13 Aug 2017

Bacon’s Pope, 1955, in Deleuze’s Francis Bacon commentary

 

by Corry Shores


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[The following is quotation. My commentary is in brackets (except for painting numbers in the quotation). Proofreading is incomplete, so please forgive my typos.]

 

 


Francis Bacon

 

Pope, 1955

 

screen shot crop

(Thanks source: artimage.org.uk)

 

Painting 57 of Deleuze’s
Francis Bacon: Logique de la sensation. Tome II - Peintures
Painting [19] of the English translation
and Painting [57] of the Seuil 2002 French

[Note: The date given for this painting in the French editions is 1954]

 

 

From the text:

Plus encore le sourire goguenard, presque intenable, insupportable, du Pape de 1954 ou de l’homme assis sur le lit : on sent qu’il doit survivre à l’effacement du corps. Les yeux et la bouche sont si bien pris sur les lignes horizontales du tableau que le visage se dissipe, au profit des coordonnées spatiales où seul subsiste le sourire insistant. [57, 59]

(Deleuze 1981a: 23c; 2002: 34a)

 

Furthermore, there is the scoffing, almost untenable, and insupportable smile of the 1954 Pope [19] or of the man sitting on the bed [11]: one senses that the smile will survive the effacement of the body. The eyes and the mouth are so completely caught up in the horizontal lines of the painting that the face is dissipated, in favor of the spatial coordinates in which only the insistent smile remains.

(Deleuze 2003a: 26a; 2003b: 28c; 2005: 21a)

 

Commentary:

[Deleuze discovers forces acting in and on the Figures in Bacon’s paintings. By means of these forces, the Figure’s body is trying to escape from itself through some opening in the body, like the mouth for example. As it is trying to escape itself, the body in a sense is dissipating or becoming effaced. The forces acting on and in the body are highly contortive. It is hard to imagine the Figure actually enjoying it or finding it pleasing in the sort of relaxed way that invites a smile. So it is odd to see the smiles on Bacon’s figures.

head detail

(askyfilledwithshootingstars.com)

(In this case, the smile seems to be scoffing, and it is “untemable” and “unsupportable” perhaps because such a smile could not endure for long under the tense conditions in the rest of the body.) So there is a disjunction of sorts between the smile and the body. The smile displays what is beginning to escape the body, because the contortive body behind the smile is what is beginning to dissipate. We are to recall the Cheshire Cat whose smile remains after the disappearance of its body.]

 

 

 

 

From the text:

 

L’hystérique, c’est á la fois celui qui impose sa présence, mais aussi celui pour qui les choses et les êtres sont présents, trop présents, et qui donne á toute chose et communique á tout être cet excès de présence. [...] Bacon peut dire avec humour que le sourire hystérique qu’il peint sur le portrait de 1953, sur la tête humaine de 1953, sur le pape de 1955, vient du « modèle » qui était « très nerveux, presque hystérique ». Mais c’est tout le tableau qui est hystérisé.

(Deleuze 1981a: 36c; 2002: 52c)

 

The hysteric is at the same time someone who imposes his or her presence, but also someone for whom things and beings are present, too present, and who attributes to every thing and communicates to every being this excessive presence. [...] Bacon explains rather testily that the hysterical smile he painted on the || 1953 portrait [11] , on the human head of 1953 [13] , and on the 1955 Pope [19] came from a “model” who was  very neurotic and almost hysterical.” But in fact it is the whole painting that is hystericized.

(Deleuze 2003a: 44b; 2003b: 50||51; 2005: 36c)

 

Commentary:

[When an image represents a situation, we might say that the image provides itself in its presence, and the represented element is given indirectly through the representation. Processing images representationally is something more or less cognitive and cerebral. Bacon’s paintings avoid representation while still providing intense sensations, and thus we are not distracted by the cognitive elements and instead are left with the raw presences of the image and its sensations. And we might also note that when we experience an overwhelming sensory experience, it attests both to the presence of those sensations as well as to the presence of whatever may be causing them, including the “forces” that are at work in imposing themselves upon our sensory apparatus. And given how overwhelming the sensations are, it attests to the excessiveness of this presence that has such a disruptive effect on our body’s workings. The Figures in Bacon’s paintings can be said to both themselves experience and express this excessive presence as well as causing us to have an overwhelming sensory experience, and thus they communicate that excessive presence to us. We might also find that in such experiences of sensory overload, our bodies begin to undergo confusions of many physical sorts, like certain components of the sensation being at odds with others. We may for example want to look away from the image in disgust while at the same time being drawn to it with rapt and eager curiosity. While under this mode of experience, we could perhaps notice certain traits of hysteria, coming especially from the lack of control of all the influences, tensions, sensations, and so on wrestling throughout our body. Deleuze’s point in these passages is that the hysteria of these Figures is something found not just in the smiles but throughout their bodies and in fact throughout the rest of the painting. For, the other elements in the painting are involved in the play of forces that give rise the Figure’s hystericized body and smile.]

 

 

Texts:

 

Deleuze, Gilles. 1981a. Francis Bacon: Logique de la sensation. Tome I. Paris: Éditions de la différence.

Deleuze, Gilles. 1981b. Francis Bacon: Logique de la sensation. Tome II - Peintures. Paris: Éditions de la différence.

FB.Fr.1981a

 

Deleuze, Gilles. 2002. Francis Bacon: Logique de la sensation. Paris: Éditions du seuil.

FB.Fr.2002

 

 

Deleuze, Gilles. 2003a. Francis Bacon: The Logic of Sensation [with translator’s introduction (Smith’s “Deleuze on Bacon: Three Conceptual Trajectories in The Logic of Sensation”) and author’s introduction to the English edition]. Translated by Daniel W. Smith. Minneapolis: University of Minneapolis.

FB.Eng.2003a

 

 

Deleuze, Gilles. 2003b. Francis Bacon: The Logic of Sensation [with translator’s preface, preface to the fourth edition by Alain Badiou and Barbara Cassin, author’s foreword, and author’s preface to the English edition]. Translated by Daniel W. Smith. Minneapolis: University of Minneapolis.

FB.Eng.2003b.2

 

 

Deleuze, Gilles. 2005. Francis Bacon: The Logic of Sensation [with translator’s preface, preface to the fourth edition by Alain Badiou and Barbara Cassin, author’s foreword, and author’s preface to the English edition]. Translated by Daniel W. Smith. London/ New York: Continuum.

FB.Eng.2003c.2

 

 

 

Images obtained gratefully from:

https://artimage.org.uk/13180/francis-bacon/pope--1955

 

.

12 Aug 2017

Bréhier (1.2) La théorie des incorporels dans l'ancien stoïcisme, “[The two planes of being: deep, real corporeality and surface incorporeality (predicates)]”, summary


by Corry Shores

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[The following is summary. Bracketed commentary is my own, as is any boldface. Proofreading is incomplete, which means typos are present, especially in the quotation. So consult the original text. Also, I welcome corrections to my interpretations, because I am not good enough with French to make an accurate translation of the text.]




Summary of
 
Émile Bréhier
 
La théorie des incorporels dans l'ancien stoïcisme
 
 

Chapitre premier:

De l’incorporel en général

 

1.2

[The two planes of being: deep, real corporeality and surface incorporeality (predicates)]

 
 
 
 
 
 
Brief summary:
Only the beings that can act and be acted upon are real beings for the Stoics. These are the corporeal bodies. They are composed fundamentally of the element Fire, which under lesser degrees of tension constitutes Air, Water, and Earth. So the whole of the cosmos is fundamentally composed of Fire, and everything in the cosmos cyclically returns to a universal conflagration. As such, what we call bodies can also be understood as regions of the universal Fire-substrate that are unified according to principles of their elemental composition, namely, of their particular mixtures and internal arrangements  of elements (which again are no more than different tensions of the Fire substrate). When we say that one body acts upon another, we can also think of it as one organized region of the universal Fire interpenetrating with another region, creating a new mixture in that general region. So when we see one body interacting with another, we might want to think that the one body causes changes to the properties of the other one. But really, the one region of Fire has intermixed with another, and neither region changed the physical properties of the compositional Fire. It is still Fire at its various degrees of tension. What does change are the arrangements of the elemental parts, which correspond to alterations in the corporeal thing’s way of being (πώς ἔχον) and thus to a change in the thing’s predicates. So when a knife cuts flesh, the two interpenetrate to create a new mixture, and corresponding to the new arrangement within the flesh is a new predicate, “being cut”. [And to the knife’s new arrangement corresponds the predicate “cutting”.] So the action of bodies cause modifications not to other bodies but rather to their predicates. These predicates are entirely incorporeal and at best can additionally manifest in our minds when we conceive them. The Stoics were always sure to make the grammatical structures of their descriptions of corporeals and incorporeals match their physical differences: causes, which can only be corporeals, are always expressed with nouns, and effects, which can only be incorporeals, are always expressed with verbs in the form of predicates. This is the Stoics’ unique philosophical innovation, which, as we will see later, revolutionized logic. In sum, their innovation is that they fashioned the world into two planes: {1} There is the plane of real and profound being, in which there are corporeals (physical bodies) that act and are acted upon by other corporeals on account of physical forces driving their interaction. {2} There is the plane of surface [and unreal] being. It lies at the metaphysical limit of the corporeal plane, remaining directly related to the interactions of corporeals, but not existing as something physically real among those interacting bodies. Here facts (predicates) play at the surface of physical being.  These facts or predicates are the effects which are caused by the corporeal interactions. (In the case of the knife and flesh, the predicate, “being cut” is also “the fact of being cut.” So the action of the knife, in how it intermixes with the flesh, causes the fact-of-being-cut to arise upon the predicative/incorporeal “surface” of the flesh.) As such, the forces driving interaction on the deeper real plane are not exhausted by having produced effects on the incorporeal plane, since these effects are not matters of physical force.
 
 
 
 
 
 
Summary
 

 

1.2.1

[The only true beings recognized by the Stoics are the active cause (τὸ ποιοῦν) and the being that the cause acts upon (τό πάσχον). There are four elements of the world: Fire, Air, Water, and Earth. Fire and Air are active, and they act transformatively upon Water and Earth, which are passive. Fire is the primordial being and the seminal reason of the world, for two reasons: {1} the other elements are absorbed into the Fire (at cosmic cycles), and {2} the other elements are degrees of tension and relaxation of Fire.]

 

The only true beings recognized by the Stoics are in the first place the active cause (τὸ ποιοῦν) and then secondly the beings that the cause acts upon (τό πάσχον). [Recall from Sambursky’s Physics of the Stoics section 1.1 that the Stoics held that the cosmos is a continuous whole surrounded by a void. The continuity of the whole is a dynamic continuity resulting from a cohering activity of a very rarified substrate called pneuma. Pneuma is composed of a mixture of the active elements, Air and Fire, while Water and Earth are the other two passive elements that pneuma serves to bind.] The active elements of the world, fire and air, act transformatively upon the passive elements [Water and Earth]. Air, Water, and Earth are consumed in the universal conflagration. Thus Fire is the primordial being and the seminal reason of the world. The other beings [presumably Air, Water, and Earth, or if not, perhaps any individual object composed of the elements] are produced by a relaxation of the tension of the primordial fire. [I may not get this last point right, so see the final sentence of the quotation below. It might be the following. Air, Water, and Earth are not the effects or the parts of Fires (êtres primitifs), but are rather different states of tension of Fire.]

Les seuls êtres véritables que reconnaissent les Stoïciens, c’est d’abord la cause active (τὸ ποιοῦν), puis l’être sur lequel agit cette cause (τό πάσχον).3 Encore faut-il ajouter que les éléments actifs du monde, le feu et l’air, donnent naissance par transformation aux éléments passifs ; les trois derniers, dans la conflagration universelle, se résorbent eux-mêmes | dans le feu, si bien que l’être primordial est le feu, la raison séminale du monde. Les autres êtres sont produits par une tension moindre, un relâchement du feu primordial. Ils ne sont ni les effets ni les parties des êtres primitifs, mais plutôt des états de tension différents de cet être.

3. Philon du mund. op. 8 (V.S.F. II 111, 18).

(11-12, note, the footnote reads V.S.F rather than S.V.F. in my version)

 

 

 

1.2.2

[The active beings are the pneumata (πνεύματα) or “breaths,” whose actions are evinced through their effects. Through these effects, they can serve as qualities of bodies, namely primary ones: being hot, being cold, being dry, and being wet, and secondary ones like colors and sounds.]

 

Among these active beings are the qualities of bodies. The active beings are the pneumata (πνεύματα) or “breaths” whose actions are evinced through their effects. The active beings as qualities are in the first place the primarily qualities that can belong to the elements, namely, being hot, being cold, being dry, and being wet. And secondly they are such sensible [secondary] qualities as colors and sounds.

Parmi ces êtres actifs se trouvent les qualités des corps ; ce sont des souffles (πνεύματα) dont l’action se montre par leurs effets. Il y a d’abord les premières qualités qui appartiennent aux éléments, le chaud, le froid, le sec, l’humide, puis les autres qualités sensibles comme les couleurs et les sons.

(11)

 

 

 

1.2.3

[We should not understand the Stoic notion of the world as being composed of distinct corporeal things that can be said to be the causes or effects of one another. Rather, beings are spontaneous principles that are different moments or aspects of one same universal being, the Fire.]

 

Bréhier notes that the world is composed not just of material beings made of the elements [Fire primarily, whose lesser degrees of tension are the other elements]. There are as well causes and principles. [I may not get the rest right, so please consult the text below. Given the Stoic cosmology of the universal fire, it is best not to think of the things in the world as being like substantial objects that can cause one another. Rather, beings should be seen as spontaneous “principles” (or let us say for now, “events”) that happen within the one same being, the Fire. But otherwise, in their doctrine of causality, one (corporeal) being cannot be said to be the effect of another (corporeal) being. (See for example the selective summary of Clement’s Stromata section 8.9.)]

Il faut remarquer que l’énumération de ces êtres, qui sont tous les êtres de la nature, ne nous fait pas sortir des causes et des principes. Le monde des Stoïciens est composé de principes spontanés, puisant en eux-mêmes vie et activité, et aucun d’eux ne peut être dit proprement l’effet d’un autre. La relation de cause à effet entre deux êtres est tout à fait absente de leur doctrine. S’il y a relation, elle est d’un tout autre genre : ces principes sont plutôt comme les moments ou les aspects de l’existence d’un seul et même être, le feu dont l’histoire est l’histoire même du monde.

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1.2.4

[Although corporeals cannot be causes or effects of one another (that is to say, they cannot change the corporeal properties of one another), they can still interpenetrate to form new mixtures, which is what really happens when we say that one body is causally influencing another body. Since everything is made of Fire, and since Fire never changes its physical nature (except for its degrees of tension, which is more a matter of distribution rather than composition), that means when one body mixes into another, neither one changes the physical properties of the other. For, their fundamental components of Fire retain their same physical Fire properties. What does change however as a result of the mixture are the arrangements and tensions of their component parts, corresponding to which are changed predicates (attributs) of the mixing bodies. Now, a predicate is not a quality. It is rather a way of being of the corporeal. So when a knife cuts flesh, the knife’s action causes the flesh’s way of being to change and to take on the predicate “being cut,” (and in the same stroke, the flesh’s passion causes the knife to take on the predicate “is cutting”). Predicates, then, are always expressed by verbs. And since they are not corporeal changes but rather correspond to them as incorporeal “events”, that places them at the “limit” or “surface” of the corporeal bodies they are predicates of.]

 

[But even though beings cannot be causes and effects of one another,] real beings can, however, enter into relations with one another, and by means of these relations, they in some sense modify one another. Clement of Alexandria says that real beings are not causes of one another but are rather causes of certain things for one another. [See especially subsection 12.1 of Stromata section 8.9.] These modifications are not themselves realities. They are neither substances nor qualities. One body cannot give new properties (propriétés) to another body. When bodies interact such that causation can be said to occur, what is really happening is that the two bodies interpenetrate and form a mixture (μῐξις or κρᾶσις). So when fire heats iron until it reddens, the fire has not given the iron a new quality (qualité) [redness or heat]; rather, the fire has penetrated into the iron and the fire’s parts now coexist among the iron’s parts. These modifications (modifications) however are not on this level of mixtures. They are not new realities (réalités), as properties (propriétés) of the things; rather, they are only attributes (attributs) (κατηγορήματα) [predicates] of the things. When the scalpel cuts the flesh, the first body (scalpel) produces upon the second body (flesh) not a new property (propriété) but a new attribute (attribut) [predicate], namely, that of being cut. [As we see, we must make some critical terminological distinctions. A property is a physical trait produced by a physical modification. One body cannot cause another body to have a property, because one body can only form a mixture with another. This mixture does not cause the mixed bodies to change their physical traits, that is, their properties; it only changes one another’s attributes or predicates. To continue this account, let me draw from an overall interpretation I gave in my commentary to Luhtala’s On the Origin of Syntactical Description in Stoic Logic section 5.6.2.4; but I will modify it to fit what Bréhier said in section 1.2.3 above. We have Fire primarily, and its various degrees of relaxation are the other elements. But overall, there is just one element, Fire. The parts of fire never change their properties. They only change their mixture arrangements. Different mixture arrangements will correspond to different predicates (here, ‘attributs’). So one thing, which as a corporeal is madee fundamentally of Fire, does not change the properties of another thing, which is also fundamentally Fire. Rather, the two sets of organized Fire particles, like the sets composing the knife and the sets composing the flesh, both enter into mixtures when they interpenetrate. But since all is just one Fire, we can think of their interpenetration as one region of the Fire moving through another region. So the region we call ‘knife’, when it is penetrated by the region we call ‘flesh’, does not thereby involve any physical change to its fundamental Fire particles. Rather, that region we call ‘knife’ now takes on the new incorporeal predicate ‘is cutting’, in accordance with its new compositional mixture. And similarly for the region we call ‘flesh’, the only change to it through this mixture is its new predicate ‘being cut’. I am not sure how to define “quality” yet. We know at least that a quality is not an attribute, because attributes are expressible by verbs. But attribute is defined as an incorporeal predicate, which is of such a physical nature that it is best expressed as a verb.] An attribute does not indicate a real quality. White and black for example [may be qualities, but they] are not attributes. For, an attribute is always expressed by a verb. This means that it is not a being, rather, it is a way of being. [It is not a thing itself, but rather] it is a category of being, πώς ἔχον. [See Luhtala On the Origin section 5.5.3.7 and Sambursky Physics section 1.4. Luhtala calls it “disposition” and Sambursky, “state”.] This way of being is somehow found at the limit of the being, that is to say, at the surface of the being. And this way of being cannot change its nature [Or, maybe, this way of being cannot change the nature of the thing it is affixed to.] Also, a way of being is neither active nor passive. For, in order for something to be passive, that would require that it be a corporeal that is suffering some action. Yet, some specific way of being, like “being cut”, is not itself suffering some action. Rather, it purely and simply is a result or effect of some interaction/interpenetration of bodies, and thus it should not itself be considered among the class of beings.

Les êtres réels peuvent cependant entrer en relation les uns avec les autres, et au moyen de ces relations, se modifier. « Ils ne sont pas, dit Clément d’Alexandrie exposant la théorie stoïcienne, causes les uns des autres, mais causes les uns pour les autres de certaines choses »1. Ces modifications sont-elles des réalités? des substances ou des qualités? Nullement : un corps ne peut pas donner à un autre des propriétés nouvelles. On sait de quelle façon paradoxale les Stoïciens sont obligés de se représenter les relations entre les corps, pour éviter cette production des qualités les unes par les autres : ils admettaient un mélange (μῐξις ou κρᾶσις) des corps qui se pénétraient dans leur intimité, et prenaient une extension commune. Lorsque le feu échauffe le fer au rouge par exemple, il ne faut pas dire que le feu a donné au fer une nouvelle qualité, mais que le feu a pénétré dans le fer pour coexister avec lui dans toutes ses parties 2. Les modifications dont nous parlons sont bien différentes : ce ne sont pas des réalités nouvelles, des propriétés, mais seulement des attributs (κατηγορήματα). Ainsi lorsque le scalpel tranche la chair, le pre- | mier corps produit sur le second non pas une propriété nouvelle mais un attribut nouveau, celui d’être coupé 1. L’attribut, à proprement parler, ne désigne aucune qualité réelle ; blanc et noir par exemple ne sont pas des attributs, ni en général aucune épithète. L’attribut est toujours au contraire exprimé par un verbe, ce qui veut dire qu’il est non un être, mais une manière d’être, ce que les Stoïciens appellent dans leur classement des catégories un πώς ἔχον. Cette manière d’être se trouve en quelque sorte à la limite, à la superficie de l’être, et elle ne peut en changer la nature : elle n’est à vrai dire ni active ni passive, car la passivité supposerait une nature corporelle qui subit une action. Elle est purement et simplement un résultat, un effet qui n’est pas à classer parmi les êtres.

(11-12)

1. Strom. VIII 9 (V.S.F. II 121, 4).

2. Stob. Ecl. I, p. 154 (S.V.F. II 153, 9).

(11)

|

1. Sextus Math. IX 211 (S.V.F. II 119, 21) ; cf. les idées d’Archédème (S.V.F. III 262, 31).

(12)

[Note, regarding Bréhier’s Stob. Ecl. I, p. 154 (S.V.F. II 153, 9). There is no English translation that I can find, but there is a similar passage by Alexander (On mixture 216, 14-218,6 / SVF 2.473): “Moreover they say that fire as a whole passes through iron as a whole while each of them preserves its own substance” (Long & Sedley 291).]

 

Some of these passages above are translated by Mark Lester and Charles Stivale in The Logic of Sense:

When the scalpel cuts through the flesh, the first body produces upon the second not a new property but a new attribute, that of being cut. The attribute does not designate any real quality

 

it is, to the contrary, always expressed by the verb, which means that it is not a being, but a way of being.

 

This way of being finds itself somehow at the limit, at the surface of being, the nature of which it is not able to change: in fact, neither active nor passive, for passivity would presuppose a corporeal nature which undergoes an action. It is purely and simply a result, or an effect which is not to be classified among beings.

(Deleuze 1969: 14; Deleuze 1990: 5; Deleuze 2004: 8)

 

 

 

1.2.5

[These predicate-effects are what we today call facts (faits) or events (événements). Predicates are incorporeals, and they are what is said or affirmed of corporeals. As such, they have no bodily existence but can enter to some extent into the mind. Causes, which are corporeals, are always expressed using nouns, and effects, which are predicates, are always expressed using verbs.]

 

The predicates, being results of the actions of corporeals, are what we today call facts (faits [and not ‘états de choses’]) or events (événements). Predicates are not corporeals or properties of corporeals; rather, they are what is said of a corporeal or what is affirmed of a corporeal. By making the predicates incorporeal, the Stoics exclude them from real beings, while at the same time, this places predicates to some extent within the mind. Sextus Empiricus says that when a body acts upon another body, the first one becomes a cause for the second, and what it causes for the second is something incorporeal. [« Tout corps devient ainsi cause pour un autre corps (lorsqu’il agit sur lui) de quelque chose d’incorporel ». See Luhtala Origins section 5.6.2.6, quoting Sextus: “The Stoics say that every cause is a body which becomes the cause to a body of something incorporeal.” (Adv. math. IX,211 = SVF 2.341, tr. Long/Sedley 1987: 333)] We see this mental/linguistic nature of the incorporeal in the concern the Stoics always have for how language expresses the predicate or effect of bodily mixture: the effect is always expressed as a verb. So for example, hypochondria should not be understood as the cause of the fever. Rather, hypochondria should be understood as the cause of the fact that the fever occurs. And in the all the examples [of Clement] that follow this one, the causes are never facts (faits) but are always corporeals expressed as substantives: stones, teacher (maître), and so on. However, the effects are always predicates like “being stable,” “making progress,” and as such, they are always expressed by verbs. [Note, regarding hypochondria, I am not sure how that relates to the spleen and fever example of Clement, Stromata section 8.9, subsection 12.2. I so far have only found a discussion of it in these terms on a google book search, here, at p.224 of Jean-Joël Duhot’s La conception stoïcienne de la causalité. The examples of the stones in the archway having the predicates “remaining together” and the teacher and student “making progress” are found in subsection 12.3 of Stromata section 8.9. For more discussion on this noun/verb relation between causes and effects, see Luhtala Origins for example sections 5.6.2.5- 5.6.2.10]

Ces résultats de l’action des êtres, que les Stoïciens ont été peut-être les premiers à remarquer sous cette forme, c’est ce que nous appellerions aujourd’hui des faits ou des événements : concept bâtard qui n’est ni celui d’un être, ni d’une de ses propriétés, mais ce qui est dit ou affirmé de l’être. C’est ce caractère singulier du fait que les Stoïciens mettaient en lumière en disant qu’il était incorporel, ils l’excluaient ainsi des êtres réels tout en l’admettant en une certaine mesure dans l’esprit. « Tout corps devient ainsi cause pour un autre corps (lorsqu’il agit sur lui) de quelque chose d’incorporel » 2. L’importance de cette idée pour eux se fait voir par le souci qu’ils ont d’exprimer toujours dans le langage, l’effet par un verbe. Ainsi il ne faut pas dire que l’hypochondrie est cause de la fièvre, mais cause de ce fait que la fièvre arrive 3, et dans tous les exemples qui suivent les causes ne sont jamais des faits mais toujours des êtres exprimés par un substantif : les pierres, le maître, etc., et les effets : être stable, faire un progrès, sont toujours exprimés par des verbes.

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2. Sexus, ibid. [Sextus Math. IX 211 (S.V.F. II 119, 21) ; cf. les idées d’Archédème (S.V.F. III 262, 31).]

3. Clem. Alex. Loc cit. [Strom. VIII 9 (V.S.F. II 121, 4)]

(12)

 

 

 

1.2.6

[There are two planes of being. {1} There is the plane of real and profound being, in which there are corporeals (physical bodies) that act and are acted upon by other corporeals on account of physical forces driving their interaction. {2} There is the plane of surface (and unreal) being. It lies at the metaphysical limit of the corporeal plane, remaining directly related to the interactions of corporeals, but not existing as something physically real among those interacting bodies. Here facts (predicates) play at the surface of physical being. They are the effects which are caused by the corporeal interactions. As such, the forces driving interaction on the deeper real plane are not exhausted by having produced effects on the incorporeal plane, since these effects are not matters of physical force.]

 

[First I will state the points Bréhier makes, and afterward I will comment.] The incorporeal fact (fait) is in some sense at the limit of the action of bodies. The form of a living being is predetermined in the germ that develops and grows. But this exterior form does not constitute a part of the living thing’s essence. Rather, the living thing’s exterior form is a result of an internal action that extends in space. And this internal action is not determined by the condition of filling out into its limits. In the same way, the action of a body, which is its internal force, is not exhausted in the effects that it produces. The effects of the body’s action do not come at any cost to its internal forces, and it does not affect the corporeal being in any corporeal way. So for example the act of cutting does not add anything to the nature or to the essence of the scalpel. The Stoics put force and thus all of reality not in events, that is, in the multiple, diverse processes that beings accomplish. Rather, they put force and reality into the unity to which belongs all the parts. In a sense, this makes them not too much unlike David Hume and John Stuart Mill, who reduce the universe to facts or events. But in another sense, the Stoics make possible a new sort of conception, which radically separates two planes of being. One the one hand, there is the plane of real and profound [corporeal] being, which includes force; while on the other hand there is the plane of [incorporeal] facts (faits), which are found playing on the surface (surface) of [real corporeal] being and which constitute an infinite multiplicity of incorporeal beings. [My comments on the above points: The incorporeal facts lie at the limit of the action of bodies. This “limit” seems to be a metaphysical limit, meaning that they lie beyond the realm or plane of corporeals, but still at the edge so to remain in an intimate relation with corporeals. It is in this sense that they lie at the surface. A living being will take on a form that is determined by the germ it develops from. But unlike what we saw with the Platonic conception in section 1.1, that form is not like an essence that causes the living thing’s parts to develop the way they do. Rather, it is caused internally by the forces at work among the corporeal elements that are able to act and be acted upon. As we have seen, the cause is corporeal but the effect is incorporeal. So the corporeal cause of development in the corporeal world, which is a matter of the physical forces at work in corporeal action, does not become exhausted in its causal action. Rather, there are just bodies acting and being acted upon by other bodies, which is a matter of new mixtures constantly being created. The effects they have are found on another plane of being, and so it is not like anything was subtracted from the physical forces, as the incorporeal plane does not admit of physical force. What is interesting to keep in mind is that only the corporeal plane is real, and the incorporeal plane is not. So the events/predicates/results of corporeal action are not found as real things among the real bodies of our world. But they are not so distant that our world bears to direct relationship to these incorporeals. Rather, they sort of dance or play at the metaphysical “surface” of physical reality. They are sort of hovering somewhere, but they have no location. They at best can only enter our minds when we conceive them.]

Le fait incorporel est en quelque façon à la limite de l’action des corps. La forme d’un être vivant est prédéterminée dans le germe qui se développe et qui s’accroît. Mais cette forme extérieure ne constitue pas une partie de son essence ; elle est subordonnée comme un résultat à l’action interne qui s’étend dans l’espace, et celle-ci n’est pas déterminée par la condition de remplir ses limites. De la même façon l’action d’un corps, sa force | interne ne s’épuisent pas dans les effets qu’il produit : ses effets ne sont pas une dépense pour lui et n’affectent en rien son être. L’acte de couper n’ajoute rien à la nature et à l’essence du scalpel. Les Stoïciens mettent la force et par conséquent toute la réalité non pas dans les événements, dans les démarches multiples et diverses qu’accomplit l’être, mais dans l’unité qui en contient les parties. En un sens, ils sont aussi loin que possible d’une conception comme celle de Hume et de Stuart Mill qui réduisent l’univers à des faits ou événements. En un autre sens pourtant, ils rendent possible une telle conception en séparant radicalement, ce que personne n’avait fait avant eux, deux plans d’être : d’une part, l’être profond et réel, la force ; d’autre part, le plan des faits, qui se jouent à la surface de l’être, et qui constituent une multiplicité sans lien et sans fin d’êtres incorporels.

(12-13)

 

From the Mark Lester and Charles Stivale translation in The Logic of Sense:

[The Stoics distinguished] radically two planes of being, something that no one had done before them: on the one hand, real and profound being, force; on the other, the plane of facts, which frolic on the surface of being, and constitute an endless multiplicity of incorporeal beings.

(Deleuze 1969: 14; Deleuze 1990: 5; Deleuze 2004: 8)

 

 

 

1.2.7

[We first needed to see how corporeals revolutionized metaphysics so that we can next examine how they revolutionized logic.]

 

We next will examine how incorporeals constitute the material of all Stoic logic. Thus incorporeals will replace the genera and species of Aristotelian logic. We needed first to see how the Stoic’s original conception of incorporeality worked in their physics in order to better grasp how it revolutionized logic.

Nous allons montrer maintenant que ces incorporels constituent la matière de toute la logique stoïcienne, se substituant ainsi dans la logique aux genres et aux espèces de la logique d'Aristote. Il était nécessaire de montrer d'abord dans la physique les raisons de cette révolution de la logique.

(13)

 

 

 

 

 

Bréhier, Émile. 1962. La théorie des incorporels dans l'ancien stoïcisme. 3rd Edn. Paris: Vrin.

PDF of a microfilm version available at:

https://archive.org/details/lathoriedesincor00brhi

 

 

Also cited:

Deleuze, Gilles. 1969. Logique du sens. Paris: Les éditions de minuit.

 

Deleuze, Gilles. 1990. The Logic of Sense. Translated by Mark Lester and Charles Stivale. Edited by Constantin Boundas. New York: Columbia University Press.

 

Deleuze, Gilles. 2004. The Logic of Sense. Translated by Mark Lester and Charles Stivale. Edited by Constantin Boundas. London / New York: Continuum [first published in English: Columbia University Press, 1990].

 

Long, Anthony A. and David N. Sedley. 1987. The Hellenistic Philosophers, vol.1: Translations of the Principle Sources, with Philosophical Commentary. Cambridge: Cambridge University Press

 
 

.

Bacon’s Sphinx, 1954, in Deleuze’s Francis Bacon commentary

 

by Corry Shores


[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

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[Entry collecting the images of the paintings in this text.]


[I am profoundly grateful to the sources of these images:

museumtv.nl

www.buzzle.com

euroartmagazine.com

Credits given at the end.]

 

[The following is quotation. My commentary is in brackets. Proofreading is incomplete, so please excuse my typos.]

 

 


Francis Bacon

 

Sphinx, 1954

 

sphinx 1951 .. www.museumtv.nl .. 1953-Francis-Bacon-Sphinx

(Thanks museumtv.nl)

 

 

Painting 81 of Deleuze’s
Francis Bacon: Logique de la sensation. Tome II - Peintures
Painting [18] of the English translation
and Painting [81] of the Seuil 2002 French

 

 

From the text:

À travers les siècles, bien des choses font de Bacon un Égyptien. Les aplats, le contour, la forme et le fond comme deux secteurs également proches sur le même plan, l’extrême proximité de la Figure (présence), le système de la netteté. Bacon rend à | l’Égypte l’hommage du sphinx, et déclare son amour de la sculpture égyptienne [...] Toutefois, si proche que Bacon soit de l’Égypte, comment expliquer que son sphinx [81] soit brouillé, traité « malerisch » ?

(Deleuze 1981a: 79|80; 2002: 116b,c)

 

Through the centuries, there are many things that make Bacon an Egyptian: the fields, the contour, the form and the ground as two equally close sectors lying on the same plane, the extreme proximity of the Figure (presence), the system of clarity [netteté]. Bacon renders to Egypt the homage of the sphinx [18], and declares his love for Egyptian sculpture [...] Yet as close as Bacon may be to Egypt, how can we explain the fact that his sphinx is scrambled, treated in a “malerisch” manner?

(Deleuze 2003a: 100ab,c; 2003b: 123c,124b; 2005:86b,c)

[Note, the painting in the French editions is cited at the end of the paragraph, and in the English editions near the beginning.]

 

Commentary:

[Bacon admired Egyptian art. Deleuze identifies certain features in Bacon’s style that can be attributed to that influence. For example, in Egyptian bas-relief, the figures are set along the 2-dimensional plane of their background.

 

media.buzzle.com 1200-10924613-egyptian-basrelief

(Thanks www.buzzle.com)

 

We often see something similar in Bacon’s paintings.

 

[1] Francis Bacon: Triptych, Three Studies for Figures at the Base of a Crucifixion, 1944.

Bacon Three Studies for Figures at the Base of a Crucifixion 1944 might be high res www.euroartmagazine.com 1197105656

(euroartmagazine.com Thanks Dr. Gerry Coulter)

 

But in this Sphinx painting, where Bacon pays tribute to Egyptian art, the Figure does not itself have very clearly discernible features, and it is not so clearly discernible with respect to its background. Deleuze wonders why.

 

[18] Francis Bacon: Sphinx, 1954

sphinx 1951 .. www.museumtv.nl .. 1953-Francis-Bacon-Sphinx

(Thanks museumtv.nl)

 

Bacon, we learn, adds manual, accidental traits to disrupt the figurative givens, which is why his art is not simply geometrical and discernible like Egyptian art.]

 

 

 

Texts:

 

Deleuze, Gilles. 1981a. Francis Bacon: Logique de la sensation. Tome I. Paris: Éditions de la différence.

Deleuze, Gilles. 1981b. Francis Bacon: Logique de la sensation. Tome II - Peintures. Paris: Éditions de la différence.

FB.Fr.1981a

 

Deleuze, Gilles. 2002. Francis Bacon: Logique de la sensation. Paris: Éditions du seuil.

FB.Fr.2002

 

 

Deleuze, Gilles. 2003a. Francis Bacon: The Logic of Sensation [with translator’s introduction (Smith’s “Deleuze on Bacon: Three Conceptual Trajectories in The Logic of Sensation”) and author’s introduction to the English edition]. Translated by Daniel W. Smith. Minneapolis: University of Minneapolis.

FB.Eng.2003a

 

 

Deleuze, Gilles. 2003b. Francis Bacon: The Logic of Sensation [with translator’s preface, preface to the fourth edition by Alain Badiou and Barbara Cassin, author’s foreword, and author’s preface to the English edition]. Translated by Daniel W. Smith. Minneapolis: University of Minneapolis.

FB.Eng.2003b.2

 

 

Deleuze, Gilles. 2005. Francis Bacon: The Logic of Sensation [with translator’s preface, preface to the fourth edition by Alain Badiou and Barbara Cassin, author’s foreword, and author’s preface to the English edition]. Translated by Daniel W. Smith. London/ New York: Continuum.

FB.Eng.2003c.2

 

 

 

Images obtained gratefully from:

https://www.museumtv.nl/app/uploads/2016/10/1953-Francis-Bacon-Sphinx.jpg

 

www.buzzle.com/articles/bas-relief-vs-high-relief-sculpture-technique.html

 

http://www.euroartmagazine.com/new/?issue=6&page=1&content=140

.

11 Aug 2017

Priest (3.1) An Introduction to Non-Classical Logic, ‘Introduction [to Ch.3, Normal Modal Logics]’, summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

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[The following is summary of Priest’s text, which is already written with maximum efficiency. Bracketed commentary and boldface are my own, unless otherwise noted. I do not have specialized training in this field, so please trust the original text over my summarization. I apologize for my typos and other distracting mistakes, because I have not finished proofreading.]

 

 

 

Summary of

 

Graham Priest

 

An Introduction to Non-Classical Logic: From If to Is

 

Part I. Propositional Logic

 

3. Normal Modal Logics

 

3.1 Introduction [to Ch.3, Normal Modal Logics]

 

 

 

Brief summary:

In this chapter, we examine some extensions of the modal logic K. We also address the question of which modal logics are most suitable for certain sorts of necessity, and we end by examining tense logics with more than one pair of modal operators.

 

 

 

 

Summary

 

3.1.1

[In this chapter we examine extensions of the modal logic system K.]

 

[Recall the modal semantics we examined in section 2.3. We said in section 2.1 that this modal logic is called K (for Kripke). Now] “In this chapter we look at some well-known extensions of K, the system of modal logic that we considered in the last chapter” (36).

 

 

3.1.2

[We also will look at the issue of determining which sorts of modal logics are most suitable for certain notions of necessity.]

 

We will also examine “the question of which systems of modal logic are appropriate for which notions of necessity” (36).

 

 

3.1.3

[We lastly look at tense logics with more than one pair of modal operators.]

 

At the end of the chapter we examine briefly “logics with more than one pair of modal operators, in the shape of tense logic” (36).

 

 

 
 
 

 

Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.

 

 

 
.

Priest (6.1) An Introduction to Non-Classical Logic, ‘Introduction [to Ch.6, Intuitionistic Logic],’ summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

[Logic and Semantics, entry directory]

[Graham Priest, entry directory]

[Priest, Introduction to Non-Classical Logic, entry directory]

 

[The following is summary of Priest’s text, which is already written with maximum efficiency. Bracketed commentary and boldface are my own, unless otherwise noted. I do not have specialized training in this field, so please trust the original text over my summarization. I apologize for my typos and other distracting mistakes, because I have not finished proofreading.]

 

 

 

Summary of

 

Graham Priest

 

An Introduction to Non-Classical Logic: From If to Is

 

Part I. Propositional Logic

 

6. Intuitionistic Logic

 

6.1 Introduction [to Ch.6, Intuitionistic Logic]

 

 

 

Brief summary:

In this chapter we will examine intuitionistic logic. It arose from intuitionism in mathematics, and it has a natural possible world semantics. We will also examine its philosophical foundations and its account of the conditional.

 

 

 

 

Summary

 

6.1.1

[Intuitionistic logic arose from intuitionism in mathematics, and it has a natural possible world semantics.]

 

Priest says that we will examine intuitionistic logic, which “has a natural possible world semantics” and which “arose originally out of certain views in the philosophy of mathematics called intuitionism.

 

 

6.1.2

[We will examine the philosophical foundations of intuitionism and also its account of the conditional.]

 

Priest says that in this chapter “We will also look briefly at the philosophical foundations of intuitionism, and at the distinctive account of the conditional that intuitionist logic provides” (103).

 
 
 

 

Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.

 

 

 
.

Priest (4.1) Doubt Truth To Be a Liar, ‘Introduction [to Ch.4 Contradiction]’, summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

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[The following is summary. My commentary is in brackets. Boldface in quotations is mine unless otherwise indicated. Proofreading is incomplete, so please excuse the typos.]

 

 

 

Graham Priest

 

Doubt Truth To Be a Liar

 

Part 2 Negation

 

Ch.4 Contradiction

 

4.1 Introduction [to Ch.4 Contradiction]

 

 

Brief summary:

Throughout the history of logic, there have been a variety of accounts of negation. One matter of contention is what can be inferred from negations that generate contradictions. The different accounts can be categorized according to whether the contradictions entail: {1} nothing (as in medieval connexivist accounts), {2} something but not everything (as in paraconsistent and relevant logics), and {3} everything (as in classical and intuitionistic logics). The view on negation that interests us is a non-trivial dialetheism where explosion does not hold, that is to say, an account in which the following inference is invalid:

α, ¬α ⊢  β, for an arbitrary β

 

 

Summary

 

4.1.1

[Non-trivial dialetheism allows for special instances of negation involved in contradictions which do not allow us to infer any arbitrary formula.]

 

[In section 2, Priest examined six accounts of truth. He says in section 2.8, the conclusion, that none of these accounts “provides any reason for rejecting dialetheism,” and in fact, “a number of them even point in its direction” (55). He further concludes now in this section that] “there is nothing in the notion of truth that prevents dialetheism from being acceptable” (75). We will now see that dialetheism holds in light of our intuitions about negation. There are however accounts of negation that rule out dialetheism” (75). For example, classical and intuitionistic logics make negation explosive (α, ¬α ⊢  β, for an arbitrary β). As such, they rule out dialetheism, “unless, of course, one is a trivialist” (75). [So probably a dialetheist is one who holds that only certain contradictions are true, and from none of those can we infer any arbitrary formula.] A good view of negation (a dialetheic one) would allow for it to hold for certain contradictions without that leading to triviality.

 

 

4.1.2

[Logical constants, like negation and the conditional, have been debated throughout the history of logic.]

 

Negation is currently considered in logic a “logical constant,” which is a class of logical constants that includes the conditional as well. Throughout the history of logic, the way to analyze such concepts has been heavily debated (75).

 

 

4.1.3

[Throughout the history of logic, there have been a variety of accounts of negation, but they can be categorized according to accounts in which contradictions entail: {1} nothing (as in medieval connexivist accounts), {2} something but not everything (as in paraconsistent and relevant logics), and {3} everything (as in classical and intuitionistic logics).]

 

Negation has seen many rival conceptions in logic. In the 20th century, for example, there were the theories of negation given in the “‘classical’ (Frege/Russell) account and the intuitionist (Brouwer/Heyting) account” (75). Priest notes that there have been rival accounts of negation throughout history. We recall from section 1.13 the three sorts of negation:

those according to which contradictions entail:

1. nothing;

2. something (but not everything);

3. everything.

(75)

Priest says that the third view includes the classical and intuitionist accounts and as well certain later Medieval accounts. The first view includes connexivist accounts from the Middle Ages. And the second view includes contemporary paraconsistent and relevant logics (76).

 

 

 

Graham Priest. 2006. Doubt Truth To Be a Liar. Oxford: Oxford University, 2006.

 

.

Bacon’s Study after Velazquez’s Portrait of Pope Innocent X, 1953, in Deleuze’s Francis Bacon commentary

 

by Corry Shores


[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

[Deleuze Entry Directory]

[Francis Bacon (painter), entry directory]

[Deleuze’s Francis Bacon: The Logic of Sensation, entry directory]

[Entry collecting the images of the paintings in this text.]


[I am profoundly grateful to the source of this image:

artinvest2000.com

Credits given at the end.]

 

[The following is quotation. My commentary is in brackets. Proofreading is incomplete, so please excuse my typos.]

 

 


Francis Bacon

 

Study after Velazquez’s Portrait of Pope Innocent X, 1953

 

Bacon. Pope Innocent X. artinvest2000 .bacon_innocent-x

(Thanks artinvest2000.com)

 

 

Painting 54 of Deleuze’s
Francis Bacon: Logique de la sensation. Tome II - Peintures
Painting [16] of the English translation
and Painting [54] of the Seuil 2002 French

 

 

From the text:

Tout le corps s’échappe par la bouche qui crie. Par la bouche ronde du pape [54] ou de la nourrice [55] le corps s’échappe comme par une artère.

(Deleuze 1981a: 23c; 2002: 33c)

 

The entire body escapes through the screaming mouth. The body escapes through the round mouth of the Pope or the nurse, as if through an artery [16, 24].

(Deleuze 2003a: 25c; 2003b: 28a; 2005:20d)

 

Commentary:

[In Bacon’s paintings, forces apply constricting pressure upon the Figures while at the same time there are forces internal to the Figure that are pushing outward, perhaps as a result of the constriction, like when squeezing a water balloon. On account of this play of forces, the Figure’s body tries to escape itself; and given the chance, it will dissipate through that escaping action. One exit for the escape is through the screaming mouth.

head detail

]

 

 

From the text:

À ce point extrême de la dissipation cosmique, dans un cosmos fermé mais illimité, c’est bien évident que la Figure ne peut plus être isolée, prise dans une limite, piste ou parallélépipède : on se trouve devant d’autres coordonnées. Déjà la Figure du pape [54] qui crie se tient derrière les lames épaisses, presque les lattes d’un rideau de sombre transparence : tout le haut du corps s’estompe, et ne subsiste que comme une marque sur un suaire rayé, tandis que le bas du corps reste encore hors du rideau qui s’évase. D’où l’effet d’éloignement progressif comme si le corps était tiré en arrière par la moitié supérieure. Et sur une assez longue période, le procédé est fréquent chez Bacon. Les mêmes lames verticales de rideau entourent et raient partiellement l’abominable sourire de « Étude pour un portrait [59] », tandis que la tête et le corps semblent aspirés || vers le fond, vers les lattes horizontales de la persienne.

(Deleuze 1981a: 24b; 2002: 34||35)

 

At this extreme point of cosmic dissipation, in a closed but unlimited cosmos, it is clear that the Figure can no longer be isolated or put inside a limit, a ring or parallelepiped: we are faced with different coordinates. The Figure of the screaming Pope [16] is already hidden behind the thick folds (which are almost laths) of a dark, transparent curtain: the top of the body is indistinct, persisting only as if it were a mark on a striped shroud, while the bottom of the body still remains outside the curtain, which is opening out. This produces the effect of a progressive elongation, as if the body were being pulled backwards by its upper half. For a rather long period of time, this technique appeared frequently in Bacon’s works. The same vertical curtain strips surround and partially line the abominable smile of Study for a Portrait [11], while the head and the body seem to sink into the background, into the horizontal slats of the blind.

(Deleuze 2003a: 26d; 2003b: 29b; 2005: 21c)

 

Commentary:

[We often see in Bacon’s paintings the Figure’s being confined within the limits of a geometrical structure, like a circular ring or platform or a rectilinear parallelepiped. But in this painting, which is during Bacon’s malerisch period, there are vertical smear stripes that seeming pull the Figure downward and sideward out of the bottom of its confining structure.

Bacon: Study after Velazquez’s Portrait of Pope Innocent X, 1953

Bacon. Pope Innocent X. artinvest2000 .bacon_innocent-x

(Thanks artinvest2000.com)

]

 

From the text:

Il faut considérer le cas spécial du cri. Pourquoi Bacon peut-il voir dans le cri l’un des plus hauts objets de la peinture [54] [55] ? « Peindre le cri… »

(Deleuze 1981a: 41a; 2002: 60b)

 

We must consider the special case of the scream. Why does Bacon think of the scream as one of the highest objects of painting? “Paint the scream . . .” [16, 24].

(Deleuze 2003a: 51a; 2003b: 60a; 2005: 42d)

 

Commentary:

[Recall from the first commentary the notion of the forces acting upon and within the Figure. To paint the scream is to paint those invisible forces.]

 

 

 

Texts:

 

Deleuze, Gilles. 1981a. Francis Bacon: Logique de la sensation. Tome I. Paris: Éditions de la différence.

Deleuze, Gilles. 1981b. Francis Bacon: Logique de la sensation. Tome II - Peintures. Paris: Éditions de la différence.

FB.Fr.1981a

 

Deleuze, Gilles. 2002. Francis Bacon: Logique de la sensation. Paris: Éditions du seuil.

FB.Fr.2002

 

 

Deleuze, Gilles. 2003a. Francis Bacon: The Logic of Sensation [with translator’s introduction (Smith’s “Deleuze on Bacon: Three Conceptual Trajectories in The Logic of Sensation”) and author’s introduction to the English edition]. Translated by Daniel W. Smith. Minneapolis: University of Minneapolis.

FB.Eng.2003a

 

 

Deleuze, Gilles. 2003b. Francis Bacon: The Logic of Sensation [with translator’s preface, preface to the fourth edition by Alain Badiou and Barbara Cassin, author’s foreword, and author’s preface to the English edition]. Translated by Daniel W. Smith. Minneapolis: University of Minneapolis.

FB.Eng.2003b.2

 

 

Deleuze, Gilles. 2005. Francis Bacon: The Logic of Sensation [with translator’s preface, preface to the fourth edition by Alain Badiou and Barbara Cassin, author’s foreword, and author’s preface to the English edition]. Translated by Daniel W. Smith. London/ New York: Continuum.

FB.Eng.2003c.2

 

 

 

Images obtained gratefully from:

http://www.artinvest2000.com/bacon_study-innocent-x.htm

 

.

10 Aug 2017

Priest (1.13) Doubt Truth To Be a Liar, ‘Some Modern Variations III: Negation as Cancellation’, summary

 

by Corry Shores

 

[Search Blog Here. Index-tags are found on the bottom of the left column.]

 

[Central Entry Directory]

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[The following is summary. My commentary is in brackets. Boldface in quotations is mine unless otherwise indicated. Proofreading is incomplete, so please excuse the typos.]

 

 

 

Graham Priest

 

Doubt Truth To Be a Liar

 

Part 1 Truth

 

Ch.1 Aristotle on the Law of Non-Contradiction

 

1.13 Some Modern Variations III: Negation as Cancellation

 

 

Brief summary:

Asserted formulas have content. And we can negate and conjoin formulas. This raises questions when we conjoin to a formula its own negation, thereby creating a contradiction. What can be said about their contents? With regard to this issue, there are three accounts of the relationship between content, negation, and contradiction. {1} The cancellation account: the content of ¬α in α∧¬α cancels the content of α, thereby leaving the whole conjunction without content. Here the contradiction entails nothing, because it has no content to carry over into an inferred conclusion. This view is seen in Ancient and Medieval logic. And, we see this sort of argument in J. Lear, who takes inspiration from Aristotle’s law of non-contradiction.  He argues that you cannot at one point assert S and then later assert not-S. For, by doing so, the not-S both cancels the content of S while adding no new content, thereby rendering their conjunction meaningless. {2} The complementation account: the content of ¬α includes all of the other content not contained in α, thus α∧¬α contains total content (all content whatsoever). This is the view of classical and intuitionistic logics.  {3} An intermediate account: the content of ¬α is a function of the content of α, but only in such a way that α∧¬α contains partial content, being neither null nor total; thus contradictions can entail some things but not others. This is the view held in relevant and paraconsistent logics. Now, the cancellation account does not work, for a number of reasons. {A} There are borderline situations that are aptly expressed as contradictions, like, it is both raining and it is not raining. But this is not saying nothing at all. {B} Our beliefs can be contradictory. We conclude one assertion from our beliefs at one point, and at another point we conclude the negation of that assertion. The negation is not nothing more than a cancellation of the prior one. It is a belief that we have that is inconsistent with another belief that we have. And since we can continue working with inconsistent information while trying to resolve the contradiction, that cannot mean it is contentless.  We see this for example when there are inconsistent scientific theories. {C} The paradox of the preface. A person writes a book. In its body, the author makes many assertions, and thus she asserts the conjunction of all of the assertions as well. But in the preface, she acknowledges that certainly at least one assertion is mistaken and is thus false. So she both asserts the conjunction of the assertions in the body while also asserting the negation of this conjunction in the preface. 

 

 

 

 

Summary

 

1.13.1

[J. Lear argues that you cannot first assert S and then afterward assert not-S. For, were you to do so, the not-S does not constitute a second assertion in addition to the first; rather, it merely cancels the first assertion.]

 

[Note, this first paragraph refers to ideas stated previously in the text, but I have not summarized them yet. Here I will quote this paragraph in full, and I will fill out the summary later if I post those prior sections.]

Let us now return to Lear. The last passage of his that I quoted (attempting to give an argument for the LNC that is independent of Aristotle’s view of substance) continues:57

One cannot assert S and then directly proceed to assert not-S: one does not succeed in making a second assertion, but only in cancelling the first assertion. This argument does not depend on any theory of substance or on any theory of the internal structure or semantics of statements. It is a completely general point about the affirmation and denial of statements.

Note that this argument is quite distinct from the one given in the first part of the paragraph. That one is about an arbitrary proposition: if the LNC fails, it rules nothing out, and so is not meaningful. The argument is specifically about contradictory propositions, and is to the effect that such a proposition has no content; a fortiori, it has no true content. The argument hinges on quite specific claims about the behaviour of negation. Let us return to it in a moment, after a few appropriate background comments.58

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57. Lear (1988), 263 f.

58. These draw heavily on Routley and Routley (1985)

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1.13.2

[There are three accounts of the relationship between content, negation, and contradiction. {1} The cancellation account: the content of ¬α in α∧¬α cancels the content of α, thereby leaving the whole conjunction without content. Here contradiction entails nothing. {2} The complementation account: the content of ¬α includes all of the other content not contained in α, thus α∧¬α contains total content (all content whatsoever). {3} An intermediate account: the content of ¬α is a function of the content α, but only in such a way that α∧¬α contains partial content, being neither null nor total; thus contradictions can entail some things but not others.]

 

[We will be thinking in terms of the content of the formula letters, like S or α. It seems that we understand this content as being something like their meaning, perhaps given in a propositional sort of form. Priest will then consider the relationship holding between the content, negation, and contradiction. He says there are three accounts of this relationship. {1} Cancellation. When you conjoin a formula with its negation, we understand that to represent the cancellation of the first formula’s content. (Suppose we first say, “It is raining,” then secondly we say, “it is not raining”. We might think of the first sentence’s meaning being cancelled, while its negation’s content is affirmed. However, when we join them as one proposition “It is raining and it is not raining”, then we are not affirming any new content. We are understanding “It is raining and it is not raining” to have no content, even though either assertion individually would.) (I may get the next point wrong, so please consult the quotation below. We next think that an inference is valid when the content of the premises contains the content of the conclusion, but I am not exactly sure how to grasp that. I suppose all the inference rules involve the conclusion having at least one of the atomic formulas in the premises, except for ex falso quodlibet. At any rate, since a contradiction has no content, then as premises we can infer just nothing from them. Priest also says we can infer other contradictions without content. But again I do not know how that works.) {2} Complementation. Here we understand the negation of a formula as meaning all the content not found in the unnegated formula. That means α ∧ ¬α includes all content. (It also means that it entails everything. I am not sure how, but maybe it is something like the following. We assert “a certain situation holds” ((like it is raining)), then next we assert “every other situation except this one holds ((it is doing every other thing but raining)). When we conjoin them, we have asserted every possible situation, thus we can derive any one of them.) {3} Intermediate position. Here we understand the content of ¬α as a function of the content of α. But the content of α ∧ ¬α has only partial content, meaning that it entails some things but not all. (Again I will guess how to understand this. Suppose we use a sort of formulation for motion like in Priest’s In Contradiction section 11.2. So at the instant the pen lifts off the paper, it is both on and not on the paper. From this content, we can infer that the pen is at least on the paper, for example. But we cannot infer that the moon is made of green cheese, or whatever else crosses our mind.)]

One may distinguish between three accounts of the relationship between negation, contradiction, and content. (1) A cancellation account. According to this, ¬α cancels the content of α. Hence, a contradiction has no content. In particular then, supposing that an inference is valid when the content of the premises contains that of the conclusion, a contradiction entails nothing—or nothing with any content; it may entail another contradiction. (2) A complementation account. According to this, ¬α has whatever content α does not have. Hence α ∧ ¬α has total content, and entails everything. (3) An intermediate account, where the content of ¬α is a function of the content of α, but neither of the previous kinds. According to this account, α ∧ ¬α has, in general, partial content, neither null nor total. Hence, contradictions entail some things but not others.

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1.13.3

[The cancellation account is found especially in Ancient and Medieval logic. The complementation account is found in classical and intuitionistic logics. And the intermediate account is found in relevant and paraconsistent logics.]

 

The third account, where contradictions have partial content and entail some but not other things, “is given in relevant and paraconsistent logics” (31). The second account, where negated content is complementary and contradictions entail everything, is found in classical (orthodox modern logics) and intuitionist logic. Priest says that the first account, where negation cancels content, “appears to have been an influential account in Ancient and early Medieval logic” (31). Priest gives some examples: “Arguably, Aristotle subscribed to something like it, since he appears to have rejected the claim that α∧¬α | entails α. (See 1.4. We will have further evidence of this later.) It appears in Boethius and Abelard. It is intimately connected with principles such as ¬(α → ¬α), which are built into modern connexive logics” (31-32).

 

 

1.13.4

[Some philosophers, like Strawson, have confused the cancellation and complementation accounts.]

 

Priest next notes that sometimes philosophers have mistakenly taken the cancellation and complementation accounts to be the same thing. One example comes from Stawson’s Introduction to Logical Theory (1952). In one part of the book, Strawson gives the orthodox account where contradictions entail everything. But then in another part he gives the cancellation account.

Suppose a man sets out to walk to a certain place; but when he gets half way there, he turns round and comes back again. This may not be pointless. But, from the point of view of change of position, it is as if he had never set out. And so a man who contradicts himself may have succeeded in exercising his vocal chords. But from the point of view of imparting information, or communicating facts (or falsehoods) it is as if he had never opened his mouth . . . The point is that the standard function of speech, the intention to communicate something, is frustrated by self-contradiction. Contradiction is like writing something down and erasing it, or putting a line through it. A contradiction cancels itself and leaves nothing.

(32, citing Strawson 2 f.)

 

 

1.13.5

[In Lear’s argument, an assertion α normally conveys information. And also normally, any new assertion will convey additional information. However, when we add the assertion ¬α to the stock of information of α, then not only have we added no new information, we have also removed the information of α.]

 

We return to Lear’s argument, which is based on the cancellation account. Priest articulates it as:

Speaker’s assertions (and here, ‘assertion’ does seem the appropriate word) normally convey information. Normally, when they make a new assertion this adds to the stock of information conveyed. But when the stock contains the information α, an assertion of ¬α adds nothing, but merely removes α.

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1.13.6

[It is not obvious in Lear’s cancellation account why the negation cannot add information rather than subtract given information.]

 

Priest will explain why this account is “sketchy and unsatisfactory” (32). [I probably do not follow this well, so please consult the quotation below. (Suppose we obtain the following bits of information. One person tells us: “The package contains something tiny”; and another person tells us: “the package is very heavy”. These are not really negations of one another, but we also become aware that: It cannot both be that the package contains something tiny and the package is very heavy. So when we learn that the pieces of information cannot both be true, then we should be able to delete either one. But we do not know which to delete. And suppose we cannot delete both. So all three sentences we must still be assertable. We simply regard the negated conjunction formulation as adding to the information already provided by each content. Using similar reasoning, we would think that if we already have the information of α, then by adding ¬α, we are adding new information rather than subtracting it. For, suppose that we did not first assert α, but rather first asserted ¬α. That would presumably have some content on its own. Let me quote so you can see.]

Even filled out like this, the account is obviously sketchy and unsatisfactory. What does an assertion of ¬α do if α is not in the information store? It must do something; negative statements do, after all, have content. So presumably that content is merely added to the store. So why doesn’t it do this if α is already there? (Inconsistent data bases are not news.) And what happens if α and β are in the information store, and ¬(α∧β) is asserted? A natural suggestion is that we delete either α or β; but we have, in general, no way of knowing which. So presumably we can only add ¬(α ∧ β) to the store. But if we can have α, β and ¬(α ∧ β) in the store, why not α and ¬α?

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1.13.7

[The cancellation account does not work. There are borderline situations that are aptly expressed as contradictions, like, it is both raining and it is not raining. But this is not saying nothing at all. And our beliefs can be contradictory. We conclude one assertion from our beliefs at one point, and at another point we conclude the negation of that assertion. The negation is not nothing more than a cancellation of the prior one. It is a belief that we have that is inconsistent with another belief that we have.]

 

Priest then explains some of the greater problems with the cancellation account. {1} Borderline situations. There are certain real situations, like certain weather conditions we have experienced, that are adequately expressed as contradictions, for example, “it both is and isn’t raining” (32). [Perhaps the idea is that there are certain sorts of precipitation that are substantial enough to qualify as at least not being not raining, so we would say it is raining, but they are also insubstantial enough that we would not feel the need to affirm that it is in fact raining, so we would also say it is not raining.] Priest says that such a borderline case “shows clearly that negation does not have to function as a cancellation operator” (32). Another example are inconsistent beliefs. Suppose we examine our beliefs, and that leads us at one point to assert α, and we keep reflecting on the beliefs, and later we come to assert ¬α. This second assertion is added information about our beliefs; it does not simply do no more than cancel the prior ones.

In any case, and for quite general reasons, the cancellation account of negation doesn’t stand up to inspection. For a start, in a borderline situation of, e.g. rain, one might say that it both is and isn’t raining. This is, perhaps, something of a special case; but it shows clearly that negation does not have to function as a cancellation operator. | Or consider another sort of situation. One can, in considering one’s beliefs, come to assert contradictory statements, and in so doing discover that they are inconsistent. The assertion of¬α in this context does not “cancel out” the assertion of α—whatever this might be supposed to mean. The assertion of ¬α is providing more information about what it is one believes, not less. And it is precisely the inconsistent nature of this information that gives one pause; if what one said had no content, it would have no unsatisfactory content, so it is difficult to see why one should bother to revise one’s beliefs at all.

(32-33)

 

 

1.13.8

[There are other ways to see how the cancellation account fails. When we have inconsistent beliefs or information, we often can still make use of them in our reasoning while we try to solve the contradiction. That would be impossible if their informational contents were cancelled. We see this for example when there are inconsistent scientific theories. Another example is the paradox of the preface. In the book’s body, the author makes many assertions and thus asserts the conjunction of them all as well. But in the preface, she acknowledges that at least one assertion is mistaken and thus false. So she also asserts the negation of the conjunction of the assertions in the preface. ]

 

Also, often when we have inconsistent information, we continues using parts of it while still in the process of resolving the contradiction. We see this with scientific principles that are known to be inconsistent. Since we can still work with the inconsistent information, we would not say that it is cancelled out. [The next example I may get wrong, so please consult the quotation below. Suppose you write a short book, and in it you make hundreds of claims. Since you assert each of them, you assert their total conjunction, which we can maybe think of being like: (α1∧α2∧...∧αn). But we know that most likely at least one of those assertions will be false, as it is close to impossible to get so many right. To warn the reader and to protect ourselves a little from harsh, unforgiving criticism, we write a preface where we state that there are most likely some mistakes in the book, certainly one at least. But if we acknowledge that at least one is false, then we are saying that their entire conjunction is false, and thus we would be asserting (α1∧α2∧...∧αn) in the body of the text, but asserting ¬(α1∧α2∧...∧αn) in the preface. These examples show that “The account of negation as cancellation therefore fails, as does the second part of Lear’s argument” (33).]

Moreover, even if one does try to resolve the contradiction in such a situation, until one succeeds, one may well continue to use parts of the inconsistent information. (Think of scientific theories that are known to be inconsistent.) It is certainly not “cancelled out”. Consider an extreme case, the paradox of the preface. A person writes a book and thereby asserts the conjoined truth of all of the claims in it. Being aware of the overwhelming inductive evidence, they also assert that there are mistakes in the book, i.e. the denial of that conjunction. This does not cancel out the claims in the book. Indeed, in this case, it might even be argued that believing the inconsistent totality of information is the rational thing to do, something that would make no sense if bits of it cancelled out other bits.60 The account of negation as cancellation therefore fails, as does the second part of Lear’s argument.

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60. See Priest (1993a) and sect. 6.2.

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1.13.9

[We now see from the last three sections that those who took inspiration from Aristotle’s first refutation were just as unsuccessful as he was.]

 

Priest writes in the last paragraph:

In the last three sections of this chapter we have looked at a number of philosophers who have been inspired by Aristotle’s first refutation. In the end, none are any more successful than was Aristotle himself. Let us now return to Aristotle’s text, and to his other refutations.

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Graham Priest. 2006. Doubt Truth To Be a Liar. Oxford: Oxford University, 2006.

 

 

Also cited:

Gabbay, D. and Wansing, H. (eds.) (1999), What is Negation?,Dordrecht: Kluwer Academic Publishers.

 

Lear, J. (1988), ‘The Most Certain Principle of Being’, in Aristotle; the Desire to Understand, Cambridge: Cambridge University Press, sect. 6.4.

 

Priest, G. (1999a), ‘What not? A Defence of a Dialetheic Account of Negation’, in Gabbay and Wansing, 101–20.

 

Routley, R. and V. (1985), ‘Negation and Contradiction’, Rivista Colombiana de Matemáticas, 19: 201–31.

 

Strawson, P. (1952), Introduction to Logical Theory, London: Methuen.

 

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