## 25 Dec 2017

### Goldschmidt (1.1.3.13) Le système stoïcien et l'idée de temps, “Temps infini et temps limité”, summary

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

Summary of

Victor Goldschmidt

Le système stoïcien et l'idée de temps

Première partie:

La théorie du temps et sa portée

A. La théorie du temps

III. La théorie du temps

1.1.3.13

Temps infini et temps limité

Brief summary:

For the Stoics, time can be understood as a line stretching infinitely into the past in one direction and infinitely into the future in another. Although time is infinite, it has parts which are either infinite or finite: time is “bound” on the far extremities by the limitless limits of the infinite past and infinite future; but past and future are limited on the inside by the finite present, being a limited limit to both past and future.

Contents

1.1.3.13

[Infinite and Finite Time]

1.1.3.13.1

[Stoic Time as “Interval” of Motion, and the Opposition of Past and Future to the Present]

1.1.3.13.2

[Time in Terms of Part-Whole Structures and the Totality Encompassing the Corporeal and Incorporeal]

1.1.3.13.3

[Time’s Unlimited Ends and Limited Present]

Summary

1.1.3.13

Temps infini et temps limité

1.1.3.13.1

[Stoic Time as “Interval” of Motion, and the Opposition of Past and Future to the Present]

(pp.35-36: “Par delà ses résonances aristotéliciennes …”)

[In sum: What makes the Stoic theory of time different from Aristotle’s is that the Stoics speak of time as being the “interval” of motion, while for Aristotle it is the “number”. Also, the Stoics oppose the past and future to the present.]

[Previously in section 1.1.3.10, we examined Chrysippus’ definition of time, and in section 1.1.3.11 we examined Aristotle’s. Then in section 1.1.3.12 we discussed how Chrysippus’ definition of time as the interval of movement echoes Aristotle’s definition of time as the number of movement. See especially section 1.1.3.12.3.] Despite the resonances between Chrysippus’ and Aristotle’s definitions of time, we see already at the beginning of the definition attributed to Chrysippus by Stobaeus that the Stoic theory has an originality to it. Now we will examine the important term “interval” in the Stoic theory, which takes the place of “number” in Aristotle. We will also see how for the Stoics the past and future stand in opposition to the present.

Par delà ses résonances aristotéliciennes, le début de notre texte fait déjà entrevoir l’originalité de la théorie stoïcienne. La suite immédiate va expliquer le terme par où cette théorie s’oppose directement à Aristote : « intervalle », substitué à « nombre »; et le commentaire mettra | d’emblée l’accent sur la thèse fondamentale : passé et futur, opposés en bloc au présent.

(35-36)

1.1.3.13.2

[Time in Terms of Part-Whole Structures and the Totality Encompassing the Corporeal and Incorporeal]

(p.36: “Le temps se prend dans deux acceptions, ainsi que la terre …”)

[In sum: The Stoic notion of time is bound up with certain Stoic part-whole structures, like the part-whole structure involved in their cosmology, where there is a totality that encompasses both the corporeal and incorporeal.]

“[T]ime is spoken of in two senses, as are earth and sea and void and the universe and its parts” (Stobaeus, in Inwood and Gerson 2008: 88. In the French as: “Le temps se prend dans deux acceptions, ainsi que la terre, la mer et le vide : (on peut en considérer) le tout ou les parties.”) We see this part-whole distinction made in another context by Diogenes Laërtius: “Both substance and matter are terms used in a twofold sense according as they signify (1) universal or (2) particular substance or matter. The former neither increases nor diminishes, while the matter of particular things both increases and diminishes” (Diogenes Laertius 1925b. Book 7, Ch.1, section 150. Copied from Perseus. In the French as “La substance, c’est-à-dire la matière, se dit dans deux sens : celle de toutes choses et celle des êtres particuliers ; la première ne s’accroît ni ne diminue ; l’autre s’accroît et diminue.”) The part-whole distinction is also made by the first two examples [either just earth and sea, or perhaps alternatively, earth and sea on the one hand and void on the other. I am not exactly sure yet how in either case there is a part-whole relation. Earth and sea would not seem to be parts related to the void as a whole. I wonder if the idea is simply that earth and sea are wholes that are divisible.] There is a third example for this part-whole structure, namely time: “Just as the void in its totality is infinite in every respect, so time in its totality is infinite on either side. For both the past and the future are infinite” (Long & Sedley 1987: I, 304; II, 301-302. In the French: “De même que le vide total est infini de toutes parts, de même le temps total est infini à ses deux extrémités ; en effet, le passé et le futur sont infinis.”) The phrase “in its totality” (“total”), which is used to designate the whole of void and time, is also what in another division incorporates the world and the void. So in Stoic cosmology, the totality is the most general term, including both being and the incorporeal condition of being. In other words, “totality” is a term that applies to both the corporeal and the incorporeal, to the “whole” (“tout”) as well as to the “parts” (“parties”) that are virtually contained in it.

« Le temps se prend dans deux acceptions, ainsi que la terre, la mer et le vide : (on peut en considérer) le tout ou les parties. » La distinction : tout-parties nous est rapportée, dans un autre contexte, par Diogène Laërce : « La substance, c’est-à-dire la matière, se dit dans deux sens : celle de toutes choses et celle des êtres particuliers ; la première ne s’accroît ni ne diminue ; l’autre s’accroît et diminue1. » Cette distinction : tout-parties, suggérée par les deux premiers exemples2, va être précisée à l’aide du troisième : « De même que le vide total est infini de toutes parts, de même le temps total est infini à ses deux extrémités ; en effet, le passé et le futur sont infinis. » – L’expression de « total », par où est désigné le tout du vide et du temps, est celle-là même qui, dans une autre division, englobait le monde et le vide3, c’est-à-dire, en cosmologie, le terme le plus général, qui comprend l’être et la condition incorporelle de l’être ; un terme, autrement dit, qui peut s’appliquer aussi bien à l’incorporel qu’à ce qui est corporel, au « tout », aussi bien qu’aux « parties » qui y sont virtuellement contenues.

(36)

1. Diog. Laërt., VII, 150 (S.V.F., II, 316) ; cf.Arius Did., 20 (Dox. Gr., 1457 sq.).

2. C’est tout ce que prétendent ces deux exemples, mais 1’analogie ne va pas plus loin ; la terre et la mer sont des ὅλα, c’est-à-dire des touts limités, comme le monde lui-même, alors que le vide est un πᾶν, c’est-à-dire un tout infini.

3. Cf. p. 27 sq.

(36)

1.1.3.13.3

[Time’s Unlimited Ends and Limited Present]

(pp.36-37: “ Quelles sont les parties du vide …”)

[In sum: For the Stoics, time can be understood as a line extending backwards to the past and forwards to the future. There is no limit to how far back and forward it goes. So you might say that time is “bound” by unlimited limits on either side. But internally it has a finite present that acts as a limited limit cutting of the past at its least past and the future at its least future.]

[Note, in the prior section 1.1.3.13.2, we used the Long & Sedley translation: “Just as the void in its totality is infinite in every respect, so time in its totality is infinite on either side”. This does not directly suggest that the void has parts, but perhaps the French version does: “De même que le vide total est infini de toutes parts, de même le temps total est infini à ses deux extrémités”. Yet, I am not sure if the idea here is about compositional parts or rather about extremities or sides. So where Long & Sedley say “in every respect” for what is “de toutes parts”, maybe we are to understand also “on all sides”. Here is the Greek for this passage: “ Ὥσπερ δὲ τὸ κενόν πᾶν ἄπειρον εἶναι πάντῃ καί τὸν χρόνον πάντα ἄπειρον εἶναι ἔφ᾽ ἑκάτερα;”. I am not certain, but I suspect that the term in question is πάντῃ/πάντα, which apparently can mean either “every way” and “on every side”. I do not know ancient Greek, but I wonder if  the sense of “both sides” lies in “ἔφ᾽ ἑκάτερα”. Yet I would note that the clause also has πάντα, so I am not sure if that should be understood as “on every side” if also we are later specifying that there are just two sides.] The Stobaeus/Chrysippus text does not explain what the parts/sides of the void are. But it is clear that the parts [/sides] are not parts [/sides] of void but are places. It would seem then, that it is no longer a matter of the parts [/sides] of time. Since the void is said to be infinite “in every respect” [/“on every side”] and time is infinite “on either side,” we could gather that the infinity in both cases is equally complete. (And we note that here time is represented by a line.) [Judging from what follows, I am supposing that the idea here is that we might at this point think that every part of time is infinite, just like every part of the void is.] But in fact, this is not the case, as is shown in the following quotation by Diogenes: “And time past and time future are infinite, but time present is finite” (“Le passé et le futur sont infinis, mais le présent est limité”). [What we have here is the following structure. Time understood as a line has two extremities, past and future, which are like its unlimited limits on the far ends. But there is a third part, the present, which is a limited limit on the inner side between past and future.]

Quelles sont les parties du vide, notre texte ne le dit pas ; mais il est clair que ces parties ne sont plus « du vide » à proprement parler, mais déjà des « lieux ». A première vue, il ne semble pas non plus être question des parties du temps. Si le vide est dit infini « de toutes parts » ; le temps, « à ses deux extrémités », on pourrait croire que l’infinitude, dans les deux cas, est également complète (le temps étant figuré par une droite). Mais il n’en est rien, ainsi qu’il ressort de l’explication suivante : « En effet, le passé et le futur sont infinis. » Ces « deux extrémités » ne sont donc pas les seules limites illimitées de la ligne temporelle ; comme le vide total peut avoir des parties : les lieux ; de même, semble-t-il, le temps, infini en passé et en avenir, pourrait, en partie, se limiter. Et c’est ce que nous dit Diogène : « Le | passé et le futur sont infinis, mais le présent est limité »1.

(36-37)

1. Diog. Laërt., VII, 141.

(37)

From:

Goldschmidt, Victor. (1953). Le système stoïcien et l'idée de temps. Paris: Vrin.

Also cited:

Diogenes Laertius. 1925b. Lives of Eminent Philosophers, vol.2. Translated by Robert D. Hicks. London: William Heinemann / New York: G.P. Putnam’s Sons.

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0258%3Abook%3D7%3Achapter%3D1

Inwood, Brad, and Gerson, Loyd P. 2008. The Stoics Reader. Selected Writings and Testimonia, edited and translated by Brad Inwood and Loyd P. Gerson. Indianapolis and Cambridge: Hackett.

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

Long, Anthony A. and David N. Sedley. 1987. The Hellenistic Philosophers, vol.2: Greek and Latin Texts with Notes and Bibliography. Cambridge: Cambridge University Press.

Stobaeus. 1884a. Ioannis Stobaei: Anthologium, vol.1. [Ioannis Stobaei, Anthologium Volumen Primum, Anthologii Librum Primum Volumen I: Libri duo Priores qui inscribi solent Eclogae Physicae et Ethicae] Edited by Kurt Wachsmuth. Berlin: Weidmann.

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