Dupréel (1.5) La consistance et la probabilité constructive, sect 1.5, ‘Hiérarchie des êtres selon la consistance’, summary

 

 

by Corry Shores

 

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[Eugène Dupréel, entry directory]

[Dupréel, La consistance et la probabilité constructive, entry directory]

 

[The following is summary and not translation. Bracketed commentary is my own, as is any boldface. Proofreading is incomplete, so typos are present, including in the quotations. Please consult the original text to be sure about the contents. Also, I welcome corrections to my interpretations, because I am not especially good with French.]

 

 

 

Summary of

 

Eugène Dupréel

 

La consistance et la probabilité constructive

 

Part 1

“La consistance”

 

1.5

Hiérarchie des êtres selon la consistance

 

 

 

Brief summary:

(1.5.1) Regarding the fate of something, we must remember that a thing can only influence and be influenced by things of the same sort. So sensible, material things can only touch and be touched by other spatial objects. The same goes for abstract entities. Numbers can only interrelate with other numbers, pure ideas with other pure ideas, propositions with other propositions, and judgments with other judgments. (1.5.2) There are three main types of beings: {1} sensible or perceptible beings (which are also spatial and material), {2} notions, which are those things that depend on a subject to know or express them, like sensations, feelings, thoughts, reveries, and so on, and {3} values, which are dynamic beings, because they lead one to commit deliberative actions.

 

 

 

 

 

 

 

 

Contents

 

1.5.1

[Inter-Affectivity as Type-Limited]

 

1.5.2

[The Three Types of Beings: Sensible Things, Notions, and Values]

 

 

 

 

 

 

 

 

 

Summary

 

 

1.5.1

[Inter-Affectivity as Type-Limited]

 

(p.12: “La consistance d’un être étant sa capacité ...”)

 

[Regarding the fate of something, we must remember that a thing can only influence and be influenced by things of the same sort. So sensible, material things can only touch and be touched by other spatial objects. The same goes for abstract entities. Numbers can only interrelate with other numbers, pure ideas with other pure ideas, propositions with other propositions, and judgments with other judgments.]

 

[So (as we noted in section 1.2.2), the consistency of a being is its capacity to endure throughout a series of its vicissitudes. With that being the case, we should note when discussing the being’s destiny that we should attend to just those sorts of vicissitudes that have some influence on its destiny. For example, an object that is simply material cannot be directly altered by things that are insensible. Rather, it can only touch and be touched by other spatial beings. Similarly, a pure idea like a number or a logical proposition can only enter into a direct relationship with other beings that are equally abstract. (Note how this rings with Spinoza’s parallelism.) A judgment can only be proven or disproven by another judgment, and a number can only be substituted by another number. And the living, thinking subject is merely the necessary intermediary for bringing these abstract entities into contact.]

La consistance d’un être étant sa capacité de durer à travers la succession de ses vicissitudes, il convient de ne porter l’attention, dans l’examen de son destin, que sur les sortes de vicissitudes capables de les atteindre. Ainsi un objet tout matériel ne peut être directement altéré par quelque chose qui n’a rien de sensible, seul peut le toucher quelqu’autre être spatial et c’est seulement sur cet être de même sorte qu’il peut porter sa résistance ; réciproquement, une idée pure telle qu’un nombre ou une proposition logique, ne peut entrer en rapports directs qu’avec d’autres êtres également « abstraits ». Un jugement ne peut être confirmé ou infirmé que par un autre jugement, un nombre admis ou nié que par la substitution d’un autre nombre. Le sujet vivant et pensant qui se prononce sur ces rapports n’est qu’un intermédiaire nécessaire, ce n’est pas de sa nature propre que dépend la relation retenue.

(12)

[contents]

 

 

 

 

 

 

1.5.2

[The Three Types of Beings: Sensible Things, Notions, and Values]

 

(p.13: “En conséquence dans la recherche de la hiérarchie des êtres ...”)

 

[There are three main types of beings: {1} sensible or perceptible beings (which are also spatial and material), {2} notions, which are those things that depend on a subject to know or express them, like sensations, feelings, thoughts, reveries, and so on, and {3} values, which are dynamic beings, because they lead one to commit deliberative actions.]

 

[So when seeking the hierarchy of beings according to their degree of consistency, we need to sort them according to their natures. We take for granted that in order to characterize consistency, we need only deal with the following three kinds of beings: {1} sensible or perceptible beings, {2} notions, and {3} values. (It is fairly straightforward what a sensible thing is, so we need not further explain it.) A notion is anything that comes to be only by means of a subject that knows and expresses it, and it can be for example a sensation, a feeling, a thought, a reverie, etc. Values are those beings that we may call dynamic, because a value is what leads to a deliberated action.]

En conséquence dans la recherche de la hiérarchie des êtres selon le degré de consistance il y a lieu de la dresser selon leurs natures respectives. On tiendra pour accordé qu’il suffit de caractériser la consistance au sein de ces trois espèces d’êtres que sont les choses sensibles ou perceptibles, les notions et les valeurs. Sous le nom de notions seront réunis tous les êtres qui ne se posent que dans leur rapport avec un sujet en condition de les connaître et de les exprimer, sensations, sentiments, pensées, rêveries etc. Quant aux valeurs ce sont ces êtres qu’on peut appeler dynamiques car une valeur est cela qui entraîne un acte délibéré.

(13)

[contents]

 

 

 

 

 

 

 

 

Dupréel, Eugène. (1961). La consistance et la probabilité constructive. (Classe des lettres et des sciences morales et politiques 55, no.2). Brussels: Académie Royale de Belgique.

PDF at:

http://www.academieroyale.be/fr/les-publications-memoires-detail/oeuvres-2/la-consistance-et-la-probabilite-constructive/.\

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Dupréel (1.3) La consistance et la probabilité constructive, sect 1.3, ‘La similitude’, summary

 

by Corry Shores

 

[Search Blog Here. Index tabs are found at the bottom of the left column.]

 

[Central Entry Directory]

[Eugène Dupréel, entry directory]

[Dupréel, La consistance et la probabilité constructive, entry directory]

 

[The following is summary and not translation. Bracketed commentary is my own, as is any boldface. Proofreading is incomplete, so typos are present, including in the quotations. Please consult the original text to be sure about the contents. Also, I welcome corrections to my interpretations, because I am not especially good with French.]

 

 

 

Summary of

 

Eugène Dupréel

 

La consistance et la probabilité constructive

 

Part 1

“La consistance”

 

1.3

La similitude

 

 

 

Brief summary:

(1.3.1) Beings’ vicissitudes can be analogously affected by shared influences, like wind blowing all the different things on a plain. We notice here that beings with analogous vicissitudes have features in common but also distinct ones too. We wonder, do differences in their fates result from differences in their features? To perform our analysis on this matter, we will begin with beings that share more common traits than differences, and we call such beings: similars. (1.3.2) When a variety of things are haphazardly mixed together, that mass can be easily disassembled by one common influence, like wind blowing on a mass of sand, gravel, and large stones. The sand will blow far away but in the same direction and probably all deposit in the same place, while the gravel will move only slightly and the large stones not at all. There groupings were sorted on account of shared powers of affection (of affecting and being affected), and elements with different powers were filtered out from one another. So while they were still their haphazard mixture (sand-gravel-stones), they had little consistency, because their various powers of affection made it such that the identity of the mass was easily disrupted. But after that sorting influence, the parts held together more readily, because they were not contaminated by other elements that would split-off from the group and thereby break the collection apart when a common influence affects the whole conglomerate. (1.3.3) We can thus observe the following. Outside influences affecting a plurality of similars probably result in {1} the similarity of the similars maintaining throughout the affective influences, and {2} the elements coming closer together on account of the separation of the different things and the increase of the consistency of the collective being that constitutes their whole, or otherwise to give rise to this collective being on account of their increased capacity to conserve under the altering factors. (1.3.4) We turn now to the effects on the interrelations between members of a sorted group of similars. External influences will cause the individuals of the group to interact more with each other. And as the group becomes more consistent, the relations between the individuals become more intimate and constant, and exterior influences tend to translate into a proliferation of mutual relations. (1.3.5) Exterior influences transfer collisional energy internally to the members, which disruptively collide into one another, now continually transferring that once external energy among each other internally as they jostle each other about. Thus the internal effect of external influences on collections is an elementary antagonism among the collection’s members. (In collections with a low degree of consistency, like the stones-gravel-sand collection being struck by wind, the members affect one another differently, causing the collection to eventually break apart. But) in collections with high degrees of consistency, like the sorted sand collection, the members affect each other similarly, and for that reason their movements come to mutually accommodate one another. Thereby, the elementary antagonism in collections with high degrees of similarity and consistency gradually decreases and eventually dissipates often without breaking the collection apart. (1.3.6) The exterior influences imposed upon collections of similars thus tend to bring about an increase in the individuals’ compatibilities, and their mutual accommodations will make them more immune to disruptive external and internal influences. This increased compatibility of the elements is a main factor in what allows the collection to endure and maintain consistency. Consider for example stones that have fallen from a seaside cliff. At first they were jagged and malformed. But by being  constantly “tumbled” around by the tides, they take on a rounded form that, on account of its increased hydrodynamic shape, is less influenced by the water currents.

 

 

 

 

 

 

 

Contents

 

1.3.1

[Studying the Role of Similarity and Difference in Beings’ Vicissitudes]

 

1.3.2

[Similarity and Increased Consistency]

 

1.3.3

[The Results of Common Influence on Similars]

 

1.3.4

[The Increased Interactivity of Individuals in a Consistent Grouping]

 

1.3.5

[Internal Elementary Antagonisms from External Influences and Their Dissipation through Consistency]

 

1.3.6

[Increased Immunity and Consistency through Mutual Accommodations]

 

 

 

 

 

 

 

Summary

 

 

1.3.1

[Studying the Role of Similarity and Difference in Beings’ Vicissitudes]

 

(p.9: “Tous les êtres suffisamment rapprochés ...”)

 

[Beings’ vicissitudes can be analogously affected by shared influences, like wind blowing all the different things on a plain. We notice here that beings with analogous vicissitudes have features in common but also distinct ones too. We wonder, do differences in their fates result from differences in their features? To perform our analysis on this matter, we will begin with beings that share more common traits than differences, and we call such beings: similars.]

 

[Recall some basic ideas from the previous section 1.2.2: We defined the consistency of a being as its capacity to maintain its identity throughout the variations or “vicissitudes” it undergoes as a result of its interactions and relations with other beings (p.7, section 1.2.2). Dupréel now notes that when beings are close enough to be modified similarly by the same influence, like the wind blowing equally on all things in the plain, then we can see that the things have common properties (that allow for their common modification by a common influence) and also particularities that distinguish them (perhaps seen in the different sorts of modifications, like the grass bending with the wind, or the rock  remaining still but very slightly eroded.) We now wonder if the differences in the beings result in differences in their fates, despite their shared or analogous vicissitudes. Normally it is a mixture of the two contraries such that it is difficult to assess what about their fates results from their differences and what from their similarities. So it would aid our analysis if we worked with beings that either have more similarities than differences or more differences than similarities. Thus we will begin by focusing on beings with strongly similar characteristics, and we will call these resembling beings: similars.]

Tous les êtres suffisamment rapprochés pour connaître des vicissitudes analogues, tel un vent qui souffle également sur tous les objets épars dans une plaine, ne manquent pas d’avoir entre eux à la fois des qualités ou propriétés communes et des particularités par lesquelles ils diffèrent les uns des autres. Nous nous demanderons si les conséquences des vicissitudes éprouvées en commun influent sur le destin de ces êtres différemment selon que domine chez eux les similitudes ou les différences. Le cas normal étant un mélange de ces deux contraires, il peut être difficile de discerner quelles conséquences sont dues à de la différence, et quelles résultent de la similitude. On les ditinguera mieux si les êtres considérés, en même temps qu’assez voisins, sont semblables par un nombre de caractères communs qui l’emporte nettement sur les différences, ou dans le cas contraire. C’est pourquoi nous fixons notre attention – au moins pour commencer – sur les êtres qui se distinguent immédiatement par une forte majorité de caractères semblables, et que nous appellerons, pour faire court, les semblables.

(9)

[contents]

 

 

 

 

 

 

1.3.2

[Similarity and Increased Consistency]

 

(p.9-10: “Que peut-il résulter de particulier ... ”)

 

[When a variety of things are haphazardly mixed together, that mass can be easily disassembled by one common influence, like wind blowing on a mass of sand, gravel, and large stones. The sand will blow far away but in the same direction and probably all deposit in the same place, while the gravel will move only slightly and the large stones not at all. There groupings were sorted on account of shared powers of affection (of affecting and being affected), and elements with different powers were filtered out from one another. So while they were still their haphazard mixture (sand-gravel-stones), they had little consistency, because their various powers of affection made it such that the identity of the mass was easily disrupted. But after that sorting influence, the parts held together more readily, because they were not contaminated by other elements that would split-off from the group and thereby break the collection apart when a common influence affects the whole conglomerate.]

 

[We wonder, what in particular could result from these similars when they undergo altering factors that are continually imposed on them by the environment? (Recall again from section 1.2.2 that the consistency of a being as its capacity to maintain its identity throughout the variations or “vicissitudes” it undergoes as a result of its interactions and relations with other beings ((p.7, section 1.2.2)).) There is a good chance that the consistencies of the similar things under common influence will remain more or less equal (that is to say, their capacity to maintain their identity will remain about the same for all of them, perhaps on account of their similar constitution and powers of affection. Thus we should expect that the beings will be altered in the same way at the same times. The next point I am not grasping so well, so I am guessing it is the following. His example is that we have masses of large stones, of gravel, and of sand. All are submitted to the same desert winds. The wind blows all the sand the furthest, all in the same direction, most likely depositing in the same depression of in front of the same obstacle. The gravel, which is heavier, moves much less than the sand, and the heavy stones remain in place. Thus there are three types of similars that began intertwined, and in that state they do not form much of a unified whole. But at the end of the wind events, they have undergone a sorting process that isolates them into groupings where each one has a higher degree of consistency than they had in their original mixture. (The idea might be the following. When they were mixed together, they had a low degree of consistency, because wind was able to alter its identity drastically by dividing it into homogenized parts that it initially was lacking. And, each part is now grouped together in a way that will more likely keep them together. Thus the sorting process increased the consistencies of the components. It would seem to be that what puts them into the common groups is their common powers of affection. And with those common powers, they will usually stand together or break apart under the same influences at the same time. Now, since the powers of affection are what define the consistency, we can say that the consistency’s identity is this shared power of affection. And since by them sharing it in common, they are naturally grouped together, and also, since they have been purified of elements with different powers of affection, they now have more consistency, because there is less chance of influences extracting parts of it with distinct powers of affection).]

Que peut-il résulter de particulier à ces semblables du fait de leur commune soumission aux facteurs altérants que leur inflige perpétuellement le milieu ? Étant très analogues du fait de leurs communes propriétés, il y a toutes chances que leur consistance soit sensiblement égale ; dès lors les altérations éprouvées par l’influence du dehors seront plus ou moins les mêmes, de même sorte ou d’égale gravité ; ils seront changés, mais en même temps et de la même manière. Retenons ici que quelque chose de spécifique se produit ainsi qui ne provient pas de telle qualité particulière, mais qui est uniquement le fait de l’égalité dans le changement subi. Soit un amas de grosses pierres, de gravier et de sable, exposé aux souffles du désert. Le vent chasse le sable au loin, dans une même direction, avec toutes chances de le déposer enfin dans quelque dépression ou devant un même obstacle ; le gravier, plus pesant, n’est écarté que de peu, tandis que les pierres lourdes sont demeurées sur place. Il y aurait donc là trois espèces de semblables qui s’entremêlaient, empêchant pour chacune un rapprochement plus complet. A la fin de l’aventure les trois espèces ont subi un triage qui en les isolant, en rapprochant les éléments de même sorte, procure à l’être collectif que constitue chacune des trois espèces, un plus haut degré de consistance. Brouillées ensemble, la consistance de ces trois sommes étant pratiquement nulle ; il est permis de considérer que c’est l’opération survenue qui leur a donné la valeur d’une existence propre et discernable.

(9-10)

[contents]

 

 

 

 

 

 

1.3.3

[The Results of Common Influence on Similars]

 

(p.10: “On dira donc que les influences ... ”)

 

[We can thus observe the following. Outside influences affecting a plurality of similars probably result in {1} the similarity of the similars maintaining throughout the affective influences, and {2} the elements coming closer together on account of the separation of the different things and the increase of the consistency of the collective being that constitutes their whole, or otherwise to give rise to this collective being on account of their increased capacity to conserve under the altering factors.]

 

[(ditto)]

On dira donc que les influences du dehors exercées sur une pluralité de semblables ont pour effet probable 1° de maintenir la similitude à travers le changement produit, 2° de rapprocher les éléments les uns des autres par l’éloignement relatif des différents et d’accroître de ce fait la consistance de l’être collectif que constitue leur ensemble, ou pratiquement de donner naissance à cet être en le rendant capable à son tour, de se conserver en dépit des facteurs altérants.

(10)

[contents]

 

 

 

 

 

Effets sur les rapports entre semblables, à l’intérieur du groupe.

 

 

 

1.3.4

[The Increased Interactivity of Individuals in a Consistent Grouping]

 

(p.10: “Plus remarquable encore est la conséquence ... ”)

 

[We turn now to the effects on the interrelations between members of a sorted group of similars. External influences will cause the individuals of the group to interact more with each other. And as the group becomes more consistent, the relations between the individuals become more intimate and constant, and exterior influences tend to translate into a proliferation of mutual relations.]

 

[(ditto)]

Effets sur les rapports entre semblables, à l’intérieur du groupe.

 

Plus remarquable encore est la conséquence des vicissitudes quelconques sur les rapports mutuels des éléments eux-mêmes (nous dirons désormais des individus, puisque les semblables évolués sont membres d’une collectivité, d’un groupe). Les influences extérieures ont pour effet normal d’ébranler plus ou moins les individus et de les précipiter les uns vers les autres. En fait, à mesure que l’être collectif devient plus consistant, plus étroits et plus constants sont les rapports entre les éléments, et l’influence du dehors tend à se traduire par un foisonnement de rapports mutuels.

(10)

[contents]

 

 

 

 

 

 

1.3.5

[Internal Elementary Antagonisms from External Influences and Their Dissipation through Consistency]

 

(p.10-11: “Il serait long de détailler les conséquences ... ”)

 

[Exterior influences transfer collisional energy internally to the members, which disruptively collide into one another, now continually transferring that once external energy among each other internally as they jostle each other about. Thus the internal effect of external influences on collections is an elementary antagonism among the collection’s members. (In collections with a low degree of consistency, like the stones-gravel-sand collection being struck by wind, the members affect one another differently, causing the collection to eventually break apart. But) in collections with high degrees of consistency, like the sorted sand collection, the members affect each other similarly, and for that reason their movements come to mutually accommodate one another. Thereby, the elementary antagonism in collections with high degrees of similarity and consistency gradually decreases and eventually dissipates often without breaking the collection apart.]

 

[When an exterior influence affects a collection of elements, the impact at first will often take the form of elementary antagonisms between the elements. The received blow disperses throughout as internal collisions, each exchanging their movement energies with each impact and reaction. But these multiple antagonisms are gradually attenuated and eventually eliminated on account of the consistency and similarity. (Consider if the collection had low consistency, like the stones-gravel-sand collection from the example. The wind is an external influence that causes the individuals to move about internally in the collection, impacting one another. Here the collisions have a noted effect, namely, to break the collection apart. But think instead of the sifted sand collection, which has greater consistency. When the wind blows it, the antagonisms between the grains will eventually dissipate without causing it to break apart as much. This seems to have something to do with the fact that the way each individual affects the others is largely the same for each, so the antagonisms over time have little notable effect.) For, the affections of each member upon the other are restrained and mostly equivalent on account of the sameness and consistency of the members, which facilitates their common mutual accommodations of one another’s influences.]

Il serait long de détailler les conséquences de l’action du dehors sur le dedans d’une collection aux éléments rapprochés les uns des autres ; on retiendra que ce retentissement prend d’abord assez régulièrement la forme d’un antagonisme élémentaire. Le coup éprouvé devient entrechoquement général, le premier bousculé recule sur un autre auquel il impose une partie de l’impulsion reçue, et le fait va se généralisant, combiné avec les inerties et les ripostes. Mais ces antagonismes multipliés ont chances de demeurer provisoires, et toujours atténués, finalement éliminés, pour cette raison que étant semblables et de consistance analogue, les lésions communiquées sont restreintes et assez exactement équivalentes, finalement éliminées dans un aménagement géné­ral, dans une commune accommodation au détriment survenu.

(10-11)

[contents]

 

 

 

 

 

 

1.3.6

[Increased Immunity and Consistency through Mutual Accommodations]

 

(p.11: “Ainsi le changement qu’impose à la collection ... ”)

 

[The exterior influences imposed upon collections of similars thus tend to bring about an increase in the individuals’ compatibilities, and their mutual accommodations will make them more immune to disruptive external and internal influences. This increased compatibility of the elements is a main factor in what allows the collection to endure and maintain consistency. Consider for example stones that have fallen from a seaside cliff. At first they were jagged and malformed. But by being  constantly “tumbled” around by the tides, they take on a rounded form that, on account of its increased hydrodynamic shape, is less influenced by the water currents.]

 

[(ditto)]

Ainsi le changement qu’impose à la collection des semblables une suite d’influences extérieures tend à se traduire par un perfectionnement de la compatibilité des individus. Leurs accommodements feront qu’ils résistent avec moins de dommage aux contacts répétés de leurs associés. Cette compatibilité acquise de ses éléments est une condition de la durée d’une collectivité, en même temps qu’elle constitue pour chaque individu un progrès de sa consistance propre. Ainsi des cailloux tombés de la falaise, incessamment « roulés » par les marées, d’anguleux et difformes qu’ils étaient d’abords, prennent une forme arrondie qui rend moins dommageables les entrechoquements et moins graves et moins durables les pressions subies.

(11)

[contents]

 

 

 

 

 

 

 

 

 

Dupréel, Eugène. (1961). La consistance et la probabilité constructive. (Classe des lettres et des sciences morales et politiques 55, no.2). Brussels: Académie Royale de Belgique.

PDF at:

http://www.academieroyale.be/fr/les-publications-memoires-detail/oeuvres-2/la-consistance-et-la-probabilite-constructive/.\

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Terence Blake’s ‘DELEUZE, DOGS, AND SCHIZOS’, Comment of June 21, 2013 at 8:49 pm

 

by Corry Shores

 

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[Boldface is mine]

 

 

 

 

Terence Blake

 

DELEUZE, DOGS, AND SCHIZOS

 

Comment of

June 21, 2013 at 8:49 pm

 

In a comment to this post Blake offers a useful translation from Deleuze and Guattari’s Kafka book:

I am basing myself in part on Deleuze and Guattari’s KAFKA, so the utterance as singularity has both ethical (they say political, but in a very general sense of political) and humorous dimensions at the same time. Humour is equated with joy. This is at the end of chapter 4 in a long footnote. “It’s the same thing: the politics of the utterance and the joy of desire” (my translation).

(Terence Blake, boldface is mine)

I note that Blake translates “énoncé” as “utterance” and not “statement” as in the other translation (see p.95 of the English and p.76 of the French)

 

 

 

 

 

 

 

 

 

 

 

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Peirce (CP1.324) Collected Papers of Charles Sanders Peirce, Vol1/Bk3/Ch2/B/§2, "Action and Perception", summary

 

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 3: Phenomenology

 

Chapter 2: The Categories in Detail

 

B: Secondness

 

§2: Action and Perception [1.324]

 

 

Brief summary:

Phenomenal experiences can be classified in accordance with their basic structural features. Secondness appears when our efforts aimed at modifying the exterior world are met with resistance from without. Our awareness in such a situation is double-sided. On the one hand we are aware of our own inner efforts, while on the other hand we are aware of the exterior resistance to those efforts and to the modifying influence they have upon us. This gives us a sense of otherness and of the not-self, and we even come to understand exterior objects in terms of their resistances to one another. Our efforts to modify the exterior world is on the side of our action, while the exterior resistance to our efforts which modifies our own thinking and ideas is on the side of perception.

[Additional reference notes: cf. Bergson’s perception, affection, and action in Matter and Memory]

 

 

Summary

 

1.324

[In secondness, we are aware of both our own inner efforts to modify the world (our actions) and as well of exterior resistance to them which modifies our inner thinking and ideas (perception). This gives us the notion of otherness or not self and more generally of objectivity.]

 

[Recall from section 1.321 how our inner world of fancy is under our domain, although the exterior world of facts can impose upon our inner world and modify our thinking by importing ideas from the outside. Peirce seems to be working with a similar notion here. So we have in our minds the image of something we expect, but then the world imposes something different upon our experiences. We “are continually bumping up against hard fact” which “forces that [inner] idea [of our expectation] into the background, and compels us to think quite differently”. Here again Peirce uses the shoulder against the jammed door analogy. In such a situation, we sense both resistance from the outside and effort on our part from the inside. We cannot have resistance without effort and vice versa. Thus there are two ways to describe the same experience of secondness. It is a double consciousness, meaning perhaps that we are doubly aware both of our inner effort and the exterior resistance to it. Now, the exterior resistance is not from us. In a sense, it is the not-self. Since the awareness is double, we therefore when being aware of secondness are doubly aware of our self and of our not-self. So when we are aware of secondness, we are aware of reaction (that is, of our reaction against exterior resistance to our efforts and its resisting reaction to our efforts.) This consciousness of reaction has two sides: {1} the side of action where our efforts to modify other things are more prominent (in our awareness) than their reaction upon us, and {2} the side of perception where their effect on us is much greater than our effect on them. This means further that our notion of otherness is based on reactivity of one thing to another actions, and in fact, we come to understand other beings’s objective existence in terms of their reactions upon one another. This idea of the other is also the idea of not, and it is fundamental to our thinking. Peirce, again, calls it secondness.]

[There is a category] which the rough and tumble of life renders most familiarly prominent. We are continually bumping up against hard fact. We expected one thing, or passively took it for granted, and had the image of it in our minds, but experience forces that idea into the background, and compels us to think quite differently. You get this kind of consciousness in some approach to purity when you put your shoulder against a door and try to force it open. You have a sense of resistance and at the same time a sense of effort. There can be no resistance without effort; there can be no effort without resistance. They are only two ways of describing the same experience. It is a double consciousness. We become aware of ourself in becoming aware of the not-self. The waking state is a consciousness of reaction; and as the consciousness itself is two-sided, so it has also two varieties; namely, action, where our modification of other things is more prominent than their reaction on us, and perception, where their effect on us is overwhelmingly greater than our effect on them. And this notion, of being such as other things make us, is such a prominent part of our life that we conceive other things also to exist by virtue of their reactions against each other. The idea of other, of not, becomes a very pivot of thought. To this element I give the name of Secondness.

(162)

 

 

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].

 

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Difference & Sensation: Deleuze's Spinozistic Affect

by Corry Shores
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The following is my presentation at the Nederlands Genootschap voor Esthetica (Dutch Association of Aesthetics) Utrecht Expertmeeting Kunstfilosofie in Utrecht, November 2011

Corry Shores

Difference & Sensation:
Deleuze's Spinozistic Affect

(Animation above is my own, made with GIMP and Unfreeze,
image from Spinoza, Opera vol. 2, archive.org, p.233)

Deleuze is commonly considered an anti-phenomenologist. However, I would like to explore the phenomenological value of his aesthetical ideas regarding affection and bodily sensation. The aim of this presentation is to offer a Spinozistic interpretation of certain concepts in Deleuze’s Francis Bacon book. For this aim, I draw primarily upon Deleuze’s writings on Spinoza’s affection. We will regard affection phenomenologically as involving a sort of affective awareness of bodily-given phenomena. We do this because Deleuze explains Spinoza’s kinds of knowledge in terms of the rhythm of affection.

Deleuze specifically refers to affective awareness as ‘the phenomenon of passage.’ It is the lived transition that we undergo when affections transfer us from one bodily state to another.


There are two primary dimensions, then, to such affective alterations.

One is the physical composition of bodies that becomes changed by the affection. The other is the dynamic of the alteration. Deleuze combines these two dimensions of affection, the compositional and the dynamic, by analyzing two sorts of infinities in Spinoza’s theory of affection, namely, extensive and intensive infinities. There is a cryptic diagram in Spinoza’s Twelfth Letter: the ‘letter on infinity.’ Deleuze’s novel interpretation of the diagram shows how it illustrates the two infinities.


Spinoza writes of the diagram that “all the inequalities of the space lying between the two circles ABCD in the diagram exceed any number, as do all the variations of the speed of matter moving through that area.”


We find similar diagrams in Spinoza’s Principles of Cartesian Philosophy. In the left diagram, both semi-circles share the same center. The space between their circumferences is everywhere the same. However, if the semi-circles do not share the same center, then the space between their circumferences will be everywhere unequal.


He also has us consider the circulation of water moving through the space between offset circles. And on account of the geometry of the non-concentric circles, every place along the circuit has a different width and hence “the fluid body that moves through the tube ABC receives an indefinite number of degrees of speed.”

The infinity diagram would then seem to be a hybrid of these two other figures.


Yet, Spinoza explains in his 81st letter that the infinity here is not obtained from the fact that there are more parts than can be counted. Instead, the diagram according to Deleuze, illustrates a mode’s infinite division into differential relations between infinitely small partitions.

Now, although Spinoza’s ‘letter on the infinite’ predates the inception of differential calculus, Deleuze locates in it what he considers to be seminal calculus notions. To explain the concept of infinitely small vanishing values, Deleuze guides us through the remarkably simple and illuminating visualization in one of Leibniz’ letters.


The diagonal line moves to the right, which diminishes the top triangle, all while increasing the bottom one; yet, because the triangles stay proportionally similar throughout the alteration, the ratio between the smaller one’s legs always remains proportional to the ratio between the larger one’s legs.

(Animation above is my own, made with OpenOffice Draw and Unfreeze)

The vanished triangle, Deleuze says, is not actually there, but is there “virtually,” because the vanishing lines have not yet entirely merged together at the corner. So the infinitely small legs of the smaller triangle are still distinct from each other and from the corner they are collapsing upon; and yet, they also do not extend beyond it. Thus, they do not bear extensive magnitudes but rather only intensive ones, which we will treat as degrees of variation. The philosophical idea here – difference without terms – is essential to Deleuze’s Spinozistic notion of affection. And it will allow us to see how Deleuze can use Spinoza’s diagram to illustrate both the intensive and extensive infinities that are involved in affection.

(Thanks en.wikipedia.org/ A.Greg)

Extensive bodies, for Spinoza, are divisible until reaching what he calls simplest bodies. Simplest bodies form compounds when ones moving at the same or at different speeds maintain a fixed relation in their mutual motions and when “the laws or nature of one part adapts itself to the laws or nature of another part in such wise that there is the least possible opposition between them.”

These infinitely small simplest bodies are never found alone, but rather only in infinite sets. These sets reciprocally unite with other infinite sets to compose a more complex body. These compound bodies are then combined with other bodies, and so on to higher orders until reaching the whole of Nature.

(Credits in order)
(colliding particles: Thanks A.Greg / en.wikipedia.org)
(blue molecule: Thanks M.L. Rahman / faculty.bracu.ac.bd)
(heart cell: Thanks Bluegrass Pundit / scinewsblog)
(heart beating: Thanks Sterile Barrier Solutions / sbsmed.net)
(circulatory system: Thanks John U / quietmoment.org)
(Egypt bridge protest: Thanks Freemanfilmsuk / youtube.com)
(Amazon river: Thanks BestofAttenborough /youtube.com)
(earth: Thanks UweTube / youtube.com)
(solar system: Thanks animated-sun.weebly.com)
(spiral galaxy: Thanks Kanal von beltoforion1 /youtube.com)
(galaxies: Thanks BrainMind.com / youtube.com)

In his letter on blood, Spinoza has his correspondent imagine a tiny worm so small that it can swim through the blood and observe how its tiniest particles collide and communicate their motion. The worm would see that the simple bodies of blood, the lymph and chyle, continually affect one another’s speeds. Yet, because they maintain their mutual affections without one destroying the other, they together make up the composite body that is our blood. The ratio of their speeds is a level of power that must stay within certain limits.


For otherwise, the simple bodies could decompose and enter into other relations. This happens, for example, when arsenic enters the blood. They will not combine. Rather, on account of their incompatible levels of power, arsenic will decompose our blood.

This sends a chain reaction of affective shockwaves throughout the body, decomposing all the other higher orders of differentially related parts. If it decreases our whole body’s power below a certain threshold, we die. Our body no longer expresses our modal essence, but instead its rearranged parts express the essences of other modes, such as the worms and soil we recompose into.

Thus, Deleuze interprets the infinity diagram as showing how a finite body extending between the limits of its size is divisible into an infinity of simplest bodies.

(Animation above is my own, made with GIMP and Unfreeze,
image from Spinoza, Opera vol. 2, archive.org, p.233)

Now to understand intensive infinities, first consider a ball on a chain swung in a circle. There are competing forces acting on the ball: on the one hand, it wants to fly outward, but on the other hand, its chain pulls it inward. As a result, the ball is always tending to go some certain way at each moment in its circular motion. If we were to cut the ball loose, it would not fly-off in a spiral, but instead outward in a straight line. This would also be the tangent to a circle’s curve at that point.

(Animation above is my own, made with OpenOffice Draw and Unfreeze)

The tangent on curves is like a tendency in the line’s change of direction at that place that is only implied in the movement. Physicists use techniques to find the instantaneous velocity of a moving object; it is something like the speed it is tending to go at that moment.


But how can a velocity be instantaneous? Well, nonetheless, it is a real quantity in the physical world, although it exists only as a virtuality.

Now, for a curve moving in a somewhat more irregular path, finding its tendency-toward-change is more complex, and here is where we might use Leibniz’ method.

(Animation above is my own, made with OpenOffice Draw and Unfreeze)


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

Sometimes we can almost feel where a certain part of the curve is heading just by judging its pattern of change. We can also create a triangle showing how the curve’s dimensions extend in a certain region. Then, like with Leibniz’ triangles, we slowly diminish the two triangle legs, and the third diagonal side gives us the tangent, which also tells us which way the curve is tending at that place.

Now, when sets of simplest bodies affectively impact the parts of our own bodies, their shocking collision corresponds with the production of an idea of that object in our imagination. “I look at the sun,” says Deleuze, “and the sun little-by-little disappears and I find myself in the dark of night; it is thus a series of successions, of coexistences of ideas, successions of ideas.” These ideas also correspond to an increase or decrease in our power of acting, and the variations are continuous.

He has us imagine that we encounter on the street our enemy Peter who makes us afraid. Yet, we suddenly turn our glance toward our friend Paul, whose charm reassures us. While moving from the ideas of Peter to Paul, we underwent a continuous increase in our power of action. These variations, Deleuze explains, are ever-altering quantities: “In other words, there is a continuous variation in the form of an increase-diminution-increase-diminution of the power of acting or the force of existing of someone according to the ideas which she has,” and “this kind of melodic line of continuous variation will define affect.”

In the 22nd letter, we find “nothing else pertains to an essence than that which it possesses at the moment it is perceived.” Deleuze reinterprets this as, “there belongs to an essence only the present, instantaneous affection that it experiences.” Deleuze offers an example of this instantaneity of an affective alteration.


We are meditating in a dark room. Then without warning, someone enters the room and abruptly turns on the lights, which completely dazzles us and renders us no longer able to maintain mental focus.

We pass between two very different states in a “lightning fast” alteration: “Two successive affections, in cuts. The passage is the lived transition from one to the other.” Every passage between affections is then necessarily an increase of power or a decrease of power. So if instead we are looking for our glasses in the complete dark, and then someone turns on a dim light, we appreciate him, because then the light increased our power of action. What we note here especially is that the affection’s increase or decrease is seen as instantaneous, which means it does not extend in time. Rather, it is an intensity.

Hence Deleuze’s other illustrative use of the diagram. A body has a certain range of affective power, and when an affection takes it beyond its limits, the body’s parts decompose into other bodies, like when arsenic enters the blood. So consider how there is a largest and smallest limit in the diagram, and throughout it is a continuum of an infinity of differential variations. Deleuze has us conceive this range of variation as representing the range of affective power that we can sustain before we decompose. So this is the intensive infinity.

(Animation above is my own, made with GIMP and Unfreeze,
image from Spinoza, Opera vol. 2, archive.org, p.233)

Now, according to Deleuze, we obtain Spinoza’s second kind of knowledge through our interactive contact with affecting bodies. As we saw with arsenic, the affections of other bodies can decompose us. Yet, in many cases when we are threatened by certain affections, we might know how to modify our own bodies so that we may sustain ourselves.

Deleuze cites an example in Dante’s Inferno. A damned soul is pelted with rain. Yet, rather than let the rain destroy him, he continually modifies the relations of his own body’s parts by twisting around, so that he may co-sustain with the rain’s affections. By making changes in the relations of our body-parts, we send waves of affective alteration throughout us on the level of our simplest bodies.


These internal self-affective shock-waves are in a dance of sorts with the external waves of affection, and their perpetuated interaction is what Deleuze here calls “rhythm.” Another example he offers is swimming. While in the water, a wave draws near us. When it strikes, we and the wave affect each other’s simplest-body arrangements. In that very instant we might be learning how to adjust to the wave’s decompositional forces. By modifying our own body’s composition, we may stay afloat and swim in conjunction with the wave, causing our body and the wave to become a compound, a larger body.

Another illustration better expresses how the rhythm of affection is a matter of differential relations. Deleuze explains that a violin and a piano playing independently do not really produce affective rhythm. However, they may achieve a rhythmic relationship during a joint performance if the violin plays in response to the piano all while simultaneously the piano performs in response to the violin. In this way, they each affectively modify one another while at the same time they modify themselves, which sustains their dual improvisation. And according to Deleuze, Cézanne also describes this rhythmic interaction when he wrote about “how to compose the canvas-easel relation with the relation of wind, and how to compose the relation of the easel with the sinking sun, and how to end up in such a way that I might paint on the ground, that I might paint lying on the ground.”

This portrayal of Spinoza’s affection will now serve to interpret some difficult terminology in Deleuze’s Francis Bacon book. Deleuze writes here that in simple sensations, rhythm “appears as the vibration that flows through the body without organs, it is the vector of the sensation, it is what makes the sensation pass from one level to another.”


The vector here is like the intensity of the affective variation to change its quantitative value. We could then conceive the body without organs as the Spinozistic body composed of continually altering differential relations. Hence, Deleuze writes that the body without organs is “an intense and intensive body. It is traversed by a wave that traces levels or thresholds in the body according to the variations of its amplitude. Thus the body does not have organs, but thresholds or levels.” As the damned soul in Dante’s Inferno twists his once protected side toward the pelting rain, waves of affective variation now impact the newly exposed part directly. It then becomes the site of sensation, where the internal waves of self-affection meet the external waves of affective variation. Yet this status is temporary, because he continually twists in the rain, making instead other parts of his body the new sites of affective reception.

Deleuze continues: “When the [internal] wave encounters external forces at a particular level, a sensation appears. An organ will be determined by this encounter, but it is a provisional organ that endures only as long as the passage of the wave and the action of the force, and which will be displaced in order to be posited elsewhere.” Sensational rhythm, Deleuze explains, can be the unpredictable variance of intensity waves that continually alters our bodily composition.

Thus Deleuze’s body without organs and its waves of sensational intensity can be viewed in light of his conception of the Spinozistic body and its continuous variations of affection, with the concept of ‘rhythm’ playing a similar role in both cases.

This provides us with a more substantial explanation for one of Deleuze’s few attacks on traditional phenomenology, in this case regarding the body without organs in contrast to the phenomenological lived body.

He writes: "this rhythmic unity of the senses can be discovered only by going beyond the organism. The phenomenological hypothesis is perhaps insufficient because it merely invokes the lived body. But the lived body is still a paltry thing in. We can seek the unity of rhythm only at the point where rhythm itself plunges into chaos, into the night, at the point where the differences of level are perpetually and violently mixed. Beyond the organism, but also at the limit of the lived body, there lies […] the body without organs."


Thus, Deleuze breaks from traditional phenomenology’s manner of conceiving the composition of the body as being made of harmoniously integrated parts that work organically with each other and with the world around them during phenomenal experiences. Nothing in its environment would stand out and appear to such a body that is completely accustomed to all the affective influences around it. Rather, for phenomena to appear to us, our bodies would need to sense things that stand out; we would need to detect differences.

A Deleuze-inspired phenomenology would explain bodily-given phenomena that appear to our affective awareness as being based on differential relations within us, throughout the phenomenal world around us, and between our bodies and the world.


Image credits:

Blue and red particles in motion
http://en.wikipedia.org/wiki/File:Translational_motion.gif
Thanks A.Greg

Blue molecule in motion
http://faculty.bracu.ac.bd/~mlrahman/Research.html
Thanks M.L. Rahman

Heart cell
http://scinewsblog.blogspot.com/2011/04/scientists-turn-blood-cells-into.html
Thanks Bluegrass Pundit

Heart beating
http://sbsmed.net/
Thanks Sterile Barrier Solutions

Circulatory system animated gif
http://www.quietmoment.org/my_weblog/2011/03/mysteries-of-the-human-body.html
Thanks John U.

Egypt protestors on a bridge
http://www.youtube.com/watch?v=rXbRdumboZ0
Thanks Freemanfilmsuk

Amazon river
http://www.youtube.com/watch?v=dn53PtW0AnA
Thanks BestofAttenborough

Earth
http://www.youtube.com/watch?v=hALtHnu4WEo
Thanks UweTube

Solar system
http://animated-sun.weebly.com/animated-solar-system.html
Thanks animated-sun.weebly

Spiral Galaxy
http://www.youtube.com/watch?v=AD9OV1Zrs4I
Thanks Kanal von beltoforion1

Galaxies
http://www.youtube.com/watch?v=X5zVlEywGZg
Thanks BrainMind.com

Spinoza. Opera, vol. 2. Edited by Carl Gebhardt. Heidelberg: Winter, 1972.
http://archive.org/details/operaquotquotre00landgoog

Geometrical Derivative animation:
http://faculty.uncfsu.edu/msiddiqu/Maple_Animations.htm
http://faculty.uncfsu.edu/msiddiqu/images/images/Gif_Folder/Definition%20of%20Derivative18.gif
Thanks Dr. Siddique of Fayetteville State University

The DeComposition of Our Body's Functions. Review and philosophical application of Compound Functions in Edwards & Penney's Calculus (Section 1.4)

presentation of Edwards & Penney's work, by Corry Shores
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Edwards & Penney's Calculus is an incredibly-impressive, comprehensive, and understandable book. I highly recommend it.

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[I your author am not a mathematician; I am merely an admirer of Edwards & Penney's wonderful calculus book. Please consult the text or other references to be certain about anything in the summary below. I mean this emphatically.]

[Other Entries in the Edwards & Penney's Calculus Series]

The DeComposition of Our Body's Functions

Review and philosophical application of
Edwards & Penney's Calculus
Compound Functions
in
Section 1: Functions, Graphs, and Models
Subsection 4: Transcendental Functions

What Do Compound Functions Got to Do With You?

Consider if we are trying to lose weight. So we go on a diet. Over the course of a day, we begin to feel our appetite increase. So this would be one function: as time increases, our appetite increases. But then, as our appetite increases, there is a decrease in our willpower to hold strictly to the diet. So our decrease in willpower is like a function compounded on the first function. Our lives are filled with many such highly complex functional relations.

Brief Summary:

Functions can be compounded one-upon-another as if the output of one machine instantly becomes the input of another.

Points Relative to Deleuze
[Under Ongoing Revision]

We might find a composition of functions in Deleuze's account of sensation, building from his portrayal of Spinoza's affection. Deleuze's example is that we are looking for our glasses in a dark room. Someone enters and turns on the light. This causes us to make a transition from the way we are affected by the dark to the way we are affected by the light. Because we are searching for our glasses, this affection increases our power to act. Consider instead if we are meditating in the dark room. Then when someone turns on the light, this dazzles us and ruins our concentration, and we lose the power to act.

Affection for Spinoza is a matter of our body's composition. What gives our body its power is the differential relations between the speeds of its simple bodies. But its simple bodies are like calculus differentials, infinitely small parts that only obtain a finite value when put into a differential relation with other simple bodies. Consider if we take poison. This will disrupt the ways the simple bodies in our body differentially relate to one another. This is why we die. Our bodies no longer express the range of differential variations that define us. Instead, they eventually express for example dirt.

Now, Deleuze also places a value on our internal decomposition when it comes to the sensations that affect us. The discord of our faculties is what makes sensations more intense [see here and here.] Also consider Spinoza's Ethics Part IV, Proposition 39, Scholium. He writes:

It sometimes happens, that a man undergoes such changes, that I should hardly call him the same. As I have heard tell of a certain Spanish poet, who had been seized with sickness, and though he recovered therefrom yet remained so oblivious of his past life, that he would not believe the plays and tragedies he had written to be his own : indeed, he might have been taken for a grown-up child, if he had also forgotten his native tongue. If this instance seems incredible, what shall we say of infants? A man of ripe age deems their nature so unlike his own, that he can only be persuaded that he too has been an infant by the analogy of other men. (Elwes translation)

From what Spinoza says about the decomposition of the body, it would seem that to change from child to man, or from poet to someone different, would be a decomposition, and thus a loss of power. But could it be that Deleuze takes the opposite view? To change from child to man is not an expression of our body's frailty. It rather shows our body's power to become something new. Imagine we get a sickness like the Spanish poet, and we no longer recognize our past selves. This would seem to be a loss of power. But that would only be so when we take the perspective of the self whom our body no longer expresses. But our bodies are always as perfect as they can be, given the conditions affecting them at any given moment. So to become someone else is not really a deprivation. It could be a testament to the power of our bodies to become new things, to express new essences. The question for Deleuze might not so much be "What can a body do?" as much as it might be "What can a body become?"

So here would be the composition of functions in this case. A certain affection might for Deleuze increase the intensity of sensation. But that means a decrease in the organization of our faculties and our body's compositional relations. Yet this again would be an increase in our body's power to become new things, to express new relations and essences. So it ultimately is an increase in our body's expressive power.

Edwards & Penney's Calculus
Compound Functions
in
Section 1: Functions, Graphs, and Models
Subsection 4: Transcendental Functions

Recall the function machine.

We can think of functions like these 'black box' machines. The machine takes-in a number from one set of values, and it gives-out a value from another set. So consider the squaring function:

The machine takes-in a 2, for example, and then gives-out a 4.

We can also compound our functions. So we can take the result of one function, and then put it into another 'function machine', if you will.

So let's begin with the function g(x). We put in x, and it gives-out u. We then have another function f(u), which is the same as f(g(x)), and we read it as, 'f of g of x'. So we plug the u into the f function, and it gives out the value for f(u). We can then call f(u), or f(g(x)) a new name. We can call it h(x). So,

h(x) = f(g(x))

This requires that all the x values in g's domain correspond (by means of g) to values in f's domain. We call the g function here the 'inner function', and the f function would then be the 'outer function' in this case.

Edwards & Penney now give an example that will illustrate something about notation for composition of functions.

We will first find f(g(x)). First note the g(x). If our number for x is larger than 1, then we will have a negative number. But when we apply it to the f function, we will have the square root of a negative number. So instead we qualify it:

But let's instead consider if we first take f(x), and then after that apply it to the g function. To avoid having the square root of a negative number, we must first begin with a positive. Then after that, there are no restrictions for the g function. So

Edwards and Penney would like then to distinguish two notations:

f(g(x))

and

f ○ g

Our example above shows that the composition of functions f and g is not the same as g and f.

f ○ g ≠ g ○ f

So the notation f(g(x)) might remind us of multiplication notation. In the case of multiplication, it does not matter what order the functions are multiplied. But as we see in the composition of functions, the order does matter sometimes.

from Edwards & Penney: Calculus. New Jersey: Prentice Hall, 2002, pp. 36-37.

Spinoza. Ethics. Transl. Elwes. available online at:
http://ebooks.adelaide.edu.au/s/spinoza/benedict/ethics/index.html