## 18 Jul 2017

### Priest (1.3) An Introduction to Non-Classical Logic, ‘Semantic Validity’, summary

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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

2. Basic Modal Logic

1.3. Semantic Validity

Brief summary:

An interpretation of an object language is a function, written v,  that assigns truth values to formulas, as for example: ν(p) = 1 and ν(q) = 0. For our classical logic semantics, the interpretation function assigns values for the connectives in the following way:

ν(¬A) = 1 if ν(A) = 0, and 0 otherwise.
ν(A ∧ B) = 1 if ν(A) = ν(B) = 1, and 0 otherwise.
ν(A ∨ B) = 1 if ν(A) = 1 or ν(B) = 1, and 0 otherwise.
ν(A ⊃ B) = 1 if ν(A) = 0 or ν(B) = 1, and 0 otherwise.
ν(A ≡ B) = 1 if ν(A) = ν(B), and 0 otherwise.

A conclusion A is a semantic consequence of a set of the premises Σ (that is, Σ ⊨ A) only if there is no interpretation that makes all the members of Σ true and A false, that is, only if every interpretation that makes all the members of Σ true makes A true as well. ‘Σ ⊭ A’ means there is not semantic consequence. A logical truth or tautology is a formula that is true under every evaluation, written for example as: ⊨ A. This also means it is a semantic consequence of the empty set of premises: φA.

Summary

1.3.1

[The interpretation of our object language in classical logic will assign a truth value to a propositional parameter, formulated for example as: ν(p) = 1 and ν(q) = 0.]

[Recall from section 1.1.5 that an interpretation can be understood “crudely” as “a way of assigning truth values.] Priest will define interpretation in classical logic. We think of it as a function that assigns truth values to propositional parameters.]

An interpretation of the language is a function, ν, which assigns to each propositional parameter either 1 (true), or 0 (false). Thus, we write things such as ν(p) = 1 and ν(q) = 0.

(5)

1.3.2

[Our interpretation schema will assign truth values for the connectives in the normal classical logical way.]

Priest then provides the evaluation schema for assigning truth values to propositional parameters. As we will see, they coincide with the normal truth tables that we know for classical logic.

Given an interpretation of the language, ν, this is extended to a function that assigns every formula a truth value, by the following recursive clauses, which mirror the syntactic recursive clauses:
ν(¬A) = 1 if ν(A) = 0, and 0 otherwise.
ν(A ∧ B) = 1 if ν(A) = ν(B) = 1, and 0 otherwise.
ν(A ∨ B) = 1 if ν(A) = 1 or ν(B) = 1, and 0 otherwise.
ν(A ⊃ B) = 1 if ν(A) = 0 or ν(B) = 1, and 0 otherwise.
ν(A ≡ B) = 1 if ν(A) = ν(B), and 0 otherwise.

(5)

1.3.3

[A conclusion A is a semantic consequence of a set of the premises Σ (that is, Σ ⊨ A) only if it is semantically valid, which means that there is no interpretation that makes all the members of Σ true and A false. This can be also understood that every interpretation that makes all the members of Σ true makes A true as well. Whenever there is not this semantic consequence, we write for example: Σ ⊭ A.]

[Priest next defines semantic consequence. Recall the two types of validity from section 1.1: {1} Semantic validity (symbolized ⊨) which preserves truth: every interpretation that makes the premises true also makes the conclusion true. {2} Proof-theoretic validity (symbolized ⊢)  which is determined by means of a procedure operating on a symbolization of the inference. Now Priest seems to be saying that if a sequent is semantically valid, then the conclusion is a semantic consequence of the premises.]

Let Σ be any set of formulas (the premises); then A (the conclusion) is a semantic consequence of Σ (Σ ⊨ A) iff there is no interpretation that makes all the members of Σ true and A false, that is, every interpretation that makes all the members of Σ true makes A true. ‘Σ ⊭ A’ means that it is not the case that Σ ⊨ A.

(5)

1.3.4

[A logical truth or tautology is a formula that is true under every evaluation, written for example as: ⊨ A. This also means it is a semantic consequence of the empty set of premises: φA.]

Iff every interpretation makes some formula true, then we call it a logical tautology or logical truth. We can write that as: ⊨ A. [I do not completely understand the next idea. When a formula is a tautology, it is a semantic consequence of the empty set of premises. I would guess the idea there is the following. Suppose you have a language where there is a particular formula that is always true on every evaluation. I suppose you could say that given the conditions of the language itself (the structure of its interpretation), you can derive the formula simply from that structure, without need to derive it from any other formula. Let us think of it another way. A conclusion is semantically valid when every interpretation that makes the premises true also makes the conclusion true. In the case of a tautology, we make say with regard to its derivation that the conclusion is already true no matter what premises are given, even if none are given. So there is no interpretation where the premises are true (or even non existent) and the conclusion false. But maybe the idea here is different than those options. I quote.]

A is a logical truth (tautology) (⊨ A) iff it is a semantic consequence of the empty set of premises (φA), that is, every interpretation makes A true.

(5)

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

.

## 15 Jul 2017

### Priest (2.2) An Introduction to Non-Classical Logic, ‘Necessity and Possibility’, summary

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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

2. Basic Modal Logic

2.2. Necessity and Possibility

Brief summary:

Modal logic deals with “the modes in which things may be true/false.” Such modes include possibility, necessity and impossibility. Modal semantics can employ the concept of possible worlds, which may be understood provisionally as a world situation that is a variation on our own, with it having slightly (or remarkably) different features. One world is possible relative to another if for example the one could actually become an outcome of the other.

Summary

2.2.1

[Modal logic is concerned with “the modes in which things may be true/false” and this includes such modalities as possibility, necessity and impossibility.]

We will examine modal logic. It “concerns itself with the modes in which things may be true/false, particularly their possibility, necessity and impossibility” (20). Priest notes that these notions are “highly ambiguous,” but we discuss that issue in chapter 3 (20).

2.2.2

[A possible world can be thought of provisionally as our world with slightly different features.]

We will examine semantics for modal logics, and these semantics “employ the notion of a possible world.” Although we elaborate this notion later, Priest offers a basic account now. A possible world can be provisionally understood by imagining our world with slightly different features.

We can all imagine that things might have been different. For example, you can imagine that things are exactly the same, except that you are a centimetre taller. What you are imagining here is a different situation, or possible world. Of course, the actual world is a possible world too, and there are indefinitely many others as well, where you are two centimetres taller, three centimetres taller, where you have a different colour hair, where you were born in another country, and so on.

(20)

2.2.3

[Possible worlds can have relations of relative possibility to one another. For example, a  possible future world situation that can actually follow from a present one is a world that is possible relative to our present one.]

There is another important notion that we will employ, namely, relative possibility. [The idea seems to be that we can think of one possible world converging with another, as for example through the flow of time taking us from our world as it is now to our world as it may be in the future. Suppose right now there is a possible situation we might find ourselves in the future, depending on the actions we take now. So right now that other possible (future) world is possible relevant to the present one. But suppose that enough time passes and we miss the opportunity to make the decisions that will take us down the path to that future situation. It will be like a missed turn on the road, and so at this later date it is not possible relative to our future situation. Recall Nolt’s diagram for this idea in section 13.2 of his Logics.

As the present moves forward, we follow a certain branch of time, cutting off our access to other braches that went off in directions time did not happen to take.]

The other intuitive notion that the semantics employs is that of relative possibility. Given how things are now, it is possible for me to be in New York | in a week’s time, 26 January. Given how things will be in six days and twenty-three hours, it will no longer be possible. (I am writing in Brisbane.) Or, even if one countenances the possibility of some futuristic and exceptionally fast form of travel, assuming that I do not leave Brisbane in the next eight days, it will then be impossible for me to be in New York on 26 January. Hence, certain states of affairs are possible relative to some situations (worlds), but not others.

(21)

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

Also cited:

Nolt, John. Logics. 1997. Belmont, CA: Wadsworth.

.

## 14 Jul 2017

### Luhtala (5.6.1) On the Origin of Syntactical Description in Stoic Logic, “Corporeals in Stoic Physics”, summary

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[The following is summary. It redoes this entry. All boldface, underlining, and bracketed commentary are my own. Paragraph enumerations are also my own, but they follow the paragraph breaks in the text. Please forgive my distracting typos, as proofreading is incomplete.]

Summary of

Anneli Luhtala

On the Origin of Syntactical Description in Stoic Logic

Ch.5 The Stoics

5.5 Stoic Logic

5.6

Stoic Physics

5.6.1

Corporeals in Stoic Physics

Brief summary:

For the Stoics, a corporeal body is understood as the capacity to act and undergo action and thus is conceived in terms of causality. The Stoics were against the idea in Plato and Aristotle that incorporeals had causal efficacy. As we see from the sources, the Stoics understood incorporeals both linguistically and physically/metaphysically. And they understood statements as being incorporeals that express how some corporeal body has certain corporeal features, mentioned in the predicate. Statements do not refer to abstract generalities but rather only to concrete circumstances happening in the world. Thus when giving examples of statements, the Stoics used proper nouns instead of common ones. Also, for the Stoics, parts of speech are corporeal even though statements are incorporeal.

Summary

5.6.1.1

[Of the definitions the Stoics gave for corporeal body, the most prevalent one is: the capacity to act and undergo action.]

The Stoics defined corporeal body in a variety of ways, including: {1} “three-dimensionality and resistance (Diog. Laert. VII,135; Apollodorus 6; Galen De qual. incorp. 10 = SVF 2.381)”; {2} “contact and separation (Nemesius De nat. hom II,46,81,6-10 = SVF 2.790)” and {3} “the capacity to act and undergo action” (Luhtala 118). Luhtala says that the third definition of having the capacity to act and undergo action was the one that “figured most prominently in the Stoic conception of body”, and she will focus on that one (118, saying in footnote that her treatment follows Hahm 1977).

5.6.1.2

[The Stoic notion of corporeal bodies as acting and undergoing action comes from Aristotle’s criticism of Platonic (incorporeal) Ideas, which Aristotle thought did not exist separately from individual particulars but rather were inherent to them, in that universals are predicated of many things.]

Hahm attributes the Stoic view of corporeality as action and undergoing of action to Aristotle’s criticism of Plato’s Ideas. For Plato, Ideas have ontology primacy, and the Ideas are “incorporeal real entities” (118). Aristotle, however, did not think that Ideas exist separately from their individual particulars but were instead “inherent in the particulars” (118).

The Stoic view of corporeality, and the adoption of the notion of action and undergoing of action as the crucial characteristic of body, owe a number of features to contemporary philosophical discussion. Hahm claims that the Stoics adopted a peculiar usage of this feature, which was already familiar to Plato and Aristotle. He relates the Stoic theory of corporeality to Plato's theory of Ideas and its criticism by Aristotle which was adopted by the Stoics.205 Plato and his successors assigned ontological primacy to incorporeal real entities, the Ideas. Aristotle, who presented many arguments against the theory of Ideas in his works, was especially keen to refute the view that the Ideas exist separate from the individual particulars, insisting that the Ideas must be considered universals inherent in the particulars. Aristotle, who regarded universals as inseparable from objects, spoke of a universal as something predicated universally of more than one thing. Hahm relates this question to the introductory paragraph of the Peri hermeneias (Hahm 1977: 7-8).

(118)

205. Of course, even the dialecticians denied the existence of Ideas.

(118)

5.6.1.3

[Since the Stoics thought that only bodies exist, that probably means they did not derive their notion completely from Aristotle, who though there were different kinds of being for corporeal and incorporeal things.]

For the Stoics, “the Platonic Ideas are thoughts in our mind and as such are nonexistent (Strob. Ecl I,136,21 = SVF 1.65; Syrianus SVF 2.364; Aet. I,10,5 = SVF 2.360)” (118). But we cannot “derive the Stoic corporealism from Aristotelian ontology in any straightforward manner” (118). Aristotelianism recognized “different kinds of being for corporeal and incorporeal things,” which is not much different than the Stoic denial of the existence of anything except corporeals [see section 5.6.0.1]. Hahm notes that the crucial notion of acting and being acted upon is found in Plato’s Sophist, where it is used in application to a notion of a soul. Aristotle does not use this notion in his metaphysical writings, but he does employ it with his physics.

The Stoics maintained that the Platonic Ideas are thoughts in our mind and as such are nonexistent (Strob. Ecl I,136,21 = SVF 1.65; Syrianus SVF 2.364; Aet. I,10,5 = SVF 2.360). But Hahm emphasizes that it would be misleading to derive the Stoic corporealism from Aristotelian ontology in any straightforward manner; to deny existence to anything but bodies is a far cry from Aristotelianism which recognized different | kinds of being for corporeal and incorporeal things, and an eternal unmoved being, the prime mover. According to him, it would be more appropriate to try to explain Stoic ontological views by tracing the origins of the crucial notion of action and undergoing of action, in terms of which the Stoics defended their view of corporeality. This notion as a feature of being can be found in Plato’s Sophist (247DE), in which it is used to assert the existence of the soul and its virtues as against materialistic arguments based on visibility and tangibility as a characteristic of being. Aristotle shows in Top. 5,9,139a4-8 that he knows of this notion; but he never used it in his own metaphysical writings. Acting and being acted up on are nevertheless vital concepts in his physical theory in which he stressed, for instance, that there can be no action or suffering without contact; he further tended to equate acting and being acted upon to moving and being moved. While admitting that there can be no motion apart from the physical body, Aristotle came very close to asserting that there can be no acting or suffering without body (Cael. 1.9.279a15-16; Gen. corr. 1.6.323a17-20; Met. 5.21.1022b15). However, he never made quite this statement, as Hahm concludes, suggesting that this was because the most important mover or agent, the eternal prime mover, was incorporeal (Hahm 1977: 9-14).

(118-119)

5.6.1.4

[The Stoics as far as we know did not defend this notion of causality involving bodies acting and undergoing action. They were interested in countering the thesis of Plato and Aristotle that says incorporeals can have causal efficacy.]

So the Stoic notion of causality gives an important place for bodies [which are causally related through action and undergoing of it.] But, Hahm notes that “we do not quite know how the Stoics argued their case” for this (119). Long and Sedley note that the capacity to act and be acted upon is never given as a defining characteristic of bodies, although it is said to be peculiar to them.  They continue to write that “In confining this capacity to bodies, the Stoics were not redefining body but radically rejecting the thesis, accepted by Plato and Aristotle, that incorporeals can have any causal efficacy. (Long/Sedley 1987: 273)” (119).

5.6.1.6

[In the Stoic sources, incorporeals are said to be unable to act or be acted upon by corporeal bodies, although corporeal bodies do have this power. In an ethical context we see predicates being labeled incorporeal, thus pointing to the linguistic nature of their argumentation regarding corporeals and incorporeals.]

Luhtala will now examine passages that discuss this notion of body “to throw light on the linguistic nature of the argumentation used by the Stoics” (119). The first set of three will all make the point that incorporeals cannot causally interact with corporeal bodies.

1. “According to them the incorporeal is not of a nature either to act or to be acted upon.”

(Sextus Empiricus, Adv. math. VIII,263 = SVF 2.363, tr. Long/Sedley 1987: 272)206

(120)

206. τὸ γὰρ ἀσώματον κατ' αὐτοὺς οὔτε ποιεῖν τι πέφυκεν οὔτε πάσχειν.

(120. Note, in Luhtala’s text, the γὰρ is omitted, but it is found in the second volume of the Long/Sedley [p.269], the online text, and in the Opera text [p.475]:

)

2. Zeno also differed from the same philosophers in thinking that it was totally impossible that something incorporeal (to which genus Xenocrates and his predecessors too had said the mind belonged) should be the agent of anything, and that only a body was capable of acting or of being acted upon.” (Cic. Act. post. I,39 = SVF 1.90, tr. Long/Sedley 1987: 272)

(120)

207. “Discrepabat etiam ab iisdem (scil. Zeno a Peripateticis et Academicis), quod nullo modo arbitrabatur quidquam effici posse ab ea (natura), quae expers esset corporis ... nec vero aut quod efficeret aliquid aut quod efficeretur posse esse non corpus.”

(120)

3. He (Cleanthes) also says: no incorporeal interacts with a body and no body with an incorporeal, but one body interacts with another body. Now the soul interacts with the body when it is sick and being cut, and the body with the soul; thus when the soul feels shame and fear the body turns red and pale respectively. Therefore the soul is a body. (Nemesius 78,7-79,2 = SVF 1.518, tr. Long/Sedley 1987: 272)207

(120)

207.

[Luhtala’s footnoted quotation follows SVF (p.117).]

[In the 1987 Nemesius text (pp.20-21), it is given as:]

Luhtala then gives a quote from [I think] Stobaeus. The first part is too enigmatic she says to comment upon, “But towards the end of the passage nouns and verbs are contrasted in a way which represents more common themes in Stoic thought. The author argues that we should wish to have ‘prudence’ and ‘moderation’ instead of ‘acting prudently’ and ‘acting moderately’ because the latter are incorporeal and predicates” (120). [See p.121 for the full quotation and its Greek original. Here I will select the more relevant part.]

For we choose what-should-be-chosen and wish what-should-be-wished and desire what-should-be-desired. For choices and desires and wishes, just like impulses, are of predicates. Yet we choose and wish and likewise desire to have goods, and so goods are choiceworthy and wishworthy and desirable. For we choose to have prudence and moderation, but not of course (to have) acting prudently and acting moderately, which are incorporeal and predicates.

(Stob. II,97 ,1 5-98,6 = SVF 3.91, tr . Long/Sedley 1987: 197)

(121, boldface mine)

Luhtala notes that “The Stoics seem to have argued that it is ethically more desirable to have prudence and moderation than to act prudently and moderately” (121). Here we are less interested in the ethical side of this argument, because we will focus on “the linguistic side of the argumentation” (121). [In the quotation, we distinguish for example ‘prudence’ and ‘acting prudently’. So] “What are contrasted here are common nouns and verbs (in the infinitive)” (121). [In the quote, ‘acting prudently’ and ‘acting moderately’ were said to be incorporeal and predicates. But there was no linguistic (or metaphysical) description of ‘prudence’ and ‘moderation’. Thus] “It is then incorporeal items of linguistic theory which are said to be less desirable than that which is represented by σωφροσύνη (‘moderation’) and φρόνησις (‘prudence’)” (121). But, “These desirable items are not linguistically specified; they are labeled neither nouns (προσηγοριαί) nor cases (πτώσεις)” (121).

5.6.1.7

[In the Stobaeus extract, we see that the linguistically designated predicate is discussed not in a linguistic context but in a non-linguistic one. We see the same sort of non-linguistic application of incorporeal predicates in some passages by Sextus Empiricus discussing truth.]

Luhtala notes now the above Stobaeus extract demonstrates “that the Stoics made use of items of linguistic theory such as predicates in contexts other than statement-making” (121). She provides the following reasoning for how we can know that in this context the linguistic concepts were not meant simply to refer to statement-making. [I do not follow this part well, so please consult the quotation below. She might be saying the following, but it is a guess. In the ethical arguments, we had the incorporeal predicates ‘acting prudently’ and ‘acting moderately’. She says that if we are to think of them just  in terms of making statements using these predicates, then they would have been joined to an incorporeal case. Perhaps she means that somehow we would be making reference to the part of the sentence that would serve as the subject of the activity. But we did not turn the discussion in that direction. Rather, these incorporeal predicates were compared to such corporeals as ‘prudence’ and ‘moderation’, which are not thought of linguistically as case, subjects, nouns, etc.]

if statement-making were at issue, the incorporeal predicate would be joined to an incorporeal πτῶσις (‘case’). But in this ethical argument incorporeal predicates are contrasted with corporeal items which are not items of linguistic theory.

(122)

[Luhtala next gives a quotation from Sextus Empiricus to show a similar sort of structure in reasoning about incorporeals. I will not summarize this well. But I will guess Luhtala is saying the following. Sextus will make a distinction between truth (ἀλήθεια) and an incorporeal, true (ἀληθὲς). When distinguishing them with regard to substance, we say that ‘truth’ is a corporeal body while ‘true’ is an incorporeal, a judgment (ἀξίωμα), and a sayable (λεκτόν). These features are those of the component of meaning (σημαινόμενα) (see section 5.5.4.0). Now, true (ἀληθὲς) is here formulated as an adjective. Luhtala says it also represents the predicate ‘to be true’. Like before, we have the non-linguistically specified corporeal body, truth (ἀλήθεια) being contrasted with the linguistically specified incorporeal, true (ἀληθὲς).]

“True is said (by the Stoics) to differ from truth in three ways, substance, structure, and function. In substance, since what is true is incorporeal, for it is a proposition and sayable; but truth is a body, for it is scientific knowledge capable of stating everything true; and scientific knowledge is the commanding-faculty disposed in a certain way, just as a fist is the hand disposed in a certain way; and the commanding-faculty is a body. In structure, since what is true is something simple, e.g. ‘I am conversing’, but truth consists of the knowledge of many true things. In function, since truth pertains to scientific knowledge but what is true does not do so at all. Hence they say that truth is only in a virtuous man, but what is true is also in an inferior man; for the inferior man can say something true.” (Sext.Emp. Pyrrh. hyp. II,81-83, tr. Long/Sedley 1987: 198)210

‘Truth’ (ἀλήθεια) is said to differ from ‘true’ (ἀληθὲς) in three ways: in substance, in composition and in potency. Where substance is concerned, ‘truth’ is a body whereas ‘true’ is incorporeal, a judgment ἀξίωμα) and a sayable (λεκτόν). The characteristics of ‘true’ are, again, those of the component of meaning (σημαινόμενα) in Stoic linguistic theory. I take the adjective ‘true’ (ἀληθὲς) to represent the predicate ‘to be true’. ‘Truth’ (ἀλήθεια) is a noun; but it is not characterized in linguistic terms, only in terms of its corporeal nature. It is contrasted with something that is linguistically specified: a propositional item, an ἀξίωμα (‘proposition’), a λεκτόν (‘sayable’), an incorporeal. This passage lends further support for my claim that the Stoics contrasted items of linguistic theory such as predicates and propositions with corporeal entities, which are common | nouns, though they are not linguistically specified. They are specified only in terms of their corporeal nature. Where structure is concerned, ‘truth’ is composite, consisting of the knowledge of many things; it is a particular state of the leading part of the soul, the ἡγεμονικόν, which is corporeal. ‘True’ is something simple, a proposition such as ‘I converse’ (διαλέγομαι). ‘Truth’ and ‘true’ differ in function in that ‘truth’ is the scientific knowledge of many things, pertaining to a wise man, whereas ‘true’ (a true proposition) is something that even a less virtuous man can say.

(122-123)

210. λέγεται διαφέρειν τῆς ἀληθείας τὸ ἀληθὲς τριχῶς, οὐσίᾳ συστάσει δυνάμει. οὐσίᾳ μέν, ἐπεὶ τὸ μὲν ἀληθὲς ἀσώματόν ἐστιν (ἀξίωμα γάρ ἐστι καὶ λεκτόν), ἡ δὲ ἀλήθεια σῶμα (ἔστι γὰρ ἐπιστήμη πάντων ἀληθῶν ἀποφαντική, ἡ δὲ ἐπιστήμη πὼς ἔχον ἡγεμονικὸν ὥσπερ καὶ ἡ πὼς ἔχουσα χεὶρ πυγμή, τὸ δὲ ἡγεμονικὸν σῶμα. ἔστι γὰρ κατ' αὐτοὺς πνεῦμα), συστάσει δέ, ἐπεὶ τὸ μὲν ἀληθὲς ἁπλοῦν τί ἐστιν, οἷον, “ἐγὼ διαλέγομαι”, ἡ δὲ ἀλήθεια ἀπὸ (τῆς) πολλῶν ἀληθῶν γνώσεως συνίσταται, δυνάμει δέ, ἐπεὶ ἡ μὲν ἀλήθεια ἐπιστήμης ἔχεται, τὸ δὲ ἀληθὲς οὐ πάντως. διόπερ τὴν μὲν ἀλήθειαν ἐν μόνῳ σπουδαίῳ φασὶν εἶναι, τὸ δὲ ἀληθὲς καὶ ἐν φαύλῳ. ἐνδέχεται γὰρ τὸν φαῦλον ἀληθές τι εἰπεῖν.

(122, copied from socratics.daphnet.org and modified to make it more similar to Luhtala’s rendition)

5.6.1.8

[Seneca discusses a Stoic ethical claim that wisdom is a Good while being wise is not. For, something can only be a good if its usefulness can be put into actuality. That can only happen if it acts as a body. Since wisdom is useful, it must be a body. But being wise is an incorporeal predicate. It cannot be a Good, because it cannot act like a body.]

Luhtala says that Seneca “is our best witness to the linguistic nature of the argumentation used by Stoic philosophers in discussing non-linguistic issues,” and we will examine a lengthy passage by him to see this (123). There is an ethical controversy attributed to the Stoics that is the following: “wisdom (sapientia) is a Good (bonum) whereas being wise (sapere) is not” (123). Seneca disagrees with this Stoic view. In the quotation below, we see the Stoics reasoning. A Good is a body. Why? Whatever is useful must be able to act as a body (in order to put its usefulness into actuality). And whatever can act is a body. A Good is useful, therefore it is a body. And wisdom is a Good, therefore wisdom is a body.  However, being wise is an accident [and thus perhaps a predicate] and so it is incorporeal. It thus cannot act or be useful. [This and the following passages seem to be cited as: Seneca, Ep. 117,2-13.]

“According to our school”, Seneca declares, “whatever is a Good (bonum) is a body (corpus), because it can act (facit); whatever acts, is a body. Whatever is a Good is useful (prodest). In order to be useful, one has to do something (faciat aliquid oportet); that which acts is a body. The Stoics say that wisdom (sapientia) is a Good; consequently, it must be called a body. But being wise (sapere) is not regarded as partaking of the same condition. It is incorporeal (incorporalis) and an accident of something else (accidit alteri), that is wisdom; therefore it neither acts nor is useful (nec facit quidquam nec prodest).”

(123, quoting Seneca)

[I do not follow the next point so well. It might be that Seneca criticizes this view by saying that two things are possible. So, the incorporeal as an accident belongs to something else. {1} It belongs inside the object. But the object is corporeal, and if belongs to the object, it must be corporeal too. To belong to the object would mean being in contact with it, and only corporeal things can make contact with other corporeal things. {2} It belongs outside the object. But if it is outside the object while belonging to it, it must be receding from the object, and only bodies are capable of motion. His next criticism it seems is that the Stoics would seem to be saying that wisdom is of a fundamentally different nature than being wise, but surely what can be said of the one should be attributable to  the other. Let me quote as I may have this wrong.]

The corporeal nature of wisdom is defended in terms of the crucial feature of the body being able to act (and undergo action). But being wise is altogether different; it is incorporeal and belongs to something else. “Is that which belongs to something”, Seneca asks, “outside the object to which it belongs, or does it inhere in the object? If it is in the object to which it belongs, it is as corporeal as the object to which it belongs. Nothing can occur without contact; that which touches, is a body. If it is outside, it withdraws after having belonged to the object. That which recedes, has motion. That which has motion, is a body. You wish that I did not say that ‘race’ (cursus) is different from ‘running’ (currere), ‘heat’ (calor) from ‘to being hot’ (calere), and ‘light’ (lux) from ‘to give light’ (lucere); I admit that these are different things, but not of an altogether different nature. If health is a matter of indifference, so is even ‘being healthy’; if ‘beauty’ is indif-| ferent, so is ‘being beautiful’. If justice is a Good, so is ‘being just’. If ugliness is a bad thing, so is even ‘being ugly’, and for heaven’s sake, if bleary-eyedness is a bad thing, so is even ‘being bleary-eyed’.”

(123-124)

Luhtala finishes this paragraph with another quote where Seneca elaborates on this Stoic distinction. [The idea seems to be that the Stoics insist that wisdom and being wise must be distinguished, because wisdom is something possessed and being wise refers to one doing the possessing or having the wisdom. See p.124 for the quotation.]

5.6.1.9

[We see in Seneca’s account a linguistic understanding of this distinction.]

Seneca was discussing action and undergoing of action, and this “echoes the Stoic view of causation which takes place between bodies”. This distinction is given in terms of active and passive verbs (124). The Stoics distinguishes ‘field’ (ager) and ‘having a field’ (agrum habere). But we do not know too much more about how to conceptualize this distinction (125). Probably the distinction began as a linguistic one, and we see Seneca give a linguistic example.

Bodies have their particular natures, such as ‘man’ and ‘horse’. They are accompanied by motions of the soul which make statements about bodies. Their proper nature is derived from bodies. When I see Cato walk, the senses reveal this to me, and the soul believes it. What I see is a body on which I focus my eyes and my mind. Then I say: ‘Cato is walking’ . What I say is not a body, but a statement about a body, which is called by some effatum (‘utterance’) , by the others enuntiatum (‘declaration’) , and by yet others dictum (‘statement’) . Therefore when we say ‘wisdom’, we understand something corporeal; when we say ‘he is wise’, we talk about a body. It makes a big difference whether you name something or say something about it.

(125)

5.6.1.10

[For the Stoics, statements are incorporeals expressing that a body has certain features. Statements do not refer to abstract generalities but rather to concrete circumstances happening in the world; thus they used proper nouns instead of common ones.]

Luhtala notes that the passage illustrates certain “principles of Stoic logic”. [The first idea seems to be that bodies have features, which are corporeal but take the form of predicates and are expressed in incorporeal statements. When discussing bodies, they are understood generally, and thus we use common nouns. But for the Stoics, statements are made in reference not to abstract generalities but rather to express real situations in the world, and thus the Stoics when discussing statements used proper nouns.]

This passage is a good illustration of the principles of Stoic logic. Statements are made of bodies, which are specified in terms of their particular natures, i.e. in terms of common and particular qualities. They are thus men or horses or individuals such as Cato. By making a statement such as ‘Cato is walking’, we abstract a feature from a body, and what we say is an incorporeal statement. It is noteworthy that when discussing the nature or bodies, Seneca mentions men and horses which are precisely the two examples of common nouns in Diogenes Laertius’ report. But when he proceeds to discuss statement-making, a proper noun occurs in the example (Cato ambulat). This is fully in accordance with the fact that the Stoic made propositions essentially about individuals.

(126)

5.6.1.11

[For the Stoics, parts of speech are corporeal while statements are incorporeal.]

[I may not get the next points right, so see the quotation below. The idea seems to be the following. For the Stoics, the individual parts of speech we utter, like nouns for example, are corporeal. I am not sure however if the part of speech as a syntactical/grammatical structure is corporeal or if it is just simply that the thing named is corporeal. The second option is more conceivable but less interesting. However, the statement itself is incorporeal.]

Seneca finally draws a distinction between ‘saying something’ and ‘speaking about something’ in a way which is reminiscent of the ancient division between the levels of naming (ὀνομάζειν) and statement-making (λέγειν). When we utter an individual nominal part of speech, such as the noun ‘wisdom’, we understand, according to the Stoics, something corporeal. When we make a statement, we understand something incorporeal. This passage throws additional light on the corporeal nature of the parts of speech as such, which must have been a source of ambiguity.

(126)

From:

Luhtala, Anneli. 2000. On the Origin of Syntactical Description in Stoic Logic. Münster: Nodus.

Other texts, cited by Luhtala:

[Note, for “Aet. I, I did not see something for it in the Bibliography.]

[Note, I could not find Apollodorus in the Bibliography.]

Cic. Act. post: Cicero. Academica posteriora.

Online text available at:

Diogenes Laertius: Lives of eminent philosophers. Translated by Robert D. Hicks. 2 vols. London: William Heinemann / Cambridge, Mass.: Harvard University Press 1950.

[Note, I did not see Galen’s De qual. incorp in the Bibliography list. Perhaps it is a part of the text that is listed:

Galen. Gelaeni de placitis Hippocratis et Platonis. Edition, translation and Commentary by Phillip de Lacy. Corpus Medicorum Graecorum. V.4.1.2. Berlin: Academie-Verlag 1978-80.]

Hahm, David E. 1977. The Origins of Stoic Cosmology. Columbus: Ohio State University Press.

Long, Anthony A. / Sedley, David N. 1987. The Hellenistic philosophers. 2 vols. Cambridge: Cambridge University Press.

[Note, I did not see Nemesius’s De nat. hom in the Bibliography list.  Perhaps it is De natura hominis.]

Sextus Empiricus: Adversus Mathematicos I-XI. Ed. with an English translation by Robert G. Bury. 4 vols. The Loeb Classical Library. London: Heinemann; Cambridge, Mass.: Harvard Univ. Press 1949.

Another version available online:

https://archive.org/details/sextiempiriciope12sext

Online text transcription at:

http://socratics.daphnet.org

[specifically here]

[Note, for Pyrrh. hyp. I did not see something for it in the Bibliography, but perhaps it is:

Sextus Empiricus. Pyrrhōneioi hypotypōseis.

Online text at:

http://socratics.daphnet.org

(Specifically here)]

Seneca: Ad Lucilium epistulae morales. Ed. by Leighton D. Reynolds. Oxford: Clarendon Press 1965.

[Note, for “Stobaeus ... Ecl.” I did not see something for it in the Bibliography, but perhaps it is Stobaeus’ Ἐκλογαί / Eclogae physicae et ethicae.]

SVF. Stoicorum veterum fragmenta I-III. Ed. Iohannes von Arnim. Leipzig: Teubner 1905-24.

Syrianus: In Metaphysica commentaria. CAG VI.1. Ed. Wilhelm Kroll. Berlin: Reimer 1902.

Texts I cite:

Nemesius. 1987. Nemesii Emeseni. De natvra hominis, ed. Moreno Morani. Leipzig: Teubner. Available online at:

https://archive.org/details/Nemesius_201604

Sextus Empiricus. 1914. Sexti Empirici Opera. Vol. 2, Adversus Dogmaticos, libros quinque (Adv. Mathem. VII-XI) continens, edited by Hermannus Mutschmann. Lipsiae [Leipzig]: Teubneri [Teubner]. Available online:

https://archive.org/details/sextiempiriciope12sext

Stoicorum veterum fragmenta, vol. I. Ed. Iohannes von Arnim. Leipzig: Teubner 1964.

PDF available at:

https://archive.org/details/stoicorumveterum01arniuoft

This entry redoes the one here, made a while ago:

http://piratesandrevolutionaries.blogspot.com/2009/06/stoic-logic-and-semantics-corporeals-in.html

.

### Voisset-Veysseyre (1) Toward a Post-Identity Philosophy, “[introductory material],” summary

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[The following is summary, and other cited texts are otherwise indicated. Bracketed commentary and boldface are my additions. Proofreading is incomplete, so please, if you will, overlook my typos and other distracting errors.]

Summary of

Cécile Voisset-Veysseyre

“Toward a Post-Identity Philosophy:

Along a Flight Line with Gilles Deleuze?”

1. [introductory material]

Brief summary:

Deleuze and Guattari had in mind a mode of philosophical thinking that is not limited to the principles and structures of standard logic.

Summary

1.1

[Corresponding to Deleuze’s and Guattari’s notion of becoming is a non-standard logic that does not hold the standard conceptions for predication and identity.]

Deleuze’s and Guattari’s A Thousand Plateaus and What is Philosophy develop a non-standard sort of logic corresponding to their notion of becoming. Its development was began in part back with Lacan’s Le Séminar IV (1956-1957), and it is also found in Derrida’s The Post Card: From Socrates to Freud and Beyond. In fact, in his Cinema 2: The Time-Image (1985), “Gilles Deleuze claimed the invention of ‘a new logic’” (1, citing Cinéma 2, p.359). [In this cited passage, Deleuze says that on account of time becoming no longer ordered by chronological succession and thus alternative pasts becoming undecidable, the true and the false become undecidable: “the true and the false become undecidable or inextricable: the impossible proceeds from the possible, and the past is not || necessarily true. A new logic has to be invented” / “le vrai et le faux deviennent maintenant indécidables ou inextricables : l’impossible procède du possible, et le passé n’est pas nécessairement vrai. C’est une nouvelle logique qu’il faut inventer” (1985: 359 / 1989: 274-275 / 2005: 263).] Voisset-Veysseyre ends by saying, “Taken in context, the notion of becoming challenges the traditional logic with the subject and its attributes as well as its correlated object; the logical notion of identity is questionable” (1).

1.2

[Deleuze and Guattari have in mind certain underlying structures or dynamics that do not operate in a manner that can be made explicit in a fixed and straightforward way.]

Voisset-Veysseyre finds some further elaboration on this non-standard sort of logic in Brian Massumi’s translator’s foreword to A Thousand Plateaus. He notes that D&G were against invariable identity, and they favored a sort of nomadic thinking that “does not repose on identity; it rides difference” (2, citing Brian Massumi, “Translator’s Foreword: Pleasures of Philosophy,” in A Thousand Plateaus, London & New York, Continuum, 1988, p. ix-xii). Voisset-Veysseyre then selects some quoted phrasings that are suggestive of features of a non-standard logic. D&G were against a sort of multiplicity that stems somehow from a unity. [Voisset-Veysseyre  then notes D&G’s notion of binary logic. Let us look closely at it first. They are talking about a sort of ramification that is like plant root propagation. One sort is binary, where one splits to two. We might think then of a stalk or trunk above ground that splits underground into two main roots, which each split to two, and so on: “the One that becomes two, the two that becomes four” (5). They call this a “binary logic”. To be clear, at this point there is no mention of truth values, but rather a sort of “logic” or consistent pattern of splitting into two. But, D&G say, “Nature doesn’t work that way: in nature, roots are taproots with a more multiple, lateral, and circular system of ramification, rather than a dichotomous one” (5). It seems a taproot is a (vertical) root with other horizontal roots coming out of it.

(Thanks wikimedia commons)

I am not sure what would be the circular system, although a rhizome root system could probably make something of a more circular structure. I am not sure. Or maybe the circularity is seen when you look down at the roots extending from the taproot and see how they come out radially. In this “natural method”, we “go directly from One to three, four, or five, but only if there is a strong principal unity available, that of the pivotal taproot supporting the secondary roots. That doesn’t get us very far. The binary logic of dichotomy has simply been replaced by biunivocal relationships between successive circles” (6). I am not sure what the biunivocal relationships are. Maybe the idea is the following. You have the relation of multiple (horizontal roots) to one (taproot). That relation goes both ways, so it is ‘bi-’. But each horizontal root is not tied directly to any other. Each is only tied to the taproot. So in that sense, maybe, it is univocal (there is only one thing to which all other things are related). The next idea is that selfhood is somehow multiple. And rhizome goes beyond the duality of the one-multiple. Voisset-Veysseyre then writes, “Many logics seem then to be possible, instead of a two valued logic: ‘There is no universal propositional logic’” (2, citing A Thousand Plateaus p.163). [In the cited D&G text, A Thousand Plateaus, they are discussing certain forces or structures – specifically, machines, assemblages, and movements of deterritorialization – that in a sense seem to operate below the structures of language and deform those structures continually. (My explanation here only comes from a very superficial reading.) These underlying factors are perhaps the “regimes of signs” but I am not sure yet. At any rate, the idea seems to be that there is no universal propositional logic, because the deforming factors are diverse and changing. What Voisset-Veysseyre gets from this and from the prior ideas is that “Many logics seem possible, instead of a two valued logic”. I would agree with the statement, but it is not clear to me yet how the concepts she has mentioned so far have bearing on the numbers of truth-values that can be assigned to statements. Voisset-Veysseyre  then notes this regime of signs that is deeper than language and that is what language is based on.]

1.3

[The older, standard logic that neuters philosophical thinking should be replaced with a mode of concept creation that is unbound by standard logical structures.]

Voisset-Veysseyre then writes, “In What is Philosophy?, logic is denounced as out of date for ‘its infantile idea of philosophy’” (3). [In this section, D&G discuss how logic confuses the concept with the proposition. It sees the proposition as what the sentence expresses intensionally. They then write, “Consequently, the philosophical concept usually appears only as a proposition deprived of sense. This confusion reigns in logic and explains its infantile idea of philosophy” (WP 22). I am not sure yet how logic sees the concept as a proposition deprived of sense. A simplistic interpretation would be that logic operates on variables for propositions, symbolized for example with capital letters,  so they lack some specific sense. But D&G are saying something else. Maybe they are saying that the concept is the sense (or intensional meaning as proposition) itself. So in being the sense of something else, the concept does not itself have any further sense. At any rate, D&G go further here to say something relevant about non-standard logics, but it is not something Voisset-Veysseyre delves into. They write, “Concepts are measured against a ‘philosophical’ grammar that replaces them with propositions extracted from the sentences in which they appear. We are constantly trapped between alternative propositions and do not see that the concept has already passed into the excluded middle. The concept is not a proposition at all; it is not propositional, and the proposition is never an intension. ... Concepts, which have only consistency or intensive ordinates outside of any coordinates, freely enter into relationships of nondiscursive resonance” (22 ... 23). Maybe the idea here is the following. A proposition is something that can enter into a logical relation with other propositions (and this is perhaps their discursivity). Propositions also are of such a nature that they present exclusive alternatives, for example, either a proposition or its negation. Now, for whatever reason (which is not crystal clear to me yet), concepts are not of a nature that they can be discursively interrelated in such an exclusive sort of way. Perhaps it is because their composition is in flux somehow or because they have vague and changing borders and are overlapping with other concepts. So while a proposition is a sense which admits of the excluded middle such that either a proposition or its negation is true, a concept in contrast somehow resides in this excluded middle zone. At any rate, Voisset-Veysseyre’s point here seems to be that Deleuze and Guattari are against standard logic in some sense or another. Her next point is that D&G are against the reductionist nature of logic that turns concepts into functions. I did not follow her next points about new logic and the utopian way. But one idea here might be that there is a mode of philosophical thinking that is not constrained by the structures of standard logic. She ends it seems by asking how philosophy can be reconceived now that standard logic is understood as insufficient.]

1.4

[The text will discuss gender, a logic of multiplicities, and post-identity nomadic/rhizomatic writing.]

Voisset-Veysseyre outlines the structure of her text. The first part will discuss issues regarding gender. The second part examines A Thousand Plateaus and What is Philosophy? to conceptualize a logic of multiplicities (4). And the third part examines nomadic and rhizomatic writing in a post-identity philosophy (4).

Cécile Voisset-Veysseyre. (2012). “Toward a Post-Identity Philosophy: Along a Flight Line with Gilles Deleuze?” Tahir. August 2011.

http://www.revuetrahir.net/2011-2/trahir-voisset-veysseyre-post-identity.pdf

Other cited texts:

Deleuze, Gilles. (1985). Cinéma 2: L’image-temps. Paris: Minuit.

Deleuze, Gilles. (1989). Cinema 2: The Time-Image. English translation by Hugh Tomlinson and Robert Galeta. Minneapolis: Athlone / University of Minnesota.

Deleuze, Gilles. (2005). Cinema 2: The Time-Image. English translation by Hugh Tomlinson and Robert Galeta. London / New York: Continuum.

Deleuze, Gilles, and Félix Guattari. 1994. What is Philosophy? English translation by Hugh Tomlinson and Graham Burchell. New York: Columbia University.

Taproot image from:

https://commons.wikimedia.org/wiki/File:Plant_taproots.jpg

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### Voisset-Veysseyre, Toward a Post-Identity Philosophy, entry directory

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Cécile Voisset-Veysseyre

“Toward a Post-Identity Philosophy:

Along a Flight Line with Gilles Deleuze?”

1. [introductory material]

Cécile Voisset-Veysseyre. (2012). “Toward a Post-Identity Philosophy: Along a Flight Line with Gilles Deleuze?” Tahir. August 2011.

http://www.revuetrahir.net/2011-2/trahir-voisset-veysseyre-post-identity.pdf

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### Bergson (5.2.1-5.2.15) La pensée et le mouvant / Creative Mind, “[All reality is change and movement, which is absolutely indivisible]”, summary

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[The following is summary. Boldface in quotation and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos. Citations give the pages for the 1938 French edition first; then the 1946 English second, and the 1965 English third.  Section and paragraph divisions follow those in the French edition; enumerations except for chapter numbers are my own.]

Summary of

Henri Bergson

La pensée et le mouvant:

Essais et conférences

[An Introduction to Metaphysics:]

The Creative Mind

5. La perception du changement / The Perception of Change

5.2. Deuxième conférence / Second Lecture

5.2.1-5.2.15

[All reality is change and movement, which is absolutely indivisible.]

Brief summary:

All reality is change. We have an inner mental life that is a flux not of distinct states but of continuous qualitative variation. And what we experience in the world are not invariable objects undergoing a series of discrete states. Rather, there is just pure durational change itself as the only substantiality, and there are not invariable things doing the changing. This means that all change and movement is absolutely indivisible. We cannot then say that a physical motion had spatialized parts to it. The movement is entire and durational (thus non-spatial) while it is happening. Only after the motion is complete can we examine the space traveled and then, if we want, divide that traveled space. But to divide the motion up, like in Zeno’s paradoxes, is to confuse movement and duration with space, which are incommensurable. So by committing this confusion we may derive Zeno’s paradoxes of motion. The evidence for the indivisibility of motion and change is phenomenological: we experience our own bodily motions as such. It is only on account of practical needs that we artificially divide the world and our mind up into immobilities. Also, we rely heavily on our vision, which is prone to artificially carve up the world into things that subsist as they move and change. But we should instead appeal to our hearing for information about real duration and change. When we hear a melody, for example, we experience a pure, indivisible, continuous variation without an invariable object as a substrate for that variation.

Summary

5.2.1

[All change and all movement is absolutely indivisible.]

Bergson asks us to break our normal habits of thinking so that we may contemplate “the direct perception of change and mobility” / “la percep-| tion directe du changement et de la mobilité” (157|158 / 167 / 142). He continues, “We || shall think of all change, all movement, as being absolutely indivisible” / “Nous nous représenterons tout changement, tout mouvement, comme absolument indivisibles” (158 / 167||168 / 142, emphasis in original).

5.2.2

[The motion of our hand from point A to B is a simple movement.]

Bergson has us consider if we move our hand from point A to B. The movement that transpires is “simple” [which may mean that it is indivisible, or complex in a non-divisible way somehow.]

Let us begin with movement. I have my hand at point A. I move it over to point B, traversing the interval AB. I say that this movement from A to B is by nature simple.

Commençons par le mouvement. J’ai la main au point A. Je la transporte au point B, parcourant l’intervalle AB. Je dis que ce mouvement de A en B est chose simple.

(158 / 168 / 142)

5.2.3

[If our hand makes no pause in its motion, it feels unitary and indivisible to us. If it does make a pause, then it does not feel like it was one motion with distinct phases; rather, it feels like two indivisible motions.]

We feel this action as being singular and indivisible. Suppose we pause at an intermediary point. How would that feel to us? As one divided motion? No, it would feel like two distinct motions. So long as it is a moving without pause, it feels indivisible.

But of this each one of us has the immediate sensation. No doubt while we are moving our hand from A to B we say to ourselves that we could stop it at an intermediary point, but in that case we should not have to do with the same movement. There would no longer be a single movement from A to B; there would be, by hypothesis, two movements, with an interval. Neither from within, through the muscular sense, nor from without ||| through sight, should we still have the same perception. If I leave my movement from A to B as it is, I feel it undivided and must declare it to be indivisible.

Mais c’est de quoi chacun de nous a la sensation immédiate. Sans doute, pendant que nous portons notre main de A en B, nous nous disons que nous pourrions l’arrêter en un point intermédiaire, mais nous n’aurions plus affaire alors au même mouvement. Il n’y aurait plus un mouvement unique de A en B ; il y aurait, par hypothèse, deux mouvements, avec un intervalle d’arrêt. Ni du dedans, par le sens musculaire, ni du dehors par la vue, nous n’aurions encore la même perception. Si nous laissons notre mouvement de A en B tel qu’il est, nous le sentons indivisé et nous devons le déclarer indivisible.

(158 / 168 / 142|||143)

5.2.4

[Because motion traverses space, we mistakenly think that the motion is divisible like the space is. But it is not. And we cannot say that the motion ever occupies a point of space at an instant of time. For, suppose we did divide the motion into smaller and smaller intervals. We would never arrive upon a point in space or time but only upon intervals of decreasing size. So while moving, the object is always passing through points; and it only occupies a point when it stops. Nonetheless, in reality, there is no rest; there is only change and motion. What appears to be at rest is simply moving at pace with our attention and thus seems like it is not moving or changing, like two trains moving side-by-side, making each train appear stationary to the other.]

Bergson will now address our tendency to want to divide up the motion into parts corresponding to spatial intervals the movement traversed. {1} We can divide the spatial interval AB into as many parts as we want. Since the movement traversed this space, we can divide the movement into as many parts as we wish, corresponding to the internal spatial intervals traversed. {2} At each instant of the motion, the hand occupied a determinate point. On the basis of these points, which correlate to instants of the motion, we can divide the motion into stages corresponding to the divided spatial intervals. Bergson then begins his responses to this sort of approach of dividing motion by means of space. He first asks {a} how can movement be applied to the traversed space? {b} And note that the space is immobile, but the movement is mobile. So how do you make something immobile coincide with something mobile? {c} How can a moving object be both moving and occupy a determinate point? If it is moving, it can only be said to be passing through a point. Were it to occupy a point, it would have stopped. [Let us take note briefly of what we may consider a correction and clarification Bertrand Russell makes with regard to this idea that to occupy a point is to be at rest. (See the entries for Bertrand Russell at the Zeno’s Paradox directory.) Russell notes that it is not enough to simply occupy a point to constitute rest. You need to remain at that point as time passes. But I think if we extract some of Bergson’s insight here, we can see a problem even with Russell’s at-at definition of motion. For Russell, there are never immediately successive points, because there is always another between any two. Now suppose we begin with one motion. And suppose we divide it into smaller and smaller intervals. Would we ever arrive upon its occupation of a point during an instant using this method? No. For no matter how small the interval, in Russell’s thinking, there is always a smaller one. And since there is no smallest decomposition, you never have occupation at a point; you only have smaller and smaller passings-through of sets of points. Thus if we begin with a unitary motion, we can never decompose it into parts that simply occupy a singular position at a singular instant. So, insofar as Russell has us think of a moving object occupying a determinate point in space, he is not dealing with a part of motion but rather with the space traversed by that motion.] Bergson further clarifies this notion of unitary motion. We think of any undivided motion as a “bound”, which endures for whatever duration of the motion, which can be any size interval, no matter how small or large. As a singular bound, it is indecomposable. But, after the bound has finished, we see that it traversed an extent of space. Since space is infinitely divisible, we imagine the motion to be so as well. But we are in error as soon as we think that we can really divide the motion up this way into immobilities. Bergson then makes the remarkable claim that in reality there are no immobilities. Whatever we consider to be an immobility is really just a movement that is going at pace alongside a moving point of reference: “when two trains move at the same speed, in the ||| same direction, on parallel tracks: each of the two trains is then immovable to the travellers seated in the other” (159 / 169 / 143|||144). [I am not entirely sure how to conceive the way this transpires in life. Perhaps the idea is that suppose we have something that we think is immobile. In reality it is changing. But it is changing at pace with our flow of awareness, perhaps. Consult the quotation to follow.]

It is true that, when I watch my hand going from A to B and describing the interval AB, I say: “The interval AB can be divided into as many parts as I wish, therefore the movement from A to B can be divided into as many parts as I like, since this movement is applied exactly upon this interval.” Or again: “At each instant of its trajection, the mobile passes through a certain point, therefore one can distinguish in the movement as many stages as one likes, therefore the movement is infinitely divisible.” But let us reflect for a moment. How could the movement be applied upon the space it traverses? How can something moving coincide with something immobile? How could the moving object be in a point of its trajectory passage? It passes through, or in other terms, it could be there. It would be there if it || stopped; but if it should stop there, it would no longer be the same movement we were dealing with. It is always by a single bound that a passing is completed, when there is no break in the passage. The bound may last a few seconds, or days, months, years: it matters little. The moment it is one single bound, it is indecomposable. Only, once the passage is effected, as the trajectory is space and space is indefinitely divisible, we imagine that movement itself is indefinitely divisible. We like to imagine it because, in a movement, it is not the change of position which interests us, it is the positions themselves, the one the movement has left, the one it will take, the one it would take if it stopped on the way. We need immobility, and the more we succeed in imagining movement as coinciding with the immobilities of the points of space through which it passes, the better we think we understand it. To tell the truth, there never is real immobility, if we understand by that an absence of movement. Movement is reality itself, and what we call immobility is a certain state of things analogous to that produced when two trains move at the same speed, in the ||| same direction, on parallel tracks: each of the two trains is then immovable to the travellers seated in the other. But a situation of this kind which, after all, is exceptional, seems to us to be the regular and normal situation, because it is what permits us to act upon things and also permits things to act upon us: the travellers in the two trains can hold out their hands to one another through the door and talk to one another only if they are “immobile,” that is to say, if they are going in the same direction at the same speed. “Immobility” being the prerequisite for our action, we set it up as a reality, we make || of it an absolute, and we see in movement something which is superimposed. Nothing is more legitimate in practice. But when we transport this habit of mind into the domain of speculation, we fail to recognize the true reality, we deliberately create insoluble problems, we close our eyes to what is most living in the real.

Il est vrai que, lorsque je regarde ma main allant de A en B et décrivant l’intervalle AB, je me dis : « l’intervalle AB peut se diviser en autant de parties que je le veux, donc le mouvement de A en B peut se diviser en autant de parties qu’il me plaît, puisque ce mouvement s’applique sur cet intervalle. » Ou bien encore : « à chaque instant de son trajet, le mobile passe en un certain point, donc on peut distinguer dans le mouvement autant d’étapes qu’on voudra, donc le mouvement est infiniment divisible. » Mais réﬂéchissons-y un instant. Comment le mouvement pourrait-il s’appliquer sur l’espace qu’il parcourt ? comment du mouvant coïnciderait-il avec de l’immobile ? comment l’objet qui se meut serait-il en un point de son trajet ? Il y passe, ou, en d’autres termes, il pourrait y être. Il y serait s’il s’y arrêtait ; mais, s’il s’y arrêtait, ce n’est plus au même mouvement | que nous aurions affaire. C’est toujours d’un seul bond qu’un trajet est parcouru, quand il n’y a pas d’arrêt sur le trajet. Le bond peut durer quelques secondes, ou des jours, des mois, des années : peu importe. Du moment qu’il est unique, il est indécomposable. Seulement, une fois le trajet effectué, comme la trajectoire est espace et que l’espace est indéfiniment divisible, nous nous figurons que le mouvement lui-même est divisible indéfiniment. Nous aimons à nous le figurer, parce que, dans un mouvement, ce n’est pas le changement de position qui nous intéresse, ce sont les positions elles-mêmes, celle que le mobile a quittée, celle qu’il prendra, celle qu’il prendrait s’il s’arrêtait en route. Nous avons besoin d’immobilité, et plus nous réussirons à nous représenter le mouvement comme coïncidant avec les immobilités des points de l’espace qu’il parcourt, mieux nous croirons le comprendre. A vrai dire, il n’y a jamais d’immobilité véritable, si nous entendons par là une absence de mouvement. Le mouvement est la réalité même, et ce que nous appelons immobilité est un certain état de choses analogue à ce qui se produit quand deux trains marchent avec la même vitesse, dans le même sens, sur deux voies parallèles : chacun des deux trains est alors immobile pour les voyageurs assis dans l’autre. Mais une situation de ce genre, qui est en somme exceptionnelle, nous semble être la situation régulière et normale, parce que c’est celle qui nous permet d’agir sur les choses et qui permet aussi aux choses d’agir sur nous : les voyageurs des deux trains ne peuvent se tendre la main par la portière et causer ensemble que s’ils sont « immobiles », c’est-à-dire s’ils marchent dans le même sens avec la même vitesse. L’ «immobilité » étant ce dont notre action a besoin, nous l’érigeons en réalité, nous en faisons un absolu, et nous voyons dans le mouvement | quelque chose qui s’y surajoute. Rien de plus légitime dans la pratique. Mais lorsque nous transportons cette habitude d’esprit dans le domaine de la spéculation, nous méconnaissons la réalité vraie, nous créons, de gaieté de cœur, des problèmes insolubles, nous fermons les yeux à ce qu’il y a de plus vivant dans le réel.

(158|160 / 168||170 / 143|||144)

5.2.5

[Zeno’s paradoxes of motion confuse the space traversed, which is divisible, with the motion, which is not. For example, Achilles is said to never overtake the Tortoise, because the Tortoise is constantly creating new distances for Achilles to cross. But Achilles’ own motion was not composed of infinitely many movements that endlessly decrease in size. It was made of a series of indivisible steps.]

Zeno’s paradoxes of motion confuse movement with the space traversed. Or if they do not make such a simplistic equivalence, they at least treat movement as being divisible like space is, without taking into account that movement is articulated in unitary segments. [Recall the paradox of Achilles and the Tortoise (described at section II.F of this entry, and discussed by Bergson in Time and Free Will §70, Matter and Memory section 4.2.6, and Creative Evolution section 4.5.10.) The Tortoise has a head start at the beginning of its race with Achilles. For Achilles to overtake the Tortoise, he must first arrive upon the Tortoise’s starting position. But by the time he gets there, the Tortoise has already advanced a little further. So now Achilles must arrive upon the Tortoise’s new position. But again, upon arriving upon it, the Tortoise will be further. So long as the Tortoise keeps moving, it will always create a new, more distant position for Achilles to cross. Thus Achilles will never overtake the Tortoise while it keeps moving.] Bergson recalls Zeno’s paradox of Achilles and the Tortoise, where “Achilles, they say, will never overtake the tortoise he is pursuing, for when he arrives at the point where the tortoise was the latter will have had time to go further, and so on indefinitely.” Bergson notes that there have been a great variety of refutations, but he proposes a simple one. He says we need to ask Achilles after he in fact overtakes the Tortoise, how did he do it? He would say that Zeno’s description does not match the way the event transpired. He did not first arrive upon the Tortoises’ first position, then second position, and on and on. Rather, Achilles will say that he took a series of steps until finally overtaking the Tortoise. So his course was a series of indivisible actions. These are the only parts we can divide his whole course into. We should not, like Zeno, divide the acts indefinitely like spatial parts corresponding to the spatial locations of the race track, because the acts are not immobilities like space and they cannot be coordinated point-by-point with an immobility like space.

I need not recall the arguments of Zeno of Elea. They all involve the confusion of movement with the space covered, or at least the conviction that one can treat movement as one treats space, divide it without taking account of its articulations. Achilles, they say, will never overtake the tortoise he is pursuing, for when he arrives at the point where the tortoise was the latter will have had time to go further, and so on indefinitely. Philosophers have refuted this argument in numerous ways, and ways so different that each of these refutations deprives the others of the right to be considered definitive. There would have been, nevertheless, a very simple means of making short work of the difficulty: that would have been to question Achilles. For since Achilles finally catches up to the tortoise and even passes it, he must know better than anyone else how he goes about it. The ancient philosopher who demonstrated the possibility of movement by walking was right: his only mistake was to make the gesture without adding a commentary. Suppose then we ask Achilles to comment on his race: here, doubtless, is what he will answer: “Zeno insists that I go from the point where I am to the point the tortoise ||| has left, from that point to the next point it has left, etc., etc.; that is his procedure for making me run. But I go about it otherwise. I take a first step, then a second, and so on: finally, after a certain number of steps, || I take a last one by which I skip ahead of the tortoise. I thus accomplish a series of indivisible acts. My course is the series of these acts. You can distinguish its parts by the number of steps it involves. But you have not the right to disarticulate it according to another law, or to suppose it articulated in another way. To proceed as Zeno does is to admit that the race can be arbitrarily broken up like the space which has been covered; it is to believe that the passage is in reality applied to the trajectory; it is making movement and immobility coincide and consequently confusing one with the other.”

Je n’ai pas besoin de vous rappeler les arguments de Zénon d’Élée. Tous impliquent la confusion du mouvement avec l’espace parcouru, ou tout au moins la conviction qu’on peut traiter le mouvement comme on traite l’espace, le diviser sans tenir compte de ses articulations. Achille, nous dit-on, n’atteindra jamais la tortue qu’il poursuit, car lorsqu’il arrivera au point où était la tortue, celle-ci aura eu le temps de marcher, et ainsi de suite indéfiniment. Les philosophes ont réfuté cet argument de bien des manières, et de manières si différentes que chacune de ces réfutations enlève aux autres le droit de se croire définitives. Il y aurait eu pourtant un moyen très simple de trancher la difficulté : c’eût été d’interroger Achille. Car, puisqu’Achille finit par rejoindre la tortue et même par la dépasser, il doit savoir, mieux que personne, comment il s’y prend. Le philosophe ancien qui démontrait la possibilité du mouvement en marchant était dans le vrai : son seul tort fut de faire le geste sans y joindre un commentaire. Demandons alors à Achille de commenter sa course : voici, sans aucun doute, ce qu’il nous répondra. « Zénon veut que je me rende du point où je suis au point que la tortue a quitté, de celui-ci au point qu’elle a quitté encore, etc. ; c’est ainsi qu’il procède pour me faire courir. Mais moi, pour courir, je m’y prends autrement. Je fais un premier pas, puis un second, et ainsi de suite : finalement, après un certain nombre de pas, j’en fais un dernier par lequel j’enjambe la tortue. J’accomplis | ainsi une série d’actes indivisibles. Ma course est la série de ces actes. Autant elle comprend de pas, autant vous pouvez y distinguer de parties. Mais vous n’avez pas le droit de la désarticuler selon une autre loi, ni de la supposer articulée d’une autre manière. Procéder comme le fait Zénon, c’est admettre que la course peut être décomposée arbitrairement, comme l’espace parcouru ; c’est croire que le trajet s’applique réellement contre la trajectoire ; c’est faire coïncider et par conséquent confondre ensemble mouvement et immobilité. »

(160|161 / 170||171 / 144|||145)

5.2.6

[Under this erroneous understanding that confuses movement with traversed space, we hold two incompatible metaphysical assumptions: {1} motion is fundamentally a passage between points, and thus it is fundamentally a mobility transpiring between immobilities, and {2} motion is decomposable into nothing more than positions dividing passages (into immobilities), and it is recomposable by taking all these positions together.]

Bergson says that this method of decomposition that confuses motion with traversed space is our usual way of understanding movement. It treats motion as if it were constituted by immobilities (spatial positions). And we think we can reconstitute movement by adding all the immobilities together. But at the same time that we decompose movement into positions, we assume as well that there is a passage between any two positions. Yet, how do we conceptualize this passage? By saying it is composed of yet more positions. We want to be able to have both concepts, that there is a mobile passage and that the passage is made of immobile positions. But as we can see, they are conceptually irreconcilable. [Bergson again ends with the notion that immobility is perhaps not even real.]

But that is precisely what our usual method consists in. We argue about movement as though it were made of immobilities and, when we look at it, it is with immobilities that we reconstitute it. Movement for us is a position, then another position, and so on indefinitely. We say, it is true, that there must be something else, and that from one position to another there is the passage by which the interval is cleared. But as soon as we fix our attention on this passage, we immediately make of it a series of positions, even though we still admit that between two successive positions one must indeed assume a passage. We put this passage off indefinitely the moment we have to consider it. We admit that it exists, we give it a name; that is enough for us: once that point has been satisfactorily settled we turn to the positions preferring to deal with them alone. We have an instinctive fear of those difficulties which the vision of movement as movement would arouse in our thought; and quite rightly, once we have loaded movement down with immobilities. If movement is not everything, it is nothing; and if to begin with we have sup- || posed that immobility can be a reality, movement will slip through our fingers when we think we have it.

Mais en cela consiste précisément notre méthode habituelle. Nous raisonnons sur le mouvement comme s’il était fait d’immobilités, et, quand nous le regardons, c’est avec des immobilités que nous le reconstituons. Le mouvement est pour nous une position, puis une nouvelle position, et ainsi de suite indéfiniment. Nous nous disons bien, il est vrai, qu’il doit y avoir autre chose, et que, d’une position à une position, il y a le passage par lequel se franchit l’intervalle. Mais, dès que nous fixons notre attention sur ce passage, vite nous en faisons une série de positions, quittes à reconnaître encore qu’entre deux positions successives il faut bien supposer un passage. Ce passage, nous reculons indéfiniment le moment de l’envisager. Nous admettons qu’il existe, nous lui donnons un nom, cela nous suffit : une fois en règle de ce côté, nous nous tournons vers les positions et nous préférons n’avoir affaire qu’à elles. Nous avons instinctivement peur des difficultés que susciterait à notre pensée la vision du mouvement dans ce qu’il a de mouvant ; et nous avons raison, du moment que le mouvement a été chargé par nous d’immobilités. Si le mouvement n’est pas tout, il n’est rien ; et si nous avons d’abord posé que l’immobilité peut être une réalité, le mouvement | glissera entre nos doigts quand nous croirons le tenir.

(161|162 / 171||172 / 145)

5.2.7

[In fact, all real change is indivisible. We erroneously think that change can be divided into states because indivisible change in the world is practically coordinated with the indivisible change of our inner experience. When our actions need to intervene in the world or when for other practical reasons we coordinate events in the world with events in our minds, we artificially designate stable states in the changes outside and inside us.]

Bergson says that this applies to any sort of change whatsoever: “All real change is an indivisible change” / “Tout changement réel est un changement indivisible”. Bergson then explains how it is that we come to erroneously understand real change as being divisible. [His first idea here might be the following, but check the quotation below. We suppose there is some change happening in the world. Let us imagine that we are heating water to a boil. So out in the world there is continuous qualitative change of the water. At the same time, our mind is in a flux of consciousness. These two fluxes flow together in simultaneity (see for example Ch.3 of Duration and Simultaneity.) Now, as the water comes to boil, we get anxious because it might overboil, so we lift the pan off the fire. We then want to say that there were distinct states of the water, namely,  it being below boiling, it being at boiling, and it cooling below boiling. These states correspond to states of our mind: our waiting for it to boil, our alarm when it boils, and our relief when it cools. But in reality, Bergson seems to be saying, the water was never in some determinate, stable state. It was always changing. And our mind was not in any determinate, stable state. It was always a flux of consciousness. But we came to regard the water having states corresponding to the appropriate actions we made with regard to it, and these actions that divided the change serve to mark off seemingly distinct and stable inner states of our experience of the change. So it is simply for practical reasons (our needing to boil the water but not too much) that cause us to delineate states of change in the world and in our inner life. But these immobilities are not really inherent to the world and our mind.]

I have spoken of movement; but I could say the same for any change whatever. All real change is an indivisible change. We like to treat it as a series of distinct states which form, as it were, a line in time. That is perfectly natural. If change is continuous in us and also in things, on the other hand, in order that the uninterrupted change which each of us calls “me” may act upon the uninterrupted change that we call a “thing,” these two changes must find themselves, with regard to one another, in a situation like that of the two trains referred to above. We say, for example, that an object changes color, and that change here consists in a series of shades which would be the constitutive elements of change and which, themselves, would not change. But in the first place, if each shade has any objective existence at all, it is an infinitely rapid oscillation, it is change. And in the second place, the perception we have of it, to the extent that it is subjective, is only an isolated, abstract aspect of the general state of our person, and this state as a whole is constantly changing and causing this so-called invariable perception to participate in its change; in fact, there is no perception which is not constantly being modified. So that color, outside of us, is mobility itself, and our own person is also mobility. But the whole mechanism of our perception of things, like the mechanism of our action upon things has been regulated in such a way as to bring about, between the external and the internal mobility, a situation comparable to that of our two trains, – more complicated, perhaps, but of the same kind: when the || two changes, that of the object and that of the subject, take place under particular conditions, they produce the particular appearance that we call a “state.” And once in possession of “states,” our mind recomposes change with them. I repeat, there is nothing more natural: the breaking up of change into states enables us to act upon things, and it is useful in a practical sense to be interested in the states rather than in the change itself. But what is favourable to action in this case would ||| be fatal to speculation. If you imagine a change as being really composed of states, you at once cause insoluble metaphysical problems to arise. They deal only with appearances. You have closed your eyes to true reality.

J’ai parlé du mouvement ; mais j’en dirais autant de n’importe quel changement. Tout changement réel est un changement indivisible. Nous aimons à le traiter comme une série d’états distincts qui s’aligneraient, en quelque sorte, dans le temps. C’est naturel encore. Si le changement est continuel en nous et continuel aussi dans les choses, en revanche, pour que le changement ininterrompu que chacun de nous appelle « moi » puisse agir sur le changement ininterrompu que nous appelons une « chose », il faut que ces deux changements se trouvent, l’un par rapport à l’autre, dans une situation analogue à celle des deux trains dont nous parlions tout à l’heure. Nous disons par exemple qu’un objet change de couleur, et que le changement consiste ici dans une série de teintes qui seraient les éléments constitutifs du changement et qui, elles, ne changeraient pas. Mais, d’abord, ce qui existe objectivement de chaque teinte, c’est une oscillation infiniment rapide, c’est du changement. Et, d’autre part, la perception que nous en avons, dans ce qu’elle a de subjectif, n’est qu’un aspect isolé, abstrait, de l’état général de notre personne, lequel change globalement sans cesse et fait participer à son changement cette perception dite invariable : en fait, il n’y a pas de perception qui ne se modifie à chaque instant. De sorte que la couleur, en dehors de nous, est la mobilité même, et que notre propre personne est mobilité encore. Mais tout le mécanisme de notre perception des choses, comme celui de notre action sur les choses, a été réglé de manière à amener ici, entre la mobilité externe et la mobilité intérieure, une situation comparable à celle de nos deux trains, - plus compliquée, sans doute, mais du même genre : quand les deux changements, celui de l’objet et celui du sujet, ont lieu dans ces conditions particulières, | ils suscitent l’apparence particulière que nous appelons un « état ». Et, une fois en possession d’ « états », notre esprit recompose avec eux le changement. Rien de plus naturel, je le répète : le morcelage du changement en états nous met à même d’agir sur les choses, et il est pratiquement utile de s’intéresser aux états plutôt qu’au changement lui-même. Mais ce qui favorise ici l’action serait mortel à la spéculation. Représentez-vous un changement comme réellement composé d’états : du même coup vous faites surgir des problèmes métaphysiques insolubles. Ils ne portent que sur des apparences. Vous avez fermé les yeux à la réalité vraie.

(162|163 / 172||173 / 146|||147)

5.2.8

[We can know that change is indivisible, because when we witness it, we experience it as such. Also, all is change, and there are no invariable objects doing those changes.]

Bergson offers as proof that whenever we directly view change or a movement, we have a feeling of absolute individuality. Bergson now makes the point that although there are changes, that is all there is. There are no invariable objects undergoing the changes. Even in movements there are no invariable objects that are doing the moving.

I shall not press the point. Let each of us undertake the experiment, let him give himself the direct vision of a change, of a movement: he will have a feeling of absolute indivisibility. I come then to the second point, closely allied to the first. There are changes, but there are underneath the change no things which change: change has no need of a support. There are movements, but there is no inert or invariable object which moves: movement does not imply a mobile.

Je n’insisterai pas davantage. Que chacun de nous fasse l’expérience, qu’il se donne la vision directe d’un changement, d’un mouvement : il aura un sentiment d’absolue indivisibilité. J’arrive alors au second point, qui est très voisin du premier. Il y a des changements, mais il n’y a pas, sous le change­ment, de choses qui changent : le changement n’a pas besoin d’un support. Il y a des mouvements, mais il n’y a pas d’objet inerte, invariable, qui se meuve : le mouvement n’implique pas un mobile.

(163 / 173 / 147, italics in the original, boldface mine)

5.2.9

[Our vision distinguishes things that come to appear as invariable objects persisting through their changes. But our sense of hearing only gives us the changes. For example, when we hear a melody, the “object” here is the melodic change itself.]

Bergson says that we develop the erroneous notion of invariable objects subsisting through change from our primary reliance on vision. Our sight separates things in our visual field, and we come to take those distinguished things as invariable figures. Sight thus prepares the sense of touch for our interactions with the world. But the other senses are better able to give us the world in changefulness. When we hear a melody, we do not perceive an invariable object that is changing but rather the change “is the thing itself”. We know this is so, because if you stop the melody at one point or at another, it is a different thing in each case. So there is no one melody that subsists throughout its changes. And we should not think of the melody being composed of the notes pictured in the score. For this is to understand it as a visualizable object with spatial properties.

It is difficult to picture things in this way, because the sense ‘par excellence’ is the sense of sight, and because the eye has developed the habit of separating, in the visual field, the relatively invariable figures which are then supposed to change place without changing form, movement is taken as super-added to the mobile as an accident. It is, in fact, useful to have to deal in daily life with objects which are stable and, as it were, responsible, to which one can address oneself as to persons. The sense of sight contrives to take things in this way: as an ad- || vance-guard for the sense of touch, it prepares our action upon the external world. But we already have less difficulty in perceiving movement and change as independent realities if we appeal to the sense of hearing. Let us listen to a melody, allowing ourselves to be lulled by it: do we not have the clear perception of a movement which is not attached to a mobile, of a change without anything changing? This change is enough, it is the thing itself. And even if it takes time, it is still indivisible; if the melody stopped sooner it would no longer be the same sonorous whole, it would be another, equally indivisible. We have, no doubt, a tendency to divide it and to picture, instead of the uninterrupted continuity of melody, a juxtaposition of distinct notes. But why? Because we are thinking of the discontinuous series of efforts we should be making to recompose approximately ||| the sound heard if we were doing the singing, and also because our auditory perception has acquired the habit of absorbing visual images. We therefore listen to the melody through the vision which an orchestra-leader would have of it as he watched its score. We picture notes placed next to one another upon an imaginary piece of paper. We think of a keyboard upon which some one is playing, of the bow going up and down, of the musicians, each one playing his part along with the others. If we do not dwell on these spatial images, pure change remains, sufficient unto itself, in no way divided, in no way attached to a “thing” which changes.

On a de la peine à se représenter ainsi les choses, parce que le sens par excellence est celui de la vue, et que l’œil a pris l’habitude de découper, dans l’ensemble du champ visuel, des figures relativement invariables qui sont censées | alors se déplacer sans se déformer : le mouvement se surajouterait au mobile comme un accident. Il est en effet utile d’avoir affaire, tous les jours, à des objets stables et, en quelque sorte, responsables, auxquels on s’adresse comme à des personnes. Le sens de la vue s’arrange pour prendre les choses de ce biais : éclaireur du toucher, il prépare notre action sur le monde exté­rieur. Mais déjà nous aurons moins de peine à percevoir le mouvement et le changement comme des réalités indépendantes si nous nous adressons au sens de l’ouïe. Écoutons une mélodie en nous laissant bercer par elle : n’avons-nous pas la perception nette d’un mouvement qui n’est pas attaché à un mobile, d’un changement sans rien qui change ? Ce changement se suffit, il est la chose même. Et il a beau prendre du temps, il est indivisible : si la mélodie s’arrêtait plus tôt, ce ne serait plus la même masse sonore ; c’en serait une autre, égale­ment indivisible. Sans doute nous avons une tendance à la diviser et à nous représenter, au lieu de la continuité ininterrompue de la mélodie, une juxtapo­sition de notes distinctes. Mais pourquoi ? Parce que nous pensons à la série discontinue d’efforts que nous ferions pour recomposer approximativement le son entendu en chantant nous-mêmes, et aussi parce que notre perception auditive a pris l’habitude de s’imprégner d’images visuelles. Nous écoutons alors la mélodie à travers la vision qu’en aurait un chef d’orchestre regardant sa partition. Nous nous représentons des notes juxtaposées à des notes sur une feuille de papier imaginaire. Nous pensons à un clavier sur lequel on joue, à l’archet qui va et qui vient, au musicien dont chacun donne sa partie à côté des autres. Faisons abstraction de ces images spatiales : il reste le changement pur, se suffisant à lui-même, nullement divisé, nullement attaché à une « chose » qui change.

(163|164 / 173||174 / 147|||148)

5.2.10

[Science decomposes things down into smaller and smaller particles understood increasingly in terms of their movements and vibrations. When we see something, we might think it is an invariable object. But that image is composed of tiny dots of color, each itself a light frequency and thus a movement.]

Bergson returns to sight to make the point that it is not necessary for us to only see invariable objects. Science decomposes things down into smaller and smaller things, understood more in terms of their motion than their substantiality. Bergson then notes that when we see something moving, the parts of our vision are colored spots, which are made of a “series of extremely rapid vibrations”. [I am not certain, but perhaps he is referring to something like the frequency of the light waves. See 165 / 175 / 148.]

5.2.11

[Change itself is the only thing with any substantiality in the sense of being something that endures. There are no other invariabilities. We see this with our inner life, which is a pure continuous flux like a melody. We are mistaken to think that there is a series of discrete and distinct psychic states modifying an invariable ego as substrate.]

Bergson says that we most encounter the “substantiality” of change in our inner life. [By substantiality he does not mean the invariable objects but change itself being the only thing that could qualify as a substrate, because change itself is the only thing that endures.] He says that certain theories of personality assume two things about consciousness, both being incorrect, and as a result they encounter a number of conceptual problems. The first incorrect assumption is that we have “a series of distinct psychological states, each one invariable”. [He also says that this series of states is thought to produce  variations of the ego by their very succession”. It is not stated whether or not the ego’s variations are a series of discrete invariable states, but I would guess they would be, as that is the form the cause takes.] The second incorrect assumption is that we have an invariable ego which “would serve as support” for the psychic variations. He first wonders how the unity of the ego could meet up with the multiplicity of the psychic variations. He next wonders how either one could have duration. Consider the flux of psychic states. Here change is superadded (s’y surajoute). [I am not sure what is meant here. I am going to guess it is the following, but please consult the text. There is only flux, which means at any present there is a variation. But what it is varying against is not present. In order to say there was change, we need to add to the present variation the past and/or future situations in order to say that a change transpires. Thus it is hard to say how the flux has duration, because in itself it is only a present variation and not something that itself endures.] Now consider the invariable ego. The ego is made of elements which do not change. [I am not sure what those elements are. Perhaps they are psychic structures of some kind.] So if its elements are invariable, how can it be said to endure? [Apparently only variable things can endure, but I am not sure why. Perhaps invariable things like structures are not temporal but some sort of idealized abstraction.] Bergson then claims that neither assumption is true. There is only the continuously varying “melody” of our inner life, and this is what constitutes our personality. [In other words, we have no stable ego.]

But nowhere is the substantiality of change so visible, so palpable as in the domain of the inner life. Difficulties and contradictions of every kind to which the theories of personality have led come from our having imagined, on the one hand, a series of distinct psychological ||| states, each one invariable, which would produce the variations of the ego by their very succession, and on the other hand an ego, no less invariable, which would serve as support for them. How could this unity and this multiplicity meet? How, without either of them having duration – the first because change is something superadded, the second because it is made up of elements which do not change – how could they constitute an ego which endures? But the truth is that there is neither a || rigid, immovable substratum nor distinct states passing over it like actors on a stage. There is simply the continuous melody of our inner life, – a melody which is going on and will go on, indivisible, from the beginning to the end of our conscious existence. Our personality is precisely that.

Mais nulle part la substantialité du changement n’est aussi visible, aussi palpable, que dans le domaine de la vie intérieure. Les difficultés et contra­dictions de tout genre auxquelles ont abouti les théories de la personnalité viennent de ce qu’on s’est représenté, d’une part, une série d’états psycholo­giques distincts, chacun invariable, qui produiraient les variations du moi par leur succession même, et d’autre part un moi, non moins invariable, qui leur servirait de support. Comment cette unité et cette multiplicité pourraient-elles se rejoindre ? comment, ne durant ni l’une ni l’autre – la première parce que le changement est quelque chose qui s’y surajoute, la seconde parce qui elle est faite d’éléments qui ne changent pas – pourraient-elles constituer un moi qui dure ? Mais la vérité est qu’il n’y a ni un substratum rigide immuable ni des états distincts qui y passent comme des acteurs sur une scène. Il y a simple­ment la mélodie continue de notre vie intérieure, – mélodie qui se poursuit et se poursuivra, indivisible, du commencement à la fin de notre existence consciente. Notre personnalité est cela même.

(165-166 / 175-176 / 148-149)

5.2.12

[This indivisible continuity of change that we directly experience as being fundamental to our awareness is real duration or time proper. But we normally conceive time erroneously as being spatial, like the note symbols of a melody juxtaposed simultaneously side-by-side on the musical staff.]

Bergson has been describing an “indivisible continuity of change”. He claims that “this is precisely what constitutes true duration.” Many might object that this notion of duration is “something inexpressible and mysterious.” But in fact this duration is “the clearest thing in the world” [because we experience it directly every moment of our consciousness.] We can think of real duration as time, so long as we qualify that it is “time perceived as indivisible.” [Now, time is often understood as being a matter of succession.] But although duration is time, we should not think of it as succession. Succession is understood as a matter of moments coming before and after, each being set beside the other. [Bergson might here, when mentioning simultaneity, be noting that this setting beside one another of moments makes them simultaneous when really they are not. See the quote below.] When we hear a melody, we have the impression that it cannot be broken up. So we should not think of the melody being broken up into notes set side-by-side and thus not in terms of this spatialized sort of succession. By putting the note symbols into the space of the musical staff, we might erroneously come to believe that the melody itself is something composed of spatially simultaneous parts. Bergson then acknowledges that we normally live our lives in the spatialized time. But real duration is something going on deep inside us. His last point might be that real duration is a single, universal time that happens exclusively in the present and that makes possible the extending changes we notice inside and outside us.]

This indivisible continuity of change is precisely what constitutes true duration. I cannot here enter into the detailed examination of a question I have dealt with elsewhere. I shall confine myself therefore to saying, in reply to those for whom this “real duration” is something inexpressible and mysterious, that it is the clearest thing in the world: real duration is what we have always called time, but time perceived as indivisible. That time implies succession I do not deny. But that succession is first presented to our consciousness, like the distinction of a “before” and “after” set side by side, is what I cannot admit. When we listen to a melody we have the purest impression of succession we could possibly have, – an impression as far removed as possible from that of simultaneity, – and yet it is the very continuity of the melody and the impossibility of breaking it up which make that impression upon us. If we cut it up into distinct notes, into so many “befores” and “afters,” we are bringing spatial images into it and impregnating the succession with simultaneity: in space, and only in space, is there a clear-cut distinction of parts external to one another. I recognize moreover that it is in spatialized time that we ordinarily place ourselves. We have no interest in listening to the uninterrupted ||| humming of life’s depths. And yet, that is where real duration is. Thanks to it, the more or less lengthy changes || we witness within us and in the external world, take place in a single identical time.

C’est justement cette continuité indivisible de changement qui constitue la durée vraie. Je ne puis entrer ici dans l’examen approfondi d’une question que j’ai traitée ailleurs. Je me bornerai donc à dire, pour répondre à ceux qui voient dans cette durée « réelle » je ne sais quoi d’ineffable et de mystérieux, qu’elle est la chose la plus claire du monde : la durée réelle est ce que l’on a toujours appelé le temps, mais le temps perçu comme indivisible. Que le temps impli­que la succession, je n’en disconviens pas. Mais que la succession se présente d’abord à notre conscience comme la distinction d’un « avant » et d’un « après » juxtaposés, c’est ce que je ne saurais accorder. Quand nous écoutons une mélodie, nous avons la plus pure impression de succession que nous puissions avoir, – une impression aussi éloignée que possible de celle de la simultanéité, – et pourtant c’est la continuité même de la mélodie et l’impos­sibilité de la décomposer qui font sur nous cette impression. Si nous la découpons en notes distinctes, en autant d’ « avant » et d’« après » qu’il nous plaît, c’est que nous y mêlons des images spatiales et que nous imprégnons la succession de simultanéité : dans l’espace, et dans l’espace seulement, il y a distinction nette de parties extérieures les unes aux autres. Je reconnais d’ailleurs que c’est dans le temps | spatialisé que nous nous plaçons d’ordinaire. Nous n’avons aucun intérêt à écouter le bourdonnement ininterrompu de la vie profonde. Et pourtant la durée réelle est là. C’est grâce à elle que prennent place dans un seul et même temps les changements plus ou moins longs aux­quels nous assistons en nous et dans le monde extérieur.

(166-167 / 176-177 / 149-150)

5.2.13

[Only change is real. There are no invariable things doing the changing.]

So both internal and external reality is “mobility itself”. There is change without things doing the changing.

Thus, whether it is a question of the internal or the external, of ourselves or of things, reality is mobility itself. That is what I was expressing when I said that there is change, but that there are not things which change.

Ainsi, qu’il s’agisse du dedans ou du dehors, de nous ou des choses, la réalité est la mobilité même. C’est ce que j’exprimais en disant qu’il y a du changement, mais qu’il n’y a pas de choses qui changent.

(167 / 177 / 150)

5.2.14

[Some might feel dizzy when contemplating the idea that reality has no fixed points of immobility. But we can obtain a sense of orientation by seeing that change itself is the most substantial and durable thing possible.]

Many will object to the notion that all is change, because they will not be able to deal with the disorienting feeling. Bergson assures such people that they can ground their sense of reality in change itself, which is “the most substantial and durable thing possible”.

Before the spectacle of this universal mobility there may be some who will be seized with dizziness. They are accustomed to terra firma; they cannot get used to the rolling and pitching. They must have “fixed” points to which they can attach thought and existence. They think that if everything passes, nothing exists; and that if reality is mobility, it has already ceased to exist at the moment one thinks it, – it eludes thought. The material world, they say, is going to disintegrate, and the mind will drown in the torrent-like flow of things. – Let them be reassured! Change, if they consent to look directly at it without an interposed veil, will very quickly appear to them to be the most substantial and durable thing possible. Its solidity is infinitely superior to that of a fixity which is only an ephemeral arrangement between mobilities. I have come, in fact, to the third point to which I should like to draw your attention.

Devant le spectacle de cette mobilité universelle, quelques-uns d’entre nous seront pris de vertige. Ils sont habitués à la terre ferme ; ils ne peuvent se faire au roulis et au tangage. Il leur faut des points « fixes » auxquels attacher la pensée et l’existence. Ils estiment que si tout passe, rien n’existe ; et que si la réalité est mobilité, elle n’est déjà plus au moment où on la pense, elle échappe à la pensée. Le monde matériel, disent-ils, va se dissoudre, et l’esprit se noyer dans le flux torrentueux des choses. – Qu’ils se rassurent ! Le changement, s’ils consentent à le regarder directement, sans voile interposé, leur apparaîtra bien vite comme ce qu’il peut y avoir au monde de plus substantiel et de plus durable. Sa solidité est infiniment supérieure à celle d’une fixité qui n’est qu’un arrangement éphémère entre des mobilités. J’arrive ici, en effet, au troisième point sur lequel je voulais attirer votre attention.

(167 / 177 / 150)

5.2.15

[We need to change our notion of the past, which says that just the present is real and that the past can only survive when remembered in the present.]

Bergson says that if we accept that “change is real and even constitutive of reality”, we will need to understand the past differently than we normally do. Usually we think that only the present exists, and the past can only survive when it is remembered in the present. In a sense, memory would be “storing them [certain parts of the past] away in a kind of box.” Bergson says this is a “profound mistake” (167-167 / 177-178 / 150-151).

[Sections 5.2.16-5.2.23 are excluded from this summary.]

Bergson, Henri. 1938 [3rd edition, 1990]. La pensée et le mouvant: Essais et conférences. Paris: Quadridge / PUF.

Available online at:

http://catalogue.bnf.fr/ark:/12148/cb372379203

Another version available at:

http://classiques.uqac.ca/classiques/bergson_henri/pensee_mouvant/pensee_mouvant.html

Bergson, Henri. 1946. The Creative Mind. English translation by Mabelle L. Andison. Westport, Connecticut: Greenwood.

Bergson, Henri. 1965. An Introduction to Metaphysics: The Creative Mind. English translation by Mabelle L. Andison. Totowa, New Jersey: Rowman & Allanheld.

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