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Gilles Deleuze was a French philosopher prominent in the late 20th century. Many articles have been written by him regarding literature, philosophy and film. Deleuze has had works in form of monographs which have mainly stemmed from the interpretation of other authors’ works such as Faucolt’s definition of space, proximity, identity and difference. This study will center on his interpretation of Faucolt’s work.

Deleuze has in the past associated his works as being a transcendental empiricism. His works have been big sellers in France and have been recorded in English speaking academic books. During 1980s and 1990s, most of his works were translated into English. This then created an impact of his works in North America; especially in Literature departments. As a result, Deleuze’s works have usually been termed as universal philosophies. Nevertheless, Deleuze has also attracted quite a number of critics; like in 1997, he was accused of abusing certain terms in his article that were scientific and mathematical in nature.

Some of Deluze’s major works were in meta-physics whereby, he contributed immensely to the understanding of identity and difference. His other works have been majorly centered upon the interpretation and analysis of Foucault’s works. In some quarters, Deleuze’s works have been termed as the most representative of Faucalt’s opinions. His works have therefore been widely used in the fields of philosophy, cinema, literature and other disciplines in very insightful and interesting ways. Deleuze has created his concepts from varied sources of credibility; such as Faucault’s works to which this study will utilize. His concepts have been termed to define the thinkers’ main concepts or the influences to which their main ideologies are yet to be understood. This study will therefore utilize some of his main insights in the understanding of the concepts of space, identity, proximity and difference.


For the proper understanding of Deleuze’s concept of Space; it should be noted that his philosophy was meant to replace Karl Marx’s ideologies regarding politics and economy together with the historical dialects of his philosophies. In Deleuze’s account of the historical process, he introduces a new term “nomad” as opposed to the concept of the “state”. The agency of the nomad principle is pit as an aggressive concept as opposed to the state. The state in this sense is considered a passive consolidator.

In proper understanding of the concept of space, nomad space is considered heterogeneous but at the same time quite smooth. On the contrary, the state is considered homogenous but striated. For example, the threads of a fabric are striated but the fabric is considered smooth; factoring in the entanglement of the fibers to form a complete material. The very spaces inhabited by nomads, for example in deserts are considered smooth. The space occupied by Eskimos in the ice regions can also be termed the same way. Deleuze further defines space by using these examples because space is further characterized by continuous landmarks and linkages. He further explains that there is no linear distinction between the earth and the sky. He also notes that there is no distance as an intermediary and therefore the visibility is limited. With these factors in consideration, there is still a strong topology that majorly relies on various points or objects rather than Haecceities.

The topology should however rely on different sets of relations such as winds, the nature of snow or sand, or even the breaking of the ice. Unlike this definition, spaces that are occupied by people who are sedentary or state spaces are usually surrounded with walls and barriers. Roads also characterize these spaces with an exhibition of constancy and regular metrics.

Mathematically, a space is between a set of points and a definition of the correlates of proximity. Mathematics also defines this space as a manifold of multiplicity. According to Deleuze, this multiplicity is not plain; it has various components to it. When Gauss and Reinmann first introduced this concept in the early 19th century, they redefined the way in which spatial problems can be defined. Einstein and other revolutionaries later used the concept to define the way physical space-time is defined.

One important feature of this ideology was to get rid of the notion that space should be defined by one dimension higher than it is. For example, to define a two dimensional object would require a three dimensional foresight. The need for the extra dimensional space arises from the use of Cartesian co-ordinates to every point of the sheet. However, if the sheet can only be studied using local data, the resultant need for space is limited.

Deleuze’s argument is that this eliminates the extra dimension to the space in study. He further adds that multiplicity is intrinsically defined without regard to external forces or recourse to an even space in which it would be defined. It is critical for Deleuze that all global embedding spaces are eliminated and all terms are viewed locally. Deleuze further argues that this is not an issue in formal philosophical nature of mathematics but an ontological issue that impacts directly on the status of the virtual space.

The structure of possibility in its virtual nature should not be made into a transcendent nature, but should always be interpreted as immanent to the world. In a multiplicity, no matter how many dimensions a space might have, it shouldn’t have a supplementary dimension that transpires upon it. This fact however makes it immanent and natural. The ontological significance such a geometric object could however be put into question. The reasoning behind it is that, multiplicity can be analyzed if the dimensions are valued from one of the degrees of freedom. The multiplicity of the dimensions therefore becomes the given space for which the state and system should be analyzed. The points in the manifold however represent the given possibilities for the points. However, certain features of topography represent the structure of the given space. State spaces are however just termed as mathematical; their topological invariants are however interpreted as being real.

Philosophers can however not use the term immanent and expect it to eliminate transcendence. A strong framework for immanence must be provided for transcendence to be eliminated. A situation could be formed whereby a person understands virtual space and comprehends its production and reproduction; though the question that would be asked would be: what ideas arise from this assumption in a material world? The world would however consist of a non-metric space that comprises of all the factors that organize the chemical, physical and social processes that result into actual systems which might comprise planets, molecules, species and the like. These systems are what inhabit our space

Metric and non-metric spaces will however be connected by intermediary spaces though it is usually extensive in nature. The virtual and intensive would therefore constitute three realms of reality which have various multiplicities that offer guidance to a number of intensive processes that actually yield in specific entities. The counter move from actual to intensive would happen regularly to guarantee multiplicities. In the material world, human thinkers would follow one among the movements: scientists emphasizing on real beings, philosophers trailing the counter motion and those that redefine possibilities virtual in nature and give them a consistent space out of actual entities.

It could therefore be summarized that philosophy and science take different directions because philosophy has a consistency but scientific perspectives have states of affairs or mixtures for references. However, through concepts, philosophy devices consistency in the state of affairs but from a scientific perspective, it actualizes the state of affairs or a body that can be referenced.


Deleuze uses the concept of difference as a mechanism for productivity as opposed to a form or attribute of identity. Deleuze’s ideology on difference differs from Kant and Hagel’s ideologies which requires reason alone. Deleuze’s ideology centers on thinking against reason. His views are supported by Faucault in the sense that his ideology is not based on merely devising a new way of thinking but from finding a new sense of sensibility. The ability to make a difference for example cannot only be understood from the basis of thought alone; action must be taken for a difference to be made. In the field of philosophy, thought can’t activate itself as a form of thinking unless it experiences obstacles which can be manifested through martial arts or science.

Unlike Hegel, Deleuze affirms that while dialect is defined by an opposition within a defined category of identity, difference is the logic behind production itself. He went on to add that opposition works in more or less the same way; only that difference is superior in that, it transcends levels and planes. Its transcending is also not just in one direction. In the definition according to Hagel, negativity is known to be among one of dialect’s primary powers. Deleuze however states that difference is thinkable just like repetition repeating itself. This can be further illustrated whereby difference is defined as forever distinguishing itself from its form. The pattern of movement in difference is normally productive but lacks opposition or negation. Necessity may also be lacking. In its place, the multiplicity of chance is witnessed. This can be equated to tossing a dice over and over with the randomness of the throw repeating itself with every number.

On the contrary, dialect eliminates the possibility of chance and establishment of the movement of the negative as an attribute of identity. This can be equated to the science of logic whereby in its instantaneous nature, is summed as being only equal to itself. However, according to Deleuze, sensitivity induces a dependency on chance into the faculty of thought development, thereby creating accidental conditions for thinking. This scenario therefore affects the condition for logical identity and creates a limit beyond any system of dialect.

As regards difference and direction, Deleuze represents his ideology in many fronts. His ideology stems from the combination of two fronts of research: repetition in which mechanical and physical attributes of repetition are concealed and differentials that are disguised. According to Delueze, appearance is not a representation but a sensory intensity that isn’t subjective or objective. Without these objectives, appearance then becomes a non- representation differential. This difference is therefore the lack of sense for the sensible, but problematic because it forces the encounter of the sensible as “given”.

Any move against representational thinking therefore becomes an infringement on the identity of the object being identified. According to Kant, difference therefore redistributes aspects of the past, present and future by fragmenting consciousness into a number of facets that are not predictable of a single facet. Deleuze notes that intensive qualities fragment by themselves and the aspect of individualism is not a contributory facet of an ego. Instead, it becomes a differential eternity multiplying itself and changing its configurations.

This therefore makes Deleuze give multiple faculties for subjectivity which in turn, become the correlates which are insensible in the sense that, it gives rise to the faculty of thought, feelings and actions. Deleuze further goes to note that each faculty only has involuntary adventures and involuntary adventures become a part of the empirical definition.


With the advancement of studies, there are a number of questions that still linger about the true definition of identity. Questions might be asked about how identity is created in relation to power or the parameters that define identity and finally whether there exists other alternatives to identity. It is now a major theory in most disciplines that identity is more negotiated than its ability to occur naturally. Some anthropologists have defined identity as a relation, gap or a difference. Some scholars have actually suggested that identity is not constructed but and identitarian jail whereby freedom can be obtained or not.

Deleuze identifies that the word identitarian is a manifestation of the current state to depict a prison. By rhyming the word identitarian with totalitarian it depicts an image of mistrust. Deleuze however notes that what works in the definition of identity also works for difference which in some quarters is termed to have outlived its usefulness. Ideas relating to identity and difference have however become suspect. For example the instructors who taught how to read the differences in culture as a production of opposites now read the binary definitions close to the nationalist and empirical enterprises. Now, new frontiers are being built from nations, regions and other units are also slowly coming into use.

Deleuze however sees a static ideology behind identity which has been the pillar of thoughts of culture during the imperial era. A profound change of paradigms is therefore being witnessed as a result of this. In some quarters however Deleuze has noted that identity can oppress; for example, in places where a black minority thrive, whatever they do is first analyzed from the point of view of identity. Other avenues should then be sought that avoid open relation to identity. The easiest positive way of defining identity based on obvious categorical definitions such as gender, age or ethnicity have become quite unsatisfactory. However the terms of any new definitions aren’t clear yet.

However, Deleuze provides the idea based on nomad thought which is among the most post-identitarian methodologies available from the pool of theoretical ideas. This concept does not advertise itself as a superior model but is free from the confines of identity. The ideology voiced out by Deleuze is therefore a break-away from past ideologies.

Deleuze has therefore swept most of the interpretations that existed in the books of meta-physics eliminating widespread notions about certain principles such as Oedipus which means a long error. It should however be noted that it was in the context of anti-colonialism that this ideology (Oedipus) was eliminated. The nomadic ideology was therefore voiced by Deleuze to liberate people from the ideologies of capitalism which included identity.

A nomad thought however simplifies the complexity of thought elements without changing the meaning or concept of their heterogeneity. The pillar of a nomad thought stems from affirmation especially when it’s thought is primarily negative. The implications of this ideology should however be analyzed in-depth. Deleuze doesn’t erase these consequences but seeks to accumulate them. This therefore means that the new ideology of nomadism is curiously linked to the older models. The relation of nomad thoughts with non-nomad thought should therefore be analyzed. Deleuze however identifies nomad thought as that which cannot negate something that isn’t self.

To do so would equate to the closed representation of the equation of representation which the new ideology seeks to replace. Non-nomad thought can only be a part of nomad thought though. The closed equation of representation can be represented as x= x= not y (I =I =not you). However, if representation is being replaced, it must find it’s rooting in the school of nomad thought which is depicted by …. +y +z + a+… (to represent an addition of major identity facets). However, if nomad thought is open enough to accommodate other theories and concepts, the epistemology of nomad thought then becomes quite interesting to analyze. However, questions are bound to arise like what constitutes a nomad thought? How is the smooth space of nomad thought differentiated from other schools of thought? How does it occur when a revolutionary thought is merged with a representational thought? Could a nomad thinker be held accountable for what he/ she have been able to represent or embrace?

Deleuze has therefore conceived in the problem of identity that it is caught up in a general process of osmosis with a lack of identitization on entities such as women, infants animals and the like. Nomad thought therefore lies out of the basis of reproduction or representation. Deleuze’s concept of nomads therefore enables us to adopt the concept itself without regard to anthropology that would only seek to incorporate the principles of anti-nomadic thinking. This claim however requires a lot of scrutiny. Its implications are therefore magnificent but somehow hard to comprehend.


In topology, proximity might define the nearness that might exist between sets of objects. Deleuze defines proximity or a map of it as one that preserves nearness. Alternatively, a map is equivalent if it could define neighborliness. The main concepts behind proximity can be defined by an axiomatic depiction of proximity space in the sense of:

Negating subsets A, B, C and D that relate to X:

X is unequal to X

A is less than B but translates to a combination of A and B.

Therefore, a combination of A and B is less than a combination of C and D but translating to A being less than D.

This signifies that A is less than B and A is less than C but translates to A being less than a combination of B and C.

A resultant equation will be that A is less than C but translates to X-B being less than X-A.

A is therefore less than B but translates to ∃E, meaning A is less than E and E less than B.

 Deleuze therefore implies that Proximity is only separated if {x} δ {y} implying that X is the same as Y. He still goes to define that proximity or a map of the same is one that negates nearness but is given by f: (X, δ) →(X*, δ*). This is only possible if A δ B in X, then f [A] δ* f [B] in X*. Therefore proximity is equivalently proximal if an inverse of its map preserves neighborliness. In the same respect it also means that C is less than*D but holding in X*, though f−1[C] is less than f−1 [D] but holding in x.

Given a space of proximity, Deleuze then defines proximity topology by letting A translate to {x}: {x} and A being a closure operator of Kuratowsk. However, if the space of proximity is separated the topology that would be realized would entail Hausdorff. Proximity maps will therefore be induced continuously on the topography. Nevertheless, the resulting topography will always be regular. Deleuze affirms that Urysohn's lemma can always be used to test this relationship. This should however be done using the latest properties of the proximal neighborliness that induces the expanding interlink of proving Lemma.

Considering the compact Hausdorff quality of space, a unique proximity exists but its corresponding topology is the given topology. Deleuze therefore asserts that two sets of objects are in proximity if and only if their closures are able to intersect each other. On other words, proximity can be used to define compactifications (the process that exists in the enlargement of a topological space) of a perfectly even Hausdorff space.

Deleuze therefore brings out the relation whereby an even space X could induce a relation of proximal nature by declaring two points for example A being near B. This relation is only possible if A could be a multiple of B and has a relation which permanent and non empty with every form of intersection between the entourage. Deleuze therefore alludes that continuous maps would therefore be continuous in a proximal nature.


Deleuze has made quite a tremendous contribution in the understanding of various concepts of space, proximity difference and Identity. His contributions have been able to insightfully provide a non representative and acoustic definition in the understanding of the contexts to which the four aspects (Space, Proximity, Identity and Differentials) are understood. Deleuze’s definition of proximity as that of which defines nearness and would enable most academic disciplines understand this concept much deeper because it is well elaborated with variables that affect this relation.

Identity couldn’t be understood better than from the insight given by Deleuze. Various issues have been identified to provide a gainful comprehension of the concept of identity. The capitalistic nature of identity has been identified and the problems it poses such as identitization are identified. The true conception of identity is therefore given to negate a more positive impact on the concept. Deleuze also uses the concept of difference as that which negates productivity. Thought cannot only be termed as having made a difference if it is not subjected to factors that cause it to react with the environment for a difference (productivity) to be realized.

The concept of space is also understood as a build-up of other existing concepts by Marx for example. Deleuze further introduces the term concept which is meant to provide a different ideology from non-nomadic ideas that still prevail in various disciplines. Deleuze gives the proper understanding of the concept of space, by the nomad space being considered heterogeneous but and at the same time smooth. He further defines it on the contrary; as the state being considered homogenous but at the same time striated. Deleuze explains his concepts better by giving examples to explain the concept of space such as the threads of a fabric being striated but the fabric being considered smooth to factor in the entanglement of the fibers to form a complete material. He further explains that the very spaces inhabited by nomads, for example in deserts are considered smooth and the space occupied by Eskimos in the ice regions can being termed the same way. Deleuze’ definitions are therefore an improvement of previous concepts of other philosophers including Foucault.ader. London: Wiley-Blackwell, 1996.

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