes are relevant. Born in South Africa in 1903, Findlay had been attracted to Fichte and Hegel as an undergraduate at the University of Pretoria, but on his arrival at Oxford in 1924 he found the Oxford form of idealism stultifying and oppressive (Findlay Reference Findlay1985). Moreover, during his Oxford years he also became critical of the subjectivistic connotations of the Fichte-leaning form of his own idealism and was increasingly attracted to the logic-driven developments of philosophy occurring at Cambridge. By 1927 he had converted to the ideas of Russell and Moore—not so much their then contemporary views, however, but the type of logically based realism expressed by Russell in Principles of Mathematics (Russell Reference Russell1903), which Russell had effectively abandoned in 1905 with his ‘theory of descriptions’.Footnote ⁵ This earlier realism had shown similarities to that of Alexius Meinong, and Findlay subsequently spent time during 1931 and 1932 at the University of Graz in Austria working on a PhD on Meinong’s metaphysics, under the supervision of Meinong’s former student, the logician Ernst Mally. Mally had published the first twentieth-century work in deontic logic—now seen as a branch of modal logic—in the previous decade (Mally 1926).

Findlay’s work on Meinong and the problems facing Meinong’s staunchly realist assumptions about non-actual objects seems to have sent him back to a non-subjectivist version of his original idealism, as the only viable framework within which Meinong’s positive contributions could be preserved. The resulting idealist/actualist features of Findlay’s own developing metaphysical position emerges at various places in critical comments made about Meinong in the thesis he published in 1933, Meinong’s Theory of Objects. Findlay’s position was further spelt out in the last of three new chapters added to a re-titled second edition, published in 1963. Moreover, hints of his later explicit re-affirmation of Hegel can be found in papers published throughout the 1940s, such as his paper on time (Findlay Reference Findlay1941), which would influence Prior, and another on Gödel (Findlay Reference Findlay1942). This Hegelianism, however, only became explicit in the 1950s, after his appointment to a chair at Kings College London (Findlay Reference Findlay1955–6, Reference Findlay1958 and Reference Findlay1963: ch. 13).Footnote ⁶

Findlay was to have an influence, albeit indirect and hidden, on directions taken within analytic modal metaphysics after the revival of modal logic in the 1950s and 1960s, not only via his influence on Prior, but also via his 1933 monograph on Meinong and, especially, the role ascribed to Mally in the effort to save Meinong’s theory of objects from crippling problems. Mally’s modification had been essentially to transform what was an ontological distinction in Meinong between existent and non-existent objects into a logical one distinguishing two different senses of predication understood as modes of determination. Mally’s distinction has been revived in recent times, for example in Edward Zalta’s distinction between ‘encoding’ and ‘exemplifying’ readings of predication (Zalta Reference Zalta1988: ch. 6), and a similar distinction, seemingly independent of Mally, can found among the actualist critic of Lewisian ‘possibilism’, Robert Stalnaker (Reference Stalnaker2012).Footnote ⁷ I take this distinction to be fundamental in relation to the modal actualist’s critique of the metaphysical consequences of the rival possibilist approach, in that it allows talk about truths in alternate possible states of the world without relying on an ontology of possible objects as truth-makers for those truths. It is just this move that appears in Hegel’s subjective logic for, I believe, the same reason. After considering the role it plays in Findlay’s distinctly idealist modification of Meinong, I will turn to its expression in Hegel’s Subjective Logic.

Meinong was a student of Franz Brentano, and his theory of objects was meant, among other things, to give an account of objects that was wide enough to encompass those of intentional attitudes, such as belief. Meinong thought that our capacity to think about non-existent objects, such as golden mountains, or even logically impossible ones, like round squares, demanded an account of the nature of those objects themselves as entirely mind-independent. The golden mountain is not a concrete existing object like Mont Blanc, but it is an object nevertheless, a non-existing one. Russell would find the resources for eliminating any such mythical entities from his own philosophy with a new approach to predication derived from Frege, but in a context that bypassed any consideration of modal discourse.Footnote ⁸ When issues of modality returned in the 1950s and 1960s, the type of truth-functional semantics earlier developed by Tarski and others for non-modal discourse presupposed by Russell was now extended to modal discourse by appeal to the notion of ‘possible worlds’.Footnote ⁹ In biting the metaphysical bullet, and advocating a realistic treatment of such worlds, Lewis effectively extended the approach to semantics developed by Tarski in the direction of an ontology like that of Russell’s erstwhile opponent, Meinong.Footnote ¹⁰

Findlay’s re-interpretation of Meinong allows us to grasp some of the detail of a conceptual path that lets us bring Hegel’s logic into the later twentieth century. Meinong had distinguished various types of things within the class of entities (Gegenstände). Most immediately, there are objecta (Objekte)—concrete objects of various sorts, which we commonly call material things, but also the individual characteristics of those things and even particular events involving those things that have particular spatio-temporal locations. Next there are non-existing objects, like the golden mountain and the round square. Thirdly, there are ‘subsistent’ (Bestehende) abstract entities, such as relations of similarity and difference; mathematical objects, such as numbers and geometrical figures; and what Meinong calls ‘objectives’ (Objektive): proposition-like abstract entities that are the contents of intentional attitudes such as those of judging or assuming, and that may or may not be the case (that is, may be factual or non-factual).

Findlay focuses on the relations between objecta and objectives. Using his example, ‘That China is a republic’ is an objective, while China itself is the objectum somehow related to it. But saying exactly how these are related would prove to be difficult. Meinong had utilized his distinction between existence and subsistence to capture the difference between objecta and objectives, but how are we to think of the relation between objects and objectives across this strange ontological divide that has one relatum in time and space and the other timeless and locationless?

Meinong had described this relation in a variety of ways. First, an objective ‘is an object of higher order’ than that of its corresponding objectum, as can be seen when one considers that an objective itself can become the objectum of a yet higher-order objective that says something of it. For example, when we say about the objective ‘snow is white’—for example, that it is a fact—the objective ‘snow is white’ now becomes the objectum ‘implicated in’ the higher objective (Meinong Reference Meinong1904: 18). Meinong, however, also describes objectives, in Findlay’s paraphrase, as higher order objects ‘built upon’ other objects of a lower order: ‘The objective that snow is white is built upon or presupposes the object snow, which is therefore its material’ (Findlay Reference Findlay1933/Reference Findlay1963: 71; Meinong Reference Meinong1910: 63).Footnote ¹¹ This ‘built upon’ conception is meant to capture the idea of some ultimate ontological foundation of atomistic objecta upon which all objectives in the universe are constructed: ‘though the proximate material of an objective may be another objective, the ultimate material of all objectives are objecta; they are the foundation on which the whole structure of objectives reposes’ (Findlay Reference Findlay1933/Reference Findlay1963: 71–72).

Meinong’s realistic ontology results from his treatment of knowledge (Erkenntnis) as the prototypical intentional attitude. It is part of the very idea of knowledge that what we know is an object as it is, independent of our thought of it (Meinong Reference Meinong1904: 3–4). In turn Meinong’s foundational ontology is paralleled by a similarly foundational epistemology, with the sensory knowledge of concrete objecta conceived as somehow providing a base upon which knowledge of higher order factual objectives can be built.

Now, given Findlay’s familiarity with the conceptual holism of Fichte and Hegel, one might expect him to challenge such an atomistic foundationalism, and he does, countering Meinong’s idea of unilateral dependence of objectives on objecta with the claim that:

This counter-claim is here given without argument, but a number of relevant arguments soon come into focus.

It will be recalled that for Meinong, relations are meant to be subsisting entities, but Meinong nevertheless distinguished between real existing ‘Verhältnisse’, relations of ‘connection’ between concrete objecta, and ideal subsisting ‘Beziehungen’ that ‘stand among’ non-existing, subsisting entities, such as mathematical entities (Findlay Reference Findlay1933/Reference Findlay1963: 143). As with the relation between objectives and objecta, Meinong describes ideal relations as grounded upon the real ones existing between objecta. Certain applications of this idea proved problematic, however. For example, Meinong had treated geometric areas as higher-order objectives, on the model of collections of concrete objecta. Thus, a red square is considered as having a structure analogous to that of a constellation of stars, the constellation itself being a higher order ‘superior’, whose inferiora are the stars. In the case of the red area, however, the inferiora are, unlike the stars, non-discrete, and this introduces a puzzle. One might treat the area as a totality of points, but how could such extensionless points be considered to be individually coloured? In fact, Meinong had rejected this analysis of such a continuum, but had offered no alternative. According to Findlay, however, the obvious alternative is to follow Aristotle, for whom a point was conceived in terms of the intersection of two lines. This amounts to determining the point itself as a ‘higher-order’ object, and has the consequence of there being ‘no ultimate infima, on which the superstructure can repose’ (Findlay Reference Findlay1933/Reference Findlay1963: 149).

Here Findlay’s objection is presented in typically Hegelian terms. On Meinong’s analysis, without being defined by higher-order objectives, the ultimate punctate constituents of any such continua would be necessarily ‘indeterminate’, that is, not simply indeterminate in relation to the limitations of our experience or knowledge, but ‘by their very nature, incapable of determination’ (Findlay Reference Findlay1933/Reference Findlay1963: 150).Footnote ¹² In this sense, objecta must be as dependent on objectives as the latter are dependent on them, much as points and lines can be thought of as mutually determining in geometry.

To address such problems, Findlay appeals to Mally’s Reference Mally1912 modification of Meinong’s theory of objects which, he believes, ‘removes many difficulties in Meinong’s theory, without abandoning the general standpoint of the theory of objects’ (Findlay Reference Findlay1933/Reference Findlay1963: 110). This modification is based ‘on a more careful analysis of the relation of the object to the objectives which concern it. In every objective an object is in some way determined, and the way in which it is determined is called a determination (Bestimmung)’ (111). A determination, he goes on, ‘is more or less identical with what is meant by the “propositional function” of Russell’ or is what is ‘usually called a “concept”—it is an incomplete or indeterminate objective’ (111).Footnote ¹³ Thus on Mally’s modification, ‘every determination determines an object, but not every determination is satisfied (erfüllt) by an object. The determination “being two-legged and featherless” determines the abstract determinate “featherless biped”… but is satisfied by nearly every human being. On the other hand, the determination “being round and square”, determines the abstract determinate “round square”, but it is not satisfied by an object’ (111).

With this, Meinong’s problematic notion of the realm of objects beyond being—an ‘Aussersein’—is no longer required. The type of ‘object’ determined without exemplification, as in the case of determination by definition, is a ‘concept’, when this is understood in a non-psychological way, as with Russell’s idea of a propositional function. Findlay notes that with such changes the Aussersein ‘is no longer a realm of full-blown objects unfortunately deprived of being, but something more nearly analogous to a space of points, which may or may not be occupied by actual objects’ (Findlay Reference Findlay1933/Reference Findlay1963: 112). I take it that Findlay’s spatial metaphor is meant to bring out two ideas: first, like points, the ‘objects’ involved are to be thought of as fundamentally abstract and in no sense concrete, and next, that as in Leibniz’s relational theory of space, the ‘points’ have natures that are entirely constituted by the relations they bear to other ‘points’.

This pushes Meinong’s theory in the direction of actualism, with the arguments counting against Meinong’s unmodified theory akin to those that have been made more recently against David Lewis’s interpretation of modal logic. On the modified account, Sherlock Holmes, for example, should not be thought of as a ‘full-blown’ concrete objectum ‘unfortunately deprived of being’, like some real Sherlock located in some non-actual alternate universe. Rather, qua abstract and non-instantiated determination, the concept ‘Holmes’ is determined by a certain range of properties constituting his being-so (So-sein): its purported bearer is a detective, has Watson as a loyal friend, and so on. Moreover, the non-instantiation of the concept ‘Holmes’ has consequences for its logical properties: such non-instantiated determinations are ‘incomplete’, in the sense that the Law for Excluded Middle does not hold of them.Footnote ¹⁴ Were we to ask a question about Holmes, the answer to which cannot be found in or inferred from the writings of Conan Doyle, then there would simply be no answer. As Findlay had pointed out, for objects of the actual world ‘we can pass beyond the determinations which we know to others which we do not know. We can ask about a certain mountain, for instance, how high it is … but we cannot say how high a golden mountain is’ (Findlay Reference Findlay1933/Reference Findlay1963: 57). ‘We speak of the world of Aussersein’, he notes, ‘but in reality the objects which have no being do not constitute a world’ (56), the Aussersein remaining ‘a strange sort of desert in which no mental progress is possible’ and which is ‘as a whole, too chaotic to be studied scientifically’ (58).

Findlay’s sceptical attitude towards Meinong’s theory of the Aussersein—that it is marked by ‘a certain immense implausibility’ (56)—would be later repeated in Prior’s reaction to David Lewis’s conception of the plurality of possible worlds as simply a ‘tall story’ (Prior and Fine 1977: 92). Prior’s rejection of non-actual entities would be expressed in turn in his treatment of tense logic and modal logics more generally.

With his tense logic, Prior had anticipated Kripke’s possible-world semantics for modal statements (Copeland Reference Copeland2002), but had resisted any analysis that would reduce a ‘tensed’ or modal claim to a structure with non-tensed or non-modal components. Conventionally understood, mathematical ‘Kripke models’ would be used to extend a Tarski-like, truth-functional semantic framework to context-sensitive, and so ‘incomplete’, intensional sentences such as tensed ones. For example, because the truth or falsity of ‘It is hot today in Sydney’ depends on when it is said, it would be treated as not expressing a complete proposition, but as a Russellian propositional function able to take objective time references as arguments. In short, the original sentence would now be treated as true or false at some specified point of time. Here Prior’s opposition was akin to Findlay’s critique of the otherwise indeterminate points supposedly making up a geometrical area.

Analogous to the treatment of tense, the analysis of ‘alethic’ modal judgements would standardly rely on the idea of such judgements being taken as true or false ‘at’ each of some set of possible worlds, and Prior would reject the idea of the reality of either temporal points or possible worlds ‘over which’ quantification could take place. The consequences of this would be to treat the original intensional sentences, such as tensed ones or ones about possibilities, as ‘metaphysically fundamental’ (Prior and Fine Reference Prior and Fine1977: 37). Prior, however, would struggle to find within the resources of his own ‘fundamental’ tense logic formal devices to match what was capable of being expressed in the models of Kripkean possible-world semantics. For his part, Prior’s former student, Fine, pursues an approach like that of Aristotelian essentialism (Fine Reference Fine1994). More recently, however, Robert Stalnaker has attempted to render another actualist reading of the possible-worlds approach, at which Prior and Fine had baulked.

The way Findlay draws on Mally’s modification of Meinong parallels the way in which Stalnaker later attempts to construe possible-world semantics in a non-Lewisian way (e.g., Stalnaker Reference Stalnaker2012: 28).Footnote ¹⁵ David Lewis treats other possible worlds as just like ours, full of concrete objects—in some possible world there would be some real Sherlock Holmes, for example. But for Stalnaker, merely possible worlds are ideal entities—maximal consistent sets of propositions akin to Meinongian ‘objectives’. Such possible worlds/propositions provide contents for modal beliefs and possess truth-values, but there are no ‘merely possible objects’ to make such propositions true or false. It is only in relation to beliefs about the actual world that one could find truth makers for such propositions; an idea Stalnaker expresses with the claim that only for beliefs about the actual world will there exist singular ‘witness propositions’, instantiated in actual objects. Given Hegel’s hostility to the existence of entities beyond the actual world, but his realistic attitude to modalities in the world, it is not surprising that a parallel way of avoiding the existence of actuality-transcending objects can be found in the two different forms of predication in his Subjective Logic. It is this, I suggest, that brings Hegel into the realm of contemporary debates about the nature of modality.

III Hegel’s predicative dualism in the Subjective Logic

Early in his discussion of judgements in his Subjective Logic, Hegel notes that a judgement—an Urteil—is not to be confused with a mere Satz,Footnote ¹⁶ by which he here seems to mean a sentence in which the linking of two name-like signs is considered to be able to convey information about two analogously related individual items. Thus in Hegel’s example, a Satz links the event of Aristotle’s death to a particular point in time (SL: 553/12.55–56). For Hegel, however, such Sätze are not judgements, and are neither true nor false, but simply correct (richtig) or incorrect (unrichtig). To express an Urteil, and aspire to truth rather than mere correctness, a Satz must be able to play a role in some piece of inferentially articulated reasoning, such as when, in countering an opposing view, one argues for the date of Aristotle’s death on the basis of evidence. In such a case, one of the terms must be a universal—for example, the putative date of Aristotle’s death must be regarded as a determination potentially predicable of other events.Footnote ¹⁷

That judgements will not be judgements without the capacity to function in inferences—that inference or ‘syllogism’ is the ‘truth’ of the judgement (SL: 593/12.95)—will become explicit subsequently when Hegel generates a series of forms of judgement with different logical shapes that finally transition into a series of inference structures. This is a theme recently taken up by Robert Brandom in his project of an ‘inferentialist’ semantics (Brandom Reference Brandom1994) which is central to his reading of Hegel (Brandom forthcoming). What is important for us is that running through both series of judgements and inferences is a recurring distinction between two different understandings of the predication relation appearing in the verbal expressions of both judgements and syllogisms: predication understood as the inherence of the predicate in the subject on the one hand, and as the subsumption of the subject under the predicate on the other (SL: 557 & 570/12.60 & 12.72; EL: §170).

Hegel’s distinction closely parallels Mally’s, in that Hegel’s two forms of predication represent different ways in which the content of a judgement can be determined for a subject, only one of which involves instantiation of the predicate in some actual, and thereby potentially locatable, specific object. Thus, determination by inhering predicates involves a necessary role for objects satisfying those predicates, while determination by subsuming predicates does not.Footnote ¹⁸ Rather, subsuming predicates determine conceptually, by exploiting intensional relations relating the predicate concept to other concepts. Hegel, however, avoids the idea common to both Prior and the orthodox possible-world semanticists he opposed. From each of these opposing perspectives, one of the frameworks—for Prior, the tensed or modal, for orthodoxy, the language of Kripke-enhanced classical logic—was regarded as ‘metaphysically fundamental’. But for Hegel, neither logical form was self-sufficient, and so neither could provide the basic logical structure of sentences. What is important to stress here is that, for Hegel, the syntax of a sentence (Satz) does not (contra Russell’s interpretation of Hegel) dictate the logical form of the judgement (Urteil) it expresses. Logical form derives more from the way the sentence functions in some particular context. Judgements with the form of inherence, he suggests, are relevant for the provision of content for judgements, while those with the form of subsumption are relevant when it is a question of inferential relations among judgements (SL: 260–61/12.63). And each judgement form presupposes the other: there can be no suggestion that this duality can be resolved by some sort of reduction of either type of predication to the other.

Hegel’s predication distinction broadly mirrors that between ‘intensional’ and ‘extensional’ construals: judgements of inherence will be in some way ‘context dependent’, while subsumptive judgements will have a more strictly propositional content. As with conventional treatments of modal sentences, the former will have translations into the latter, but, like Prior, Hegel rejects the idea that the logical framework of subsumptive judgements provides some ultimate medium into which context-sensitive judgements can be translated. Subsumptive judgements will themselves need to be translated into some further ‘inherence’ judgement to find their ‘truth’, but these in turn cannot be ultimate, and they can be translated into further subsumptive judgements. Moreover, such cycles of translation result in a progressive complexification of both subject and predicate terms in the series of judgements leading ultimately to the ‘Judgement of the Concept’, which is shown to be an implicit inference.

Against this general background, let us trace Hegel’s first steps. We find predication as inherence first exemplified in the most immediate judgement of Dasein (SL: 557–68/12.59–70), which, while usually translated as ‘judgement of existence’, could equally be called judgement about what-is-there.Footnote ¹⁹ Hegel clearly has in mind a type of immediate and perceptually based ‘de re’ judgement about some specific, perceivable and ostensively indicable object—(this object existing ‘there’ (‘da’)).Footnote ²⁰ These are the judgements in which the existence of concrete entities that instantiate the predicates involved—the particular rose referred to in Hegel’s examples, ‘the rose is red’ and ‘the rose is fragrant’, for example (SL: 558–59/12.61)—contribute to the determination of the judgement’s meaning. Such de re judgement form will recur, with increasingly complex conceptions of the res involved. For example, later, with the categorical judgement, the ‘res’ will be understood as a genus rather than some individual instance, but Hegel will avoid any metaphysical commitment to any type of ‘higher order’ Meinongian entity existing over and above the spatio-temporally particular members making it up.

Hegel’s judgement of existence in its initial form, which he calls the ‘positive judgement’, looks like a Meinongian judgement about a single objectum, but for Hegel this judgement type could play no foundational role, because it lacks truth. The positive judgement is ‘not true’ but ‘has its truth’ in the next form of judgement, the ‘negative judgement’ (SL: 562/12.64), which will develop into the reflective judgement, the first instantiation of a judgement type with subsumptive predication.Footnote ²¹ One reason such an immediate judgement lacks ‘truth’ is that it is neither true nor false in the conventional modern sense, as revealed by one of Hegel’s other examples, the indexical ‘it is daytime now’ (562/12.64). As Hegel had pointed out in the Phenomenology of Spirit (PhG: §95), were such a judgement taken to be true at a particular time, it would be become false at some later time.

It is negation, as introduced by a ‘negative judgement’, that introduces a new level of logical complexity that will develop through the series, and usher in the judgement of reflection. Hegel describes two levels of negation: effectively, the first negation produces the predicative structure that Cambridge logician (and critic of Russell) W. E. Johnson described as involving ‘determinates’ of a ‘determinable’ (Johnson Reference Johnson1921: ch. XI). When one says, for example, ‘the rose is not red’, negation, Hegel points out, can be taken as applying only to the determinateness of the predicate, because one does not thereby imply that the rose is not coloured. Rather, ‘it is … assumed that it has a color, though another color’ (SL: 565/12.68; EL: §173). Considered in this context, the predicate ‘red’ has gone from functioning in an initial quasi-name-like way, purporting to pick out some individual instance of redness, to saying something more general. Now ‘red’ can be regarded as picking out some particular determinate region of some kind of ‘colour space’. As Johnson made clear, such a conception of necessity cannot be reduced to the that which follows ex vi terminorum: that a thing’s being red all over necessarily excludes its being green all over does not follow from any definition of redness. The determinable-determinate distinction cannot be reduced to the genus-species distinction. Johnson’s distinction is seemingly yet another version of the type of predicative dualism that Findlay took from Mally.Footnote ²²

But this type of Johnsonian first negation, Hegel points out, still leaves an otherwise positive judgement (SL: 565/12.68; cf. EL: §173), in the sense in which the positive rejoinder, ‘It is yellow!’ would count as the ‘negation’ of this assertion ‘This rose is red’. Thus, the first negation type is subject to a second that ‘negates the determinateness [Bestimmtheit] of the predicate of the positive judgement, its abstract universality, or, considered as content, the singular quality that it possesses of the subject’ (SL: 566/12.68). Using Johnson’s terms, we could say that, while the first negation is restricted to the predicate qua particular determinate of its determinable, the second negates the more general determinable that the first predicate instantiates. This second negation has resulted in a new logical structure. It is the ‘external’ negation typical of modern classical logic, in which the scope of the negation operator is the complete proposition expressed by the sentence. We now have a model for the type of judgement using ‘subsumptive predication’, the logical form of which now gets spelt out in the discussion of the ‘judgement of reflection’.

In the judgement of reflection, predication is now understood as subsumption of the subject under the predicate, and the subsumed subject term, Hegel says, is now determined as a ‘singularity as such’—that is, as what is usually discussed as a ‘bare particular’ without determination by some ‘kind’ term, as in the earlier judgement of existence. And, also in contrast to the earlier judgement, the predicate is now understood as an ‘essential universal’ that ‘constitutes the basis against which the subject is to be measured and determined accordingly’ (SL: 569/12.72). That is, the subject of a predicate ‘P’ is determined as that of which ‘P’ is truly said, the subject being judged simply in terms of whether or not it is ‘subsumed’ under the predicate.

Abstracting from the peculiarities of ways of being red, the predicate will be free of the phenomenal connotations that it had in the earlier judgement of existence—any ‘singular quality’ that inheres in the subject (SL: 566/12.68)—and this, I suggest, is because such judgements do not rely on available existing objects to determine their contents phenomenally.Footnote ²³ We can see the significance of this from the fact that core types of judgements of reflection are ones employing ‘particularly’ and ‘universally’ quantified subject terms (SL: 570–72/12.73–75). From the limitations of the earlier positive judgement of existence, it is clear that we cannot think of, say, ‘all roses are plants’ as simply shorthand for a string of positive judgements: ‘“this rose is a plant” and “that rose is a plant” and “this other rose is a plant” …’, eventually indicating all the roses. A more appropriate way of thinking of such a judgement as thinking of it as not about particular roses but more about the concept ‘rose’, stating that it is instantiated in this, this, this, and so on.

This was effectively the pattern of predication presupposed by Russell in his critique of Hegel’s alleged reliance on subject-predicate structure: we should not regard a sentence such as ‘All unicorns are hooved’ as, following Aristotle, really about the kind unicorn—an approach that ran into difficulties with non-existent referents such as this. Rather it merely says that if the concept ‘unicorn’ were true of something, then so too the concept ‘hooved’ would be true of it. Rather than about unicorns (which do not exist), the judgement could be described as a higher-order judgement about the concept ‘unicorn’, attributing to it a certain property—the property of being such that whatever instantiates it also instantiates the concept ‘being hooved’. Thus, this also provided Russell with a way of avoiding Meinong’s non-existing objects. That something like this is understood by Hegel’s ‘subsumptive predication’ becomes apparent when we examine how he conceives of the transition of inherence judgements into subsumptive ones.

Hegel describes the procedure that generates his taxonomy of judgement forms as involving an ‘exchange of significance’ between the subject and predicate terms of the Satz that expresses the judgement, and this might be simplified if we focus on the difference between the sentence expressing the judgement and the judgement expressed—that is, between Satz and Urteil. While Hegel considers subject and predicate as grammatical terms (SL: 552/12.55), he thinks of the logical structure of judgement as involving relations among the different conceptual determinations of singularity, particularity and universality (SL: 530–49/12.33–52). We might then think of these different conceptual determinations as able to be distributed differently over the grammatical subject and predicate places of the expressed sentence. Hegel excludes those structures in which subject and predicate terms are both conceived as expressing the same conceptual determination (as in universal subject and universal predicate). However, besides the familiar structure of singular subject and universal predicate, he also allows sentences in which the subject term is conceived of as universal and the predicate term singular.

Considered from the perspective of the sentence, qua array of tokens ordered in time and space, subject and predicate terms can, as Frank Ramsey pointed out, be easily reversed: we can say either ‘Socrates is wise’, or ‘Wisdom is a characteristic of Socrates’ (Ramsay Reference Ramsey1925: 404). While these may have the same truth-values, it is clear from the perspective of everyday language that while the former is about Socrates, the latter is about wisdom. Reversal of subject and predicate terms has allowed the judgement to go from being about an individual to being about a concept, and to say something of a concept is to bring it under a higher order concept. Here the sentence says about the concept ‘wisdom’ that it has the property of being instantiated in Socrates. The simple syntactic trick of making the nominalization of the predicate ‘wise’ into a subject should, however, not be thought as requiring the existence of a new type of object, ‘wisdom’, that the new sentence is about.

Hegel exploits such a consequence of the manipulability of sentence structure. Thus, he cycles between these two general forms, generating his string of increasingly complex judgement forms. That is, he cycles between context-sensitive sentences ‘about’ particular objects to ones ‘about’ the concepts that such objects instantiate. This process seems to objectify concepts, fitting in with the picture of Hegel as a type of Aristotelian ‘conceptual realist’ for whom ‘concepts’ (essences) are mind-independent entities ‘out there’ in the world, entities to which our ‘subjective’ concepts can somehow correspond. But, I suggest, Hegel’s predicative duality is designed just to avoid this ontology, just as Findlay’s use of a similar distinction was his way of avoiding Meinong’s version of a similar realism.Footnote ²⁴

We see this when Hegel’s subsumptive judgements of reflection transition into a type of higher-order de re judgement of inherence—the categorical judgements that the conceptual realist takes to be about ‘secondary substances’ or ‘essences’. Isolated from this dynamic process, such judgements might indeed seem to be about ‘objective’ concepts, in the style of the conceptual realist, but it is this very isolation that deprives them of determinacy. Taken by themselves they are no more judgements than had been Hegel’s sentence relating the date of Aristotle’s death. And this dynamic alternation of judgement forms only stops when it is shown that the ‘truth’ of judgements in general is the syllogism, explicitly affirming that judgements only find their truth as judgements when they are functioning as parts of larger inferential wholes.

I suggest that this all counts against the conceptual realist who has taken Hegel’s idealism as an ontological thesis: among the entities making up the world are Aristotelian essences or natures that Hegel (somewhat confusingly) calls ‘concepts’. Hegel’s account of judgement does not support this interpretation. Rather, it supports his earlier categorical affirmation that what is—i.e., reality—is what is ‘actual’ (wirklich). I will conclude by touching on how this actualist dimension of Hegel implies a different understanding of the nature of his ‘idealism’.

IV Actualism as idealism

The creator of modern modal logic in its pre-Kripkean phase, C. I. Lewis, had linked modal logic, qua intensional logic, to the logic of the earlier idealists, and had opposed it to the extensional approach to logic of the likes of Boole and Russell (Lewis Reference Lewis1930), with its links to empiricism and materialism. It is not surprising, then, that besides Lewis, the earliest ventures into modal logic in the twentieth century were by logicians associated with the phenomenological movement, such as Findlay’s teacher Mally. As many have pointed out (e.g., Prior Reference Prior1968) intensional logics (spelt with an ‘s’) seem appropriate to the study of intentional states (spelt with a ‘t’). It is in this sense that logics of belief and practical intentionality have come to be treated as species of ‘modal’ logic. It would be thus appropriate for Hegel qua idealist to have an intensional logic, but what does his idealism amount to as a metaphysical position?

Idealism has commonly been taken to be an ontological affirmation that the world is, somehow ‘mental’—a conception more associated with Berkeley than the German idealists.Footnote ²⁵ The conceptual realist Hegelian is rightly critical of this misunderstanding, and attempts to correct it with the idea that, for Hegel, the fabric of the objectively knowable world contains something like Aristotelian mind-independent ‘essences’ (concepts). The actualist, however, is likely to regard essences so conceived as problematic, and as being still too close to the transcendent Platonic ideas from which they derived. For the actualist, the mistaken world-as-a-mind thesis will be regarded as a misinterpretation of the unproblematic idea that, because the actual world contains us, then, given the fact of our being minded, it thereby contains ‘mind’.Footnote ²⁶ There will be thus a significant dose of Kantianism in this reading of Hegel’s metaphysics, in that, as with Kant, the traditional project of metaphysics, as an investigation of the nature of some ‘mind-independent’ reality, is rejected.Footnote ²⁷ Philosophy is redefined, as with Kant’s critical turn, but not, as Kant had it, as an investigation of some mind-shaped appearance behind which exists an unknowable world ‘in itself’.

For the actualist, we might say, Kant’s apparent world simply becomes the actual world to which we all belong, but because we each experience and know this world from some particular location within it, such knowledge will always contain traces of indexicality. And yet this ‘immediate’ cognitive relation to the world is always open to ‘mediation’, in that we can come to know how the world might be for other differently-located beings. In this sense, the mutual translatability of Hegel’s two forms of predication serves the logical function of making clear how it could be that our cognitive relation to the world is always mediated by the capacity to recognize others as minded beings, and recognize ourselves in their recognition of us. Like modern modal logics, then, Hegel’s logic must permit reasoning not simply about objects per se, but entities to which we ascribe intentional contents.

Again, we might turn to Stalnaker for help in conceiving how an actualist Hegel might regard the status of both mind and modality in the world. As I read Stalnaker, mind and modality come as a package, as aspects of the actual world in which we live. Thus he regards possible worlds, or alternatively, propositions,Footnote ²⁸ as ‘abstract objects whose existence is inferred or abstracted from the activities of rational agents’ (Stalnaker Reference Stalnaker2003: 32). They are effectively posits required if we want to think systematically about the contents of the minds that we recognize in others and which we attribute to ourselves. Without this explanatory role they would be vacuous notions. ‘It is thus not implausible’ he goes on, ‘to suppose that their existence is in some sense dependent on, and that their natures must be explained in terms of, those activities’ (32). But we need to appeal to possibilities to make sense of the intentional states of others, and so mind and modality are inseparable. This, I suggest, is broadly the type of ‘idealism’ to which Hegel, qua actualist, is committed. Were we to try to conceive of a world without minds in it, given that there would be no place in that world for propositions, nor for ‘possible’ alternatives to it, there would there be no place for ‘essences’, or ‘higher order objects’ either. Hegel’s idealism is, then, more metaphysically deflationary than that portrayed by the conceptual realist.

In this paper I have sketched an account of Hegel as a ‘modal actualist’, and have linked it to an understanding of the nature of his ‘idealism’. This understanding, which reconceives the traditional metaphysical project as a systematic investigation of the actual world is, I have suggested, expressed within both parts of his Science of Logic: in the Objective Logic we are told that the proper conception of ‘Being’ is Wirklichkeit, a modally rich conception of the actual; in the Subjective Logic we are presented with some of the logical structures needed to think of the actual world when conceived in this way.Footnote ²⁹