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Pt3.Ch6.Sb2 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘The Calculus’. summary

by Corry Shores
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[Hegel, Deleuze, and the Critique of Representation, Entry Directory]

[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]

 

Henry Somers-Hall

 

Hegel, Deleuze, and the Critique of Representation.

Dialectics of Negation and Difference

 

Part 3: Beyond Representation

Chapter 6: Hegel and Deleuze on Ontology and the Calculus

Subdivision 1: The Calculus

Brief Summary:

Deleuze’s and Hegel’s anti-representationalist philosophies can be compared on the basis of their different interpretations of differential calculus and Kant’s antinomies.

Summary

Calculus deals with “quantities whose relations to one another vary.” (162) Somers-Hall deals mostly with speed, the relation of time to distance. Early developments in the study of rates of change come from Oresme. To find velocity, draw a graph with time as one axis and distance traveled as the other. To determine the speed we look at change in distance over change in time, which also gives us a diagonal between those time-space coordinates on the graph. This only gives us average velocity. If we wanted to know the velocity at any moment, it would have to be at constant speed. But for motion with inconstant velocity, we cannot use this method. Instead we need to draw a tangent to the curve to determine the velocity at that moment. But a point cannot have a direction. Leibniz’s solution is to begin with the diagonal between the point in question and some other arbitrarily selected point (which gives the average velocity within the bounds of that time frame), and then bring the arbitrary point infinite close to the one in question. This slides the diagonal to indicate the velocity at that point. In fact, we can do this merely working with the graph’s functions in their numerical form. (163d)

For Hegel, calculus’ method is expressed in the formula [see §608 of this entry]

or

The second one is the gradient function for a curve, change in x over change in y. Let’s first examine

(Thanks Dr. Siddique / faculty.uncfsu.edu)

So the i  on the bottom is the x value. And our function gives us y = f(x). So we will find the y values by using the function formula. On the top, we have two applications of the function. The second one tells us what point along the y axis is right above the first x value.

 

Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.

Clark & Chalmer’s Extended Mind

 

 

I Introduction

The authors explain they will advocate “an active externalism, based on the active role of the environment in driving cognitive processes.” (2) [Cited pages in accordance with online pdf http://www.philosophy.ed.ac.uk/people/clark/pubs/TheExtendedMind.pdf]

 

II.

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x

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Deleuze Cinema, BK1 Ch1 Pt1 Pr1 Movement thesis 1 intro: space is distinct from movement.

 

by Corry Shores
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[The following is summary; original text is given below. My own comments are in brackets.]

[Citation format:
(C1: [1983 French]; [1986 English]; [2005 English])
(C2: [1985 French]; [1989 English]; [2005 English])
Page break: ‘||’ for 2005 English, otherwise ‘|’ ]

 

Gilles Deleuze

Cinema 1
Cinéma 1

Ch1
Theses on Movement: First Commentary on Bergson
Thèses sur le mouvement: premier commentaire de bergson

Pt1
Première thèse: le mouvement et l’instant
First thesis: movement and instant

Pr1
Movement thesis 1 intro: space is distinct from movement

Summary

 

Bergson has three theses of movement.

Thesis 1: Movement is distinct from the space covered.

We cannot consider movement and space as being of the same sort of thing. They are essentially different.

 

The temporality of space and motion in the first thesis on movement:

a) Space is past, it is what has previously been covered by the movement.

b) Movement is present, it is the act of covering which secondarily produces space, temporally speaking.

 

The metrics of space and motion:

a) The space covered is divisible into qualitatively homogeneous parts. [One meter of distance is divisible into two half meters of distance.] In face, space is infinitely divisible into parts.

b) Movement is indivisible in this sense, or at least we can say that  if we do divide it, the parts are heterogeneous: “movement […] cannot be divided without changing qualitatively each time it is divided.” [Movement is like complete change and not just change in place. Spatial distance does not measure the change of movement, it measures the change of place. Movement is more than displacement. Movement is not constant departure of place, rather it is constant departure of state. The status of things is constantly altering. In physical motion, there is both the qualitative change of state of the things in motion (and the whole of all things), but as well, there is the change in place.]

“the spaces covered all belong to a single, identical, homogeneous space, while the movements are heterogeneous, irreducible among themselves.”

 

 

Deleuze, Gilles. Cinéma 1: L'image-mouvement. Paris: Les éditions de minuit, 1983.

Deleuze, Gilles. Cinema 1: The Movement-Image. Transl. Hugh Tomlinson & Barbara Habberjam, London / New York: Athlone; Minnesota: University of Minnesota, 1986.

Deleuze, Gilles. Cinema 1: The Movement-Image. Transl. Hugh Tomlinson & Barbara Habberjam, London / New York: Athlone, 1986; Continuum 2005.

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