Peirce (CP1.15-1.26) Collected Papers, V1, §1 “Nominalism”

 

by Corry Shores

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[The following is summary. Boldface and bracketed commentary are mine. Proofreading is incomplete, so please forgive my typos.]

 

 

Summary of

 

Charles Sanders Peirce

 

Collected Papers of Charles Sanders Peirce

 

Volume 1: Principles of Philosophy

 

Book 1: General Historical Orientation

 

Chapter 1: Lessons from the History of Philosophy

 

§1: Nominalism [1.15 – 1.26]

 

 

 

Brief summary:

Peirce thinks that logic is in a bad state and that this has partly to do with the philosophical history of the nominalist/realist debate. Peirce places himself in the realist camp, but in a novel way. He holds that there are three modes of being: {1} positive qualitative possibility, {2} the being of actual fact, and {3} the being of law that will govern facts in the future. “Firstness” is something being as it is regardless of what can be said of it through its interactions with other things. This mode consists of positive qualitative traits like redness, which exist primarily as possibilities that secondarily can become evident through relational interactions with other objects. “Secondness” is brute actuality, as seen when something undeniably exerts itself upon us, or when we face external resistance to our own exertions. “Thirdness” is the present givenness of future predictable conditions, knowable now on account of general laws that will probably remain in effect.

 

 

Summary

 

1.15

[Peirce sees logic as being in a bad condition, although Medieval logic was quite advanced for its time]

 

Pierce thinks recent works in logic were “in a bad condition,” and regarding philosophy, only ethics was not at that time in a bad state. 

Very early in my studies of logic, before I had really been devoting myself to it more than four or five years, it became quite manifest to me that this science was in a bad condition, entirely unworthy of the general state of intellectual development of our age; and in consequence of this, every other branch of philosophy except ethics – for it was already clear that psychology was a special science and no part of philosophy – was in a similar disgraceful state.

(p.3)

 

However, Peirce found the logic of Medieval scholars to be “marvellously exact and critical” in comparison to the “general condition of thought” (pp.3-4).

 

 

1.16

[Nominalists think that laws and general types are figments of the mind, while realists hold that they are real.]

 

This period of Medieval logic that Peirce is referring to is “the age of Robert of Lincoln, Roger Bacon, St. Thomas Aquinas, and Duns Scotus” (p.4). During this period the debate over nominalism and realism was “settled in favor of realism” (4). Peirce characterizes the positions in this way. The nominalists held that laws and general types are figments of the mind, while realists held that they are real. Yet by saying that laws and general types are real, we are working more in metaphysics than in logic. [I am not sure, but I think the next point is the following. We might have common-sense beliefs regarding whether laws and general types are real or nominal. And saying that they are real is to make a metaphysical determination. However, if we analyze the beliefs as they are as beliefs, examining their meaning, to see if they imply that laws are either objective or subjective, then we are doing logic rather than metaphysics. Let me quote, as the idea here is not clear to me. I do not know for example if by common-sense beliefs he means realist beliefs, or beliefs regardless of whether they are realist or nominalist. Perhaps the idea is that we are to put aside the realist/nominalist debate, and instead (a) explicitly state our beliefs about laws and general types, (b) do an analysis of what exactly is meant by those statements expression the beliefs to (c) determine if they imply we believe laws and general types are objective (similar to a realist view) or subjective (similar to a a nominalist view.]

But as a first step toward its solution, it is proper to ask whether, granting that our common-sense beliefs are true, the analysis of the meaning of those beliefs shows that, according to those beliefs, laws and types are objective or subjective. This is a question of logic rather than of metaphysics – and as soon as this is answered the reply to the other question immediately follows after.

(p.4)

 

 

1.17

[Scotist realists in the 14th century were in power until the humanists replaced them.]

 

In the 14th century, the political climate was such that the Scotists, who were realists, were the party in power, although there were was a small nominalist movement that was opposed to papal power and instead favored civil government. But soon there was a rise of humanism, and at the same time Scotism died out (p.4). [I might have misunderstood the history as Peirce describes it. See the text.]

 

 

1.18

[The humanists were inspired by classical nominalists.]

 

Peirce portrays the humanists as being weak thinkers, as they instead favored a more artistic style of expression and took up the “three easiest of the ancient sects of philosophy, Epicureanism, Stoicism, and Scepticism.” The Epicureans, like John Stuart Mill, “were extreme nominalists”. The Stoics were nominalists, and they did not put any stock in inductive reasoning. The Sceptics go a step further and did not believe “any scientific knowledge of any description to be possible”. This includes arithmetic, geometry, and other sorts of sciences [that we would think are possible even without inductive reasoning]. Thus Sceptics were nominalists [I suppose because they would claim that any knowledge we would possibly have would at best be unrelated to reality.] (p.5)

 

 

1.19

[This humanist trend extended into such thinkers as Descartes, Locke, Berkeley, Hume, Leibniz, Kant, and Hegel]

 

So among this Romantic movement “was a tidal wave of nominalism”. Descartes, Locke, Berkeley, Harley, Hume, Reid, Leibniz, Rémusat, Kant, and Hegel were all nominalists. In fact, “all modern philosophy of every sect has been nominalistic” (p.6).

 

 

1.20

[Peirce however is a realist.]

 

Peirce declared himself a realist in a paper published in 1871. Although he has revised his position many times since then, he still has not changed his fundamental realist orientation. And in fact, science “has always been at heart realistic, and always must be so” (6).

 

 

1.21

[Modern philosophers, who are nominalists, recognize only one mode of being, namely, existence, which is the being of an individual or fact, and it consists in the object’s crowding out a place for itself in the universe and reacting by brute force or fact against all other things.]

 

[Peirce will now describe modern philosophers as holding a core belief that to me seems to also express a realist position, so I am confused by the realist/nominalist distinction. I briefly consulted Mayorga’s From Realism to “Realicism”: The Metaphysics of Charles Sanders Peirce. The situation seems to be the following. Nominalists think universals exist merely as concepts or names, while realists think they exist in reality. Let me quote her:

The problem of universals, that is, the problem of determining what kind of ontological status universals have, has been a source of fascination and frustration for philosophers for more than two thousand years. What are universals? Simply put, they are the general concepts (or ideas or words) we develop in order to make sense of the world around us. If we want to claim to have knowledge of the world as it truly is, we need to determine exactly what kinds of things our concepts are and the connection they have with the world at large. The problem of universals deals with trying to determine the nature of these concepts, and consequently, the nature of their connection with the world.

By the 1300s, the problem had become a central one for philosophy. This was the time of John Duns Scotus, a Franciscan monk from Scotland, otherwise known as “The Subtle Doctor” because of the subtlety and profundity of his work. Duns Scotus was a proponent of moderate, or scholastic realism, as the position came to be called, which claimed that universals are somehow real. The opposing stance was nominalism, which said that universals are concepts or names (nomina in Latin, hence the term), or words, and therefore not real. For a while, the realist position was the more popular, but for many reasons, the subsequent rejection of dogmatic scholastic ideas led to the acceptance of the much simpler doctrine of | nominalism, associated primarily with William of Ockham. Scotus’s (and his followers’) abstruse and recondite style of writing did not help their case much either. Eventually, the realistic position came into such disfavor that the term originally used to simply designate the followers of Duns Scotus, the “dunces,” as they were called, eventually came to acquire the pejorative meaning it has today.

(Mayorga p.1-2)

The core belief of modern philosophers is that there is only one mode of being, namely that there are individual things or facts with their own independent existence, and these things or facts interact with other ones. Later Peirce says that realists think there are two modes of being. I am still a little confused about how to characterize realism and nominalism with regard to modes of being. Let me quote.]

The heart of the dispute lies in this. The modern philosophers – one and all, unless Schelling be an exception – recognize but one mode of being, the being of an individual thing or fact, the being which consists in the object’s crowding out a place for itself in the universe, so to speak, and reacting by brute force of fact, against all other things. I call that existence.

(Peirce p.6)

 

 

1.22

[Aristotle instead recognized two modes of being. Something is primarily in the mode of a possibility of formation, in matter, and secondarily it develops into a formation, in the mode of being called form.]

 

For Aristotle, however, there are two modes of being, form and matter. (In fact, for Aristotle there is a hint of a third mode). The mode of matter is an embryonic form of being, and matter develops to take on form. A seed for example develops into a tree, so the “being of a tree in its seed” is an instance of “an embryonic kind of being”. It can also be “the being of a future contingent event, depending on how a man shall decide to act.” [So it would seem then that matter is the primary mode of being, and the form comes secondarily, as it is the result of a development.] Realists, however, reverse “the order of Aristotle’s evolution by making form come first, and the individuation of that form come later.” [I do not follow that idea, but perhaps Peirce is saying that realists assume that something has its given form automatically and only through transformation will it change, rather then something beginning as a possibility within something else. I am guessing. So I quote:]

Aristotle, on the other hand, whose system, like all the greatest systems, was evolutionary, recognized besides an embryonic kind of being, like the being of a tree in its seed, or like the being of a future contingent event, depending on how a man shall decide to act. In a few passages Aristotle seems to have a dim aperçue of a third mode of being in the entelechy. The embryonic being for Aristotle was the being he called matter, which is alike in all things, and which in the course of its development took on form. Form is an element having a different mode of being. The whole philosophy of the scholastic doctors is an attempt to mould this doctrine of Aristotle into harmony with christian truth. This harmony the different doctors attempted to bring about in different ways. But all the realists agree in reversing the order of Aristotle's evolution by making the form come first, and the individuation of that | form come later. Thus, they too recognized two modes of being; but they were not the two modes of being of Aristotle.

(pp.6-7)

 

 

1.23

[Peirce holds that there are  three modes of being: {1} positive qualitative possibility, {2} the being of actual fact, and {3} the being of law that will govern facts in the future.]

 

[Now, although Peirce has declared himself a realist, which in light of what he just wrote should mean that he recognizes two modes of being, he now says that he in fact recognizes three modes of being.  Exactly what constitutes the realist position is not entirely clear to me so far. Peirce is perhaps outlining a new sort of realism.]

Peirce thinks that there are actually three modes of being: {1} positive qualitative possibility, {2} the being of actual fact, and {3} the being of law that will govern facts in the future. He says that we can directly observe these modes of being in whatever we might be turning our attention to.

My view is that there are three modes of being. I hold that we can directly observe them in elements of whatever is at any time before the mind in any way. They are the being of positive qualitative possibility, the being of actual fact, and the being of law that will govern facts in the future.

(7)

 

 

1.24

[Secondness (the second mode of being) is brute actuality; it is the undeniability of other things acting upon us and affecting us; and we experience it also when facing an exterior resistance to our actions.]

 

Peirce begins with the second mode of being, which he said above was “the being of actual fact”. When something is actual, that means it happens at some time and at some location. So it has that sort of specificity [which obtains its determinate specificity by comparison with its relation to other times and locations.] For this reason, an event’s actuality consists in its relations to all other existing things in the universe. Moreover, actuality is “brute” in the sense that it has an undeniability to it, on account of the fact that when something really is acting upon us and effecting us, we cannot just wish that influence and contact away. We experience in the mode of encounter this second mode of being when we feel resistance against our activities.

Let us begin with considering actuality, and try to make out just what it consists in. If I ask you what the actuality of an event consists in, you will tell me that it consists in its happening then and there. The specifications then and there involve all its relations to other existents. The actuality of the event seems to lie in its relations to the universe of existents. A court may issue injunctions and judgments against me and I not care a snap of my finger for them. I may think them idle vapor. But when I feel the sheriff's hand on my shoulder, I shall begin to have a sense of actuality. Actuality is something brute. There is no reason in it. I instance putting your shoulder against a door and trying to force it open against an unseen, silent, and unknown resistance. We have a two-sided consciousness of effort and resistance, which seems to me to come tolerably near to a pure sense of actuality. On the whole, I think we have here a mode of being of one thing which consists in how a second object is. I call that Secondness.

(7)

 

 

1.25

[The first mode of being (firstness) is something being as it is regardless of what can be said of it through interactions with other things. This mode consists of positive qualitative traits like redness.]

 

The first mode of being (firstness) is something being as it is in itself regardless of anything. But, Peirce seems to think that the second mode is a confirmation of existence, as it becomes evident to one thing that another exists. So taken all by itself, something’s existence is just a possibility that can only be actuated through interaction with other beings. Peirce says that the first mode of being is to be understood in terms of positive [and not relational] qualities. So something in its firstness can be red as a pure expression of color and not as a color that is to be understood in comparison with other colors or tones of the same color, or with other things with color. We assume that exterior objects bear this mode of firstness, because we treat them as possibly having qualities that may not even be evident to us at that moment, although they could become evident under the right circumstances. Thus exterior objects have certain positive qualities regardless of whether other objects, like we ourselves, become aware of them through our contact with the objects.

Besides this, there are two modes of being that I call Firstness and Thirdness. Firstness is the mode of being which consists in its subject's being positively such as it is regardless of aught else. That can only be a possibility. For as long as things do not act upon one another there is no sense or meaning in saying that they have any being, unless it be that they are such in themselves that they may perhaps come into relation with others. The mode of being a redness, before anything in the universe was yet red, was nevertheless a positive qualitative possibility. And redness in itself, even if it be embodied, is something positive and sui generis. That I call Firstness. We naturally attribute Firstness to outward objects, that is we suppose they have capacities in themselves which may or may not be already actualized, which may or may not ever be actualized, although we can know nothing of such possibilities [except] so far as they are actualized.

(7)

 

 

1.26

[The third mode (thirdness) is the present givenness of future predictable conditions, knowable now on account of general laws that will probably remain in effect.]

 

[The idea behind thirdness seems be the following. The future is something that now exists as possibility. But there are two sorts of possibility. There is indeterminable and determinable possibility. The third mode of being is like the determinable kind of possibility. We can safely make predictions about the future so long as there is some law or general rule in effect now and presumably also in effect throughout the future too, on the basis of which the future can be determined in the present. Let us consider a possible example. We do not know how we will die, but we do know that we will die. Our existence now has three modes of being. We express qualities that may or may not factor into the existence of other things that would be affected by our qualities or be aware of them. The second mode of our being is that about our lives which is interactive, interrelational, and interaffective with other beings. And lastly, that about our lives which is predictable like the future given now and lived now is the third mode. We might want to ignore the fact that we will die, but it is there as a predicable possibility in every moment of our living. So, one mode of our being is us existing with determinable features of our future given immanently every moment now. And this is on account of certain laws that are currently evident to us, namely, the laws of the human body’s tendency toward eventual decomposition.]

Now for Thirdness. Five minutes of our waking life will hardly pass without our making some kind of prediction; and in the majority of cases these predictions are fulfilled in the event. Yet a prediction is essentially of a general nature, and cannot ever be completely fulfilled. To say that a prediction has a decided tendency to be fulfilled, is to say that the future events are in a measure really governed by a law. If a pair of dice turns up sixes five times running, that is a mere uniformity. The dice might happen fortuitously to turn up sixes a thousand times running. But that would not afford the slightest security for a prediction that they would turn up sixes the next time. If the prediction has a tendency to be fulfilled, it must be that future events have a tendency to conform to a general rule. "Oh," but say the nominalists, "this general rule is nothing but a mere word or couple of words!" I reply, "Nobody ever dreamed of denying that what is general is of the nature of a general sign; but the question is whether future events will conform to it or not. If they will, your adjective 'mere' seems to be ill-placed." A rule to which future events have a tendency to conform is ipso facto an important thing, an important element in the happening of those events. This mode of being which consists, mind my word if you please, the mode of being which consists in the fact that future facts of Secondness will take on a determinate general character, I call a Thirdness.

(8)

 

 

Peirce, C.S. Collected Papers of Charles Sanders Peirce, Vol 1: Principles of Philosophy.  In Collected Papers of Charles Sanders Peirce [Two Volumes in One], Vols. 1 and 2. Edited by Charles Hartshorne and Paul Weiss. Cambridge, Massachusetts: 1965 [1931].

 

Also cited:

Mayorga, Rosa Maria Perez-Teran. From Realism to “Realicism”: The Metaphysics of Charles Sanders Peirce. Plymouth, UK: Lexington Books / Rowman & Littlefield, 2007. 

 

.

Somers-Hall, (Ch.1), Deleuze’s Difference and Repetition, ‘Chapter 1. Difference in Itself’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Chapter 1. Difference in Itself

 

Very, very brief summary:

Chapter 1 of DR critically examines representational systems. They are unable to describe the fundamental world of intensive variation where determinate essential distinctions do not hold. Aristotle’s representational system of genus-species classification also is not even consistent, as it requires that the fundamental category of being be univocally defined while everything else under it equivocally defined. There are four solutions to the problems of representational systems such as Aristotle’s: 1) The univocity being in Duns Scotus, Spinoza, and Nietzsche. 2) The infinite representation of Hegel’s and Leibniz’s systems. 3) The perspectivism of Merleau-Ponty’s phenomenology. And 4) The partial participations in Plato’s system of division. Of these solutions, Spinoza’s and Nietzsche’s are the most successful.

Very brief summary:
The first chapter of DR is about the inability of representational systems to be self-consistent and/or to describe the fundamental intensive layer of reality, which is unrepresentable. A system is representational if it is based on the subject-predicate structure of judgment that allows for distinctions of the type “this is not that”. Aristotle’s representational system defines things using subject-predication on the basis of the genus-species structure (a man is an animal that thinks). One problem is the highest genus, being, cannot be defined using this structure, since no genus is higher than it. Aristotle’s solution is an equivocal conception of being, where it has various senses related to each other through their relation to a focal meaning of being. But this makes his system inconsistent, since everything else must be defined univocally. There are four sorts of possible solutions to the problems of representational systems. 1) Univocity. Scotus says that our finite being is a different degree than God’s infinite being. Spinoza has one being or substance, but it is internally differentiated modally. Nietzsche sees the world univocally as being a field of dynamically related intensive power variations that only secondarily and artificially is divided into a world of distinct subjects. 2) Infinite representation. Hegel’s dialectic is an infinite movement which generates the categories of the understanding, and is thus infinite representation. However, it is based on clear-cut oppositions which our complicated and ambiguous world does not conform to. Leibniz’ monads have a representational subject-predicate form, but since they have an infinity of inter-relational predicates, it is infinite representation. Leibniz however still has the opposition difference between our world and the other possible ones. 3) Perspectivism. Merleau-Ponty teaches us that really all things are merely perspectives, and we artificially posit whole things that are opposable to others. But he centralizes the body as the origin of all our perspectives and is thus using identity. 4) Plato’s Partial Participations. Plato sees the world as being made of things which never classify cleanly, since none are fully faithful to ideal forms. However, Deleuze notes that the origin of this system is still a representational world of distinct forms rather than the immanent world of intensive variation.


Brief summary: 
The world is fundamentally sub-representational. It is a field of intensive differences. Only secondarily do we divide it up into determinate things using the representational subject-predicate structure of judgment that enables us to say ‘this is an x” and thus also “this is not that’. But Deleuze notes how such representations cannot tell us about the more fundamental unrepresentable level of the world. Aristotle’s system of classification is one way that we use representational thinking to divide the world. We divide genuses into species that differ in kind according to an essential difference, and we define any species by designating first its genus then its specifying difference (man is an animal that thinks). At the lowest level the divisions terminate with individuals that differ not in kind but in number and in accidental traits. At the highest level is being, which cannot fit the structure required by the system, since it cannot have a genus above it. Aristotle’s solution is to say that there is one focal concept of being, and it equivocally takes a number of different but related senses. This introduces inconsistency into his system, since the fundamental category is defined equivocally, but all the rest by necessity are defined univocally.  Duns Scotus’ solution is to use a univocal definition of being. He says that the difference between our finite perfection and the infinite perfection of God is a matter of intensive degrees of difference. But in the end, Scotus claims that the intensive difference between God and humanity is so great as to qualify as difference in kind, and thus it is not a fully univocal being. Spinoza, however, has a more univocal being. For him, there is one being that is internally differentiated into intensive modal variations. On the one hand these modes serve to differentiate and determine being, which is required for being to have any sense at all. However, the modes do not in reality (but only in our imagination) actually constitute distinct individuals but are rather expressions of one substance. Thus it is a univocal sense of being. Nietzsche as well has a univocal sense of being. For him, it is a mistake to see there being different subjects in the world each with moral values and obligations to other subjects. Rather, there is a field of dynamically varying intensive power relations that express as much power as they can. It is only when a weak party wants to externalize blame for their weakness that they arbitrarily carve up the world into victims and perpetrators. Seeing just a field of power relations is the nomadic view, while arbitrarily carving up that field is the sedentary view. When we take the sedentary view, we might say that one moral actor could have acted better, thus that we ourselves could have lived a better life. We would not then affirm the eternal returnability of our lives. However, if we take the nomadic view, then we think that expressions of power relations were always at their fullest, and thus nothing is wrong or missing in our lives. Hence we could affirm its eternal returnability. In this way, being is univocal (since it is one field of relations) and affirmative. The other way to avoid the problems of Aristotle’s representational system is to use infinite representation. Hegel for example sees the dialectic as an infinite movement which generates all other things. The dialectic also generates the categories of our understanding, and we use concepts and terms to represent the dialectic, and since also it is an infinite movement, it is an infinite representation. However, Hegel’s dialectic still has problems of representation. For example, it still has identities and also its notion of opposition is too crude for application in the real world where things are more ambiguous. Leibniz also uses infinite representation. For him there are an infinity of basic small parts of the world, called monads. Since these monads are subjects that are defined by a set of predicates, they are understood representationally. But since a) all monads are in relation to each other, b) also all those relations are expressed as predicates, and c) there are an infinity of such relations, the predicates of each monad are infinite. And thus this is infinite representation. But Leibniz still uses an oppositional notion of difference, since our existing world stands opposed to the inconsistent ones that God did not select. Phenomenology at first seems to present a world that is not made of opposing objects. We are never given things fully as whole objects in perception. As such, our world is made merely of phenomenal differences without opposing objects. However, phenomenology also tells us that we nonetheless posit the objects as whole things. Merleau-Ponty recognizes that fundamentally however our world is no more than a perspective. But since he places the body at the origin of those perspectives, his system is still based on a fixed identity, and thus it still is representational. Lastly, Plato’s method of division seems to avoid the problems of representation in Aristotle’s similar system of division. For Plato, things are not divided precisely, since inclusion under a type of thing is always a matter of being more or less like the ideal form for that thing. As a result, there are often imposters that get included with the better examples. The world then for Plato is one where there cannot be clear distinctions between things, since it is not always clear under which category they belong, and they can belong very well to one and just marginally well to another. However, Deleuze’s problem is that Plato traces the origin to a realm of ideas where the distinctions are clear-cut, rather than to an immanent world of intensive difference where such clear distinctions between things do not hold at this most basic level.

Summary

(1.1 Introduction) We live in a world of difference, but none of it in itself is overtly differentiated. To do this, we might designate different parts representationally by saying “this is an x” and using the subject-predicate structure of judgment. However, the grounds of representation that may explain whence and how representation comes about is sub-representational and thus cannot be represented. This deeper, unrepresentable sort of difference Deleuze wants to explore. (1.2 Aristotle’s Conception of Difference) Aristotle has a concept of difference that is bound up with this genus-species classification system. A genus is like a category, and it is divided into species, which share the general trait of the genus, but they have a specifying difference that distinguishes them within that genus. Thus difference in kind between the species is Aristotle’s notion of difference. It is an essential difference, rather than an accidental one. A genus can be a species within a higher genus, and a species can be a genus to lower species. The divisions terminate at the level of individuals, which do not differ in kind but rather they differ only in number and on account of accidental differences. (1.3 Aristotle’s Conception of Being) There is a problem in Aristotle’s system with the highest genus, being. Since there is no higher genus, it cannot be defined as being part of a group of other species sharing the same genus but differing on account of some essential distinction. Aristotle needs this concept of difference but he cannot have a higher genus. His solution is to say that there is one focal concept of being, but there are a number of senses of being that are different from one another. These different senses are like paronymous meanings, which are morphologically related but not identical, as for example ‘grammarian’ and ‘grammar’. But this solution introduces an inconsistency in the system. All species lower than being get their sense only from univocal meanings, which allow clear distinctions between species. However, the highest and most fundamental category only gets its sense by means equivocal meanings. (1.4 Duns Scotus) Medieval theologians follow Aristotle’s system, but they want to place God above being. They do this by understanding being equivocally through analogy. There is the being of our finite world, on the basis of which, we might by means of analogy understand what God’s infinite being would be like. Duns Scotus argues that this solution does not work. The only way we would be able to know that finite and infinite being are analogical is if we already knew what infinite being is like, when in fact we do not. So our own finite perfection cannot serve as the basis for knowing God’s infinite perfection. But for Scotus, the problem in these attempts that use analogy is that they assume that the finite and the infinite are different in kind, when really they are different in degree. This is an intensive understanding of the sense of being, and it allows for a univocal understanding of being. This also means that God is not higher than being, since being/perfection is not a property but rather a mode of substances. Since this is heretical, Scotus claims that since the difference in degree between God and humanity is so great, that indeed there is a difference in kind between God and humanity. Deleuze would instead prefer a more univocal sense of intensive variation. (1.5 Spinoza) Spinoza also has a univocal sense of being. For him, there is just one substance. But it is internally differentiated essentially, through its attributes, and it is further self-differentiated through intensive modal degrees of each attribute. Substance for Spinoza is not like a category that can be divided up into the individuals of the world. However, all the modes express substance modally. So even though the world may seem to be composed of many substances, there is really only one that is expressed through many intensive modal variations of it. (1.6 Nietzsche) Nietzsche also has a univocal understanding of being. We understand being as power. And the world is not fundamentally composed of distinguishable subjects. This is a fabrication created by the weak who want to externalize blame for their weakness. Instead, there are just competing forces that express themselves to their fullest. This is a nomadic view of the world, since it sees there being just a play of dynamic differential relations and not substantial things doing the actions. It is also affirmative, since in these relations the power is affirmed as much as it can be. The sedentary view instead sections-off parts of the field of dynamic differential relations and designates subjects with moral values. The more one such partition dominates another, the more it is said to be immoral. Since this has a this-and-not-that structure, and since it thinks that power should be self-limiting, it is based on negation, and it is secondary to the more original field of differential power relations (1.7 The Eternal Return) We see Nietzsche’s univocity of being in nomadic distributions further expressed in his notion of the eternal return. If we section-off the world in a sedentary way that generates moral subjects, then we might say that such a subject, ourselves especially, could have made more moral choices. In that case, we would not want to live our lives exactly the same way eternally, since we could have lived it better. However, were we to take the nomadic view, where being is understood as a dynamic of intensive power variations, then we would say that nothing could have been better, and thus we would affirm the eternal returnability of our lives. (1.8 Infinite Representation) We just saw how the univocal understanding of Being can remedy the problem of Aristotle’s system. Deleuze says another way is an infinite representation. A finite one uses limits to determine things. Infinite representation sees all things as existing moments of an infinite concept that encompasses everything. (1.9 Hegel) Aristotle’s system is finite representation, since it fixes everything in a stable system definitional limits. Hegel’s dialectic is an infinite movement. And since it generates the categories that we use in representational thinking, it is thus infinite representation. But there are still problems with it. 1) The source of the dialectic movement is not representable. However, Hegel represents it with concepts and terms. 2) Hegel’s infinite has a pattern-instance structure that is similar to Aristotle’s genus-species structure. Thus, Hegel does not get rid of a central identity. 3) Hegel’s basic structure of opposition is too crude to apply to the real world where there is much more ambiguity, overlap, mixing, etc. (1.10 Leibniz) Leibniz also has an infinite representational system. For Leibniz, the world is made of an infinity of parts called monads. Each has predicates which define it. Thus the world conforms to the subject-predicate structure of representation. However, each monad is related to the infinity of other ones. And for each such relation it has a predicate expressing that relation. Thus each monad has an infinity of predicates, and therefore it is infinite representation. Since in Leibniz’s world there are so many coexisting differences, we might think that he is operating using a non-oppositional notion of difference. However, he also thinks that this world stands opposed to other inconsistent worlds which were not chosen by God to be. So his system does have oppositional difference. (1.11 Phenomenology) Phenomenology offers a possible way to see the world as being composed of non-oppositional differences. Our knowledge of things in the world is always partial, since our perceptions are limited by our spatial and temporal perspectives. It would seem then that we only see the world in a fragmentary way, where there is a field of phenomenal differences, but no different things with their own determinate limits. However, phenomenology also tells us that we posit the fragmented things as whole things, thereby placing them into oppositional relations with other posited things. Merleau-Ponty recognizes this, and his phenomenology might also be based not on identity; however, because our body is for him always the center of perception, his system is based on a fixed identity. (1.12 Plato) Plato’s method of division might also seem at first to improve upon Aristotle’s system and to regard the world as composed of non-oppositional differences. For Plato, we can classify by dividing general groupings into more specific ones while maintaining a rough definition for the things we are trying to classify. But the divisions are not always so clear-cut. Inclusion into a grouping is relative, depending on how well the specimen is faithful to the ideal model for the thing we are trying to define and classify. Thus we can have less faithful imposters or pretenders getting mixed up with the more faithful examples. Deleuze’s problem with this system is that instead of tracing the origins to an immanent field of intensive difference, Plato instead traces them to a separate world of clear-cut Ideas.

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

 

 

 

 

 

Somers-Hall, (5.4), Deleuze’s Difference and Repetition, ‘5.4 The Three Characteristics of Intensity (232–40/291–300)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

Chapter 5. The Asymmetrical Synthesis of the Sensiblence

 

5.4 The Three Characteristics of Intensity (232–40/291–300)

 

 

Brief summary: 

Extensity, which is of the realm of the extensum, is fundamentally different from intensity, which is of the realm of the spatium. The most important difference is that intensity is more fundamental than extensity, since extensity takes on its features as a result of intensity explicating into certain extensive expressions. The main distinguishing feature is their divisibility: The extensum, as it is extensive, is a multiplicity that is homogeneously divisible, meaning that each division produces parts that are of the same nature. Two meters (of something) can be divided into two equal (and identical) parts. The spatium, as it is intensive, is a multiplicity that is heterogeneously divisible, meaning that each division produces parts that are of a different nature. Each moment, our consciousness synthesizes the past with the present into a whole mental state. But each successive moment of consciousness is qualitatively different from prior ones. For example, with each new note of a melody, the character of that melody as a whole changes. Were we to divide our consciousness between the way it once was when we heard a prior note with the way it is now, having heard more notes that have altered the melody’s character, we would have two parts of consciousness that differ qualitatively. Thus, they differ in nature. Deleuze emphasizes three important features of intensity: 1) because it is not metrically homogeneous like extensity, it does not divide into equal parts, and thus intensity includes the unequal in itself; 2) since an intensive difference does not involve one thing being the negation or denial of another, but rather is a matter of pure differential relations, intensity affirms differences; and 3) because it explicates into extensities, intensity is an implicated, enveloped, or embryonized quantity.

 

Summary

SH now asks, “what are the characteristics we find in intensity? We first note important differences between intensity and extensity. When you combine two extensive magnitudes, like two spatial distances, you get one whose value is the numerical total of the two. That is not how intensive magnitudes work, however. For example, if you combine fluids of different temperatures, the new temperature is not the addition but rather the average of the two. “intensity understood prior to its location in extensity will have different characteristics to extensity itself” (174). So for Deleuze, the “nature of | the extensum and the spatium as a whole are radically different,” but he also focuses on the differences between intensive and extensive elements and also the differences in the ways each kind of element relates to others of its own type (174-175). Deleuze’s account discusses cardinal and ordinal numbers, while all the while in the background is Bergson’s account of two multiplicities. [SH discusses Bergson’s multiplicities in his Hegel, Deleuze… book, Pt2.Ch3.Sb4]. For Deleuze, intensity has three characteristics: 1) it includes the unequal in itself, 2) it affirms differences, and 3) it is an implicated, enveloped, or embryonized quantity (SH 175).

1) Intensity includes the unequal in itself.
SH will follow Delanda’s analysis in his Intensive Science and Virtual Philosophy. Extensive quantities, we noted, maintain their nature when added, [and perhaps intensive quantities do not. If intensive quantities change their nature when added, I am not entirely sure how the prior example of combining fluids with different temperature applies, since I would think they keep the same nature even if they average. For, they would form a fluid with its own temperature that could be added to yet another, repeating the same process.] Extensive quantities “can be measured numerically, and […] these measurements are comparable (or commensurate) with one another” (175). [The next ideas are slightly complicated, but they are straightforward. It seems we need to establish different orders of ordinal numbers, since within each order certain values are suggested or desired, but that order cannot express them. Another order is then posited which can express those other values. So we begin with natural numbers, which do not have decimal values between them. So among the natural numbers, we have 2, 7, and 8, for example. We can divide 8 by 2 and get 4, which is also a natural number. But if we divide 7 by 2, we get something greater than 3 but less than 4. So we need to turn to another order of numbers, fractions, which would give us seven halves, in this example. But fractions do not allow all quantities to be expressed, since for example there is the value of pi, for which there is no exact ratio of integers that could express it. So we need another order of numbers, the real numbers (which will include both rational numbers, that is, those that can be expressed in fractional form, as well as irrational numbers, which cannot be expressed fractionally). So again, within each order, there is an incommensurability that cannot be expressed within that order and which thus calls for another order to express it.]

As Deleuze notes, this difference reflects one of the key features of extensive magnitudes: that they can be measured numerically, and that these measurements are comparable (or commensurate) with one another. Now, if we look just at the natural numbers (0, 1, 2, 3 . . .), we find that frequently we come across magnitudes that cannot be expressed in these terms. For instance, provided we remain with the natural numbers, we cannot divide 7 by 2, as the result is not itself a natural number. The obvious solution to this difficulty is to introduce another order of numbers that does allow us to relate these two quantities to each other, in this case, fractions. Similarly, we will discover that fractions do not allow all quantities to be related to one another, leading to the instigation of a new order of numbers: real numbers (such as √2 or π). In each case, we have an incommensurability between quantities that cannot be cancelled within the order of numbers themselves, but only by instigating a new order of numbers.
(SH 175)

[So we note that fractions proceeded from natural numbers, and reals from fractions.] Now we ask, from what order of numbers do natural numbers proceed ? (175). We turn now to the difference between ordinal and cardinal numbers. Cardinal numbers can have identities in the sense of forming equivalents and compositions. So the difference in value from one to three is the same as from two to four (175). Ordinal numbers, however, “just give us a sequence without requiring that the difference between the elements is the same in each case (thus, the difference between first and third does not have to be the same as the difference between second and fourth)” (SH 175). [Cardinal numbers can be said to have a metrical distance. For example, the “distance” between one and three is the same “distance” as between two and four. (That of course sounds right, but I wonder if numerical differences obtained through subtraction imply a geometrical sort of distance like on a number line. I guess the idea is that so long as the differences between units are standardized, that this creates a sort of metric.)] Ordinal numbers can also be thought of as having distances, but it is not metrically consistent or measurable like with cardinal numbers [so first is more distant from third as it is from second, but that does not mean we can say there is the same distance from first to second as there is from second to third.]

Since ordinal numbers do not operate on the basis of metrical units spanning between their values, “the kinds of operations we can perform with cardinal, natural numbers cannot be performed, meaning that we cannot produce equalities within this domain. Rather, it is only by the addition of a common measure between numbers (and thus the conversion of ordinal numbers to cardinal numbers) that we can begin to talk about equalising quantities” (176); [we then turn to a Deleuze quote. It seems we first need to understand the spatium as having distances enveloped in it, which might be like how the syntheses of space somehow explicate extensive space from an intensive spatium. What is happening here is a bit vague in my mind. The next thing is that when ordinals are converted to cardinals, it involves such an explication of the spatium.] “ ‘In fact, ordinal number becomes cardinal only by extension, to the extent that the distances enveloped in the spatium are explicated, or developed and equalised in an extensity established by natural number’ (DR 233/292)” (SH 176). SH continues:

We can note that, in these cases, we have a model that parallels the account of intensity we have seen so far. An uncancellable difference (intensity) gives rise to a new domain (extensity) within which that difference is cancelled. ‘Here, however, we rediscover only the duality between explication and the implicit, between extensity and the intensive: for if a type of number cancels its difference, it does so only by explicating it within the extension that it installs. Nevertheless, it maintains this difference in itself in the implicated order by which it is grounded’ (DR 232/292).
(SH 176)

We saw how heat was cancelled in its own domain of energy and temperature [but this is not a case of intensities in the intensive spatium, but rather of intensities explicated into the extensive physical world of energy transfers.] Yet, intensity is not equalized in its own domain of intensity. It can only be equalized after being explicated into the constituted realm of extensities. “Whereas in the thermodynamic model, difference is cancelled within its own domain, leading to the idea of the heat death of the universe, for Deleuze difference can only be equalised in a constituted realm, leaving it unequalised in its original domain” (176). Cardinal numbers, as we have gathered, presuppose extensive space. [I am not sure I get the next point about time and ordinal numbers. The Bergson quote seems to be saying that a succession of increasing numbers needs a spatial structure, since without it, each successive number would displace the prior and we would never have more than just one thing at a time. Then it seems SH is saying that Deleuze follows Bergson’s claim that a) cardinal number requires space, and also that b) there is a temporality to ordinal numbers, perhaps since they are understood only in terms of their succession, but I am not sure I follow correctly, and c) this temporal succession requires space. The final point that quotes from the Deleuze lecture, in the SH quotation below, I do not grasp so well. Time arises in an ordinal series. But it arises secondarily as a spatialized time. Perhaps the idea is that is that the pure form of time is somehow intensive, and in some way it is ordinal succession, and out of it somehow arises an extensive time of cardinal succession. I probably have that wrong, and even so, I do now grasp how that works. Let me quote:]

As cardinal numbers are constituted from elements that are absolutely identical with one another, they presuppose an extensive space. Bergson makes the point as follows [the following up to citation is Bergson quotation, and bracketed text within it and within the next Deleuze quotation is SH’s]:

And yet [numbers] must be somehow distinct from one another, since otherwise they would merge into a single unit. Let us assume that all the sheep in the flock are identical; they differ at least by the position which they occupy in space, otherwise they would not form a flock. But now let us even set aside the fifty sheep themselves and retain only the idea of them. Either we include them all in the same image, and it follows as a necessary consequence that we place them side by side in an ideal space, or else we repeat fifty times in succession the image of a single one, and in that case it does seem, indeed, that the series lies in duration rather than in space. But we shall soon find out that it cannot be so. For if we picture to ourselves each of the sheep in the flock in succession and separately, we shall never have to do with more than a single sheep. In order | that the number should go on increasing in proportion as we advance, we must retain the successive images and set them alongside each of the new units which we picture to ourselves: now, it is in space that such a juxtaposition takes place and not in pure duration. (Bergson 1910: 77)

Thus, Deleuze follows what he takes to be Bergson’s claim that ‘space [is] a condition of number, even if only an ideal space, the time that arises in the ordinal series arising only secondarily, and as spatialized time, that is to say as space of succession’ (L 00/00/70).
(SH 176-177)

[All this material was to explain how intensity includes the unequal in itself, but I am not sure how to sum up how that is so. I suppose that it contains the unequal within itself, because equalization is only possible when intensity is explicated and thus when it is not within itself. Therefore, it seems, within intensity is only unequality somehow. The ordinals for example do not have a standarized metric, so in a sense their differences are unequal, perhaps.]

2) Intensity affirms difference.
The first claim “aimed to show that intensity couldn’t be understood in terms of extensity” (177). The second claim is that intensity “also cannot be understood as a quality” (177). Deleuze supports this claim with another one: qualities are understood  in terms of negation, but intensity, when characterized by difference, is not understood in terms of negation. Recall how for Aristotle’s notion of definition, the difference between species involves a negation. [see again for example section 1.6, and before that section 1.2. As we noted, in Aristotle’s system of division, things are differentiated on the basis of clear defining limits that determine what is special and proper to each thing. These limits serve to define what makes one thing what it is and what makes something else not that thing but rather something different entirely, and thus Aristotle’s system makes use of negation.]

As we saw in Chapter 1, within the Aristotelian notion of definition, a difference presupposes negation. That is, when we wanted to talk about the essence of man, we did so by attributing a property to him called a difference. This difference allowed us to divide the genus into two opposed classes: the rational and the non-rational. Negation was thus fundamental to the process of definition, and to the specification of properties. We can sum up this characterisation of difference with the claim that if x differs from y, x is not y.
(177)

[For the next point, recall from section 1.4 how for Scotus, there is a difference in quantitative intensity between God’s infinite perfection and the finite perfection of our world. So also, our finite (im)perfection is not to be understood as a negation of God’s infinite perfection. Rather, we are different degrees on the same scale of the intensive variation of being. We also saw, again from section 1.6, how the negation-based models involve a notion of extensive space, since if one thing is not another, they cannot occupy the same place, whether that by physical space or a sort of “conceptual space” you might say. But intensive differences never involve one being a negation of another. I am not entirely sure I understand how to conceive intensities, unlike extensities, which I can picture in my mind more readily. I wonder if the idea is something like this: say you have two intensive magnitudes of heat, with one being greater than the other. What makes one have its own value is understood only by its relation to the other, or to some third value, perhaps zero (or becoming-zero or infinitesimally-away-from zero or something like that). Since each of the intensive values is such only in relation to the other, what defines each of them is not that one is the negation of the other, (that it is “not the other”), but instead that together they differentially relate, and it is that relation itself which defines them jointly. Perhaps one problem with this heat example I used is that differences in heat are not intensive in the way we mean it here, since they have been explicated in such a way that they may be assigned numerical values which themselves are extensive. At any rate, the next idea I think comes from a possible objection, which is that an intensity can diminish to zero, thus intensities can be negated. But Deleuze notes that when it comes to physical intensities, there is no zero value. I am not sure, but perhaps the idea is that intensities can get smaller and smaller to the infinitely small, but never to zero, and when we say ‘zero’ for some intensive value, we really mean infinitely little. I am not entirely sure why this is. Maybe it is because intensities are always the difference between values, but total zero has no value and thus it cannot enter into a differential relation with other intensities.]

As we saw in Chapter 1, this constraint on the concept of difference was not inherent to difference itself, but only difference thought in terms of extensity. Scotus’ intensive conception of difference avoided the need to define it in terms of negation. We can, in effect, note that the introduction of negation into difference rests on the need to see contrary properties as not inhering in the same object, or occupying the same ‘space’. Since intensity is prior to the emergence of both objects and (extensive) space, these restrictions do not apply to it. As Deleuze points out, even if we do look at intensity as it occurs within extensive space, we do not find the strict absence of intensity: ‘It is said that in general there are no reports of null frequencies, no effectively null potentials, no absolutely null pressure, as though on a line with logarithmic graduations where zero lies at the end of an infinite series of smaller and smaller fractions’ (DR 234/294).
(SH 177)

[The next idea is that negation can be applied to properties, but not to intensities. From the Plato example, one instance of a property seems to be ‘equal to’ or at least just physical size. But I am not sure what would be other properties. They would not for example I guess be the ones mentioned above, like frequency and pressure. They would be extensive sorts of things I suppose like spatial dimensions, and perhaps physical distributions of component parts (or maybe not, if density is an intensity). But I wonder if these properties includes color, which can be understood quantitatively (and perhaps intensively) in terms of light wave frequency or qualitatively, with each basic color being different in kind from the others (blue is not more or less of something than red is, in how it appears). At any rate, for the next idea, recall how for Plato, contrary properties, like objects that under certain conditions appear equal, and under others appear unequal, shock us to think more about the Ideas we use. Deleuze also thinks that contrary qualities have this power. Yet, Plato thinks that the shock turns our mind toward timeless Ideas. Deleuze, however, thinks that the contrary properties arise because their source is (somehow) intensive difference. Thus, these shocking moments are an invitation to think more directly about the intensive basis of thought.]

Thus, whereas negation can be applied to properties, we never actually discover the negation of an intensity, but only its difference from other intensities. Deleuze here supports Plato’s insight that the fact that objects | can possess contrary properties presents a shock capable of leading to thinking. Rather than seeing these contrary properties as leading us to contemplation of a timeless realm of Ideas, Deleuze argues that they refer us to a field of intensive difference responsible for the change in qualities we find in the world around us. What makes the qualities in becoming contradictory is that they actualise an underlying intensive difference, and it is this difference that provides the real opening to thought.
(177-178)

3) Intensity is an implicated, enveloped, or embryonized quantity.
SH explains that this third characteristic of intensity is derived from the first two. [We now make a distinction between cardinal numbers and qualities. Cardinal numbers are divisible, but qualities are not. The reason we can divide cardinal numbers is because both their unity and their division are matters of mental actions. They are unified insofar as we mentally treat the value as a whole unit, but they are divided insofar as we regard them as a collection of smaller values. There is also discussion in the quote about continuity and discontinuity. I do not follow it readily, so I will just quote it and return to it if it factors in later. The next idea is that intensity can be divided, but not like extensities can be, since intensity is not metrically homogenous.  But I do not understand how it can be divided. What we know is that if you divide an intensity, it changes the nature of what was divided, with the example being Bergson’s notion of consciousness or duration. I am not exactly sure how you divide consciousness in the first place, and then how the result of the divisions would be different in kind. Perhaps we might check section Pt2.Ch3.Sb4 from his Hegel, Deleuze book. But it gets a bit clearer when we look at the Bergson example (I am just not sure how it works for intensive things other than consciousness). He notes how if we listen to a melody, each new note or moment changes the character of the melody as a whole, just as each new moment of consciousness more generally changes the whole of consciousness on the whole. It seems Bergson gives one way in this melody example how we might divide our consciousness. He says that we can dwell on one note, while the melody continues developing in the moving present, and when we do so, we notice a difference between how the melody sounded back when that note was playing with how it sounds now, after more development has taken place. It seems then we can “divide” consciousness temporally by considering different moments making up present consciousness. What we notice is that each is different qualitatively. (One moment of the melody is not more or less than another. They instead have different characters). I am not sure Bergson would consider consciousness an intensity, but perhaps it is meant to illustrate more the idea of a type of multiplicity, of which Deleuze includes intensities, which change in nature when divided. For, SH’s next point is that the two types of multiplicity (ones that when divided produce parts that are the same in nature and ones that when divided produce parts that are different in nature) “can be mapped onto the extensive and intensive in a relatively straightforward manner” (179)]

Finally, as a third characteristic, ‘intensity is an implicated, enveloped, “embryonised” quantity’ (DR 237/297). This third characteristic is derived from the previous two. We have seen that cardinal numbers are divisible. Deleuze makes the claim in a lecture on Bergson that this is because, since they are a collection of equal units, dividing them is simply an intellectual operation [the following up to citation is Deleuze quotation]:

The divisibility of the unit; for a number is a unity only by virtue of the cardinal colligation, that is to say the simple act of the intelligence that considers the collection as a whole; but not only does the colligation bear on a plurality of units, each of these units is one only by virtue of the simple act that grasps it, and on the contrary is multiple in itself by virtue of its subdivisions upon which the colligation bears. It’s in this sense that every number is a distinct multiplicity. And two essential consequences arise from this: at once that the one and the multiple belong to numerical multiplicities, and also the discontinuous and the continuous. The one or discontinuous qualifies the indivisible act by which one conceives one number, then another, the multiple or continuous qualifying on the contrary the (infinitely divisible) matter colligated by this act. (L 00/00/70)

Qualities, on the other hand, are not divisible. It makes no sense to talk of dividing rationality, or animality, for instance. Now, intensity is not like quality, in that it can be divided. It is not composed of equal elements, however, but is rather a sequence of asymmetrical relations, such as we find with the ordinal numbers (it is asymmetrical in that second is defined by being ‘in between’ first and third, but first and third are not ‘in between’ second). Thus, ‘a temperature is not composed of other temperatures, or a speed of other speeds’ (DR 237/297). If an intensive multiplicity is not simply constituted from pre-existing elements, then division is true division, leading to a change in the nature of what is divided. Here we can turn to Bergson’s alternative form of multiplicity. For Bergson (at least at this stage of his philosophical development), this alternative form of organisation is that which we find in our conscious | states, although for Deleuze this mode of organisation is not simply a feature of our perception of the world, but rather of the world itself. As we can see, Bergson’s account of the perception of a melody presents clearly the way in which dividing non-extensive multiplicities leads to a change in their nature [the following up to citation is Bergson quotation]:

Pure duration is the form which the succession of our conscious states assumes when our ego lets itself live, when it refrains from separating its present state from its former states. For this purpose it need not be entirely absorbed in the passing sensation or idea; for then, on the contrary, it would no longer endure. Nor need it forget its former states: it is enough that, in recalling these states, it does not set them alongside its actual state as one point alongside another, but forms both the past and the present states into an organic whole, as happens when we recall the notes of a tune, melting, so to speak, into one another. Might it not be said that, even if these notes succeed one another, yet we perceive them in one another, and that their totality may be compared to a living being whose parts, although distinct, permeate one another just because they are so closely connected? The proof is that, if we interrupt the rhythm by dwelling longer than is right on one note of the tune, it is not its exaggerated length, as length, which will warn us of our mistake, but the qualitative change thereby caused in the whole of the musical phrase. We can thus conceive of succession without distinction, and think of it as a mutual penetration, an interconnexion and organization of elements, each one of which represents the whole, and cannot be distinguished or isolated from it except by abstract thought. (Bergson 1910: 100–1)

The two different notions of multiplicity can be mapped onto the extensive and intensive in a relatively straightforward manner [the following up to citation is Deleuze quotation:]

Therefore there are two types of multiplicity: one is called multiplicity of juxtaposition, numerical multiplicity, distinct multiplicity, actual multiplicity, material multiplicity, and for predicates it has, we will see, the following: the one and the multiple at once. The other: multiplicity of penetration, qualitative multiplicity, confused multiplicity, virtual multiplicity, organized multiplicity, and it rejects the predicate of the one as well as that of the same. (L 00/00/70)

These two forms of multiplicity can be related to the extensum (extensity in general), and the spatium (the field of intensive difference as a whole).
(178-179)

[Recall the three spatial syntheses from section 5.3. Quoting from our brief summary: “1) Intensive differences are localized by being distributed into various spatial locations, and they move from place to place according to how they interrelate and interact (in thermodynamics, for example, heat moves from its location to where cold is located, normally). 2) The extensive space into which these intensities are distributed and the qualities belonging to those things in extensive space come about somehow by means of intensive depth. 3) These distributions of intensities and their explications into extensive properties and other qualities continues to remain fresh and in a perpetual state of renewal.”] “The three spatial syntheses show how these two multiplicities are related” (SH 179). [It seems the idea is that they are related by the process of explication. I think I grasp what the results of explication are (namely, explicated intensities in the extensive realm, perhaps in the form of numericalized intensive properties, extensive properties, and qualities) but as a process or activity, I still do not quite understand how explication works. I have questions like, where are the deeper intensive differences that become explicated? Are they in the same location as the explicated ones? How does the transition from one realm to the other transpire? Or is it that there are extensive givens, but acting on them somehow are forces of variability, and explication is the effects of the variation?] SH concludes this section by turning us to the next one: “The final question to be addressed is how the intensive multiplicity is | related to the Idea. In answering this question, we will also have to deal with the problem of individuation, or the emergence of the subject from an a-subjective field of intensity” (SH 179-180).

 

 

 


Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

L:

Deleuze, Gilles, lecture of date 00/00/70.
French:
http://www.webdeleuze.com/php/texte.php?cle=107&groupe=Conf%E9rences&langue=1
English: 
http://www.webdeleuze.com/php/texte.php?cle=111&groupe=Conf%E9rences&langue=2


Bergson, Henri (1910), Time and Free Will, trans. F. L. Pogson, London: Allen and Unwin.

DeLanda, Manuel (2002), Intensive Science and Virtual Philosophy, London: Continuum.

 

 

 

 

 

 

Somers-Hall, (1.5), Deleuze’s Difference and Repetition, ‘1.5 Spinoza (40/49–50)’, summary

by Corry Shores
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[Henry Somers-Hall, Entry Directory]
[Henry Somers-Hall’s Deleuze’s Difference and Repetition, Entry Directory]

 

[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

 

Chapter 1. Difference in Itself

1.5 Spinoza (40/49–50)

Very brief summary:

Spinoza has a univocal conception of God/substance/being. There is one substance, but it expresses infinite essences and infinite intensive modal determinations, which are quantitative degree-variations of an essence. Thus although substance is univocally one, it is infinitely self-differential internally.

Brief summary:

Spinoza is a philosopher of univocal being, and under Deleuze’s original interpretation, Spinoza is a philosopher of univocal self-differential being. For Spinoza, there is one infinite substance, which is also both God and the world in all its entirety. Since substance is infinite, that means its essence is infinite. In fact, it has infinitely many essences. The essence as our minds understand it would be substance’s ‘attribute’. Our minds are able to comprehend just two of substance’s infinitely many attributes, namely, thought and extension (the ‘realm’ of ideas and the parallel ‘realm’ of physical bodies). There is one substance, but it expresses itself through (at least these) two unique essences. And there are infinitely more. But since there are infinitely many, we cannot characterize substance on the basis of the sum of all its essences, since there is no limit and thus no determinate totality of essence. However, each essence is different from the others. And yet, consider how all of substance’s modifications or determinations are expressed in each attribute. For one attribute to differ from another then, is for substance to internally differ from itself, since each attribute fully contains substance and yet the essences are not identical. Thus, since there are infinitely many essences that fully express all of substance’s determinations, that means there are infinitely many self-differential relations that constitute substance’s essentiality. So instead of conceptualizing substance by means of this or that essence or by means of all essences taken in sum, we can instead conceptualize substance as being infinite self-differentiation. In addition, all of substance’s modal determinations are like intensive degrees and as such are in a way part of an unbroken continuum of variation. Thus both on the levels of essence and determination, substance is a univocal multiplicity: it is one thing but it is thoroughly composed of self-variation (self-differentiation).

Summary

 

[We previously saw how Duns Scotus is for Deleuze the first major thinker on univocity. Scotus made being be a matter of degree, with God having an infinite amount of being and we a finite amount. In an Aristotelian / Aquinian system we would make God’s and humanity’s being be different in kind, since God is transcendental. Thus although we use the term being for both us and God, we are using the term equivocally. Scotus says that instead there are different degrees of being, with God having an infinite amount and we a finite. In this way, being is said of both God and humanity, but it is meant univocally. This view sees being as admitting of intensive variations.] Spinoza is for Deleuze the second major thinker of the metaphysical concept of univocity. For Scotus being is abstract, where for Spinoza it is something we encounter in life, and is thus a matter of pure affirmation. [I am not sure why Scotus would say we never encounter being in our experiences. We encounter beings, why not being? Perhaps this is because being is considered only something we can understand about beings but not directly experience in them. And what makes encountering being in life a matter of affirmation? Perhaps this results from an immanent understanding of divinity which does not deny our world any being, value, or reality.] SH will review Spinoza’s basic notions of substance, attributes, and modes. Descartes defined substance as something which depends on nothing else for its existence. Descartes thinks that for example the mind and the body are not dependent on one another for their existence, and thus they are numerically distinct substances. He even thinks that we have as many numerically distinct substances as we have minds and bodies (SH 35).  Spinoza’s definition of substance is similar. For him a substance is whatever exists in itself [that is, not as a part or attribute of something else] and is conceived in itself [that is, does not have a genus above it which is needed to conceptualize it, and it does not require any other concepts to (co-definitionally) conceive it.] For Descartes, there are numerical distinctions between the many different minds and bodies, and these are real and substantial distinctions. There really are some number of different substances. Spinoza argues against this. [Take first Descartes’ view. We have your mind and my mind. We cannot distinguish them on the basis of their attributes, since both are mind, that is to say, there is no difference attributionally. We can only distinguish them on the basis of their modalities, with this being my mind, having the attribute mind, and that being your mind, with the attribute mind. Spinoza says we cannot distinguish substances by means of modifications. His reasoning is not easy to grasp. Consult Proposition 5 of Book 1 of his Ethics. It seems he is saying the following. The conceptualization of a substance does not involve the conceptualization of other concepts, including its modalities. Therefore, if we are only able to conceive of a certain substance by also conceiving of one of its modalities, then we are misconceiving it (See Ethics Book 1, Prop. 5). Thus, we could not properly distinguish substances on the basis of their modes. We already eliminated the only other way to distinguish them, their attributes. That means that no difference between one substance and another can be conceived. It seems that we must also assume that whatever is inconceivable is impossible. Since any substance being numerically distinct from another is inconceivable, there must not be numerically distinct substances. Instead, there must only be one substance.]

Spinoza defines substance as follows: ‘By substance I understand that which is in itself and is conceived through itself, that is, that the conception of which does not require the conception of another thing, from which it has to be formed’ (Spinoza 1992: Part I D3). Spinoza is here very close to Descartes’ definition of substance as ‘a thing which exists in such a way as to depend on no other thing for its existence’. At this point, however, an important difference arises in regard to how we distinguish substances. For Descartes, the fact that a substance exists implies that it is numerically distinct from other substances. Thus, for Descartes, the mind and the body are two actually distinct substances. In fact, we have more than just two substances. Each person has a separate mind, or soul, and so there are a number of real, numerically distinct, substances which share the same attribute. How does this relate to the question of how to distinguish or determine entities? For Descartes, ‘there are numerical distinctions which are at the same time real or substantial’ (EPS 30). Spinoza disputes this claim, arguing that substances with the same attribute could only be distinguished by their particular mode (i.e. whether the substance of thought is your or my thought). As substance is logically prior to its modes, it is impossible to distinguish substances with the same attributes numerically (Spinoza 1992: Part I P5). This does not just mean that there is only one substance, but as it falls outside of numerical distinctions, substance is better described as singular (without number).
(SH 35)

We move now to attribute. “In Descartes’ terms, an attribute is the essence of a substance, so, for instance, the essence of material substance is extension. So in answer to the question, ‘what is it to be a material substance?’, we would reply, ‘it is to be extended’ ” (SH 36a). And as we saw, for Descartes, substances are numerically distinct. We would distinguish one from another merely by indexical means, for example, by saying: “ ‘this is my body, and that is yours’ ” (SH 36ab). [Here, bodies are instances of extended substances. I am not exactly sure, however, what is meant by: “Extension plays a purely definitional role in this case” (SH 36). What is being defined, and how is it being defined? It seems in this context, we define one substance as different from another, and we do so by pointing them out separately. Is that separation extensional?] But since for Spinoza there cannot be more than one substance, that means thought and extension are two expressions of being’s essence. That is to say, there is one substance that has at least these two attributes, and not many substances sharing these two attributes.

As Deleuze notes, this problem is similar to the one Scotus dealt with, namely, if God is simple (that is, not composed of parts), then how can God (understood as substance) have many attributes?  [Regarding the following, I am not certain if this is a reference to the prior section’s (1.4) ideas regarding intensive difference or if it is a general summarization of Scotus ideas we have not seen yet. The conclusion we come to is that for Scotus, the different attributes of God such as truth, goodness, and unity are somehow formal but not real features of God’s infinite being. If we are continuing with the prior ideas, then perhaps this means that intensively speaking there is no essential difference between God’s infinite goodness and our finite goodness, but our minds can make that distinction when we take into account just how very different they are in degree. Or maybe he is saying that there is no real difference between God’s goodness and his truth and unity, although there is a formal difference. I will quote it.]

Scotus’ solution was to rely on the notion of a formal distinction between the different attributes so that while they were not actually distinct as things separate from one another, they were nevertheless formally distinct in that they picked out genuine differences for reason within the infinite being. Truth, goodness and unity were therefore formally, but not really, distinct features of the infinite being (Scotus uses a similar logic for the Trinity).
(36)

For Spinoza, attributes also are formally distinct but not really distinct, since “they express the essence of the same substance” (SH 36). SH then describes key differences between Scotus’ and accounts of God’s attributes Spinoza’s accounts of God’s / substance’s attributes. Difference 1) [This first difference I do not entirely grasp, but it seems that for Scotus the attributes are not real but are rather ways that our minds understand the nature(s) of God, while for Spinoza it might be either or both subjective and objective, which may be similar to the distinction SH is making between formal and real.] “First, Scotus’ attributes are really just what Deleuze calls ‘signs’ for the intellect. They express a way in which the nature of God is to be taken up by the finite subject. It is to an extent ambiguous how they are to be read in Spinoza. His definition of ‘what the intellect perceives of a substance, as constituting its essence’ can be read both as subjective (by focusing on the intellect’s perception) or as objective” (36). The second difference: Scotus’ God is separate from the world, while for Spinoza the world and God are not distinct. [In cases where God is distinct, that in a sense might be a denial of our world, that is, a denial of its substantiality, reality, goodness, perfection, and so on. However, were we to see God as absolutely immanent to our world, then perhaps that would be affirmative in the sense that we deny nothing of the reality or worth of our world.]

Second, for Scotus, God is a separate entity to the world, whereas for Spinoza, as there is only one substance, the expression of the essence of God in the attribute cannot merely be a formal feature. Rather, the expression is the world. For Spinoza, therefore, the intellectual and physical realms are just the expression, or explication, of the | essence of God. In this sense, ‘instead of understanding univocal being as neutral or indifferent, he makes it an object of pure affirmation’ (DR 40/49). Whereas the essence of God is known formally for Scotus (as a ‘sign’), it is now known expressively and concretely. We therefore have a progression between the nature of God being known analogically for Aquinas; univocally, but only in a formal manner for Scotus; and now univocally and affirmatively for Spinoza.
(SH 36-37)

With Spinoza’s “expressionism” in mind, we turn now to modes. Previously we saw that for Descartes there are numerical distinctions which are real [in the sense that distinct substances are each on their own and are numerically countable.] Spinoza does not think that there are such real numerical distinctions [between substances, but it seems there are numerical distinctions between attributes, since they are qualitatively different and are separately nameable.] Modes, however, modify the one substance, and are not distinct [from substance, since they inhere to it and depend on it for their existence, and also perhaps, they are not distinct from each other, if they are intensive degrees of the attribute, that is, of an essence of substance.] Modes, unlike substance, cannot be thought as though they were separable from the substance they modify. Spinoza [in Ethics Book 1, definition 5] defines modes as “the affections of substance; that is, that which is in something else and is conceived through something else’ (Spinoza 1992: Part 1 D5)” (SH 37). We saw already modal distinction in Scotus. They were intensive differences of some substantiality, like degrees of perfection of being. However, modes still in a way are numerically distinct. [This seems to be incompatible with SH’s above claim that they are not distinct. If we mean, distinct from one another, perhaps previously he means not really distinct as there is only one substance to which all of them modify, and thus are not substantially separated from one another, but in the second case they are numerically distinct in the sense that they can each be distinguished in our minds on the basis of their degree.]

Earlier on, I mentioned how Spinoza disagrees with Descartes’ equation of real and numerical distinction. Spinoza instead argues that substance is really distinct, but not numerically distinct. Modes operate in the opposite manner. Modes are modifications of a singular substance, and so are not really distinct. They are, however, numerically distinct from one another. If modes are to be distinct, but not seen as existentially distinct from one another (as they are all moments of a singular substance), we need some other way of distinguishing them. This is in essence the same problem that we found in Scotus’ attempt to develop a univocal conception of being which was at the same time applicable to finite and infinite beings. Scotus’ solution was to replace Aquinas’ notion of the finite/infinite distinction (which was founded on limit) with a distinction founded on intensity. Thus being is like the concept of whiteness. While we can formulate a concept of whiteness separately from the intensity by which it manifests itself, such a concept would be inadequate. Intensity is the mode by which whiteness manifests itself. According to Deleuze, Spinoza develops a similar account of the nature of finite modes. Just as intensity is only modally distinct from whiteness, finite modes are only modally distinct from substance itself.
(SH 37)

SH then discusses the role that univocity plays in Spinoza’s philosophy. In sum, on account of the univocity of substance, it is determined not by conceptual difference but rather by a difference internal to it. [[We will need to work through this I think. Let us begin with an assessment of what this means. I am going to suppose that the main idea here is that we have two different conceptions of reality. In the Aristotelian/representational conception, we view everything in reality as having a certain sense or essence that is determinable by distinguishing it from the sense or essence of something else. This necessitates a fundamental multiplicity, since everything needs something else for its own unique being, and so even the supposed one ‘unique’ being (of beings) itself must somehow have multiplicity built into it in order for it to have any sense. We saw one way that could be is equivocity. Now consider the other view of reality. This view also regards everything as having an essence. However, essence is not determined by means of differences between substances, as there is only one substance anyway. Yet, that one substance has many essences. The nature of substance then is not some singular essence, since there are many. But also, there are infinitely many essences, according to Spinoza. Since there is no limit to substance’s essences, each of which differ from one another qualitatively, then we cannot say that substance is the sum of all its essences. For, there is no such numerical sum. However, we can generally characterize this situation. Each essence of substance differs from all the others. We can say for any pair of them that they express not only the quality of each essence but also they express the difference between them. Since both are expressions of substance, one such pair expresses one way that substance has an internal difference, or we might put it in other words that such a pair expresses one of substance’s self-differentiations. Substance is truly one and univocal. However, its essences are inconsistent. Substance is by nature self-differential, self-inconsistent. And there is an infinity of different essential expressions. Thus we can say generally speaking that the most fundamental nature of substance is that it is infinitely self-differentiating. The essence of substance is self-differentiation. SH perhaps is making a different point. Perhaps the self-differentiation he refers to is the intensive difference of modal differences and not essential difference of attributes. I quote for your judgment.]]

What is the role, therefore, that univocity is playing in Spinoza’s philosophy? First, we can see that the nature of substance itself is not given according to a categorial form of definition. In order to define something for Aristotle, we need a genus and a difference. This led to the problem | of the highest genus, as the highest genus would seem to require a higher identity in order to be defined, but the presence of such a higher identity would imply that the highest genus was not, in fact, the highest genus. In such a case, determination relies on a numerical distinction between terms. We must be able to separate the rational animals from the nonrational animals (as separately existing entities) in order to define man as a rational animal. We define something by saying that it is ‘this and not that’. Spinoza’s substance, however, has an essence which is expressed through the attributes. This essence is not one that can be given in terms of the categories, however, as Spinoza’s substance is not subject to any form of numerical distinction – it is singular. On this basis, it cannot be determined through the ‘this and not that’ structure of representation, even in relation to a possible but non-existent object. Substance does have a structure and an essence, however, as is shown by the finite modes which as a whole express substance, and which are distinguished from one another in terms of their intensity. Substance is determined by a difference, but it is not a difference between concepts (everything is substance), but rather a difference that is internal to substance. This is therefore one of the most difficult ideas in Deleuze’s metaphysics: substance expresses its essence by differing from itself. This is made possible on the basis of the univocal conception of being, whereby all modes express the same being. Spinoza’s system therefore makes no distinction between different ways in which things exist. Although the world appears to be made up of different substances, in actual fact, everything is simply an expression of the same substance.
(37-38)

 

 

 

 

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

DR:
[Deleuze] Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

EPS:
[Deleuze] Expressionism in Philosophy: Spinoza, trans. Martin Joughin, New York: Zone Books, 1990.

Spinoza (1992), Ethics, trans. Samuel Shirley, Indianapolis: Hackett Publishing.