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Diagrammatic ImmanenceCategory Theory and Philosophy$

Rocco "Gangle

Print publication date: 2015

Print ISBN-13: 9781474404174

Published to Edinburgh Scholarship Online: September 2016

DOI: 10.3366/edinburgh/9781474404174.001.0001

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Spinoza and Relational Immanence

Spinoza and Relational Immanence

Chapter:
(p.20) Chapter 1 Spinoza and Relational Immanence
Source:
Diagrammatic Immanence
Author(s):

Rocco Gangle

Publisher:
Edinburgh University Press
DOI:10.3366/edinburgh/9781474404174.003.0002

Abstract and Keywords

This chapter reviews the organisational structure of Spinoza’s Ethics, focusing on the concepts of unity and relation. It examines the tension between the geometrical order of the textual presentation and the interpretative questions raised by treating the text as a guide to praxis. It then focuses on the Spinozist doctrine of affective individuation and the role of the third kind of knowledge in Spinoza’s system.

Keywords:   Benedict Spinoza, Ethics, Geometrical order, Individuation, Affects

The more we understand singular things, the more we understand God.

Spinoza, Ethics Vp24

A distinctive feature of Spinoza’s thought is that it rejects any explanatory mechanisms grounded in mystery or de jure unknowability, in particular any explanatory criteria of experience and knowledge that would rely on ‘objects’ external to the mind. While Spinoza concedes that ‘a true idea must agree with its object’, he understands philosophical explanation to be grounded properly not in truth but in adequacy: ‘By adequate idea I understand an idea which, insofar as it is considered in itself, without relation to an object, has all the properties, or intrinsic denominations of a true idea.’1 From a Spinozist point of view, then, empiricism in anything like the Lockean style is a philosophical non-starter. For Spinoza, it will never be sufficient to rest any explanation of experience, knowledge or power on the sheer fact that it is given. No doubt one always begins with what is given, but on Spinoza’s terms philosophy fails to think adequately if the given functions for it as an answer and not solely as a relative starting-point. Thought itself is a transitive activity and a continuous process, and so beginnings are as such exterior to thought. Because for a philosophy of immanence nothing can be absolutely exterior to thought, such thinking cannot countenance absolute beginnings. Among other reasons this is why the undivided term ‘God, or Nature’ in Spinoza must be understood not as a foundation or ultimate principle but rather as an incontrovertible milieu: real immanence.

If certainly no Lockean empiricist, Spinoza does seem to be grouped readily among the early modern ‘rationalists’. And sure enough, Spinoza shares with Descartes and Leibniz a resolute willingness to blur if not entirely efface the distinction of logic – and mathematics – from metaphysics. For reason as such, conceptual and formal relations, not the experiential contents of the senses, (p.21) are eminently knowable. Hence metaphysics as the rational science of reality’s ultimate structure is feasible. Yet unlike Descartes and Leibniz, Spinoza makes no important contributions to mathematics and indeed demonstrates no exceptional aptitude in that arena. Perhaps this is because in Spinoza the deductive character of mathematics is immediately ontologised. There is no separable context in Spinoza’s metaphysics for positing merely abstract entities like forms or numbers that would serve as the proper regional domain of deductive structure. For Spinoza rational deductive structure simply and immediately is what is. Metaphysics directly implicates ontology, without remainder.

Moreover, in both Descartes and Leibniz space is reserved for the decisive mystery of the will. In Descartes – Augustinian and Pelagian by turns – the human will’s arbitrary power raises human beings almost to godlike status (it is the only thing infinite in us, other than the idea of God). And in Leibniz the will accounts for the single divine choice of which among the merely possible worlds to actualise in fact. Yet Spinoza rejects both human and divine will as philosophically explanatory. Among at least these three, then, it is only Spinoza who articulates a genuinely thoroughgoing rationalism, that is, a deductive determinism excluding any real power attributable to the will. In this respect, Spinoza appears to be aligned with the strict necessitarian materialism of such seventeenth-century thinkers as Hobbes and Gassendi, although the Spinozist God remains equally irreducible to causal mechanics. Mechanical causation, while certainly exhibiting necessity, still remains a form of exterior determination and does not attain the more radical necessity of immanence. In any case, as compared with Descartes and Leibniz it is Spinoza alone among the ‘rationalists’ who has the courage to equate the belief in an arbitrary power of wilful decision with the objective stupidity of a rock that once thrown thinks it has chosen so. For Spinoza only a mind that has failed to think things through adequately would identify true liberty with mere individual choice.

In opposition to such voluntarist conceptions of human action, Spinoza rejects any conception of mind that holds will and intellect separate, thus allowing for discontinuity between what is understood and whether and how one affirms or denies its truth. In contrast to the Cartesian and Sceptic-Academic distinction of perception from judgement, for instance, Spinoza asserts in Part Two of the Ethics that ‘[i]n the mind there is no volition, or affirmation and negation, except that which the idea involves insofar as it is an idea’.2 One

(p.22) major difference between Spinoza and Descartes is found then in the conception of the self implied by this unity of will and intellect. By identifying will and intellect Spinoza rejects the Cartesian egoic conception in which the self or subject is able to stand removed from the objects of its regard and to judge or know them in relative freedom. In Spinoza’s conception, human beings are not sites of subjective transcendence but rather immanent parts of nature. In his preface to Part Three, Spinoza writes:

Most of those who have written about the affects, and men’s way of living, seem to treat, not of natural things, which follow the common laws of Nature, but of things which are outside Nature. Indeed they seem to conceive man in Nature as a dominion within a dominion [imperium in imperio]. For they believe that man disturbs, rather than follows, the order of Nature, that he has absolute power over his actions, and that he is determined only by himself.3

The geometrical order of the Ethics, to which we will return, serves in this way as a metaphor for Spinoza’s theory of mind.4 The mind in its everyday functioning is like an ambiguous demonstration cut off in part from the axioms and theorems that support it. Reasonable thinking and reasonable life, on the contrary, are like coherent demonstrations, explicit truths, consistent integrations of principles, contexts and consequences.

On this basis Spinoza’s deep mistrust of natural language becomes intelligible. He dismisses what he calls the ‘first kind of knowledge’, or ‘knowledge through signs’, because he understands such signs to be merely arbitrary connections between certain sounds or combinations of letters and pseudo-concepts or ‘picture-thoughts’ in the imagination. Words for Spinoza are little more than historical sedimentations of the same human puffery that asserts the will’s power to choose. The very conventionality of natural language damns it philosophically. Like Wittgenstein two and a half centuries later, Spinoza will think with maximum caution in face of ‘the bewitchment of our intelligence by means of language’.5 And at least like the Wittgenstein of the Tractatus, Spinoza aims to remedy the inevitable falsifications and inadequacies of natural language with a formal presentation and a formal understanding. For Spinoza such formally adequate modes of thinking are embodied directly in the ‘geometrical method’ of the Ethics.

Gone with dependence on human words in order to think is any need among canons of philosophical explanation for external (p.23) ‘reasons to be’ in Spinoza. The single, absolutely infinite network of immanent causation replaces the traditional reliance on (and shuttling between) efficient and final causality. Unlike every theologised or crypto-theologised demand for causal sequences to end their chain in divine creative fiat or spontaneous eventful upsurge, Spinoza’s philosophy takes existence plainly to be the default of essence.6 The irony is that only such a thoroughgoing rationalism opens thought to immersion in a rose-like Real that is absolutely ‘without why’.7

Thus we come to the core of Spinoza’s immanent metaphysics. For Spinoza Nature (or God, since they are the same thing and words do not matter) is not only infinite, but absolutely infinite: ‘By God I understand a being absolutely infinite, that is, a substance consisting of an infinity of attributes, of which each one expresses an eternal and infinite essence.’8 It follows that all negations and limits within being can only be local and selective. The import of Spinoza’s all-too-misunderstood remark omnis determinatio est negatio is not at all the reality and ubiquity of negation but rather the ultimate unreality of any final or absolute determination.9 There are no absolute cuts between one thing and the next in Spinoza’s metaphysics, only more or less attenuated relations corresponding to variable degrees of commonality. Such relations (the affects and common natures) are themselves constitutive of higher-order entities, in such manner that the boundary between relatum and relatio is always at best localised and relatively unstable. To put it in more Spinozist terminology, the clear conceptual and systematic distinction between modes of substance on the one hand and the affects and common natures that structure these on the other does not in fact differentiate two separate real types of being but rather provides complementary perspectives on infinite substantial expression itself. What is, is expressed as structure. Ontology is just local metaphysics.

To develop the reading just sketched, this chapter begins by reviewing the overall structure of the Ethics and examining the role of unity and relations within it. It then turns to the geometrical order of the text and shows how this method of presentation raises unique interpretive issues for treating the Ethics as an ethics, that is, as a guide to praxis. These same issues arise in a transposed form in the problem of modal individuation and are partly resolved there. When the Spinozist account of individuation is in turn applied to language, a thoroughly affective theory of linguistic representation comes to light, indicating how the powers inherent to language express only a limited region of the potentials of thought. Finally, this sequence concludes (p.24) by considering the role of the third kind of knowledge, traditionally one of Spinoza’s most contentious notions, in light of the preceding analyses, and proposing a pragmatic and implicitly diagrammatic interpretation of this singular conception of thought’s power.

Unity and Relations in Spinoza’s Ethics

It will be helpful first to review the main outlines of Spinoza’s text. As indicated by its full Latin title – Ethica Ordine Geometrico demonstrata, et In quinque Partes distincta – Spinoza’s Ethics is articulated in five main segments, or parts.10 Two interpretive tasks follow from this division: (1) following the transitions and developments from one part to the next; and (2) understanding the five-part series as a whole in the unity of its sense.

Part One – ‘Of God [De DEO]’11 – presents the most general features of Spinoza’s metaphysics: the unity of substance, the infinite attributes, and the modifications, or modes of those attributes. These three terms – substance, attribute and mode – become the basic metaphysical framework for Spinoza’s ensuing discussions. In a concentrated series of propositions and demonstrations Spinoza quickly establishes the existence and unity of a single substance – God, or Nature – in which all things exist.12 From the essence of this single substance necessarily ‘follow infinitely many things in infinitely many modes […]’.13 Spinoza argues at length that all things are as they are through the necessary consequences of the divine nature – the primary emphasis throughout is on causal order and necessity: ‘Things could have been produced by God in no other way, and in no other order than they have been produced.’14

The passage from Part One to Part Two, ‘Of the Nature and Origin of the Mind [De Natura & Origine MENTIS]’, marks a specification within this all-encompassing field of a domain with particular relevance for human beings. Among the infinite attributes of the one substance, Spinoza examines the two of which human beings consist as singular modes – thought and extension. Spinoza begins Part Two with God’s power of thinking and concludes as in Part One with an affirmation of necessity as the identity of will and intellect.15 Yet in distinction from Part One, Spinoza here emphasises ‘how much knowledge of this doctrine is to our advantage in life’.16

The hinge that both separates and links Part Two with Part Three is a shift from the more general and static discussion of ideas and bodies in Part Two towards a consideration of their interactive (p.25) affects, their ways of affecting and being affected by one another.17 Part Three is entitled ‘The Origin and Nature of the Affects [De Origine & Natura AFFECTUUM]’, that is, the relational actions and passions of bodies (and their corresponding ideas). Here Spinoza outlines the dynamics of the affects and specifies a number of increasingly complex and differentiated human affects arising from the ‘primary’ trio of desire, joy and sadness and including such familiar emotions as love, hate, devotion, hope and fear, gladness, remorse, pity and gratitude.18

In passing from Part Three to Part Four the dominant note of Spinoza’s text shifts from description to prescription. The theme of Part Four is ‘Of Human Bondage, or the Powers of the Affects [De SERVITUTE Humana, seu de AFFECTUUM VIRIBUS].’ Thus the main subject of Part Three, the affects, continues, but here in relation to the ‘desire to form an idea of man, as a model of human nature which we may look to’ in order to understand the negative consequences of the affects’ powers over us.19

Ethical prescription also motivates Part Five, ‘Of the Power of the Intellect, or on Human Freedom [De POTENTIA INTELLECTUS, seu de LIBERTATE Humana].’ The respective titles of the two final parts thus signal how the movement from Part Four to Part Five is expressed through a pair of coordinated transitions: an analytic shift from affective to intellective power and an emancipatory movement from bondage to freedom. In Part Five the theme of God’s unity from Part One returns in the form of the ‘idea of God’ to which singular ideas are necessarily referred in the ‘intellectual love of God’.20 In this there appears a key to understanding not just the series of steps from one part to the next but the immanent unity of the series itself.

Throughout the text, Spinoza’s immanent metaphysics (developed most fully, it should be noted, in a book entitled Ethica) emphasises unity, particularly the unity of God and Nature in Part One and the unity of body and mind (the identity of extended and thinking modes, in Spinoza’s terminology) in Part Two. The very form of these ‘unities’ raises particular problems for interpreting Spinoza’s thought. The terms in which Spinoza presents them are not unique to Spinoza, of course, but are in each case inherited from tradition, whether theological or philosophical, ancient or contemporary. His novel account of immanence is thus cobbled from diversely given materials, and the account itself consists primarily in how these materials themselves are conceptually transformed by being syntactically rearranged.21 This occurs at each of the three primary levels of (p.26) Spinoza’s theoretical apparatus – substance, attribute and modes – and the problem of formal unity and relational difference manifests itself differently at each level.

At the level of substance, as we have seen, Spinoza affirms the unity of a single substance. Spinoza inherits the question of unity at this level especially from medieval Jewish and Muslim theologians, for whom God’s unity is a primary subject for thought and the relationship between God and the created universe is an important and contentious theme.22 In treating this traditional theme, Spinoza breaks with traditional interpretations of God’s transcendence by identifying the terms God and Nature together in the concept of one universal substance, which he defines as ‘what is in itself and is conceived through itself, that is, that whose concept does not require the concept of another thing, from which it must be formed’.23 This single substance, itself alone ‘absolutely infinite’ and from which ‘must follow infinitely many things in infinitely many modes’, may be designated equally well in Spinoza’s view as Deus or Natura, God or Nature.24 This substance is one, or unity in an ultimate, almost Parmenidean sense.

At the level of the attributes, the problem of unity appears primarily as the relation or identity of the two attributes in which human being is involved, those of thought and extension.25 Like the unity of God and Nature, the question of the essence of the relationship here is also a problem Spinoza inherits from tradition. In this case, however, it is the newly established Cartesian tradition that Spinoza inherits and whose disjunct terms he sets in parallel order. More broadly still, the problem appears at this level in the distinctions among all the attributes in their infinite diversity, since for Spinoza there are an infinite number of attributes, not only those of thought and extension. As the relation between this level and the preceding one, the problem of unity appears also with regard to the metaphysical distinction between substance and attributes themselves.26 The attributes are many, yet the unity they share and express is the unity of substance.

Finally, the problem of unity comes into play equally at the level of individual modes (singular bodies and the ideas, or minds, of those bodies).27 This is expressed first of all in Spinoza’s identification of ideas and bodies. In contrast to the Cartesian distinction of thinking and extended substances (minds and bodies), Spinoza identifies ideas and bodies as expressions of one and the same mode of substance under distinct attributes. Here too the unity of and relation between (p.27) the levels of substance and modes becomes an issue. The modes are individuated unities, yet they are plural and relational in essence. Still, they are modes of one substance. But in what sense?

This problem of formal unity arises for substance, attributes and modes in distinct ways, yet extending across and linking these three levels of Spinoza’s theoretical framework is the question of ethical practice. Spinoza’s metaphysics implies and expresses an ethics. Spinoza’s Ethics is in fact an ethics in precisely the sense that its primary bearing is upon how one lives and acts. To this extent the philosophical problem of unity is expressed primarily as a problem of practical relation, first of all as the signifying relation between Spinoza’s text and the possible contexts of its reading or use. It is clear especially in the contrast between Parts Three and Four on the one hand and Part Five on the other that reason is Spinoza’s answer to the question of how one should live if one is to be free. Reason is itself the passage from the bondage of passion to the freedom of action, from the external power of the affects to the power of human freedom. Reduced to its most basic formulation, Spinoza’s answer appears much like the answer given by the ancient Stoics: one’s life should be lived in accordance with reason. From an ethical perspective, rationality is only secondarily a means of knowledge. Primarily, reason is a mode of conduct. In other words, reason itself for Spinoza is a form of practical relation. As essentially practical, reason enacts and produces the unity of part with part and of part with whole, and in this way reason expresses unity not because it subsumes a diversity of themes under a common theoretical form, but because it involves a relational way of being that is one of agreement (convenire).28

At stake is the distinction and relation internal to any ethical text between its theoretical meaning and its practical programme. On the one hand, there are the various logical and conceptual relations that constitute the systematic structure of the Ethics. On the other hand, there are the various relations of bodies, ideas and whatever else there may be that constitute the actual world itself (regardless of whether one accepts the premises and conclusions of Spinoza’s metaphysics). Readers of the Ethics are inevitably caught up in these concrete worldly relations in myriad ways, and any interpretive strategy that would take the Ethics as a practical guide for action is faced with the task of outlining possible relations of agreement between the internal system of the Ethics and the wider and more complex world of human activity to which that text’s meaning is addressed. The problem expressed here is, more generally, that of signification for (p.28) ethics: how does one indicate, model or describe modes of practical relation in a way that facilitates effective translation into unforeseen contexts? In particular, how does one accommodate a discourse of ethical prescription within the framework of a necessitarian and thoroughly rationalist metaphysics? If there is a mystery in Spinoza, it is not the mystery of the cosmic or trans-cosmic All. It is the mystery of the mystery: how can there be (the illusion of) separation, mutilation or fragmentation of beings at all? Without a gap or crack between what is and what ought to be, why should there be an Ethics in the first place? What is a primer in immanence for?

The problem of practical relation as it appears in Spinoza’s Ethics may be clarified by way of an analogy drawn from the mathematics of Spinoza’s own day. Descartes’ Geometry, published in the generation just prior to Spinoza’s intellectual maturity, first established modern analytic geometry as the mapping of algebraic relations between real numbers onto geometrical relations between lines and figures in a Euclidean plane.29 In Descartes’ text, ‘l’unité’ serves a central terminological and methodological role. ‘Unity’ represents the arbitrary choice of a fixed geometrical magnitude, ‘one line’, as Descartes writes, ‘which I shall call unity [que je nommeray l’unité] in order to relate it as closely as possible to numbers’.30 Once chosen, this unique magnitude (corresponding to the quantity 1) stands in fixed proportion to all other possible finite magnitudes in a Euclidean space. Since relations between the parts of geometrical figures may at every point be expressed or measured by the construction of lines, that is, magnitudes, it becomes possible on this basis to express geometrical relationships in terms of relations of numbers. This transformation of geometrical form into numerical proportion thus enables the rigorous, isomorphic translation of geometry into algebra. Establishing the conditions of possibility for such translation constitutes one side of Descartes’ methodology; the other consists in using the established relation to then solve specific problems.31

How does Descartes’ method work? To make Cartesian analytic geometry feasible, one must first designate an arbitrarily long, finite, continuous line segment as corresponding to the discrete quantity ‘one’ (or unity). It then becomes possible to express infinitely many (Euclidean) geometrical relations as corresponding uniquely to definite mathematical (numerical/algebraic) relations and vice versa. Thus Descartes’ method institutes and enables a far-reaching and systematic correspondence – algebra to geometry – by first establishing a single, minimal correlation, the number one to the length of a chosen (p.29) line segment.32 The large-scale correspondence of algebraic and geometric relations does not proceed tautologically of itself (no point, no line is in itself a number), but is rather constituted hypothetically by the choice of a determinate ‘unity’. To call such a choice hypothetical is not to question its validity (which can be demonstrated clearly to anyone who examines its results or effects), but only to emphasise its original contingency. It is to recognise that while its logical modality is not itself that of necessity, precisely this particular kind of choice does necessarily make a large-scale, rigorously demonstrable one-to-one correspondence of algebraic and geometrical relations possible. While in a certain sense it does not matter which definite magnitude is chosen as ‘unity’, the very possibility of analytic geometry as a mathematical science depends on the choice of some such definite magnitude. We may thus distinguish the relative necessity that a singular magnitude be chosen (for the definite purpose of establishing a correlation of algebra and geometry) from the relative indifference of what magnitude is in fact actually chosen.

The form of discursive presentation in Spinoza’s Ethics may be understood as analogous to the relation-forming function of ‘unity’ in Descartes’ Geometry. In reading the Ethics, practice is the mode of interpretation that translates text to context. Yet in relating the ideas expressed in the axiomatic system of the Ethics to the complex fields of worldly experience, a ‘unity’ has to be established bringing these systems of different kind into relation. A common term needs to be posited to make them commensurate. The discursive form of the Ethics offers itself as a model for this common term, but it is only interpretive practice itself that is able to play the role concretely.

According to the theoretical framework of Spinoza’s Ethics, the very relation between the two orders – the textual and the worldly – must be understood from within the perspective of an immanent metaphysics. So what ‘unity’ would suffice to relate text and context? In Part One of the Ethics Spinoza shows how certain traditional arguments against attributing corporeality to God proceed ‘from the fact that they suppose an infinite quantity to be measurable and composed of finite parts’.33 In line with Spinoza’s implied position here, any finite unity would thereby be insufficient to make the absolute infinity of a single substance proportional to any finite part of itself. Required instead would be an infinitely developmental form of relation, a relational process or method able to test and correct itself without limit rather than a static identity relating text and application according to a uniform model. Rather than (p.30) answering the question who or what provides the unity of practice in Spinoza’s Ethics, we must instead ask how the unity functions according to these criteria. The unity bridging text and context, theory and practice for Spinoza must itself be relational in an at least potentially infinite manner.

Descartes’ analytic geometry enabled the rigorous translation of algebraic and geometric relations on the basis of a posited ‘unity’ of linear magnitude. For Descartes’ method the positing of the choice is necessary but the particular choice made remains indifferent. Yet if we follow the line of thought from the analogy above, we must note that the reader of Spinoza’s Ethics already finds him or herself immersed in a field of cultural, social, political and linguistic particularity, engaged in specific projects and constituted as an individual personality involved in concrete relations. The ‘unity’ relating text and context is already at least partially given in principle as the set of habitual practices in which any reader of the Ethics is already engaged. Yet in its general applicability, the Ethics cannot speak to its readers in their concrete singularity but must offer whatever ideas and practices it enfolds in a single, unified way to a general audience.34 Whatever relation the Ethics means to establish between text and context must be expressed in the work’s own communicative form. The text of the Ethics anticipates and addresses this necessity by casting its themes and arguments according to a particular form of abstraction: the geometrical method, a practical diagram of purely conceptual relations.

Demonstrating Geometrical Order: Spinoza’s Diagrammatic Method

The Ethics presents itself to its readers in geometrical order, an order at once programmatic and hermeneutic. To a significant extent it is this presentational form of definitions and axioms, propositions and demonstrations borrowed from Euclid’s Elements that unifies the five main parts of the Ethics and the passages from one part to the next.35 Interpreting the Ethics accurately requires following and understanding the various series of progressive demonstrations with diligence and care. Indeed, the Ethics’ geometrical order appears both to indicate and to typify the kind of thinking which Spinoza understands to possess ‘the power of ordering and connecting the affections of the body according to the order of the intellect’, the very power of reason.36

(p.31) The geometrical order has two sides. On the one hand it serves as a genre of philosophical presentation, a way of communicating ideas and their logical relations.37 In this respect the geometrical order or method may be distinguished from other forms of philosophical presentation, such as those developed in the ancient and medieval schools and those in general use today: dialogues, lectures, essays, articles, dissertations, all the various genres of philosophical saying.38 One way the geometrical order is unusual among these other alternatives is in its degree of apparent depersonalisation. In distinction from the pro and contra method of Scholastic disputation, for example, which presumes distinctly opinionated individuals or at least points of view, a Euclidean proof does not weigh two sides of an argument, but rather arrives at demonstration through purely ideal constructions whose possibility and validity remain independent in principle of any particular mind. Such constructions are enabled by formal deductive steps taken from clearly defined terms, posited axioms and the set of theorems already proven at any given stage, a set of constructive resources that continues to grow as new theorems become available. Since the original definitions and axioms are not themselves derived logically, but are simply posited as such, the only internal criteria available for such systems are derivability and consistency.39 What motivates Spinoza to cast his Ethics in this self-contained and impersonal manner?

The answer appears by way of indicating the second side of the geometrical order – not the order of presentation itself but the order of intelligible relations that the presentation is meant to manifest in and for its readers. In both Spinoza and Euclid the fixing of terms and axiomatic rules for constructing theorems appears to eliminate the role of the author as an independent mind, one individual communicating to others. The truths expressed in the propositions are – assuming the demonstration is valid – straightforward logical relations independent of the form of their expression and not in themselves subject to dispute. Surely someone had to write the text before us which we ascribe to Euclid, yet once its demonstrations are correctly understood, the very form of the text effaces any authoritative value we might ascribe to that singular name.40 More generally, the status of authority in Euclidean proof takes an interesting shape: on the one hand no claim to authority is made in the conventional sense – at no point does Euclid refer to any external legitimating authority (history, scripture, common sense) and in this respect the validity of the theorems is to be found nowhere outside (p.32) of the demonstrations themselves. Yet on the other hand, this very freedom from external authority is enacted in the imperative mood, not the indicative – Euclid’s reader becomes convinced of the truth of the theorems by ‘letting’ the demonstrations prove themselves. The actual geometrical demonstrations are inseparable in this way from series of commands to construct diagrams of relations either in some material substrate such as ink on paper or in the pure imagination: ‘Draw a line perpendicular to AB at C’, ‘Let there be a circle of radius R’, ‘Extend AB to infinity’.

Thus to follow Euclid’s reasoning is to see and thereby directly to understand the necessity of his conclusions by taking the same series of constructive and deductive steps in the order given programmatically by the text. One attains adequate ideas by following determinate instructions and then perceiving the incontrovertible results. Spinoza’s text is meant to suggest by its very form that a philosophical ethics may be organised in the same fashion. Spinoza refers to geometrical demonstrations as the ‘eyes of the mind, by which it sees and observes things [mentis … oculi, quibus res videt, observatque]’.41 By this, Spinoza suggests that diagrammatic demonstrations in the Euclidean sense do not merely lead to an insight, but are that very insight itself. To make this quite clear, consider a common geometrical property, for instance the equality of the sum of the angles of any triangle and that of two right angles. Even to question the possibility of such an equality one must first have conceived the idea of a triangle as such. Yet in adequately conceiving the idea of a triangle one must also have implicitly conceived the necessary logical concomitants of that idea (three vertices, three sides, a bounded figure and so on), these properties being involved necessarily in the concept of any triangle. Included among these many properties is the special property that the sum of the triangle’s three angles is necessarily equal to the sum of two right angles. How does one make this necessity explicit? Constructing a diagram in accordance with the demonstration made in Book I, Proposition 32 of Euclid’s Elements should be sufficient to convince any interested reader.42 In general, diagrammatic demonstrations of this kind make such implicit yet necessary consequences both vivid and clear, and a valid demonstration of this sort is thus a constructive act of the mind that is in the very process of its activity an understanding and affirmation of the truth it discloses.

For Spinoza, this way of proceeding moves contrary to the ‘picture-thinking’ of representation since the mind’s power to affirm or (p.33) deny the object of its thought cannot be detached from the intrinsically dynamic form of that thought itself, the active evolution of its necessary properties. Spinoza writes, ‘We must investigate, I say, whether there is any other affirmation or negation in the mind except that which the idea involves, insofar as it is an idea […] so that our thought does not fall into pictures.’43 And elsewhere, ‘For to have a true idea means nothing other than knowing a thing perfectly, or in the best way. And of course no one can doubt this unless he thinks that an idea is something mute, like a picture on a tablet, and not a mode of thinking, namely, the very [act of] understanding.’44

Spinoza’s interpreters have disagreed over how seriously to take the Ethics’ geometrical order as an essential component of its meaning. These readers may be sorted roughly into two camps: those for whom the geometrical order is primarily a formal trapping for philosophical views that could just as well be translated into other idioms without loss; and those for whom the geometrical form of argumentation is inseparable from the Ethics’ own distinctive philosophical content. The former camp includes figures such as Wolfson who claims in a classic study of Spinoza that one could reconstruct the whole of the Ethics by simply cutting up and rearranging the texts of various classical, medieval and early modern thinkers whom Spinoza drew on as sources, with the majority of these fragments coming from but three thinkers: Aristotle, Maimonides and Descartes.45 More recently Curley follows Wolfson in seeing the geometric treatment of Spinoza’s thought as at least partly obscuring the actual historical origins of Spinoza’s ideas, in particular his contentious dialogue with his immediate, early modern predecessors, especially Descartes and Hobbes, ‘a dialogue the geometric presentation served to conceal, and was, perhaps, partly designed to conceal’.46

The second camp includes thinkers such as Gueroult who take the geometrical presentation of the Ethics to be essential to Spinoza’s thought, not just in form but equally in content.47 Indeed, for this camp the form or structure of Spinoza’s presentation constitutes the very meaning it is meant to convey. Thus in reading Spinoza’s text Gueroult himself redoubles Spinoza’s method through his own commentary, laying out in a structural manner the paths of deduction as they develop from proposition to proposition. For Gueroult the demonstrations themselves function as genetic ideas, replicating the processes of origination and development intrinsic to their specific objects: God, or substance in Part One, and the Mind, or power of thinking in Part Two.48 Some philosophers strongly influenced (p.34) by Marx such as Althusser and Negri – who rightly aim to link Spinoza’s metaphysics explicitly with his separate analyses of society and collective power in the Theologico-Political Treatise and the unfinished Political Treatise – tend also to take this view since the impersonal, scientific rigour of geometrical proof promises to function as a kind of fulcrum for overcoming ideological misconceptions and developing emancipatory forms of thought.49 For Negri, despite dismissing it at one point as ‘fatuous’ and ‘the price that Spinoza paid to his epoch’, the geometrical method nonetheless constitutes ‘the methodologically constructed possibility of arranging the totality in propositions without shattering its intrinsic wholeness’.50 The Ethics’ geometrical order according to Negri becomes at once a representation and a repetition of the constructive pluralist ontology it describes: ‘The causal and productive geometric method is neither unilateral nor unilinear; it corresponds to the versatility that the univocality of being produces.’51

What distinguishes the two camps is primarily how the Ethics is understood in relation to earlier philosophical and theological traditions. Wolfson and Curley tend to see continuity (albeit dissembled by the form of the text itself) where Althusser and Negri (and to a lesser extent, Gueroult) see rupture or ‘anomaly’. What is at stake in the dispute is thus largely a matter of questioning the power of formal abstraction relative to thought’s historical production and reception.52 If the geometrical or demonstrative method is truly no more than a secondary and unnecessary appendage – an extrinsic form – then we as readers remain free to disregard it and to penetrate beyond it to Spinoza’s own historically conditioned philosophical views, the real content of the text. But if the demonstrative method is intrinsic to the actual sense of the Ethics as a way of thinking at least partially independent of historical and linguistic context, then not only must we attend carefully to its mode of presentation and follow its method in following Spinoza’s thought, we must also call into question the presumption that such a work of philosophy functions in the first place to represent and defend philosophical ‘views’ at all.53

In general, as one emphasises the geometrical presentation of the Ethics, one necessarily emphasises the practical component of reading the text in a corresponding way. One moves from a disputational or dialogical model of philosophy to one closer to the formal deductive systems arising well after Spinoza, like those in twentieth-century logic which are at heart mathematical. At its limit, such a (p.35) view would deny that Spinoza’s text has any relevant linguistic or referential content at all but is instead simply a set of formal operations and the relations they constitute. If the formal deductive method were to be entirely abstracted from its concrete instantiation in the Ethics as that text has come down to us, then nothing would warrant linking the method to any of the specific discursive contents of the Ethics at all. Spinoza’s thought would become an attempt merely to indicate a pure method saying nothing, a deductive programme devoid of linguistic sense, a pure geometrical order without figure or form.54 Rather than a set of philosophical judgements subject to discussion and debate, the Ethics on this reading would be something like a complex formal algorithm, expressible most nearly as a formal language. We will see how Hvidtfelt Nielsen develops such an approach to the Ethics in some detail below.

It should be clear in any case that the Ethics as Spinoza wrote it cannot simply be reduced to its geometrical presentation in this fashion. Critics of a strictly geometrical, demonstrative or deductive reading of the Ethics are quick to point out that Spinoza’s demonstrations do not match the deductive rigour their geometric form would suggest.55 If Spinoza meant his formal demonstrations to serve as the core method for following his thought, why would he have handled them so freely? There is in addition the undeniable importance of those parts of the text that in no way function within the deductive system proper. Each of Parts Three, Four and Five of the Ethics begins with a preface not contained in the text’s network of explicit axioms, propositions and demonstrations but pertaining in essential ways to the philosophical meaning of Spinoza’s thought. There is also the summarising Appendix to Part Four, in which Spinoza presents the conclusions drawn in the previous demonstrations in a more discursive fashion so that they may be ‘seen at a glance’. There is as well Spinoza’s own admission that the Ethics pertains neither to ‘medicine’ nor to ‘logic’, both of which need to be developed as supplements to his work.56 More importantly, Spinoza’s frequent and often lengthy ‘scholia’ – commentaries and digressions from the strictly deductive framework – contain many of his finest insights and most important philosophical claims. To read the Ethics merely as a formal deductive system would imply disregarding these sections of the text, and a strictly formalist reading would be forced to ignore them entirely. Outside the geometrically demonstrative framework, they would thus be outside the Ethics ‘proper’. This implies that there is more in the hermeneutical dimension of Spinoza’s text than (p.36) the merely programmatic dimension of geometrical proof would suggest.

Clearly, a purely formalist reading of the Ethics is untenable. But so too is a reading that would ignore the logic of geometrical order entirely and that would reduce its power of formal abstraction entirely to historical and contingent factors. Both sides must be held together despite their tension; the Ethics is both a culturally and historically embedded text addressed to situated readers and a formal structure in part irreducible to history. The geometrical order disengages from the person and time of Spinoza, but in order to understand this order in relation to its possible applications in practice, we must look at the concrete context in which Spinoza originally composed his Ethics, as well as the relevant features of any context in which it might be applied.

Scholars such as Israel have shown in detail the historical importance of Spinoza for the development of modern European conceptions of reason and freedom.57 Yet the ideas of Spinoza circulated primarily through second-hand accounts of his theoretical claims, not through first-hand trials of his ethical and practical prescriptions – although it was the ethical consequences that were thought to follow from Spinoza’s ideas that especially worried his critics.58 Even in contemporary scholarship, to the extent that the practical orientation of the Ethics is recognised explicitly, Spinoza’s geometrical method is often conflated directly with his concept of reason. It remains generally accepted that Spinoza’s philosophy at least tends in the direction of the identification of philosophical and mathematical reasoning associated with later Enlightenment rationalists such as Wolff.59

Yet recall our earlier reference to Descartes’ Geometry and the analogy we drew there to the interpretive problem of Spinoza’s Ethics. The analytic geometry developed by Descartes holds a central place in the development of modern mathematics primarily because of its emphasis on relation. This concept remains fundamental both to the objects and the procedures of mathematics. As a popular historian of mathematics puts it:

We see [analytic geometry] not as a geographic scheme of location or an exercise in blending algebra and geometry or a painless path to Euclidean and more advanced geometries, but as a means of expressing relationships (relations, in mathematical terminology) of all kinds and making important deductions about them. This point of view makes analytic geometry the very core of mathematics, since many mathematical subjects – for example, trigonometry, (p.37) calculus, ‘complex analysis’, probability, mathematical statistics, and even one essential part of logic – are theories of general or special relations.60

In other words, analytic geometry – the initial frame for Newton’s and Leibniz’s subsequent development of the calculus – may be seen as the ‘very core’ of modern mathematics precisely to the extent that it formalises and enacts a logic of relations.

Yet the category of relation is by no means limited to the realm of formal mathematics. Relations may certainly be abstract, merely possible and thoroughly ideal but they are also discernable everywhere as concrete, actual and inescapably real. They respect no fixed limit between the conceptual and the real, and they require a rethinking of the easy identification of what is real with what is seemingly most concrete. In fact, relations are situated within an immanent conceptual ‘space’ sui generis varying continuously across infinite degrees of concreteness and abstraction, singularity and generality. Where are the ‘things’ such relations relate?

Individuation

The philosophy of Spinoza takes the indivisible unity of the whole of nature as its starting-point, its primary hypothesis.61 This emphasis on unity brings to the point of identity the terms tradition had kept absolutely distinct: God and creation, or nature. The oneness of this single substance is identified in Part One of the Ethics with absolute infinity.62 Consider a spectrum of conceptual determination stretching from pure singularity to perfect generality. Where along the spectrum would this singular concept – the infinite idea of God, or nature – itself fall? At one of the poles? Which pole – the singular or the general? Nature, it seems, would be both singular and general – at both poles at once, embracing the entire spectrum.

In light of the comprehensive unity of nature, how are we to understand the unity of some particular finite thing – a grandfather’s tuba, for instance, or some tarantula on a California backroad? What makes such a thing one thing, it itself? A subject-predicate structure and model of language leads traditionally to an understanding of individual things as distinct substances – hypostases – to which qualities and events may be attributed. Yet Spinoza holds that only one substance truly exists – Nature, or God. What we normally consider to be individual things are understood to be modes, or affections (p.38) of this single substance.63 What is the unity of such a mode? The problem arises at all levels of our hypothetical spectrum. At each stage or degree from the purely singular to the perfectly general we may pose the question of unity anew: what is the unity of the kind or species ‘plant’ or the concept of a ‘living thing’ or indeed a ‘thing’ as such? How would Spinoza understand the individual differences and stratifications within our imagined spectrum? In the unity and continuity of God, or Nature, where and how is discreteness manifest?

The problem of individuation took on new importance in early modern philosophy due to the emergence of a mechanistic conception of bodies and the Cartesian distinction of thinking and extended substances. The philosophical successors to Descartes, Spinoza among them, inherited this problem and addressed it each on his own terms.64 This problem has engaged Spinoza’s commentators as well on a variety of levels – metaphysical,65 epistemological66 and political.67 One concern common to these various strata lies in asking how what constitutes the unity of an individual thing (whether a body, an idea or an essence in general) should be formulated in relation to Spinoza’s distinctive conception of the unity of nature as a whole.

Spinoza claims that all individuals ‘though in different degrees, are nevertheless animate’, but qualifies this claim by interpreting the ‘different degrees’ of animation as different degrees of power determined by varying capacities to act and perceive.68 Bodies are animated to a greater or lesser degree as they are capable of doing or experiencing more or fewer things:

[I]n proportion as a body is more capable than others of doing many things at once, or being acted on in many ways at once, so its mind is more capable than others of perceiving many things at once. And in proportion as the actions of a body depend more on itself alone, and as other bodies concur with it less in acting, so its mind is more capable of understanding distinctly.69

On this view a table, for example, does have a soul – its mind or ‘idea’ – but a table’s soul is capable of very few kinds of internally determined action. What a table does is in fact almost entirely exhausted by what is done to it.

What all the various degrees of animation share is how they constitute distinct individuality through the relative motions and affects of their component parts. Spinoza defines an individual as a composite of bodies which ‘communicate their motions to each other in a certain fixed manner’. The complete definition is as follows:

(p.39) When a number of bodies, whether of the same or of different size, are so constrained by other bodies that they lie upon one another, or if they so move, whether with the same degree or different degrees of speed, that they communicate their motions to each other in a certain fixed manner, we shall say that those bodies are united with one another and that they all together compose one body or individual, which is distinguished from the others by this union of bodies.70

The relations of movement and rest among the component parts of this whole, taken together, constitute the essence or ‘nature’ of the individual in question. The ‘manner’ of this communication of motions is thus a fundamental component of the individual as such. How a body’s various parts communicate their motions is a crucial aspect of what that thing is, its nature and unity.

The unity of a composite body is thus defined by Spinoza in terms of differential relations that compose it as a singular whole: ‘Bodies are distinguished from one another by reason of motion and rest, speed and slowness, and not by reason of substance.’71 This explains why they are modes of one substance and not independent substances themselves. Under the attribute of extension, such modal components are typically manifest as relative trajectories of bodies in space that may or may not affect one another in a variety of ways.

Affective relations are thus a sort of multi-scale ontological glue; in binding modes to one another, they constitute the modes themselves as local systems or parcels of variable relations that affect other such systems in similarly variable yet also partly regular and determinate ways. This progressive ‘scaling-up’ of individuating relations has no finite limit: ‘if we proceed in this way to infinity, we shall easily conceive that the whole of nature is one individual, whose parts, that is, all bodies, vary in infinite ways, without any change of the whole individual’.72 This is the ‘infinite mediate mode’ which Spinoza elsewhere calls ‘the face of the whole universe’.

To summarise, Spinoza’s theory of individuation in the Ethics has four essential characteristics. Together, these provide the necessary framework for understanding individual modes as affective diagrams:

  1. (1) Modes are relatively stable systems of relations among component parts. These systems themselves become stable internally when certain of their relations take on a canonical or determinative status with respect to others. Such determining relations are typically ‘local equilibria’ within some space of possible states.73

  2. (p.40) (2) A duality of determination and indetermination is constitutive of modes as such. No mode can be fully determinate because all of a mode’s constituent relations are characterised by variable affordances with at least some degree of elasticity. On the other hand no mode can be fully indeterminate because it would then be independent of all relation and hence a substance, not a mode.

  3. (3) Every mode exists by virtue of being relationally situated vis-à-vis its local environment in an immediately affective way. Existent modes are actual, and the relations in which they are embedded at any particular moment are immediately responsible for the increase or decrease of those modes’ powers to affect and be affected by other modes. Two consequences follow:

    1. A. Each mode consists of a duality of internal (system) and external (environment) relations.

    2. B. Each mode involves a duality of active (determining) and passive (determined) affects.

  4. (4) Processes of modal individuation are never absolutely discrete, but are always finally determined through the ultimate continuity of nature as a unique substance. Modes are local inflections of a universal relational field, not separate ‘things’.74

Take note of Figure 1.1. The diagram on the left is meant to suggest in an intuitive way the dynamics of modal consistency. Its arrows represent affective relations, and its dots represent modes individuated at some level of organisation ‘lower’ than that pictured. Such a distinction of levels or scales is essential to Spinoza’s conception

Spinoza and Relational Immanence

1.1

(p.41) of individuation and its structural dependence on the doctrine of affects.75 The diagram on the right shows how the mode individuated by the relatively stable affective relations pictured on the left becomes capable by that very process of individuation of entering into higher-order affective relations with other modes. To put it more exactly, it is only in respect to such higher-order relations that the process of individuation at the lower level can even be registered or identified.76

Individuation is thus always a matter of degree, never a binary criterion for membership in some special metaphysical kind, ‘entities’, distinguishable from properties or relations. The question ‘how many individuals are there?’ is meaningless for Spinoza, or, taken strictly, the answer is simply one: God-or-Nature. Anywhere we locate a set of bodies moving together with any degree of regularity – that is, practically anywhere we look or can imagine looking, short of absolute chaos – we are able to identify an individual in Spinoza’s sense. The problem of individuation is thus primarily a matter of identifying the continuous ‘selective’ processes by which sets of relative motions attain relative consistency.

How does a set of component parts attain the consistency of a relatively fixed set of motions? How do individuals become individuals in any determinate sense? The question of what constitutes an entity can only be answered by indicating the process or event that consolidates or renders consistent a given set of relations of movement into a single, integrated whole for something else which they affect and by which they are affected. An individual is such that its component motions are united for something other than itself according to some specific way of affecting the latter. In contrast to the dyadic subject-predicate structure of representational judgement, the affective structure in Spinozist individuation involves essentially three term relations: X affects Y in manner Z. Affects are thus intrinsically potentialities or powers.77 They range in their very essence across a spectrum of possible instances or expressions. See Figure 1.2. The arrow highlighted on the right in Figure 1.1 above is here elaborated as a range of possible relations to a variety of different individuals varying within conditions or affordances intrinsic to the affective relation (the arrow) itself.

In the human sphere, this is the point at which the Spinozist conception of individuation intersects with the phenomenological. In perception and lived experience objects are individuated for us. The place where this experience of individuation becomes itself public and communicable is language.78

(p.42)

Spinoza and Relational Immanence

1.2

Language, Affect and Form

Unlike the image of thought guided by linguistic representation, a conception of thought like that of Spinoza that thoroughly saturates thinking within the immanence of relationality does not require a constitutive break between the vehicle and the object of thought. On the Spinozist view, language itself is directly relational, as are all forms of experience, perception and knowledge. Yet such worldly relations obviously possess a status distinct from the pure relations investigated by mathematics. In particular, the relations expressed in and through human language are meaningful and thus subject to interpretation in a different sense than, say, a theorem of geometry. The context for practical application of the Ethics must be understood to include these sorts of meaningful relations as well. One challenge for Spinoza in attempting to link geometrically ordered relations of adequate knowledge to practical or ethical relations in the world is to find a criterion and method by which this linkage itself might be conceived and understood adequately.

(p.43) Rather than presuming a more or less properly functioning technology of language and text with which to generate and perform philosophy with artfully chosen words, for Spinozist thought it is necessary to work instead at each step of cognition within an immanent framework that is at once both singular and universal and that would thus bypass from the very beginning any necessary reliance on a presupposed mediating level of linguistic or conceptual generality. It is here that Spinoza’s relational account of individuation comes to the fore as an explanatory account of language as such. On Spinoza’s terms, it is only on the basis of an account of modal individuation as universal, multi-scale, affective relationality that language and linguistic representation may themselves be understood, rather than the reverse.

The problem of language from this point of view is just one slice of the more general question of how individual modes and their affects are able to reside somehow ‘between’ the singular and the universal. At or very near the pole of singularity along our previously discussed spectrum we encounter some particular, individual thing – a sprig of mint, say, or rather this sprig of mint. Simply by identifying such a particular thing as belonging to some definite kind, however – as mint, in this case – we find we have already moved along our spectrum some minimal degree in the direction of the opposite pole, that of generality. As we are then enveloped or led back in thought to more general kinds (herb→plant→living thing→thing) we approach the pole of maximum generality, where we would expect to find the most general forms of being, or categories.79

It is a commonplace that human beings are distinguished from the rest of nature by their collective participation in language: anthropology– the logos of ‘humankind’, or anthropos – states a pleonasm. Not only is language the medium of communication about all sorts of things, it is also the primary domain in which human individuals are recognised as such; it is in and through participation in language that human beings speak to and for one another. In the terms of our discussion of individuation we might say that the affect of linguistic communication individuates both human nature as well as the natures of singular human beings. This is not to say that language exhausts or even originates essential humanity, only that language is one very important thing humans do through which we are what we are. In this way we pass from the communication of the motions of the composite parts of bodies and natures in general to the singular problem of communication in the sense of human language.

(p.44) Language is the point where the question of individuation may be asked of ‘universals’, or general ideas as they arise in contexts of human communication, giving rise to debates that have traditionally been framed in terms of nominalism and realism. Spinoza appears at first sight to be clearly a nominalist. If any two moving bodies can be described by a ratio of motions (for example, the ratio of the vectors corresponding to their velocity and direction) and are thereby considered to be ‘communicating’ their movements, then any pair of moving bodies chosen at random would constitute an individual. Such individuals and the general types by which they are called would be mere names. Similar cases would hold for any number of bodies, and as a result all possible sets of relations of movements of actual bodies would have to be considered individuals. If communication is thus understood as merely abstract, quantitative relation (ratio in the mere sense of a mathematical ratio), then individuation loses any qualitative aspect and becomes simply an arbitrary assemblage of parts. In fact, however, Spinoza has provided a guard against this thoroughly nominalist conception through his doctrine of the affects. The question of whether two or more bodies are truly communicating their movements must be displaced onto the question of whether and how they actually affect one another. To genuine affects would then correspond genuine individuals. More importantly, different kinds of communication of movement would thus correspond to discrete and distinguishable affects. Thus the manner in which two or more bodies affect one another corresponds to the way they communicate their movements and therefore determines what sort of individual those bodies compose. The reality of distinguishable affects implies and envelops the reality of any structures that might conceptualise those affects or name them. The affects thus absorb and ‘immanentise’ any transcendent conception of logos as an a priori linguistic condition of thought.

Language would in this way be understood in terms of the kinds of affects it makes possible and the affective relations it sustains. We have seen how Spinoza’s ‘parallel postulate’ claims that ‘[t]he order and connection of ideas is the same as the order and connection of things’.80 This identification of ideal and material orders makes the problem of linguistic meaning an especially thorny one. The difficulty may be illustrated through the following example: a woman reads. This act of reading constitutes a complex, embodied event. It is a matter of bodies in motion, communicating affects in a variety of ways. She sits at a café on a busy street. She sips her coffee. In one (p.45) hand she holds a large, blue book. Her eyes scan the page, a rhythmic iteration from left to right in conjunction with a slower movement from top to bottom. The words – differentiated as patterns of black ink on a white page – evoke a series of sounds and images that combine and retroactively charge one another to produce the unity of a complex sense, a meaning for or before her.

How, on Spinoza’s terms, are we to understand the woman’s experience of this text’s meaning? The seeming implication of Ethics IIp7 is that if meaning occurs in thought and is thus a complex of ideas, a sufficient description of this event of meaning will necessarily be parallel to a corresponding description of a complex of physical events. Meaning would be reduced to a set of related physical events, or rather identified with those events according to the parallel postulate. Yet our everyday experience of meaning mitigates against this. It is not just that the description is not detailed enough (that we must, for example, go all the way to a description of photons reflecting off the fibres of the page, individual neural firings in the woman’s brain, and so on). Rather, what we mean (and experience) in the term ‘meaning’ would seem to be in principle irreducible to any such description.

Philosophers coming from perspectives as different as Althusser and Nielsen have seen this aspect of Spinoza’s thought as a positive opportunity for eliminating or at least minimising the domain of meaning and advancing a consistent philosophical materialism.81 The elimination of meaning in this way would accompany the elimination of the egoic subject as the ground of thinking. The domain of meaning would be effectively evacuated because the unity of a subject for whom meaning would, precisely, mean will have been exchanged for the standpoint of radical immanence. Thought, then, would no longer be the privileged domain of a subject, but rather the unity of an infinite attribute the order and connection of whose parts would be strictly parallel to that of the world of things. In our example, the woman would no longer be thinkable as a ‘kingdom within a kingdom’. She would be, rather, a local inflection in a continuous field of material (ideal) relations. Does such a conception entail the annihilation of meaning?

It is important to remember that the relations constituting the field are not themselves objects of possible representation, but are instead actual affects. In Spinoza’s thought, the affective mingling of bodies (and the realm of ideas conceived as strictly parallel to this mingling) dissipates every illusion of thought as a mirroring of subject and representation. And it does seem as though the very generality and (p.46) communicability of meaning would mitigate against any reduction of meaning to absolutely singular affective events. Yet perhaps the problem with our exemplary image of the woman reading is that by its very nature as example it has already fallen under the generalised illusion of representational thought, of presuming that the meaning of a text and the representation of that meaning must both somehow be thought-pictures. Surely something is present to the woman’s mind as the object of her intentional regard, but any implicit theoretical model that already places conditions on what sort of ‘something’ that object might be tends to beg the question of how thought actually relates to what it thinks. In the end, the doctrine of the affects does not preclude representation, but merely circumscribes it and displaces its auto-foundational role in theorising thinking.

In particular, the dynamic character of the affects precludes any neutral, or strictly representational model of textual interpretation. Because ideas for Spinoza are always affective, and the interpretation of a text – like everything else – involves the movement and ordering of ideas, interpretation is itself necessarily affective through and through. Among other things, then, one cannot adequately grasp the meaning of Spinoza’s own text without simultaneously recognising the implications of one’s very act of interpretation within the meaning thus generated. This self-reflective exigency is something the Ethics shares with any text that either implies or explicitly develops a more or less comprehensive theory of meaning or interpretation.82 Yet the singular strategy of the Ethics involves leading any work of interpretation – in particular, the act of reading – back to a dynamic interplay of affects that renders them increasingly rational.

Spinoza ultimately reduces all affects to the three ‘primitive’ affects of desire, joy and sadness. Because of the universality of the affects, no interpretive method or procedure can be abstracted from the interplay and movement of affective dynamics. Not even a single step in any interpretative process is exempt from this reduction to the affects. Thus a Spinozist mode of reading opens the possibility at every stage to ask the question: What affects are being mobilised at this point in the reading? For Spinoza, the answer will always necessarily be plotted along the three dimensions of desire, joy and sadness and the multitude of affects generated through combinations and interactions of these. These are not rational foundations, but component vectors of a real space of relational becoming. Rationality, for Spinoza, consists of gradients of increasingly active relationality along pathways through this affective space (transitions from passive (p.47) to active affects). Such gradients of affective power explain linguistic reason, or logos, as a special case rather than requiring explanation in terms of the latter.

Consider the demand for logical consistency. Apparent contradictions in meaning between two parts or phases of a single text (or often separate texts by a single author) are cause for displeasure, even a kind of righteous indignation in careful readers. Indeed, much contemporary philosophical work consists in demanding consistency from canonical and authoritative texts, and policing those texts for logical inconsistencies. This highly ritualised process of assertion and critique takes place against the background of a presupposition that is usually taken for granted to the point of becoming practically invisible – the presupposition that consistency is somehow philosophically required, that a self-contradictory text ought necessarily in this respect to be devalued. But why without begging the question should we demand consistency of an argument or text at all?

A Spinozist analysis of reading calls such presuppositions into question and renders them potentially explainable on the basis of investigating the actual affects deployed in any singular case or across some discernable class of cases. In Spinoza’s view any interpretive criterion that actually functions in any specific context however broad or narrow, even one as apparently basic as simple logical consistency, must be understood through its singular affective connections always traceable back to those of desire, joy and sadness. Thus texts and the varied processes of reading are taken out of a strictly representational framework and brought back to the individually and collectively affective contexts within which they circulate. Meanings no longer serve as representational contents, but are rather active strivings and dynamic passages for individuals (which are just relatively local collectivities) and collectivities (which are just relatively regional individuals). Therefore, to return to the example, the criterion of logical consistency is inseparable from – indeed for Spinoza, strictly identical to – the ensemble of affects it engenders: the pleasure of seeing ideas cohere, the conviction aroused in a listener, the smugness of a pat argument, the interpretive frustration in the face of manifest contradiction, and a potentially infinite list of others.

It would be mistaken, however, to see this turn to the affects as something like a mere psychologisation of logic or a cheap reduction of logical criteria to mere feeling. The affective interpretation of logical consistency, for example, does not reduce consistency to affect but rather understands logical consistency in terms of its (p.48) intrinsic relation to possible ways of affecting and being affected by texts, arguments and so forth in practical ways across multiple situations. Whatever logical principle of validity is contained in the demand for consistency, for the unity of thoughtful expression, that principle itself is manifest only in and through the specific affective relations it engenders for individuals and collectivities, from private readers of Spinoza’s Ethics, say, to communities as general as those of ‘rational language-users’.

It must be remembered that for Spinoza affects always correspond to transitions in some particular essence’s power to act. For Spinoza, all bodies, and especially bodies as affectively complex as human beings, are in constant flux, becoming more powerful and active in certain respects while being inhibited and weakened in others. Thus language itself must be understood as a dynamic field of real relations both empowering and enfeebling human beings in countless ways across innumerable contexts.83 On the basis of such an understanding, the sense of philosophical language in particular becomes transformed. How philosophy is communicated must be integrated into both the idea of what philosophy is and the sense of what it says.

How, on this basis, should we interpret the Ethics itself and the affects it mobilises? What happens when we examine Spinoza’s own text from the standpoint of language and individuation just given? Following Spinoza’s own methods, the distinction between natural language and logical form comes to the fore, a dimension of Spinoza’s thought in which rhetoric and logic are problematically and interestingly entwined. In the present context, conceiving of language in terms of affective, signifying relations between individuals who are themselves essentially, or naturally relational helps us to understand Spinoza’s writings themselves as linguistic texts that nevertheless work practically to reorient language towards its intrinsically formal dimension.

It is helpful here to turn to the interpretation of Spinoza advanced in Nielsen’s detailed study, Interpreting Spinoza’s Arguments.84 According to Nielsen, Spinoza’s geometrical order of presentation and his affective-materialist conception of language work together to transform natural language use itself into the mimesis of a formal language. Nielsen’s reading of linguistic practice in the Ethics finds in the text’s logical form a kind of ethical prototype that anticipates the formal systems of logic developed by later analytic philosophers. Notable is Nielsen’s reduction of this logic to practice. Nielsen understands Spinoza’s use of the geometrical method as an attempt (p.49) to produce within an inherited Scholastic Latin vocabulary something akin to the formal deductive systems that were only to emerge much later in the early twentieth century and that have become ever more sophisticated up to our current day. For Nielsen, Spinoza’s aim in producing a deductive system was to pass from the ambiguities inherent within conventional language to the unqualified, formal certainties of logic. Thus, Nielsen’s abstraction of a formal method from the Ethics provides a thoroughgoing critique of the linguistic form of the Ethics itself. In Nielsen’s view, ‘[Spinoza’s] usage was meant to help readers escape being trammeled by their ordinary verbal meanings (affects), and so to enable them to undertake the attempt at thinking along the same deductive lines as Spinoza thought he had been following in his writing.’85

Yet Nielsen emphasises that Spinoza is not only producing a formal logic, but intends by means of this logic to be able to reach scientific truths about the actual world. Formal truth and referential truth must thus somehow coincide, despite Spinoza’s distinction between true and adequate ideas. Nielsen writes:

Spinoza had to solve two problems. Besides discarding ordinary usage, he also had to provide referents for his theory of mind. He tried to solve the first problem by turning his Latin into a predecessor of a formal system. The second problem he believed would disappear the moment one would realize (and utilize) the concurrence of logic and science. Whenever usage is logical it will, simply by its being so, enable users to speak (and think) of real existing physical events.86

This coincidence of logical form and epistemological reference is supposed to be guaranteed both by the parallel postulate and by the doctrine of the common notions. Thus, Nielsen sees Spinoza as presenting a form of logical realism – logical and natural truths straightforwardly coincide. To think according to the formal demands of logic is necessarily to come to correct conclusions about actual states of affairs.

For Nielsen, formal logic empowers its users to critique and modify their linguistic practices, particularly the ways they relate linguistic utterances to specific meanings. Nielsen views Spinoza’s overall method as a self-reflective process through which the pre-critical use of meanings becomes thoroughly sceptical. Thus students of formal logic would ‘conceive of verbal meanings, not as objects to be understood, but as transitions in our mental dispositions’.87

(p.50) To make sense of this, Nielsen shows how Spinoza’s Ethics deals with language on two distinct levels. It provides, first and foremost, a unique theory of mind in which linguistic meanings must be construed according to Spinoza’s doctrine of ideas. Nielsen calls this the ‘essential part’ of Spinoza’s notion of language, distinguishing from this a conception of linguistic usage or practice that he calls a ‘minor part’.88 These two levels of meaning and usage interact at the heart of the argumentative structure of the text of the Ethics itself. Nielsen thus reads the Ethics as an endlessly self-deconstructing text.89

On the basis of the theory of meaning and that of usage, a theory of verbal meaning may be constructed according to which natural language meanings come out as initerable and affective events. Applying this result to Ethica itself, a text of a, once, very natural language, would make what Ethica might mean an ever changing subject inaccessible to reason (cognition).90

In other words, by taking the Ethics to be a kind of formal, interpretive operation that converts natural language meanings into unrepeatable, affective events and by then treating the text of the Ethics itself as the object of this same operation, the ‘meaning’ of the Ethics dissolves into a series of discontinuous and self-contradictory happenings. The Ethics thus becomes a complex version of the ‘liar’s paradox’ in which an inhabitant of Crete exclaims that all Cretans are liars, although at a practical rather than theoretical level.

If this were the last word in interpreting the Ethics, then we would be left with a thoroughgoing scepticism with respect to its practical sense. Yet Nielsen does not use this as an argument against the cogency of Spinoza’s argument. Instead, he sees this paradox – and Spinoza’s own recognition of it – as the root cause of Spinoza’s use of the geometrical method of demonstration as the form of his reasoning. Because Spinoza was aware of the inevitable ambiguities of natural language and was striving for the kind of knowledge represented by mathematics and exact physical science, Nielsen argues, he embedded his natural language assertions in a complex and self-critical logical structure that undoes natural language meaning at every step. In this way even while the natural language ‘sense’ of the text negates itself, the Ethics’s logical form remains intact and indeed positively and progressively infiltrates the cognitive practices of its careful readers somewhat as sketched in Figure 1.3. Nielsen writes, (p.51)

Spinoza and Relational Immanence

1.3

In my opinion, Spinoza clearly realized this implication of applying the theory of Ethica to Ethica itself as a text of natural language. He was aware of the self-defying nature of his theory, but believed that he could counteract it by installing in the Latin of his text the semblance of a logical structure.91

The logical structure Nielsen refers to is not simply the axiomatic-deductive system that Spinoza borrows from Euclid. It is, more importantly, the self-referential logic that allows the Ethics to refer to its own natural language practices at the same time that it undermines them. Nielsen goes on to remark that ‘[Spinoza’s] idea was brilliant, but […] the logic of the time was not ripe for his design.’92

According to Nielsen a proper reading of Spinoza’s Ethics from the standpoint of its own theory of meaning is directed teleologically towards overcoming meaning as such. In Nielsen’s view, only the well-formed and logically precise statements of science are capable of being used in a rational (and repeatable) way without attributing meanings to those statements:

If the acts of ordinary verbal meaning are inherently initerable – as I believe they are – then obviously we cannot make them iterable without thereby changing them into something which cannot be verbal meaning anymore. But what we can do is use our acts of verbal meaning as gradual preparations for one day dispensing with verbal meanings altogether.93

In Nielsen’s view, Spinoza was motivated by the desire to produce a formal system along the lines of contemporary second-order (p.52) symbolic logic, and while the Ethics itself is not adequate to that desire, we as later readers benefiting from the developments in logic over the past three and a half centuries (especially the last hundred years) may be able to reconstruct an Ethics closer in fact to Spinoza’s own intentions.

Nielsen’s analysis reveals the practical mechanism in Spinoza’s text (self-reflective scepticism) that produces the effect of impersonal discourse and impels both logical formalisation and a negation of ordinary language use. In evacuating meaning, Nielsen’s Spinoza abstracts philosophy from the context of interpersonal address and response. The problem is that logical formalism – while generated initially out of a natural language context – appears capable of transcending that context to the point of annulling it.

Nielsen’s study reveals something interesting and important about the mixture of natural language meaning and formal structure in the Ethics. His analysis shows that a basic incongruity holds between the two domains, and more importantly it traces how this incongruity is demonstrated or performed in the text itself by referring the text’s meaning in part to the logical structure that frames it and by taking the text’s logical structure as operative on the natural language meanings that it frames. Yet Nielsen never conceives Spinoza’s project in terms of its own concrete initerability, in particular its momentous contributions to transformations in the actual cultural and historical field within which Spinoza himself worked.

Whether or not Nielsen’s reading is ultimately successful, we must stress the limits within which his reading moves. Nielsen’s bias is that of the formal logician for whom logical rigour is a basic criterion and goal. As a frame for his entire analysis Nielsen explicitly limits himself to the second kind of knowledge, claiming ‘We want no truck with infinity, nor any other merely abstract entities; neither could we afford one, lest we jeopardize the whole idea of our investigation.’94 To repeat, the ‘whole idea’ of Nielsen’s investigation is to find in Spinoza’s Ethics a mode of practical understanding that would escape the equivocal senses of everyday language. In short, Nielsen brackets the infinite at the same time and with the same gesture by which he brackets the singularly concrete (the ‘initerable’). Both are a function of the ambiguities of natural language meanings. What Nielsen demonstrates with extraordinary rigour in his study (and the detail of his analysis can scarcely be indicated here) is that a formalist reading of the practical logic (language as use) inherent in the Ethics can be both consistent with Spinoza’s text and highly relevant to current debates (p.53) concerning the rigorous use of symbol systems in scientific practice when restricted to this domain. Yet to limit oneself to what Spinoza calls the second kind of knowledge (adequate but merely general ideas) is to limit oneself to only part of the Ethics. Spinoza’s text also refers to and makes use of the third kind of knowledge, and it is precisely here that a wedge may already be inserted into the apparently formal and logical closure of Spinoza’s text.

Spinoza’s Third Kind of Knowledge

In early 1678, less than a year after Spinoza’s death, a coterie of his friends published and distributed his Opera Posthuma with the Ethics included, the author’s identity indicated only by the initials ‘B. D. S.’95 With this act, the Ethics, the culminating product of decades of Spinoza’s solitary thinking, intensive study and dialogue with others – the three primary foci of his intellectual life – passed beyond the limits of his own immediate world and became part of a larger cultural and intellectual heritage.96 Today Spinoza is read and discussed in dozens of languages throughout the world. In the passage from the personal, individual and regionally limited to the public, historical and globally connected we may recognise a familiar figure of the modern notion of reason. Seen in light of the subsequent developments of philosophy, Spinoza’s work may appear as a constitutive factor in the turn to such a view of modern reason. Is this image of reason valid? Is it applicable to Spinoza’s Ethics?

As we have already seen, the ethical consequences of Spinoza’s thought appear first of all as a problem implicated in the very form of Spinoza’s discourse. The way Spinoza’s text presents itself to be read implies certain specific interpretive practices. This is evident particularly in the system of axioms, definitions and theorems that constitute the Ethics’ ‘geometrical order’. The form of the Ethics implies an ethics of interpretation.

The interpretive practices entailed by the Ethics’ discursive form are closely linked to Spinoza’s notion of reason, ‘the power of the intellect’.97 For Spinoza, reason entails freedom. Part Five of the Ethics, according to Spinoza’s preface, ‘concerns the means, or way leading to freedom’, a path he outlines in an exposition of the intellect’s power over the affects and an examination of ‘what kind of dominion it has for restraining and moderating them’.98 It is important that this dominion of the intellect over the affects is by no means absolute.99 The practice of reason takes place always in a shifting (p.54) context of affective life and contingent events. While reason may develop general principles of conduct on the basis of experience and inference, the practical application of reasonable principles remains contingent upon the specifics of individual cases.100 This is clear from Spinoza’s discussion of maxims from later in Part Five:

The best thing, then, that we can do, so long as we do not have perfect knowledge of our affects, is to conceive a correct principle of living, or sure maxims of life [certa vitae dogmata], to commit them to memory, and to apply them constantly to the particular cases frequently encountered in life. In this way our imagination will be extensively affected by them, and we shall always have them ready.101

The role of Spinoza’s Ethics as a whole may be understood as that of a complex maxim of this type, and the problems involved in its interpretation and application need to be understood accordingly. The use of general maxims in handling particular cases recalls the Aristotelian problem of phronesis.102 As Aristotle recognises, the philosophical investigation of ethics ‘does not aim at theoretical knowledge’ since ethics is by nature oriented towards something other than knowing a subject matter. Ethics is a matter of practical self-transformation: ‘we are inquiring not in order to know what virtue is, but in order to become good’.103 In this regard, any discursive presentation of ethics is confronted with a kind of paradox: what is said is typically general; what is done is always singular. Aristotle recognises the difficulty of providing a theoretical account of particular practices, ‘for they do not fall under any art or precept but the agents themselves must in each case consider what is appropriate to the occasion, as happens also in the art of medicine or of navigation’.104 Even a philosophy that posits or produces theoretical certainties still finds itself irremediably unsure in confronting the contingencies of practice.

The Ethics must be applied, and the means of application are themselves part of the subject matter of ethics as a mode of philosophy. How are we to conceive of a mode of relation comprehending both the specific interpretive difficulties of Spinoza’s text and the problem of practical application in general? By examining the problem of language and signification under the aegis of Spinoza’s immanent and relational ontology, we have been led naturally to a broadly pragmatic conception of signs and meaning. Epistemology in Spinoza is integrated into ontology, and knowledge is always a (p.55) matter of power and processes of individuation. Conversely, for Spinoza, ontology is essentially epistemic. What is, precisely in the degree and amplitude of its being, knows.

In Part Two of the Ethics, Spinoza distinguishes three kinds of human cognition, or knowledge (cognitio).105 What differentiates the three kinds is the manner in which they are formed or received by the mind. The first kind of knowledge arises either (1) ‘from singular things which have been represented to us through the senses in a way which is mutilated, confused, and without order for the intellect’, which Spinoza calls ‘knowledge from random experience’; or (2) ‘from signs, for example, from the fact that, having heard or read certain words, we recollect things, and form certain ideas of them, like those through which we imagine the things’.106 Either of these sources leads to potentially faulty judgements which Spinoza designates with two names, opinion and imagination. The second kind of knowledge, in contrast to the first, arises ‘from the fact that we have common notions and adequate ideas of the properties of things’.107 This Spinoza calls reason. Finally, the third kind of knowledge ‘proceeds from an adequate idea of the formal essence of certain attributes of God to the adequate knowledge of the essence of things’.108 Spinoza’s name for this highest sense of knowledge is intuitive knowledge.109

The basic sense of Spinoza’s first and second kinds of knowledge is clear enough. To know that Ulaan Bataar is the capital of Mongolia because the atlas says so and to act on that knowledge – say, to buy an airline ticket with the intention of travelling there – is to follow the first kind of knowledge. To understand gravity by investigating the common properties of falling bodies or to comprehend a general theorem of geometry is to know according to the second kind of knowledge. The sense of the third kind of knowledge is less clear.110 When do we as knowers ‘proceed from an adequate idea of the formal essence of certain attributes of God to the adequate knowledge of the essence of things’, and in what sense would this knowledge be intuitive? Despite its initial appearance in Part Two, the third kind of knowledge plays no explicit role in the Ethics until it reappears in Part Five. There, in the context of Spinoza’s discussion of active freedom, immortality and the ‘intellectual love of God’, the third kind of knowledge appears in the following affirmation: ‘The greatest striving of the mind, and its greatest virtue is understanding things by the third kind of knowledge.’111 In other words, the third kind of knowledge would constitute a maximum for the mind’s (p.56) desire and its power. The sense of this maximum is then explicated as a relation between the unique essences of singular things and the singular idea Dei. In any case, it is clear that the difference between the second and the third kinds of knowledge is relevant to Spinoza’s discussion primarily (if not solely) in Part Five where Spinoza provides his image of human freedom and offers his view on human immortality. Evaluation of the third kind of knowledge usually goes hand in hand with how these issues are interpreted and understood.

In Part Five of the Ethics, after having clarified the famous third kind of knowledge which manifests ‘the greatest striving of the mind, and its greatest virtue’,112 Spinoza shows that in so far as this third kind of knowledge provides knowledge of singular things, rather than rational generalities, it provides especially powerful ways of affecting the mind. In proposition 36, we read:

The mind’s intellectual love of God is the very love of God by which God loves himself, not insofar as he is infinite, but insofar as he can be explained by the human mind’s essence, considered under a species of eternity [sub specie aeternitatis]; that is, the mind’s intellectual love of God is part of the infinite love by which God loves himself.113

The point to stress is that Spinoza makes a distinction here between God’s self-love as infinite and God’s self-love ‘insofar as he can be explained by the human mind’s essence’. Only the latter is accessible to and realisable by the finite intellect. The finite intellect participates in God’s own self-love by means of the third kind of knowledge – the ‘intellectual love of God [amor intellectualis Dei]’. This form of knowledge knows singular things sub specie aeternitatis, that is, it knows them not as possible or merely represented, but as actually and singularly existing and therefore, by means of God’s essence as the necessary cause of all that exists, as necessary in God. Spinoza makes this clear in the demonstration of proposition 30. There he writes:

Eternity is the very essence of God insofar as this involves necessary existence (by ID8). To conceive things under a species of eternity, therefore, is to conceive things insofar as they are conceived through God’s essence, as real beings, or insofar as through God’s essence they involve existence.

‘Knowledge through singular things’ would seem to suggest a discrete subject knowing discrete, particular objects, but by using the context of Part Two of the Ethics to refigure here the apparent (p.57) meanings of Part Five, this phrase comes to stand for an immediate and active knowledge through the affects by which one has been individualised. Scientia intuitiva is not the intellectual cognition of an intelligible object, but rather the affection of active and communicative relations with other individuals. The third kind of knowledge is the very act of becoming a (relative) individual in and through certain kinds of relations. The passage into modes of relationality ‘conceived through God’s essence’ constitutes the third kind of knowledge.

Spinoza makes clear that knowledge of the third kind – intuition through singular things – is to be cultivated by the wise person even above knowledge of the second kind, or reason (which is itself universally true and indubitable). General reason – due to its necessity and thus its power to resist transitory affections – can provide the source for relatively strong affects.114 Yet the third kind of knowledge is even more powerful and therefore more excellent. Spinoza shows ‘how much the knowledge of singular things I have called intuitive, or knowledge of the third kind (see IIP40S2), can accomplish, and how much more powerful it is than the universal knowledge I called knowledge of the second kind’.115 In a remarkable moment of textual self-reflection, Spinoza uses his own treatise as an example:

For although I have shown generally in Part I that all things (and consequently the human mind also) depend on God both for their essence and their existence, nevertheless, that demonstration, though legitimate and put beyond all chance of doubt, still does not affect our mind as much as when this is inferred from the very essence of any singular thing which we say depends on God.116

In other words, knowledge of generality cannot affect us as powerfully as knowledge through singularity. Importantly, such singularity must be instantiated directly in concrete relations. It can only be indirectly mediated by the representational powers of language that always generate the appearance of separating what words are from what they do. For similar reasons, singularity cannot be formalised adequately in any system of merely general relations. There is no illustrative example of such a singularity outside of a determinate function in a determinate context that is knowable only from within that context – in this case, Spinoza’s own treatise. This would apply first of all to the interpretation of the Ethics itself. It has the structure of an immanent sign. Despite Spinoza’s own disparaging remarks (p.58) about using signs, the third kind of knowledge involves semiotic functioning.117

Although the knowledge gained in Part One of the Ethics concerning the nature of God is beyond doubt, it remains only knowledge of the second kind and its affective power for particular human beings is relatively limited. Any reader of the Ethics – or community of readers – will understand the text primarily as signifying a set of interrelated claims. After having passed through the analyses of the affects in Part Two, however, and having come to understand the bondage of inadequate ideas and the liberatory and active power of adequate ideas in Parts Four and Five, the readers of the Ethics have – it can be hoped – begun to relate the general truths of Part One to their present circumstances. They will have internalised the truth of Part One in so far as it pertains to the activities of their own essence. In the case of a community, this essence involves particularly the ways and means they communicate. The affective power of this knowledge will be significantly stronger than knowledge of the second kind because its associative resonance for a particular mode is so much greater. It puts the Ethics in a role of correction, not origin.

By explicitly including the third kind of knowledge as a component of the Ethics, Spinoza challenges from within the seemingly totalising logic of a book (or a method) that would say (or do) everything. With the recognition of the third kind of knowledge, Spinoza acknowledges the limits of his own text. Or, if one prefers, the text calls itself into question by indicating an even more powerful potential. Only by entering into contingent relations with the ideas and practices of separate individuals is the Ethics capable of engendering the third kind of knowledge. By holding room for a level of knowledge (and experience) that is neither in conflict with the general truths of the second kind of knowledge nor reducible to them, Spinoza’s text remains communicatively open. Rather than simply reiterating a universal logic, it also holds itself accountable to unforeseeable communication with other discourses.

Garrett interprets the third kind of knowledge in terms of Spinoza’s geometrical method and the inferentialism it implies.118 The Euclidean method of geometrical proof constantly uses inferences that may be drawn from the construction of geometrical figures. A circle, for example, may be defined as the set of points in a plane equidistant from a given point. Yet this description – more precisely, this construction – necessarily implies other properties that (p.59) may not be immediately apparent (such as the property that given any two straight, intersecting line-segments the endpoints of which are on the circle and which do not pass through the circle’s centre, the line-segments will not bisect one another).119 Some of these properties may be counter-intuitive and surprising. Only by carefully following the steps of the relevant proof does the entailment of the property by the original construction become apparent. One of the pleasures of geometry is coming to understand how numerous and complex are the properties implied by even the simplest geometrical forms. In an analogous fashion, Garrett reads Spinoza as saying that ‘the transition toward the third kind of knowledge is the recognition of how our minds are eternal in and through what follows from them’.120 For Garrett, the structure of the Ethics itself is irregular, with ‘certain crucial ideas’ having greater weight and value than others, particularly the ‘idea of God’ [idea Dei].121 These salient ideas are rich with implications and entailments. In them are consolidated and condensed (Spinoza uses the verb involvere) many other ideas and the various series of consequences following from them. For Garrett the third kind of knowledge would consist in an intuition of the implicit consequences of our ideas, consequences that may not be apparent immediately. The third kind of knowledge would involve comprehending in a practical manner how effects are generated out of causes in the form of entailments made explicit through relational constructions – diagrams – and how, in particular, such consequences are entailed by the ideas that compose our own minds. To think according to the third kind of knowledge would be to enact and to understand the singular effects of our ideas and simultaneously to understand ourselves through the diagrammatic effects our ideas and actions imply.

Read on the basis of the third kind of knowledge, the Ethics is thus transformed from a representational and explanatory system, a theoretical model of everything that is, to a pragmatic tool, a corrective instrument of thought and practice. Here the therapeutic dimension of Spinoza’s text comes to the fore. Singular forms of thought and practice may use the Ethics (or rather, the forms of thought it entails) to clarify and correct themselves relationally. The geometrical method of presentation indicates a clear direction for expounding philosophy in a practical and immanently relational mode, but in Spinoza’s own text it is perhaps not yet a methodological tool fully adequate to its purpose. Spinoza’s is a diagrammatic metaphysics that still at least partly seeks its most effective expression.

Notes:

(1.) Benedict Spinoza, Ethics Ia6, IId4. Spinoza clarifies: ‘I say intrinsic to exclude what is extrinsic, namely, the agreement of the idea with its object’, E IId4, exp. All citations from the Ethics – hereafter abbreviated ‘E’ – are from Edwin Curley’s translation, with the standard form of reference to Spinoza’s text by part number in Roman numerals, ‘a’, ‘d’, ‘p’ and so on to represent ‘axiom’, ‘definition’, ‘proposition’ and then final number.

(2.) E IIp49. Ultimately for Spinoza ‘[t]he will and intellect are one and the same’. E IIp49c. Michael Della Rocca has analysed this proposition in detail, particularly with respect to the divergences it implies from Descartes’ thinking, in ‘The Power of an Idea: Spinoza’s Critique of Pure Will’.

(3.) E III, preface.

(4.) Yirmiyahu Yovel writes of the geometrical order as a ‘metaphor’ in this sense. See Spinoza and Other Heretics, vol. I, pp. 139–40.

(6.) Although the theme of essence and existence is an especially subtle one in Spinoza, I take the discussion in E Ip11 to be definitive: ‘a thing necessarily exists if there is no reason or cause which prevents it from existing’. Essentially, Spinoza reduces existential modality to the binary necessary/impossible and reserves essence as an incommensurable category irreducible to the possible, like Deleuze’s later concept of the virtual. A clear and relatively thorough analysis of the relevant conceptual issues is provided in Valtteri Viljanen, Spinoza’s Geometry of Power.

(7.) This reading is thus contrary to Michael Della Rocca’s emphasis on the Principle of Sufficient Reason in his Spinoza. A careful study of the problem of freedom and necessity in Spinoza appears in Henri Atlan, Sparks of Randomness, especially vol. 1, ch. 2 and vol. 2, chs 4 and 6.

(8.) E Id6.

(9.) The phrase ‘omnis determinatio est negatio’ is in fact a misquote by G. W. F. Hegel taken from Spinoza’s letter to Jelles (letter 50 in the Complete Works) that Hegel uses to critique Spinoza in his Lectures on the History of Philosophy, vol. 3, p. 267.

(11.) I have preserved the idiosyncratic capitalisation from the Latin contents page. The standard scholarly edition of the Ethics in Latin is that of Gebhardt. I have used the Gebhardt edition as it appears alongside (p.61) the French translation of Pautrat in Ethique (Paris: Seuil). References to Spinoza’s Latin throughout the following are drawn from this edition. I have preserved the ampersands but not the dropped s’s from the Gebhardt typography.

(12.) E Ip1–p15.

(13.) E Ip16.

(14.) E Ip33.

(15.) E IIp48.

(16.) E IIp49s(iv).

(17.) In this way the discussion of common notions in Part Two (E IIp37– p39) functions as a kind of prolepsis of Part Three and the succeeding parts.

(18.) See E IIIp11s and the summary of definitions of the affects at the end of Part Three.

(19.) E IV preface.

(20.) E Vp14–p36. We will examine the intellectual love of God, or ‘third kind of knowledge’, at the close of the present chapter.

(21.) Zourabichvili refers to this as Spinoza’s ‘strategy of the chimera’. Spinoza’s rhetorical strategy in this regard is analysed more fully in Rocco Gangle, ‘Theology of the Chimera’, in Smith and Whistler, eds, After the Postsecular and the Postmodern.

(22.) See, for instance, Maimonides, The Guide for the Perplexed. The Platonic and Aristotelian influences on Jewish philosophy, going back at least to the Hellenistic period with thinkers such as Philo of Alexandria, represent the confluence of the Greek philosophical and Hebraic revelatory traditions. This concern with Greek philosophy was reintroduced into Jewish thought through contact with Muslim intellectual culture in the eleventh and twelfth centuries. See Ze’ev Levy, Baruch or Benedict, especially ch. 1.

(23.) E Id3. See the discussion of the sources and sense of this definition in Wolfson, The Philosophy of Spinoza, vol. 1, pp. 61–78.

(24.) E Ip10s, Ip14c1, Ip16.

(25.) Within each attribute, the exact same necessary causal order is manifest. See E IIp7: ‘The order and connection of ideas is the same as the order and connection of things.’

(26.) In Part I substance is defined (E Id3) as ‘what is in itself and is conceived through itself, that is, that whose concept does not require the concept of another thing, from which it must be formed’, while attribute is understood (E Id4) as ‘what the intellect perceives of a substance, as constituting its essence’. There are thus infinitely many attributes (including thought and extension), but all of them express one and the same substance (E Ip11).

(27.) E IIp7s: ‘[A] mode of extension and the idea of that mode are one and the same thing, but expressed in two ways.’ The human mind is thus (p.62) nothing other than the idea (under the attribute of thought) of the human body (under the attribute of extension) in E IIp11, and furthermore ‘The mind does not know itself, except insofar as it perceives the ideas of the affections of the body’ (E IIp23). See also E IIp13.

(28.) The common notions are the primary source of such agreement. The term ‘agreement’ itself appears in a variety of contexts in Spinoza’s five-part discussion of how to live, such as in his claim that ‘All bodies agree in certain things [Omnia corpora in quibusdam conveniunt]’ (E IIp13s Lemma2). See also IIp23.

(29.) La Géometrie initially appeared in 1637 as the third appendix to Descartes’ Discours de la Méthode pour bien conduire sa raison et chercher la vérité dans les sciences. It is available in English translation with the French original en regard as The Geometry of Rene Descartes, trans. Smith and Latham.

(30.) The Geometry of Rene Descartes, p. 2.

(31.) It would be misleading to characterise Descartes’ ‘invention’ of analytic geometry as completely without precedent. Interpreting geometrical magnitudes as numbers occurs as early as Book VII of Euclid’s Elements (Def. 1 of that Book defines unit as ‘that by virtue of which each of the things that exist is called one’). Further contributions to what would become the Cartesian line of thought are to be found from the third-century bce geometer Apollonius of Perga to Nicole Oresme (fourteenth century ce) and Francois Viète (late sixteenth century). See the discussion in Edna E. Kramer, The Nature and Growth of Modern Mathematics, pp. 134–66.

(32.) Consider, in an analogous fashion, how the planar coordinate system which has become associated with Descartes’ name functions through the assignment of an arbitrary point of ‘origin’ and the fixing of perpendicular axes orienting the entire plane in definite relation to this origin. In a more metaphorical analogy, the role of l’unité in the Geometry might be compared (and contrasted) with the role of the cogito in Descartes’ general philosophical/scientific method.

(33.) E Ip15s.

(34.) The publishing world into which the Ethics entered was in many respects a new and rapidly evolving one. See Jonathan Israel, Radical Enlightenment, chs 5–7. The appearance of the Ethics in this context should be read in light of the emergence of a European and specifically Dutch ‘public sphere’ in the 1600s. For an analysis of these and later developments especially in Germany, England and France, see Jürgen Habermas, The Structural Transformation of the Public Sphere.

(35.) Although each part begins with a new set of definitions and axioms, the results of previous parts are preserved and instrumentalised in the demonstrations of propositions in succeeding parts. The form itself of proposition and demonstration remains common to all five (p.63) parts. Within the Ethics the geometrical order functions according to Spinoza’s own understanding of a ‘common notion’ as ‘equally in the part and in the whole’. See E IIp37–p39.

(36.) E Vp10.

(37.) While the Ethics is perhaps the best-known example of this form, Spinoza’s text is not unique in this regard. See the discussion in Wolfson, The Philosophy of Spinoza, vol. 1, pp. 40–7, and ch. 2 generally.

(38.) Any distinction between ordo and more is irrelevant to our purposes here.

(39.) Indeed Steinberg has argued that Spinoza’s use of the geometrical order reflects more generally a ‘nonlinear’ and ‘holistic’ conception of knowledge-justification for philosophy. Such a reading emphasises the complex, inner coherence of the constructed system of theorematic consequences rather than their relations of founded dependence upon the initial axioms and definitions. Diane Steinberg, ‘Method and the Structure of Knowledge in Spinoza’.

(40.) In this light Hampshire interprets Spinoza’s use of geometrical order in terms of a ‘rationalist’ desire common to many of Spinoza’s contemporaries, including Bacon, Descartes and Leibniz. In Spinoza this desire extends to the very form of his treatise: ‘[Spinoza] wished to be entirely effaced as individual and author, being no more than the mouthpiece of pure Reason’, Hampshire, Spinoza and Spinozism, p. 32, cited in Steinberg, ‘Method and the Structure of Knowledge in Spinoza’, p. 152.

(41.) E Vp23s. Deleuze shows how Spinoza’s notion of demonstration follows from his conception of the difference between nominal (or abstract) and real (or genetic) definitions, Spinoza: Practical Philosophy, pp. 61–2.

(42.) For a detailed study of how diagrams function in Euclid, see Reviel Netz, The Shaping of Deduction in Greek Mathematics. A related, more formal analysis of such diagrammatic reasoning from a broadly Kantian perspective is found in Jesse Norman, After Euclid.

(43.) E IIp48s.

(44.) E IIp43s, emphasis added.

(47.) Martial Gueroult, Spinoza, 2 vols. See also Pautrat’s preface to the French translation of the Ethics, Seuil.

(48.) See especially Gueroult, Spinoza, vol. 2: L’Âme, ch. 16. For a discussion of the structuralist approach of Gueroult see Deleuze’s review of the first volume of Gueroult’s work on Spinoza, ‘Spinoza et la methode generale de M. Gueroult’, in L’île Déserte et Autre Textes, pp. 202–16.

(p.64) (49.) Althusser gives an account of his own discovery of Spinoza: ‘I discovered in [Spinoza] first an astonishing contradiction: this man who reasons more geometrico through definitions, axioms, theorems, corollaries, lemmas, and deductions – therefore, in the most ‘dogmatic’ way in the world – was in fact an incomparable liberator of the mind’, ‘The Only Materialist Tradition, Part I: Spinoza’, in Montag and Stolze, eds, The New Spinoza, p. 4.

(50.) Antonio Negri, The Savage Anomaly, pp. 177 and 47. These remarks show clearly that for Negri it is less the geometrical order of presentation than the geometrical form of thought that remains essential.

(51.) Ibid., p. 47.

(52.) Derrida’s complex reading of Husserl’s On the Origins of Geometry raises similar questions in the context of phenomenology and the mathematical sciences.

(53.) Bernard Pautrat goes so far as to claim that any accessory notes or commentary on Spinoza’s text would be extraneous, just as one does not annotate a mathematical proof: ‘[O]n n’annote pas un traité de mathématique, on le lit, on tente de le comprendre, on l’assimile […].’ ‘Avertissement’ to Ethique, pp. 9–10.

(54.) Compare the notion of logical form in Wittgenstein’s Tractatus Logico-Philosophicus in which a tautological system of relations undergirds the unity of an infinite collection of worldly ‘atomic facts’.

(55.) Bennett, for instance, asks, ‘How could someone as supremely able as Spinoza have been satisfied with demonstrations so many of which are invalid and unrescuable?’ A Study of Spinoza’s Ethics, p. 27. This is not simply a rhetorical question but raises the important issue of the relation between the logical form of Spinoza’s arguments and their implicit motivations.

(56.) E V preface.

(58.) Ibid., part III. The TTP was much more widely read than the Ethics until after Kant.

(59.) See Volkmar Poppo’s negative reaction to eighteenth-century Wolffians in his Spinozismus Detectus discussed in Israel, Radical Enlightenment, pp. 542–3.

(61.) Strictly speaking, the unity of the whole of nature is deduced in the Ethics, not hypothesised. This is the function of the first fifteen propositions of Part One (E Ip1–p15). Yet this series of deductions itself follows from the set of definitions and axioms with which Spinoza begins. These axioms and definitions are themselves the conditional framework for Spinoza’s subsequent claims. Taken together, they serve as a collective hypothesis: begin here, if you would, and see what follows.

(p.65) (62.) E Ip8.

(63.) See E Id5 and Ip15. Bennett’s interpretive solution of this basic problem in Spinoza through his ‘field metaphysic’ is an initial point of reference in what follows. Bennett shows how modes for Spinoza are best conceived as adverbial properties, regional ways of being. See A Study of Spinoza’s Ethics, pp. 92–6.

(64.) See the discussion in Thomas M. Lennon, ‘The Problem of Individuation among the Cartesians’, in Barber and Gracia, eds, Individuation and Identity in Early Modern Philosophy, pp. 13–39.

(65.) Don Garrett’s overview of the question brings together the views of several other scholars, including Curley, Bennett, Lachterman, Gueroult and Matheron. ‘Spinoza’s Theory of Metaphysical Individuation’, in Barber and Gracia, eds, Individuation and Identity in Early Modern Philosophy, pp. 73–101.

(66.) Della Rocca addresses the individuation of ideas in light of concerns with knowledge and representation by coordinating two problems: (1) in what sense does a mind have an idea of some particular thing?; and (2) how is the identity of mind and body conceived with respect to the causal independence of the attributes of thought and extension? Michael Della Rocca, Representation and the Mind-Body Problem in Spinoza, esp. ch. 2, pp. 29–38. See also Robert Brandom, ‘Adequacy and the Individuation of Ideas in Spinoza’s Ethics’, ch. 4 of Tales of the Mighty Dead, pp. 121–42.

(68.) E IIp13s.

(69.) E IIp13s.

(70.) E IIp13a2’’, definition of individual. This ‘physical digression’ in Spinoza’s Ethics is analysed more fully in Rocco Gangle, ‘Theology of the Chimera: Spinoza, Immanence, Practice’, in Smith and Whistler, eds, After the Postsecular and the Postmodern.

(71.) E IIp13L1.

(72.) E IIp13L7s.

(73.) These local equilibria are typically ‘metastable’ in the sense developed by Simondon. See the discussion of this concept in Levi Bryant, Difference and Givenness, pp. 217–19.

(74.) This is in accord with Bennett’s interpretation of extended substance in Spinoza as what he calls ‘the field metaphysic’ in A Study of Spinoza’s Ethics, p. 92 and more generally, ch. 4. For a related systems-theory account of individuation in contemporary science, see Sunny Auyang, Foundations of Complex-System Theories, ch. 3 and How is Quantum Field Theory Possible, chs 19–20.

(75.) This need not imply that the levels or scales of individuating organisation are absolute (since the only non-relative scale is that of God itself, (p.66) which is ‘absolutely infinite’). For a proposal of how to reorient thinking both metaphysically and scientifically in a ‘scale-free’ manner, see Thalos, Without Hierarchy.

(76.) The question of whether it may be consistently posited that such relations go ‘all the way down’ without depending upon foundational atoms of one sort or another may be at least partially addressed mathematically in terms of the consistency of non-wellfounded models of set theory. It is a standard expedient in certain mathematical arenas to simply define the ‘content’ of any node in some system of relations as the set of its relations in the system. This fractal-like structure does not necessarily lead to any paradoxes or inconsistencies. For details, see Jon Barwise and Lawrence Moss, Vicious Circles, parts 2 and 3.

(77.) This need not imply that only potentiality is real. Affects are not merely potentials; they also directly and immediately affect and are affected by other modes. See David S. Oderberg, ‘No Potency Without Actuality’, for an interesting analysis of this problem in terms of directed graphs.

(78.) While Spinoza in the Ethics is generally dismissive of language as a dependable mode of access to adequate ideas, equating natural linguistic practice with the ‘knowledge through signs’ of the imagination, his sensitivity to the formal structures of language is evident in the detail and sophistication of his Hebrew Grammar, in Complete Works.

(79.) The Greek kategorein meant originally to accuse in the public gathering-place, the agora. The term has always retained some of this public and communicable connotation. In Aristotle, for instance, the categories are conceived as modes of discourse; in Kant, as universal structures of experience.

(80.) E IIp7.

(81.) Consider Althusser’s notion of history as a ‘process without subject’. See ‘ The Only Materialist Tradition, Part I: Spinoza’, in Montag and Stolze, eds, The New Spinoza.

(82.) A theory of the disciplinary specificity of philosophy based on a similar conception of self-reference is proffered in Thomas-Fogiel, The Death of Philosophy: Reference and Self-Reference in Contemporary Thought.

(83.) To speak in Saussure’s terms, parole here takes precedence over langue. Yet parole must be understood in this context primarily as affective rather than as representational or propositional. The problem of language’s force comes to the fore. See François Laruelle, Machines textuelles, for a rich account of this theoretical problem.

(85.) Ibid., p. 158, with ‘escaping’ in the original corrected here to ‘escape’.

(p.67) (86.) Ibid.

(87.) Ibid., p. 6. Following a parallel line of thought, Aaron Garrett has related meaning to method as the core sense of Spinoza’s philosophy. Garrett summarises his position in terms of a threefold thesis, claiming ‘that [1] Spinoza’s philosophy is a kind of self-clarificatory therapy for those capable of self-clarification; that [2] this self-clarification arises not just from reflection but also from other sorts of knowing; and finally that [3] the choice of the method by which to establish appropriate knowledge and the vehicle or means by which to present it, as a consequence, is absolutely central’. Aaron V. Garrett, Meaning in Spinoza’s Method; the citation is from p. 7 (bracketed numbers added).

(89.) Indeed, Nielsen draws explicit parallels between Spinoza’s rhetoric and Derrida’s method of deconstruction, but these are left largely undeveloped.

(90.) Ibid., p. 28.

(91.) Ibid.

(92.) Ibid. One recent innovation in logic that Nielsen marshals in his updating of Spinoza is Saul Kripke’s theoretical and notational introduction of the formal analysis of ‘possible worlds’. In accord with the reduction of metaphysical issues to questions of linguistic usage that characterises the ‘linguistic turn’ in Anglo-American philosophy, possible worlds ought to be considered merely ‘stipulations which we may make when trying to describe the use of certain utterances’. Ibid., p. 78.

(93.) Ibid., pp. 76–7, with ‘using’ in the original corrected to ‘use’.

(94.) Ibid., p. 141.

(95.) For details of the initial publishing of the Ethics, see Israel, Radical Enlightenment, pp. 285–94.

(96.) For a recent narrative of Spinoza’s life and works in the context of both his Jewish heritage and the developments of seventeenth-century Dutch economics and politics see Steven Nadler, Spinoza: A Life. For a concise synopsis of the major streams of the critical reception of Spinoza’s work from the early modern period to the present, see Pierre-Francois Moreau, ‘Spinoza’s Reception and Influence’, in Don Garrett, ed., The Cambridge Companion to Spinoza.

(97.) Title of E V.

(98.) E V preface.

(99.) Spinoza emphasises that it is not possible to overcome the affects through mere willpower. Instead, ‘much practice and application are required to restrain and moderate them’. E V preface.

(100.) In this may be seen one major difference between Spinoza and Hegel. For Spinoza the practice of philosophy is related foremost to the (p.68) individual, not to the historical movement of reason as trans-individual Spirit. This does not imply that Spinoza is insensitive to the role of reasonable practice at the level of history and politics, but it does mean that the locus of philosophy in such large-scale developments is first of all a matter of individual thought and action. For a study of some of the apparent similarities and real differences between Spinoza and Hegel, see Pierre Macherey, ‘The Problem of the Attributes’ in Montag and Stolze, eds, The New Spinoza. For studies of Spinoza’s thought linking his philosophical methods to the rise of political liberalism, see Stephen B. Smith, Spinoza’s Book of Life: Freedom and Redemption in the Ethics.

(101.) E Vp10s.

(104.) Ibid., 1104a, p. 953.

(105.) E IIp40s2. It is important to note that Spinoza uses the term cognition [cognitio] to refer not only to knowledge in the conventional sense (as justified true belief) but more generally as the act of thinking. Despite this, the Latin cognitio and its genitive form cognitionis are generally translated in English as ‘knowledge’.

(106.) E IIp40s2.

(107.) E IIp40s2.

(108.) E IIp40s2.

(109.) Scholars have debated the importance of what Spinoza calls the third kind of knowledge for Spinoza’s thought more generally. Reception of Spinoza’s third kind of knowledge has ranged from Bennett’s frank dismissal contending ‘that Spinoza is talking nonsense and that there is no reason for us to put up with it’ to Gueroult’s painstaking analysis culminating in the identification of the active power of the third kind of knowledge and the genetic method of geometrical demonstration of the Ethics itself, both of which express ‘truth in action [le vrai en action]’. Bennett, A Study of Spinoza’s Ethics, p. 85; Gueroult, Spinoza, vol. 2: L’Âme, p. 477. Between these two extremes it is also worth noting Negri’s balanced but mostly critical comments in chapter 7 of The Savage Anomaly asserting that the sequence of propositions Vp25–p27 concerning the third kind of knowledge constitute ‘a reemergence that deals with desire and hope more than it deals with the progress of the system’. For Negri, this is a drawback. For the reading considered here, it may instead be a (self-critical) strength. Wilson’s lucid analysis of the issues at stake concludes that the third kind of knowledge leaves its interpreters with ‘a riddle’: ‘What is it, exactly, to come to perceive the “inmost essences” of singular things (p.69) as they follow from the necessity of the divine nature?’ Margaret D. Wilson, ‘Spinoza’s Theory of Knowledge’, in Garrett, ed., The Cambridge Companion to Spinoza, ch. 3.

(110.) The mathematical example (based on numerical proportions) that Spinoza subsequently provides to clarify his meaning is only marginally helpful. In many respects it raises more questions than it answers. See the final paragraph of E IIp40s2.

(111.) E Vp25.

(112.) E Vp25.

(113.) E Vp36.

(114.) E Vp6, Vp7.

(115.) E Vp36s.

(116.) E Vp36s, emphasis added.

(117.) The apparent contradiction is resolved by distinguishing between dyadic and triadic models of signification (to be described in Chapter 3). When Spinoza disparages signs, it is in a dyadic sense. The third kind of knowledge is semiotic in the triadic sense.

(119.) This property is demonstrated in Euclid, Elements, Book 3, Proposition 4.

(121.) Ibid. It is worth noting in this regard what Spinoza says in E IIp8 regarding the relationship between the ideas of singular modes and the infinite idea of God, namely that due to the relationship’s very uniqueness one cannot provide an alternate example that would illuminate it: ‘If anyone wishes me to explain this further by an example, I will, of course, not be able to give one which adequately explains what I speak of here, since it is unique’ (E IIp8s). Nevertheless, Spinoza does go on to provide an example, a geometrical example that must therefore be understood analogically.