Showing posts with label Hegel and Spinoza. Show all posts
Showing posts with label Hegel and Spinoza. Show all posts

12 Jul 2010

Resonance and Phenomena: Sensations of Intensity


by Corry Shores
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[The following is material from my presentation at this year's Istanbul Resonance(s) Deleuze and Guattari conference at Istanbul Bilgi University, July 2009. I had an incredible time, learned much I now gratefully know, and I met many wonderful people. And let me also wish the best to those attending the Deleuze International Studies conference now in Amsterdam.]



Corry Shores

Resonance and Phenomena: Sensations of Intensity


Deleuze is sometimes labeled an anti-phenomenologist. And in fact we find him at times openly critical of phenomenology. This does not mean Deleuze was uninterested in phenomenal appearances. In fact, we might find that he does better to account for the phenomenality of phenomena. So instead of phenomenology’s motto, “back to the things themselves,” Deleuze would perhaps have us go “back to the phenomena themselves.” Consider how some appearances impress themselves more profoundly upon us, that is, be more phenomenal, like how shocking events are more pronounced than the other mundane appearances of that day. In other words, if we want to account for what it is that makes a phenomenon phenomenal, we might favor Deleuze’s theory, because it emphasizes the differences involved in phenomenal experiences, rather than the similarities that constitute unified phenomenal objects.

We will focus on the idea of heterogeneous quantity, which is very difficult to conceive. Normally we regard quantities as homogeneously-composed of standardized units. A meter we divide into a hundred centimeters, an hour into 60 minutes. We assume that we can continually make further standardized divisions as many times as we want. In this way, it is quantitatively homogeneous.

Now instead, we will need to form a conception of a quantity which cannot be divided ultimately or infinitely into standardized units. This would be a heterogeneous quantity, which Deleuze calls rhythm. It is composed fundamentally of quantitative variations rather than standardized units.

First we will look at Deleuze’s account of Kant’s sublime to help explain what he means by sensation in his Francis Bacon book. Yet, the Kant material becomes less helpful when Deleuze characterizes sensation in terms of waves of intensity. As a provisional solution, we will consider briefly what Deleuze has to say about Spinoza’s affect. I do not think the Spinoza material can replace the ideas that we obtain from Kant. Nor do I think that everything Deleuze says about Spinoza accords with what he says in the Logic of Sensation. I propose these Spinozist ideas so we might better conceptualize Deleuze’s notions of resonance, rhythm, and phenomena.

I suggest first some illustrations. Consider a crystal goblet resonating to a singer’s voice. The glass seems to hum and move to the sound, as though there were a harmonious relation or affinity between the voice and the crystal. But the resonating crystal bends and distorts like a liquid, being pushed-and-pulled in many different incompatible ways all at once, until it shatters into a chaos of shards. So I suggest another image for Deleuze’s resonance. Recall what happens when we try to force together two powerful magnets, same-pole against same-pole. Each makes the other tremble and shake. This is not because of some affinity, but rather on account of the oppositional forces they communicate to one another. They have a sort of incompatibility that tries to force an extent of distance between them. When we push them together, that inherent tendency-toward-distance expresses itself more profoundly in the magnet’s resonant shaking. As we reduce the extensive magnitude between them, we seemingly increase another magnitude that is somehow like distance, but which is perhaps more properly called depth. There is no spatial extent between the contracted magnets, but there is a chasm of difference implied in how forcefully they wrestle with one another. These other sorts of magnitude implicitly express themselves in extensive space and time, and yet are not found extending explicitly in either. They would be intensive rather than extensive magnitudes. The effect of such intensities could be the resonances which express these underlying incompatibilities.

For another illustration, consider when we try to focus our attention on the ticking of a clock. Normally it is in the background of our awareness. When we turn our attention to it, this ticking becomes more apparent and phenomenal. But for how long are we able to pay attention to each and every tick of the clock, before our minds begin to wander? Very quickly, the ticking disappears from the forefront of our awareness; it ceases to be as phenomenal. The ticking is homogeneous and redundant, so eventually nothing about it will stand-out. But what if the clock malfunctioned and began ticking in irregular patterns? Would it not spontaneously appear from the background of our awareness and dominate our attention?

When discussing heterogeneous rhythms, Deleuze refers us to the ideas of music composers Boulez and Messiaen. Boulez speaks of rhythm in terms of music that has an irregular pulse. He says that one way he accomplishes this is by dividing the time into such a nuanced pattern that only a machine could perform it with perfect precision. This causes the human performer to produce a rhythmic pulse that continually defies a regime of regularity. According to Messiaen, a military march is not rhythmic, because there is nothing about its regular pattern that interferes with the listener’s pulse, breathing, or heartbeats, and thus she receives no shock. He continues, “the march, with its cadential gait and uninterrupted succession of absolutely equal note-values, is anti-natural. True marching is accompanied by an extremely irregular swaying: it’s a series of falls, more or less avoided, placed at different intervals.” What seems to underlie these notions is that rhythm is characterized by motion and change; and if the same standardized patterns are repeated without variation, then the motion stagnates and loses its rhythmic feel.

In Difference & Repetition, Deleuze distinguishes between two types of repetition in music. The first is cadence-repetition, which perhaps we could associate with the normal ticking of a clock: it divides time into regular intervals and is an “isochronic recurrence of identical elements;” that is, it is made-up of equal, homogeneous metrical lengths. The other sort he calls rhythm-repetition, which perhaps we might relate to the malfunctioning clock. Its incommensurable and unequal periods create distinctive points or privileged instants. Each instant is privileged, perhaps because none can be assimilated into a common ratio that homogenizes the whole pattern. Deleuze also has us consider how Fred Astaire’s waltzing involves too much internal rhythmic variation to be reduced to 1, 2, 3; and he cites the more complex rhythmic patterns of Turkish music as another example.

Now, Deleuze explains that for Kant, there is an underlying heterogeneous rhythm responsible for the phenomena that appear to us. When our faculties function normally in sensation, the object we encounter is given to us with extensive magnitudes: it extends in space and time. Yet for Kant, the phenomenal object is not something that merely bears extensive magnitudes, it itself is a magnitude. Daniel Sutherland writes “we might think of a walking stick as having a magnitude of one meter... in contrast, Kant thinks of the walking stick as being a magnitude.” Objects appear to us with temporal and spatial features; thus, to be a phenomenal object is to be a magnitude, and we may estimate how great the extent of the magnitude is. When we confront an object, we do not grasp its extensive dimensions all at once; for, no matter how small the object is, a passage of time is required to scan its full spatial extent. It is not until we take all the extensive parts together that we comprehend the object and take it as a whole; but this is done through a succession of apprehensions of the parts which are then retroactively synthesized into a whole. The imagination does this by reproducing the representations of the previously apprehended parts and then uniting them all into a synthetic representation of the entire object.

Deleuze gives this example. When seeing a tree, we might apprehend the parts by looking first to the top, then move our eyes bit-by-bit towards the bottom, thereby assessing that the tree has a height of ten people. But when seeing the mountain behind the tree, we look-it up to the top and assess it as ten trees tall. So the unit of measure varies according to the circumstance, but in each case, it seems to be in due proportion with the object it measures. What must be involved in these acts of comprehension, Deleuze suggests, is an aesthetic comprehension of the unit of measure, based on an evaluation of the “rhythm” of the succession of apprehensions, as though they had a quantifiable rate.

Yet, as sublime experiences demonstrate, the rhythm cannot be fully assessed by an equal, steady, and consistent comparison of homogeneous parts; rather, this rhythm is continually heterogeneous and uneven. Yet there are times that, in a way, we fall to a level below our extensive units of measure, to the more catastrophic source of our phenomena, which is an irregular rhythm emerging from chaos. For Kant, we encounter the mathematical sublime when our series of apprehensions of something is greater than our capacity to comprehend them. In this case, it is boundless or too great for us to tame with standardized extensive units. Because it lacks a standard of comparison, it is incommensurable. Without a way to comprehend our apprehensions, we become disoriented from the influx of sense input that we cannot process.

Although Kant does not use this concept of rhythm, Deleuze thinks it is nonetheless implied in Kant’s sublime. But then sublime experiences only uncover the irregular rhythm already underlying the way the world is given to us. This chaos is not some exceptional circumstance, but seems instead to be the condition for all phenomena whatsoever.

We find Deleuze using these principles of rhythm, chaos, and discord when discussing the sensations that Francis Bacon’s paintings induce. Bacon does so primarily by means of his diagramming technique: when standing before a blank canvass, he faces clichés and preformed figures that his imagination projects upon the white space, which he then begins to paint. But then, he gambles, and makes random expressive strokes overtop of these imagined and proto-formed figurations, introducing catastrophe and chaos into the painting. Bacon then “reads” these expressive strokes as though they were a graph or diagram, by observing the many alternate ways that the image is tending to change. Then, Bacon develops a multiplicity of these divergent and incompossible tendencies, which deforms the figure, and causes irregularities in the way our bodies sense the painted images; in fact, our body’s organic operation can be thrown so much into disorder that it might be more properly considered a Body without Organs.

So when we see one of Bacon’s figures, what we sense is something that continually defies our attempts to recognize it. Our experience of it is one of continual variations. And it is in this way that Bacon’s works give us sensations, which Deleuze says are essentially rhythms. He writes: “in the simple sensation, rhythm is still dependent on the figure; it appears as the vibration that flows through the body without organs”. Any single figure in Bacon’s works will send an intensive wave of varying amplitudes through the disorganized Body without Organs.

He also writes that every figure is a shifting sequence or series. And also, even in one wave, he explains, there is already a vibrating resonance. Perhaps this is because the wave’s chain of varying differences are forced one-upon-another like our contracted magnets, causing the sequence to vibrate from within itself. Yet the random disruptions of Bacon’s diagram-technique often mangle two figures together. When figures are coupled in the painting, they then produce in our bodies two different varying waves. These may confront one another, and communicate their difference of level, causing both to resonate. Note also that Bacon painted a number of triple-paneled works. These triptychs, then, bring different coupled figures into relation. There then would be three layers of resonance: that within each wave, that between coupled waves, and that among the couples taken altogether. Here Deleuze borrows again from Messiaen to characterize the rhythms of the triptychs. Each figure plays one of three roles, and they continually and unpredictably exchange these parts they play, depending on how we experience the painting at any given moment. One character gives us a sense of increase, another decrease, and the third is like the point of reference gauging the relative motion of the other two. Messiaen describes them as three actors performing a play. The active character beats down the passive one, all while the attendant witnesses this violent drama.

Deleuze’s commentary on Kant’s sublime serves well to explain the role of chaos in sensation. But this account is based on Kant’s doctrine of the faculties, and it is not clear how the discord between the faculties of understanding and imagination relates to the continuous coupled waves of intensity that traverse the body without organs and whose differences in level are responsible for sensation. Perhaps we might turn elsewhere for other useful concepts, which are still relevant to our discussion regarding the way our bodies are affected by the world around us. One possibility would be to consider some of the concepts Deleuze uses when explaining affection in Spinoza. According to Deleuze’s account, things that we encounter in the world make an impression on our bodies, which as well produces an (inadequate) idea of that object in our imagination. Deleuze says: “I look at the sun, and the sun little-by-little disappears and I find myself in the dark of night; it is thus a series of successions, of coexistences of ideas, successions of ideas.” These ideas either increase or decrease our power of acting, and the variations are continuous. He illustrates in this way. We encounter Peter on the street. He is an enemy who makes us afraid. Then suddenly we turn our head to see Paul, whose charm reassures us. While moving from the idea of Peter to Paul, there was a continuous increasing variation in our forces of existing and powers of acting. Deleuze says that these variations are perpetual. He continues, “In other words there is a continuous variation in the form of an increase-diminution-increase-diminution of the power of acting or the force of existing of someone according to the ideas which she has.” He then explains, “this kind of melodic line of continuous variation will define affect”. So we see Peter, which produces an affection. It is a level of power to act. But at that moment, there is a passage of increase or decrease that causes us to feel joy or sadness. These instantaneous tendencies to increase or decrease are the affects rather than mere affections. They carry with them not just a level of power but also the forces and tendencies trying to make that level of power alter its quantity. Deleuze explains that these instantaneous passages from one degree of power to another are intensities. So intensity is not so much the total quantity of power one has at a given moment, but rather it is more like the power of the tendencies that are working to change that quantity.

Note how in Difference and Repetition, Deleuze explains resonance in the following way. First we consider a heterogeneous series. It is defined by the intensive differences between the terms within it. Then we consider two or more heterogeneous series found together. They resonate on account of the differences they communicate to one another. When two different heterogeneous series are forced together, a phenomenon flashes between them.

So we might construct the following account. Something affects us, like a figure in a Bacon painting, and it does so in a continually varying way. Its variance stems from the rhythmic heterogeneity in how we are affected by it. The diagramming technique is what prevents us from constituting the figure as a recognizable object. Nonetheless, the figure never ceases being phenomenal. This could perhaps be because the phenomena that appear to us are not objects, but are rather the shocks or flashes we undergo when something defies our expectations or when incompatible tendencies are forced together. So, by basing phenomena on difference, it appears Deleuze does well to account for what makes them so phenomenal in the first place.



15 Jul 2009

A Variation on Infinity, §11, Logic of Expression. Simon Duffy



[The following summarizes part of Simon Duffy's extraordinary book, The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze. My commentary is in brackets. Duffy's work is remarkable, so I highly recommend this book. If it costs too much, perhaps encourage your library to obtain a copy.]





A Variation on Infinity


Simon Duffy

The Logic of Expression:
Quality, Quantity and Intensity in Spinoza, Hegel andDeleuze

Chapter 1
"Spinoza from the point of view of an idealist or a materialist dialectic"


§11 The adequate and the inadequate idea of the actual infinite


Macherey follows Hegel’s translation of Spinoza’s geometrical example in the 12th letter, “The Letter on the Infinite.” There is an irregular distribution of space between lines AB and CD.

Thus there are many “inequalities of space” between the two lines.

Macherey considers them in terms of the variation that might appear if there was motion from end to end:

The ‘inequalities of the space’ should then be understood to refer to ‘the set of the differences between these unequal distances’, or, what Macherey emphasizes as ‘the variation’ of these ‘differences’, which is determined by the rotation of the segments from AB towards CD, ‘in the sense of hands of a watch’. This set, which is ‘the sum of the inequalities of distance included in this ... total space’, is a continuous and therefore infinite variation. (27bc, emphasis mine)

For Hegel, the differences are limited by the maximum, AB, and the minimum, CD. But for Macherey, the variations are limited by how much they may vary. So the difference between the length of AB and CD is the margin that limits the range of variation.

According to Hegel’s interpretation, it would not matter if the circles were concentric or not. He merely considered infinity as the infinite divisibility of continuous magnitudes. But for Macherey, the actual infinite is the infinite variation of differences in the middle-space. Substance expresses itself through an infinity of different qualities or attributes. Extension is one of them. Finite extended things, then, would be modes or modifications of substance as expressed extensionally. When we use our reason to understand the limited expanse in the geometrical example, we see that it is caused by infinite substance, and for that reason the mode itself is infinite by force of its cause. However, if we use our imagination to conceive the infinity between the limits, then we begin to imagine it being divided into smaller and smaller parts on to infinity. This would be to inadequately understand it as unlimited or indefinite. (27-28)

According to Spinoza, some things are indefinite because we cannot describe them in terms of numbers. But even though we cannot give them a number, we can still know that certain ones are larger or smaller than certain other ones. (28a)

When we conceive of the geometrical example with our imagination, we can consider it as being divisible into an infinite number of variations. Ones with a greater range of variation could then be seen as having a greater infinity of differences. Hegel thinks that this would be the bad infinite. For, to say that one infinity is larger is to indicate that it has a greater number of parts. But number does not apply to the actual infinite, so we cannot say that one actual infinite is greater or lesser than another, says Hegel. (28b.c)

According to Macherey, we encounter such contradictions when we conceive the infinite by means of the imagination, “which wants to represent everything by numbers.” (28d) However, reason can clearly and distinctly conceive the notion of the continuous without encountering paradoxes. (28-29)

Macherey disagrees with Hegel’s interpretation. For Hegel, Spinoza’s geometrical example first indicates an infinity that is a negation of the finite: when we infinitely divide something, there is always something beyond or more than the finite parts that division produces. But this is the bad infinite. When we negate this notion, we realize that the actual infinite is such because no number applies to it in the first place. So Spinoza’s geometrical example illustrates the dialectical mediation leading to the actual infinity by means of the negation of negation. [again, see this entry for more.] But for Macherey, the example depicts both infinites at the same time. For when we use our imagination, we inadequately conceive it as indefinite and unlimited. And when we use our reason, we adequately understand it as infinite by force of its cause. (29b)

So no negation is involved for Macherey. We adequately and positively know the infinite as resulting from the infiniteness of its immanent cause: substance. Hence Hegel’s formulation omnis determinatio est negatio does not apply [for more see this entry and this one.]

We only partially understand the infinite when we use our imagination. But when using reason, we may have “knowledge of the third kind.” (29-30)



Duffy, Simon. The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze. Aldershot: Ashgate Publishing, 2006.



Affirming the Infinite, §10, Logic of Expression. Simon Duffy



[The following summarizes part of Simon Duffy's extraordinary book, The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze. My commentary is in brackets. Duffy's work is remarkable, so I highly recommend this book. If it costs too much, perhaps encourage your library to obtain a copy.]





Affirming the Infinite


Simon Duffy

The Logic of Expression:
Quality, Quantity and Intensity in Spinoza, Hegel andDeleuze

Chapter 1
"Spinoza from the point of view of an idealist or a materialist dialectic"


§10 The problem of the ‘bad infinite’



Previously we discussed Hegel’s misinterpretation of Spinoza’s infinite. It is not merely the infinite divisibility of finite extensions. Conceiving it so is often the doing of our imaginations rather than our more able rational faculties.

Macherey builds from Gueroult’s commentary to argue that Hegel misses Spinoza’s point: finite things are not infinite by force of their cause. Finitely-extended modes are nonetheless infinite insofar as they express the infinite of substance, which is their immanent cause. (25c)

Macherey evokes the distinction between

1) what is infinite by its nature. Substance is absolutely infinite; and

2) what is infinite by force of its cause. The attributes or modes of substance are infinite in this way.

He further distinguishes

1) what is infinite because it has no limits; and

2) what is infinite because it cannot be determined by numbers. It is unlimited or indefinite despite the fact that it is bound within a maximum and minimum.

When we use reason, we may adequately understand things. But our imagination is inadequate for this purpose. Substance is absolutely infinite. We can only conceive it through reason, and not through imagination. We can, however, imagine substance’s affections. But when we do so, we understand them inadequately as unlimited and indefinite. Only reason can adequately understand affections as infinite by force of their cause. (26a)

Unless we maintain these distinctions, we will run into contradictions when conceiving the infinite.

According to Macherey, the bad infinite is the unlimited or indefinite. It is the same thing as the actual infinite. When using reason, we understand it adequately as the actual infinite, but when using our imagination, we inadequately conceive it as the bad infinite.

For Macherey, we adequately understand something when we grasp it affirmatively in terms of its cause. Hegelian dialectic views the infinite in terms of negations, and hence does not understand it adequately.

According to Macherey, the actual infinite, as apprehended adequately in the mode, ‘is not different to that infinity constitutive of substance, but is formally the same’. The actual infinite is therefore the immanent expression in the affections, or the finite modes, of infinite substance, which is their cause. (26-27)



Duffy, Simon. The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze. Aldershot: Ashgate Publishing, 2006.


14 Jul 2009

Good Infinities Gone Bad, §9, Logic of Expression. Simon Duffy

[The following summarizes part of Simon Duffy's extraordinary book, The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze. My commentary is in brackets. Duffy's work is remarkable, so I highly recommend this book. If it costs too much, perhaps encourage your library to obtain a copy.]





Good Infinities Gone Bad

Simon Duffy

The Logic of Expression:
Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze

Chapter 1
"Spinoza from the point of view of an idealist or a materialist dialectic"

§9 Infinite actu and the ‘bad infinite’


Hegel discusses Spinoza’s bounded infinite in Science of Logic and the History of Philosophy. And he refers specifically to Spinoza’s geometrical example in the 12th Letter.

Hegel interprets Spinoza as saying that the space between AB and CD is filled with an infinity of “inequalities of space.” (21d) One might think then that the infinite for Spinoza results when we try to count all the infinitely many unequal spaces. Just as soon as we think we counted them all, more pop-up in-between the ones we just counted. Hence this would be an infinity resulting from a continuously incomplete series. However, Hegel claims that this is not how Spinoza actually viewed infinity. For Hegel, a continuum is by nature not divisible into any number of parts. Hence, we misrepresented a continuous value when we regard it as being made-up of a determinate number of discrete elements. And there is nothing incomplete about Spinoza’s infinity, because it is all entirely there between the two boundaries. Such is the “actual infinite.” (22b.c)

So the actual infinite can be found within the finite. We would instead be dealing with the “bad infinite” if we were to think of infinity as more finite parts than can be counted. (22c)

The bad infinite is a negation of the finite, (because it says that the finite is never enough, and the infinite is always something more). The actual infinite is a negation of the bad infinite, (because it says that the infinite is found within bounds, and need not always be more more more.) Thus the actual infinite is “the negation of negation.” (22-23)

Hegel portrays mathematicians as incorrectly conceiving the infinite in the “bad” way. Spinoza thinks instead that mathematicians conceive the infinite correctly, however. He says that something is infinite for them not on account of the number of its parts, but rather because it is not expressible by any number. So we need not consider the actual infinite in terms of a contradiction or negation. It is not something that exceeds number. It is merely something that cannot be expressed by numbers. Hegel does not recognize this of mathematicians. He wants to contrast the mathematical (bad) infinite with the philosophical (good/actual) infinite. This fits his dialectical logic. The bad mathematical infinite is the first negation, and the philosophical infinite is the negation of negation.

Hence we see that Hegel misrepresents Spinoza’s characterizing the mathematical infinite as being the same as the actual infinite. Instead for Hegel, the mathematical infinite is a sort of dialectical stepping-stone leading to the philosophical infinite:

The infinite, when opposed to the finite, is conceived as the bad infinite, which is then sublated and subsumed in the actual infinite, that is, the finite realizes itself as actually infinite. This is how Hegel resolves the relation of the infinite to the finite from the point of view of his interpretation of Spinoza. (24a)

Yet Hegel’s interpretation of Spinoza’s geometrical example misses its subtle but important peculiarities. [See Macherey’s commentary.] The circles are off-set. Hegel’s rendition could also be expressed if the example were of concentric circles. For he also thinks that the infinity of points on a line also exemplifies the actual infinite. In his view, all finite things contain the philosophical infinite in this way. (24c)


Duffy, Simon. The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze. Aldershot: Ashgate Publishing, 2006.



20 Jan 2009

Simon Duffy. The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze, Chapter 1, §7 "Et determinatio negatio est"




[The following summarizes Simon Duffy's extraordinary book, The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze, Chapter 1, §7.
Duffy's work is remarkable, so I highly recommend this book. If it costs too much, perhaps encourage your library to obtain a copy.]




Simon Duffy. The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze,

Chapter 1 "Spinoza from the point of view of an idealist or a materialist dialectic",

§7 "Et determinatio negatio est"

We might say that the book lying on the table has many pages, that is, many parts, and the book itself is the whole encompassing those parts. But then we might stand further away, and take into account the whole desk with all its accompanying objects. The whole work area itself is then a whole, whose parts are the many objects contained in it and on it. We could stand even further away and consider the desk as a part of the whole office, then consider the office as a part of the whole building, then the building as a part of the whole city, and so on. [We might even venture to say that all of reality is one whole that only arbitrarily is broken into parts.] In other words, under these considerations, part and whole seem to be arbitrary divisions our mind makes for its given purposes.

Spinoza likewise does not consider parts and wholes as real things. Rather, they are useful mental fabrications, "beings of reason" he calls them. He writes in his Short Treatise:

part and whole are not true or real entities, but only things of reason, and consequently there are in Nature neither whole nor parts.

So we may consider the book as sharing a boundary with the desk. Or we may not grant such a boundary, and consider the whole work area as complete in itself, with its own arbitrarily designated boundary with the other things in the office. Each time we arbitrarily designate a boundary, we are fabricating a being of reason, rather than identifying a real being. What constitutes the boundary between the desk and the book is a negational determination: the book is not the desk and it lies outside it, and vice versa. But really there never was such an internal opposition to all of reality.

However, in our minds, we may construe such a distinction in which there is a mutual negational determination. Hence Spinoza in his 50th letter to Jelles writes determinatio negatio est. [For more on this letter, see Macherey's commentary.]

As Duffy has explained, Hegel wants to write Spinoza into his dialectical history, so to render Spinoza's substance metaphysics as a lesser developed stage in his dialectical system. This turns upon Hegel's suspicious misreading of Spinoza's determinatio negatio est. Hegel reads it as omnis determinatio est negatio, "all determination is negation." This is a misleading misreading, because it suggests that Spinoza meant that for all of being, determination is negation. But really, Spinoza just meant, for only the beings of reason, determination is negation. (18c-19)

In the 50th letter, Spinoza speaks of determination when referring to figures. But Duffy shows that even Hegel himself does not consider figures as identical with the beings bearing them [see §206 of Hegel's Science of Logic.] Here is Duffy's notable contribution to this debate. He has found compelling evidence that even Hegel himself knew he had no grounds to overgeneralize Spinoza's claim.

So for Spinoza, a determinate mode is a unique entity only in our imagination. Modes are produced by substance, and modes modify substance. So in that sense modes are determined by substance. But substance is one with its modes. For, modes are immanent expressions of substance. Modal determinations are merely fabrications of the imagination.

Hence Hegel has "no justification" for interpreting Spinoza's theory of imaginary determinations as implying that all determination is negation. For, substance determines its own modes without them also negating substance. (19a.d)



Duffy, Simon. The Logic of Expression: Quality, Quantity and Intensity in Spinoza, Hegel and Deleuze. Aldershot: Ashgate Publishing, 2006.