Goldschmidt (1.1.3.15) Le système stoïcien et l'idée de temps, “Aiôn et présent”, summary

 

by Corry Shores

 

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[The following is summary. Bracketed commentary is my own, as is any boldface. Proofreading is incomplete, which means typos are present, especially in the 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

 

1.1.3.15

Aiôn et présent

 

 

 

Brief summary:

For the Stoics, there are two modes of temporality. {1} There is the time of the actual present, and this present exists and has some limited extensive duration. And {2} there is the unlimited time reaching infinitely into the past and future, with the division between the two being the present as an infinitely divided, mathematical instant. While Chrysippus did not make a terminological distinction despite speaking of time in each of these senses, Marcus Aurelius does in fact distinguish them terminologically by calling the eternal, infinite sort of time “αἰών”. He uses this notion to make the point that in the context of eternal time, our life is but an insignificant finite interval, and so we should not be troubled too much in life, given its ultimate insignificance. Now, aiôn-time (including both the limitless past and future and the infinitely divided mathematical instant that is the “present” and the limit between the two) is incorporeal and thus irreal, while the lived, specious present that we know by our senses is the real corporeal present.

 

 

 

Contents

 

1.1.3.15

[Aiôn and the Present]

 

1.1.3.15.1

[The Irreality of Past and Future and the Reality of the Present]

 

1.1.3.15.2

[Eternal/Infinite Past and Future “Aiôn” time and the Limited Interval of Our Lifetime]

 

1.1.3.15.3

[The Incorporeality of the Aiônic Past and Future and Its Mathematical Present]

 

 

 

Summary

 

1.1.3.15

Aiôn et présent

 

1.1.3.15.1

[The Irreality of Past and Future and the Reality of the Present]

 

(p.39: “ On ne saurait donc dire, à la suite de Proclus …”)

 

[In sum: There are two senses of time. There is time as infinitely extending into the past and future. It is irreal, in that rather than existing like corporeals do, it subsists as an incorporeal. And there is another time, that of the actual present. This time is real and exists. The present is a limit to the infinite time, just as place is a limit to the unlimited void.]

 

We thus cannot draw Proclus’ conclusion that all this argumentation tends to deny the reality of time, namely, that since time is never actual, it therefore does not exist. This is only true however for the past and the future [which are said to “subsist” rather than exist, and thus have a sort of irreality to them, even though they have a “somethinghood”]. But the present does exist and is actual. This makes their theory of time analogous to their theory of space, as is seen in the following diagram:

 

void (infinite on all sides)

-----------------------------
place (limited)

 

=

time (infinite at each of its extremities: past and future)

-----------------------------

time (limited: present)

 

 

[I have not read the part on place and void yet, so I cannot decipher the diagram right now. But in a previous section on this topic, Goldschmidt examines the following Stobaeus quotation:

Stobaeus I:161,8-26. SVF 2.503, part:

The void is said to be infinite. For what is outside the world is like this, but place is finite since no body is infinite. Just as anything corporeal is finite, so the incorporeal is infinite, for time and void are infinite. For as nothing is no limit, so there is no limit of nothing, as is the case with the void. In respect of its own subsistence it is infinite; it is made finite by being filled, but once that which fills it has been removed, a limit to it cannot be thought of.

(Long and Sedley I, p.294)

In the French:

« On dit que le vide est in fini ; car tel est le vide en dehors du monde ; le lieu, en revanche, est limité, étant donné qu’aucun corps n’est infini. Or, de même que le corporel est limité, de même l’incorporel est infini ; en effet, le temps est infini, ainsi que le vide. Car, de même que le rien n’est aucune limite, de même il n’y a aucune limite au rien ; or tel est le vide. Selon sa propre nature, en effet, il est infini; il se limite cependant, quand il est rempli ; mais quand est supprimé ce qui le remplit, impossible de lui concevoir une limite »³.

3. Arius Did., 25 (Dox. gr., 160, 24sqq. = S.V.F., II, 503)

(Goldschmidt p.26).

Perhaps Goldschmidt is describing the following structure with his diagram, but this is a preliminary guess. The void has no limit. It is incorporeal, and it has no element of place in it. But when it is filled by something, that something is corporeal, is limited, and has place. We have a similar structure with time. There is time understood as unlimited at both its extremities of the past and the future. It is incorporeal and has no real moments in it, thus it has no real temporal “places” filling it. But a real present can come to be said to have a location associable with the unlimited time. Such a present is limited, corporeal, and has temporal “place”.] [Let me note something about place in infinite time. We can say that if it is linear, it has determinate places along the line, as some come before others. Thus we might want to say that infinite time has temporal “place” to it. And so we might designate one part as coming before another. But at best these temporal places could only be relative to one another and not have an assigned place on the continuum. This is because there is no first or last moment that would orient all the rest. Perhaps we might designate some point as the present and use that as the point of origin to give determinate place to all the rest. I am not certain. It could also be that infinite time has no such present, because the present is real and time is irreal. In other words, this kind of time seems to have order without place. Imagine designating a point in this line of time, and speaking of that point’s “place”. But under consideration that there is infinitely much coming before it, we might imagine that place shifting forward in relation to it, as if getting pushed further into the future in the context of a past that fills up further into the past. In the context of the infinite future, we might think of its place shifting backward into the past under that relation. It is somewhat dizzying to think of a moment’s place in an infinite stretch. Let me put it another way. Suppose we designate a moment in infinite time. We might think that any such moment stands in the exact middle of the line, because going forward and back from it are infinities. But this holds for any point on the line. Thus every point is right in the middle of time and so none would have any ultimate place. A moment can have place in relation to another moment (being so much before or after it), but a moment cannot have place in relation to time itself. And even the relative place is not secure, because neither of the two related points in time have an ultimate place on the line, so their interval has no place in the same way either point has no place.]

On ne saurait donc dire, à la suite de Proclus, que « toute cette argumentation tend ... à nier la réalité du temps : il n’est jamais actuel et par conséquent n’existe pas »³. Cela n’est vrai que du passé et de l’avenir. Mais le présent, lui, existe et est actuel, en sorte que la théorie du temps est exactement analogue à celle de l’espace⁴ :

 

le vide (infini de toutes parts)

--------------

le lieu (limité)

 

le temps (infini à chacune de ses extrémités : passé et futur)

----------------

le temps (limité : présent)

 

(39)

3. Incorporels, p.59.

4. E. Bréhier a parfaitement indiqué cette analogie (« Ce temps est au milieu du temps infini comme le lieu du monde dans le vide », Incorp. p. 55), malheureusement, sans en faire bénéficier son interprétation d’ensemble de la théorie du temps.

(39)

 

 

1.1.3.15.2

[Eternal/Infinite Past and Future “Aiôn” time and the Limited Interval of Our Lifetime]

 

(p.39: “ Sans doute, la théorie eût-elle été plus scolairement intelligible …”)

 

[In sum: The Stoic notion of time as extending infinitely to the past and future is seen implicitly in Chrysippus’ definition of time in its two senses, but it is given terminological distinction by Marcus Aurelius, who calls it αἰών. He speaks of how our life is a limited interval (similar to a broadened present) set within an infinite gulf of the limitless past and future of the αἰών. In comparison to eternity, our life is of infinitesimal significance, and so we should not over-dramatize the difficulties in our life.]

 

This Stoic theory of time [with its two senses, namely, {1} an irreal, unlimited time extending infinity into the past and future and {2} a real limited time of the actual present] would have been as intelligible as their theory of void and place had Chrysippus used two terms for time to designate the two types of temporality. But perhaps Chrysippus thought this distinction was already obvious, given that it is more or less a distinction between the present on the one hand and the past and future on the other hand. Also, he does suggest this distinction when saying that “time is spoken of in two senses” (Inwood and Gerson 2008: 88. In the French: “Le temps se prend dans deux acceptions”). But even if we insist that Chrysippus was imprecise, we nonetheless find the conceptual distinction given a proper terminological distinction in Marcus Aurelius. He speaks of an infinite time, corresponding to the void, and he calls it αἰών, normally translated by “eternity” (“éternité”). To see the origin and development of the term αἰών, we can look to Onians’ The Origins of European Thought: About the Body, the Mind, the Soul, the World, Time and Fate. (See this entry: Selections on Aion and Chronos [Αἰών; Χρόνος] in Onians’ Origins of European Thought). There we learn that “αἰών” referred to the “vital liquid” and came to mean “life-time”, “period of time”, and then “eternity” [see page 251: “This conception of Χρόνος, the usual meaning of which is ‘Time’, may be related to that of αἰών, which was not only the procreative life-fluid with which the ψυχή was identified, the spinal marrow believed to take serpent form, but also came to mean ‘lifetime’, ‘period of time’ and so ‘eternity’.”] But, as Goldschmidt notes, this means that [although it means eternity] it also means the limitation that the Stoics reserved for present time. [I am not certain, but perhaps Goldschmidt is saying that αἰών originally referred to the limited, durational, specious present and then later evolved to mean eternity.] Goldschmidt cites the following places where Marcus Aurelius uses αἰών.

 

Meditations IV, 3:

 

ἀλλὰ τὸ δοξάριόν σε περισπάσει; ἀπιδὼν εἰς τὸ τάχος τῆς πάντων λήθης καὶ τὸ χάος τοῦ ἐφ᾽ ἑκάτερα ἀπείρου αἰῶνος καὶ τὸ κενὸν τῆς ἀπηχήσεως καὶ τὸ εὐμετάβολον καὶ ἄκριτον τῶν εὐφημεῖν δοκούντων καὶ τὸ στενὸν τοῦ τόπου, ἐν ᾧ περιγράφεται: ὅλη τε γὰρ ἡ γῆ στιγμὴ καὶ ταύτης πόστον γωνίδιον ἡ κατοίκησις αὕτη; καὶ ἐνταῦθα πόσοι καὶ οἷοί τινες οἱ ἐπαινεσόμενοι;

(Marcus Aurelius 1916: 68-70. Text copied from Perseus [so capitals excluded for example])

 

Est-ce la gloriole qui te divertira? Considère la rapidité de l’oubli de toutes choses, l’abîme de l’éternité, sans borne derrière comme devant nous, la vanité d’un nom qui retentit, la mobilité et l’irréflexion des gens qui paraissent vous louer, et l’étroitesse du lieu qui limite la renommée. Qu’est-ce que toute la terre? Un point. Et de ce point quelle minuscule partie nous habitons ! Et là même combien d’hommes, et quels hommes! te loueront?

(Marcus Aurelius 1924: 31-32)

 

Or shall the little affair of character and glory disturb you, when you reflect how all things shall be involved in oblivion; and the vast immensity of eternal duration on both sides; how empty the noisy echo of applauses; how fickle and injudicious the applauders; how narrow the bounds within which our praise is confined: the earth itself but as a point in the universe: and how small a corner of it the part inhabited: and, even there, how few are they, and of how little worth, who <92> are to praise us!

(Marcus Aurelius 2008: 48)

 

But will that paltry thing, Fame, pluck thee aside? Look at the swift approach of complete forgetfulness, | and the void of infinite time on this side of us and on that, and the empty echo of acclamation, and the fickleness and uncritical judgment of those who claim to speak well of us, and the narrowness of the arena to which all this is confined. For the whole earth is but a point, and how tiny a corner of it is this the place of our sojourning! and how many therein and of what sort are the men who shall praise thee!

(Marcus Aurelius 1916: 69-71)

 

But perhaps the desire of the thing called fame will torment thee. – See how soon everything is forgotten, and look at the chaos of infinite time on each side of [the present], and the emptiness of applause, and the changeableness and want of judgement in those who pretend to give praise, and the narrowness of the space within which it is circumscribed [and be quiet at last]. For the whole earth is a point, and how small a nook in it is this thy dwelling, and how few are there in it, and what kind of people are they who will praise thee.

(Marcus Aurelius 1882: 123)

 

Here we see that αἰών [αἰῶνος] is used to mean the infinite time extending both into the past and into the future. Goldschmidt then cross references the Stobaeus/Arius text we have been often referring to [see especially section 1.1.3.10].

 

See lines 20-21 below, especially “τὸν χρόνον πάντα ἄπειρον εἶναι ἔφ᾽ ἑκάτερα”:

Stobaeus Eclogae I p.106, 5 W. (Arii Did. fr. 26 Diels) in SVF 2.509:

(SVF 1964b: 164)

 

And lines 11-13 below:

Stobaeus, Eclogae I, p.106:

(Stobaeus 1884a: 106)

 

Just as the void in its totality is infinite in every respect, so time in its totality is infinite on either side.

(Long and Sedley 1987: I, 304; II, 301-302)

 

And just as void as a whole is infinite in every direction, so too time as a whole is infinite in both directions.

(Inwood and Gerson 2008: 88)

 

While the term αἰών is not used here, we see the same structure of time being infinite both into the past and future. Goldschmidt then cites Meditations 12, 7.

 

Meditations XII, 7:

 

Ὁποῖον δεῖ καταληφθῆναι ὑπὸ τοῦ θανάτου καὶ σώματι καὶ ψυχῇ: τὴν βραχύτητα τοῦ βίου: τὴν ἀχάνειαν τοῦ ὀπίσω καὶ πρόσω αἰῶνος: τὴν ἀσθένειαν πάσης ὕλης.

(Marcus Aurelius 1916: 326. Text copied from Perseus)

 

Dans quel état, quand la mort nous surprend, doivent être notre corps et notre âme ? — La brièveté de la vie, l’immensité des temps passés et futurs, la faiblesse de la matière.

(Marcus Aurelius 1924: 168)

 

Reflect on the condition of body and soul befitting a man when overtaken by death, on the shortness of life, the yawning gulf of the past and of the time to come, on the impotence of all matter.

(Marcus Aurelius 1916: 327)

 

Consider, in what state shall death find you, both as to body and soul? <284> Observe the shortness of life; the vast immensity of the preceding, and ensuing duration; and the infirmity of all these materials.

(Marcus Aurelius 2008: 146)

 

Consider in what condition both in body and soul a man should be when he is overtaken by death; and consider the shortness of life, the boundless abyss of time past and future, the feebleness of all matter.

(Marcus Aurelius 1882: 297)

 

As we see, here αἰών [αἰῶνος] refers to a time that spans infinitely into the past and future. Goldschmidt also notes that in this quote, that aiôn-time and inert matter are understood in the sense of the “whole”. [I am not exactly what he means here. Maybe he is saying that the aiôn-time is incorporeal, but has a whole, just as inert matter and its present time, is a whole; or otherwise that the aiôn-time makes a whole in its combination with inert matter (and its present temporality).] We look next at Meditations 12, 32:

 

Meditations XII, 32:

 

Πόστον μέρος τοῦ ἀπείρου καὶ ἀχανοῦς αἰῶνος ἀπομεμέρισται ἑκάστῳ: τάχιστα γὰρ ἐναφανίζεται τῷ ἀιδίῳ: πόστον δὲ τῆς ὅλης οὐσίας: πόστον δὲ τῆς ὅλης ψυχῆς: ἐν πόστῳ δὲ βωλαρίῳ τῆς ὅλης γῆς ἕρπεις. πάντα ταῦτα ἐνθυμούμενος μηδὲν μέγα φαντάζου ἢ τό, ὡς μὲν ἡ σὴ φύσις ἄγει ποιεῖν, πάσχειν δὲ ὡς ἡ κοινὴ φύσις φέρει.

(Marcus Aurelius 1916: 340. Text copied from Perseus)

 

Bien petite est la part de l’immense et profonde éternité qui est dévolue à chacun, et elle s’évanouit si vite dans l’infini des temps 1 Bien petite est, pour chacun, sa part de l’universelle substance comme de l’âme universelle. Et qu’est-ce, en la vaste terre, que cette motte où tu rampes? Réfléchis sur toutes ces choses, et tu concevras que la vraie grandeur consiste | à régler tes actions sur ta nature propre, et à souffrir comme le veut la commune nature.

(Marcus Aurelius 1924: 175-176)

 

How small a part is appointed to each one of the infinite immense duration? For, presently, it must vanish into eternity: How small a part of the universal matter? And, how small, of the universal spirit? On how narrow a clod of this earth do you creep? When all these things are considered, nothing will appear great, except acting as your nature leads; and bearing contentedly whatever the common nature brings along with it.

(Marcus Aurelius 2008: 151)

 

How tiny a fragment of the boundless abyss of Time has been appointed to each man! For in a moment it is lost in eternity. And how tiny a part of the Universal Substance! How tiny of the Universal Soul! And on how tiny a clod of the whole Earth dost thou crawl! Keeping all these things in mind, think nothing of moment save to do what thy nature leads thee to do, and to bear what the Universal Nature brings thee.

(Marcus Aurelius 1916: 341)

 

How small a part of the boundless and unfathomable time is assigned to every man? for it is very soon swallowed up in the eternal. And how small a part of the whole substance? and how small a part of the universal soul? and on what a small clod of the whole earth thou creepest? Reflecting on all this consider nothing to be great, except to act as thy nature leads thee, and to endure that which the common nature brings.

(Marcus Aurelius 1882: 302)

 

Here we see the present-eternal in its part-whole relation, for we are appointed a small part of matter in the infinitely immense duration of αἰών [αἰῶνος]. The next reference is Meditations 5, 24:

 

Meditations V, 24:

 

Μέμνησο τῆς συμπάσης οὐσίας, ἧς ὀλίγιστον μετέχεις, καὶ τοῦ σύμπαντος αἰῶνος, οὗ βραχὺ καὶ ἀκαριαῖόν σοι διάστημα ἀφώρισται, καὶ τῆς εἱμαρμένης, ἧς πόστον εἶ μέρος;

(Marcus Aurelius 1916: 120. Text copied from Perseus)

 

Souviens-toi de l’universelle substance où tu participes pour si peu, et de la durée éternelle dont une tranche si brève, si mince, t’a été réservée, et de la destinée dont tu es une partie, mais combien petite !

(Marcus Aurelius 1924: 59)

 

Remember how small a part you are of the universal nature; how small a moment of the whole duration is appointed for you; and how small a part you are of the object of universal fate, or providence.

(Marcus Aurelius 2008: 66)

 

Keep in memory the universal Substance, of which thou art a tiny part; and universal Time, of which a brief, nay an almost momentary span has been allotted thee; and Destiny, in which how fractional thy share?

(Marcus Aurelius 1916: 121)

 

Think of the universal substance, of which thou hast a very small portion; and of universal time, of which a short and indivisible interval has been assigned to thee; and of that which is fixed by destiny, and how small a part of it thou art.

(Marcus Aurelius 1882: 156)

 

In these we note the idea of the finite interval (διάστημα / “intervalle”) of our life within the infinite span of aion-time. On this topic of the finite interval (διάστημα) of our life falling between the infinite gulf of past and future, he cross-references Meditations 4, 50:

 

Meditations IV, 50:

 

Ἰδιωτικὸν μέν, ὅμως δὲ ἀνυστικὸν βοήθημα πρὸς θανάτου καταφρόνησιν ἡ ἀναπόλησις τῶν γλίσχρως ἐνδιατριψάντων τῷ ζῆν. τί οὖν αὐτοῖς πλέον ἢ τοῖς ἀώροις; πάντως πού ποτε κεῖνται, Καδικιανός, Φάβιος, Ἰουλιανός, Λέπιδος ἢ εἴ τις τοιοῦτος, οἳ πολλοὺς ἐξήνεγκαν, εἶτα ἐξηνέχθησαν: ὅλον, μικρόν ἐστι τὸ διάστημα καὶ τοῦτο δἰ ὅσων καὶ μεθ̓ οἵων ἐξαντλούμενον καὶ ἐν οἵῳ σωματίῳ; μὴ οὖν ὡς πρᾶγμα. βλέπε γὰρ ὀπίσω τὸ ἀχανὲς τοῦ αἰῶνος καὶ τὸ πρόσω ἄλλο ἄπειρον. ἐν δὴ τούτῳ τί διαφέρει ὁ τριήμερος τοῦ τριγερηνίου;

(Marcus Aurelius 1916: 96. Text copied from Perseus)

 

C’est un secours ridicule, mais pourtant utile à qui veut mépriser la mort, que de faire la revue des hommes dont l’attachement à la vie fut tenace. Eh bien ! qu’ont-ils fait de plus que ceux qui ont expiré avant l’heure ? Où gisent enfin Kadikianos, Fabius, Julianus, Lépidus, et tous leurs pareils, qui portèrent tant de gens en terre et y furent eux-mêmes portés ensuite? En somme, bien petit est l’intervalle, et parmi combien de souffrances, avec quels hommes, dans quel faible corps on le passe ! Ce n’est donc pas une affaire. Contemple en effet derrière toi l’immensité des temps, et cet autre infini devant toi. Voyons ! Dans ce gouffre, quelle différence y a-t-il entre une vie de trois jours et une vie triple de celle du Gérénien ?

(Marcus Aurelius 1924: 46)

 

‘Tis a vulgar meditation, and yet a very effectual one, for enabling us to despise death; to consider the fate of those who have been most earnestly tenacious of life, and enjoyed it longest. What have they obtained more than those who died early? They are all lying dead some where or other. Caedicianus, Fabius, Julian, Lepidus, and such like, who carried out the corpses of multitudes, have been carried out <111> themselves. In sum, how small is the difference of time! and that spent amidst how many troubles! among what worthless men! and in what a mean carcase! Don’t think it of consequence. Look backward on the immense antecedent eternity, and forward into another immensity. How small is the difference between a life of three days, and of three ages like Nestor’s?

(Marcus Aurelius 2008: 57)

 

An unphilosophical, but none the less an effective, help to the contemning of death is to tell over the names of those who have clung long and tenaciously to life. How are they better off than those who were cut off before their time? After all, they lie buried somewhere at last, Cadicianus, Fabius, Julianus, Lepidus, and any others like them, who after carrying many to their graves were at last carried to their own Small, in any point of view, is the difference in length, and that too lived out to the dregs amid what great cares and with what sort of companions and in what kind of a body! Count it then of no consequence. For look at the yawning gulf of Time behind thee, and before thee at another Infinity to come. In this Eternity the life of a baby of three days and the life of a Nestor of three centuries are as one.

(Marcus Aurelius 1916: 97)

 

It is a vulgar, but still a useful help towards contempt of death, to pass in review those who have tenaciously stuck to life. What more then have they gained than those who have died early? Certainly they lie in their tombs somewhere at last, Cadicianus, Fabius, Julianus, Lepidus, or any one else like them, who have carried out many to be buried and then were carried out themselves. Altogether the interval is small [between birth and death]; and consider with how much trouble, and in company with what sort of people and in what a feeble body this interval is laboriously passed. Do not then consider life a thing of any value. For look to the immensity of time behind thee, and to the time which is before thee, another boundless space. In this infinity then what is the difference between him who lives three days and him who lives three generations?

(Marcus Aurelius 1882: 140)

 

[Here now is the Goldschmidt quotation:]

 

Sans doute, la théorie eût-elle été plus scolairement intelligible si, comme dans le cas du vide et du lieu, Chrysippe avait employé, pour distinguer ces deux temps, deux termes différents. Mais la distinction entre présent, d’une part, et passé et futur, d’autre part, a dû lui paraître suffisante, sans compter la précision : « Le temps se prend dans deux acceptions. » – En tout cas, s’il y a, de la part de Chrysippe, une négligence sur la terminologie, on peut dire qu’elle est réparée chez Marc-Aurèle, chez qui le temps infini, correspondant au vide, prend un nom précis, celui qu’on a coutume de traduire⁵ par : éternité (αἰών)⁶.

(39)

5. Sur l’origine et le développement de ce mot, voir maintenant les analyses de R.B. Onians, The origins of European thought about the body, the mind, the soul, the world, time and fate, Cambridge, 1951. – Il est notable que ce mot désignant primitivement le « liquide vital » en vient à signifier « life-time », période, puis : éternité (Onians, p. 251), c’est-à-dire qu’il implique cette limitation que les Stoïciens réservent au temps présent.

6. Marc-Aurèle, IV, 3, 7: τὸ χάος τοῦ ἐφ᾽ ἑκάτερα ἀπείρου αἰῶνος (cf. notre texte | d’Arius: Τὸν χρόνον πάντα ἄπειρον εἶναι ἔφ᾽ ἑκάτερα). Ces extrémités sont le passé et le futur: XII, 7: Τὴν ἀχάνειαν τοῦ ὀπίσω καὶ πρόσω αἰῶνος; la suite immédiate de ce texte τὴν ἀσθένειαν πάσης ὕλης, mentionne la matière, c’est-à-dire que le temps-aiôn et la matière inerte sont pris ici dans le sens du « tout » (p. 36. n. 1). La distinction : tout-partie est appliquée aux deux termes dans XII, 32 : Πόστον μέρος τοῦ ἀπείρου καὶ ἀχανοῦς αἰῶνος ἀπομεμέρισται ἑκάστῳ … πόστον δὲ τῆς ὅλης οὐσίας et, avec emploi technique du mot « intervalle » dans V, 24 : Μέμνησο τῆς συμπάσης οὐσίας, ἧς ὀλίγιστον μετέχεις, καὶ τοῦ σύμπαντος αἰῶνος, οὗ βραχὺ καὶ ἀκαριαῖόν σοι διάστημα ἀφώρισται, καὶ τῆς εἱμαρμένης, ἧς πόστον εἶ μέρος ; cf. IV, 50, 3 (διάστημα), 5 (βλέπε γὰρ ὀπίσω τὸ ἀχανὲς τοῦ αἰῶνος καὶ τὸ πρόσω ἄλλο ἄπειρον. – Voir plus loin, §§ 99-101.

(39-40)

 

 

1.1.3.15.3

[The Incorporeality of the Aiônic Past and Future and Its Mathematical Present]

 

(p.40: “Ainsi n’est incorporel que ce temps-aiôn …”)

 

[In sum: The only incorporeal temporality is the infinite past and present of aiôn-time along with the mathematical instant obtained by infinitely dividing the past and future.]

 

So the only incorporeal temporalities are {1} the aiôn-time as the infinite time of past and future along with {2} the mathematical instant obtained by infinitely dividing the aiônic past and future. But we now wonder, if the present that is extended and known by sensation exists, what is its mode of existence and how is it limited in extent?

Ainsi n’est incorporel que ce temps-aiôn, temps infini en passé en avenir, et cette instant mathématique qui, lui-même, se divise à l’infini en passé et futur¹. Mais si le présent, étendu et saisi par la sensation, existe, en quoi consistera son mode d’existence, et comment en est limitée l’étendue ?

(40)

 

 

 

 

 

From:

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

 

 

Also cited:

 

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.

 

Marcus Aurelius. 1882. Meditations of Marcus Aurelius Antoninus, Emperor of the Romans. English trans. by George Long. Chicago: Shaver.

PDF available at:

https://archive.org/details/meditationsofmar01marc

Online Text available at:

http://classics.mit.edu/Antoninus/meditations.4.four.html

 

Marcus Aurelius. 1916. The Communings with Himself of Marcus Aurelius Antoninus, Emperor of Rome, Together with His Speeches and Sayings. English translation by C. R. Haines. London: Heinemann / New York: Putnam.

PDF available at:

https://archive.org/details/thecommuningswit00marcuoft

Online text at:

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3atext%3a2008.01.0641

 

Marcus Aurelius. 1924. Les pensées de Marc-Aurèle. French translation by A.-P. Lemercier. Paris: Alcan.

PDF available at:

https://archive.org/details/lespensesdemar00marc

 

Marcus Aurelius. 2008. The Meditations of the Emperor Marcus Aurelius Antoninus. English translation by Francis Hutcheson and James Moor. Edited by James Moore and Michael Silverthorne. Indianapolis: Liberty Fund.

PDF available at:

https://archive.org/details/MeditationsOfTheEmperorMarcusAureliusAntoninus

 

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.

PDF available at:

https://archive.org/details/adw8682.0001.001.umich.edu

 

SVF. 1964b. Stoicorum veterum fragmenta, vol.2: Chrysippi Fragmenta Logica et Physica. Ed.  Hans von Arnim. Stuttgart: Teubner.

PDF available at:

https://archive.org/details/stoicorumveterum02arniuoft

 

 

 

 

 

 

 

.

Selections on Aion and Chronos [αἰών; χρόνος] in Onians’ Origins of European Thought

 

by Corry Shores

 

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The Origins of European Thought: About the Body, the Mind, the Soul, the World, Time and Fate

 

Selections on Aion and Chronos

[αἰών; χρόνος]

 

 

Brief summary:

In ancient Greek mythology, philosophy, and literature, there are (at least) two important names for time. First note some cosmological ideas. Around the world flows a river, Ὠκεανός, which is the source of all generation in the world. And, a body’s procreative element is the ψυχή, which is both a liquid and also appears under the form of a serpent. Likewise, Ὠκεανός is thought to be the primal cosmic procreative power or ψυχή, being as well both liquid and serpent. The Orphic version of this serpent is called Χρόνος, which is also the word for the usual meaning of “time”. Euripides also names the circling stream around the universe as Χρόνος. And for the Orphics, Χρόνος is mated to Ἀνάγκῃ, which means “necessity”. For the ancient Greeks, time and fate are also understood in terms of movements circling around the earth. The other word for time is αἰών, which like Χρόνος, is understood in terms of the waters and a serpent circling around the world. In Homer, αἰών means a couple things. It can mean a vital fluid from our marrow or cerebral system that comes out as tears and sweat. As such, it can be understood as the fluid that we are drained of as we age and that we lose when we die. So αἰών also means “lifetime”. As a fluid that gives life, it is thus related to the Ὠκεανός, which is also the life-fluid of the world, and, as a circling movement around the world, is time and fate. For Pindar αἰών is both the life-fluid and a compelling destiny or δαίμωνthat controls life. Αἰών, then, also means “eternity.” And Heraclitus uses the word to mean “the power controlling the changes of the world” (Onians’ words, p.251). In Heraclitus’ conception of αἰών as this cosmic principle, it is like a child playing a game.

 

 

 

Selections

[The following are quotations]

 

On the assumption that its nearest cognates are ἀεί and aevum it is generally agreed that the fundamental meaning for Homer and later is ‘period of existence’ and so, from the meaning ‘lifetime’, that of ‘life’ is derived. But the passages, from which this is inferred for Homer, can be put thus: “If I go home, my αἰών will exist for a long time.’

(200, citing Homer Il. IX, 415f)

 

And elsewhere in Homer αἰών clearly is not a period of time but a ‘thing’ of some kind like ψυχή persisting through time, life itself or a vital substance necessary to living. At death ‘ψυχή and αἰών leave’³ a man, or we are told merely that ‘αἰών leaves’⁴ him or that he ‘is deprived’ of it⁵ or of it and ψυχή.⁶

(200, citing, 3: Il. XVI, 453. 4: Il. V, 385; Od. VII, 224. 5: Il. XXII, 25. 6: Od. IX, 523f).

 

Later also, as we know, tears and sweat were thought to be the same liquid.² It is this liquid which Homer calls αἰών.

(p202, citing the Problemata, 884 b 22ff).

 

‘nor were his eyes ever dry of tears, but there flowed down the sweet αἰών as he lamented for his return’ …. This has hitherto been ignored and paraphrased away: ‘his life ebbed’, etc., but its natural interpretation in fact is that the liquid flowing down was αἰών and that it is the same liquid which is said to be ‘wasted’ when husband or wife weeps.

(201, citing maybe Od. V, 151 ff.)

 

This liquid was, we saw, thought to be concentrated particularly in the head, to be dependent upon the cerebro-spinal fluid and ‘marrow’.

(205)

 

For Aristotle 'the living creature is by nature moist (“liquid”, ὑγρόν) and warm, and to live is to be such, but old age is cold and dry and so is what has died... it is inevitable that one who grows old should dry up’.² It was thus natural to regard the liquid (αἰών) as the life, the stock of life inevitably diminishing with the passage of time, the measure of lifetime like the diminishing sand in the glass.

(215, citing De Long, et Brev. Vit. 466 a, 19ff. Cf. De Gener. Anim. 784 a, 34, etc.)

 

The thought traced that it is the ‘fluid’ in which life is and by which life is generated not only appears from Homer onwards in the recognition and worship of rivers as the generative powers (see pp. 229 ff.), but it also has its cosmic correlate.

(247)

 

For Homer the ‘generation’ (γένεσις) ‘of all’ (πάντεσσι) is the river ‘Ὠκεανός’¹ (Okeanos) which surrounds the earth and is associated with ‘mother Tethys’.

(247, citing Il. XIV, 246; cf. 201, 302. Cf. patrem rerum, Virgil, Georg. IV, 382; parens rerum, Anth. Lat. (Riese) 718, 14).

 

We shall see that Ὠκεανός was believed to be a bond around | the earth, apparently of serpent form even as Acheloos, the primal river or water, was conceived as a serpent with human head and horns. The procreative element in any body was the ψυχή which appeared in the form of a serpent. Ὠκεανός was, as may now be seen, the primal ψυχή and thus would be conceived as a serpent in relation to procreative liquid. The conception of Ὠκεανός has no basis in observation. It can now be explained as the imagined primal cosmic ψυχή or procreative power, liquid and serpent.

(248-249, citations removed)

 

While identified with or believed to be in the procreative liquid, the ψυχή was πνεῦμα. We can now understand as a survival of the earliest Greek conception the picture attributed by Epiphanius to Epicurus, who said almost the last word of Greek science about the structure of the universe. He is credited with saying that ‘the all was from the beginning like an egg, and the πνεῦμα in serpent wise around the egg was then a tight band as a wreath or belt around the universe’ ...  It is the same conception which appears in two versions of the Orphic cosmogony which we may now correlate: (1) that the world egg was begotten by a wind ...; (2) that it was engendered by a serpent which arose out of water and slime; the upper part of the egg became Ὠκεανός and the lower part Earth, including Τάρταρος in its nether depths .... We can perhaps also better understand at one and the same time why in this Orphic version the serpent was called Χρόνος and why, when asked what Χρόνος was, Pythagoras answered that it was | the ψυχή of the universe.¹ According to Pherekydes it was from the seed of Χρόνος that fire and air and water were produced. This conception of Χρόνος, the usual meaning of which is ‘Time’, may be related to that of αἰών, which was not only the procreative life-fluid with which the ψυχή was identified, the spinal marrow believed to take serpent form, but also came to mean ‘lifetime’, ‘period of time’ and so ‘eternity’. For Pindar αἰών meant not only the life-fluid but also a compelling destiny, a δαίμων controlling life.⁷ It is the name Heraclitus gave to the power controlling the changes of the world.⁸ For the Orphics Χρόνος was mated to Ἀνάγκῃ, ‘Necessity’, which also, according to the Pythagoreans, lies around the universe.⁹ Below¹⁰ it will appear how for the earliest Greeks time and fate were circles. The process of time was the movement of the circle around the earth.

((250-251, many citations removed.

1: See Plut. Quaest. Plat, VIII, 4 (1007 A f.). For Χρόνος as a circling stream around the universe see Eurip. Fr. 594 (Nauck) = Krit. B 18 Diels: ἀκάμας τε χρόνος περί τ' ἀενάῳ / ῥεύματι πλήρης φοιτᾷ τίκτων / αὐτὸς ἑαυτόν.)

7: See pp.405f.

8: See pp.252f.

9: See p.332.

10: Pp. 442ff.

))

 

He [Heraclitus] calls the cosmic | principle αἰών and conceives it as a child playing.

(253)

 

[Note, the following are from other sources, but they expand on this last quote by Onians. They give the Heraclitus text:]

 

XCIV (D. 52, M. 93) Hippolytus, Refutatio IX.9.4

αἰὼν παῖς ἐστι παίζων, πεττεύων· παιδὸς ἡ βασιληίη.

“Lifetime is a child at play, moving pieces in a game. Kingship belongs to the child.”

Notes:

Lifetime: aiōn, vitality, life; lifetime, duration, time; cognate with aiei, forever.
moving pieces: pesseuōn, playing pessoi, a board game perhaps involving dice, like backgammon and modern Greek tavli.

(Kahn 1979: 70-71)

 

Some other translations:

Time is a child playing draughts, the kingly power is a child’s.

From: Samuel Béreau / 

http://philoctetes.free.fr/heraclitefraneng.htm

 

Eternity is a child playing draughts, the kingly power is a child’s.

From: John Burnet

https://en.wikisource.org/wiki/Fragments_of_Heraclitus

 

Other translations listed at

https://en.wikiquote.org/wiki/Heraclitus

 

 

 

 

Kahn, Charles. 1979. The Art and Thought of Heraclitus. An Edition of the Fragments with Translation and Commentary. Cambridge: Cambridge University.

 

 

 

 

 

 

 

 

 

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The Origins of European Thought: About the Body, the Mind, the Soul, the World, Time and Fate

 

 

Selections on Aion and Chronos [αἰών; χρόνος] in Onians’ Origins of European Thought

 

 

Onians, Richard Broxton. 1951. The Origins of European Thought: About the Body, the Mind, the Soul, the World, Time and Fate. Cambridge: Cambridge University.

 

 

 

 

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Goldschmidt (1.1.3.14) Le système stoïcien et l'idée de temps, “Divisibilité du temps”, summary

 

by Corry Shores

 

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[The following is summary. Bracketed commentary is my own, as is any boldface. Proofreading is incomplete, which means typos are present, especially in the 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

 

1.1.3.14

Divisibilité du temps

 

 

 

Brief summary:

Chrysippus has a seemingly self-defeating notion of time. He says that no time is completely present, and yet only the present exists. This would seem to suggest that time does not exist. Chrysippus further clarifies that no time exists in the present in the strict sense rather than in the broad sense. The strict sense of the present is not something we actually experience. At best, we can form of concept of it as a limit between the past and future. Under such a conception,  we can think of the present as admitting of no past or future. But time can be said to exist in the broad sense when we think of how we experience the specious present as having some duration. So our senses tell us that there is time in the present, but this is only one sense of the term “present”, namely, the experienceable present. However, the other sense of “present,” the strict sense, is grasped not experientially but only mentally through mathematical procedures. If this sort of present has any reality, we can never actually grasp it as a real component of time. The reason for this has to do with the Stoic ideas regarding the infinite divisibility of continua, including bodies (as spatially extending things) and time (as a temporally extending and perhaps durational thing). When bodies or time are understood mathematically, we can divide them to infinity until arriving upon an infinity of indivisibles. This is already problematic, because suppose we divide a cone into an infinity of stacking circles. We begin by assuming that the cone has a smooth surface. So each ring and its neighbor cannot be of different sizes, because then the cone’s surface would be jagged. But, if they are all the same size, we have a cylinder and not a cone. We encounter a similar problem when we divide bodies and time infinitely. Suppose a body is divided into an infinity of indivisible parts. Those parts would need to lack extension, or else they would be divisible. But parts without extension cannot be parts of extending bodies, because their additive sum would not have extension. (Also, it is not clear how division can arrive upon them, because anything with extension when divided would seem to produce parts with extension, for otherwise the thing being divided would not have extension to begin with.) Similarly for time. Suppose we could infinitely divide time into instants. On the one hand, we cannot obtain indivisibles through division of divisibles. On the other hand, were we to have indivisibles of time and space, their sum could not be said to compose larger structures, because none have any extent or duration. So Chrysippus is saying that such indivisibles produced by a mathematical procedure of infinite division are beings of reason, and if they do have any reality, we can never know them in their actual reality. For in actual practice, we can only continue our divisions endlessly, never arriving upon the limit. Thus, in one sense (the broad sense) time is “real” and in anther sense (the strict sense) time is irreal (it subsists as an incorporeal something without existing corporeally).

[Note: it could instead be that time is simply real (lacking even non-existing susbistance) and the mathematical notion of infinitely divisible time is a misconception that tells us nothing about temporality itself. I will revise this if in the next section that seems to be the case, but I had the impression the next section would propose the Aiôn time which might capture the sense of the mathematical present and also the subsistence of the past and future.]

 

 

 

Contents

 

1.1.3.14

[The Divisibility of Time]

 

1.1.3.14.1

[The Non-Presence of Time and the Existence of the Present and Subsistence (Non-Existent Somethinghood) of the Past and Future]

 

1.1.3.14.2

[The Present in the Strict and Broad Sense. The Non-Presence of Time (Past and Future)]

 

1.1.3.14.3

[The Continuous Divisibility of Corporeality]

 

1.1.3.14.4

[The Mathematically Infinite Divisibility of Bodies and Time. The Impossibility of Actual Infinite Divisibility]

 

1.1.3.14.5

[Chrysippus and the Reality of Time]

 

 

 

Summary

 

1.1.3.14

Divisibilité du temps

 

1.1.3.14.1

[The Non-Presence of Time and the Existence of the Present and Subsistence (Non-Existent Somethinghood) of the Past and Future]

 

(p.37: “C’est ce qu’affirme très clairement sa thèse…”)

 

[In sum: For the Stoics, no time is completely present, and yet only the present exists, while the past and future subsist. We note the oddity here that it would seem we are to conclude that no time exists, even if the present exists.]

 

[We are continuing with Chrysippus’ definition of time as given by Stobaeus. See section 1.1.3.10.] “He says most clearly that no time is wholly present” (Long and Sedley 1987: I, 304; II, 301-302. “C’est ce qu’affirme très clairement sa thèse : aucun temps n’est entièrement présent.”) But the text continues to claim that “only the present belongs; the past and the future subsist, but belong in no way (Long and Sedley 1987: I, 304; II, 301-302) / “only the present exists, whereas the past and future subsist but do not at all exist” (Inwood & Gerson 2008: 88. “seul, le présent existe ; le passé et le futur subsistent, mais n’existent pas du tout”). Although this might seem like a contradiction, we should not think of it as such, as Stobaeus claims that Chrysippus says this “most clearly”.

« C’est ce qu’affirme très clairement sa thèse : aucun temps n’est entièrement présent. » Mais la suite du texte soutient que « seul, le présent existe ; le passé et le futur subsistent, mais n’existent pas du tout ». S’il y a là une contradiction, elle ne peut être qu’apparente, puisqu’elle se trouverait dans un même passage où le doxographe, pour sa part, ne voit rien que de « très clair ».

(37)

 

1.1.3.14.2

 

[The Present in the Strict and Broad Sense. The Non-Presence of Time (Past and Future)]

 

(p.37: “ La thèse : « Aucun temps n’est entièrement présent »…”)

 

[In sum: the present can be understood in two senses. 1) In the strict sense as the physically real present that is the limit between past and future, admitting of no parts of them. 2) In the broad sense, as the specious present we experience, where it simply appears as if in the present there is also a little bit of the past that is passing away and little bit of the future that is now coming into being. So in reality, the past and the future do not exist. They rather are sayables that can only “exist” by being expressed by thoughts in the mind.]

 

The claim that no time is entirely present is reformulated in the conclusion: “Consequently no time is present exactly, but it is broadly said to be so” (Long and Sedley 1987: I, 304; II, 301-302) / “Consequently, no time is present in the strictest sense but only in a broad sense” (Inwood and Gerson 2008: 88. In the French: “Aucun temps n’est rigoureusement présent, mais on le dit (présent) selon une certaine étendue.”) So it is in the “strict” or “exact” (“rigoureux”) sense that time is not “wholly present” (“entièrement présent”). We see the sense of this distinction in the parallel text in Stobaeus attributed to Posidonius. Here “strict” or “exact” (“rigoureux”; perhaps ἀπαρτισμὸν in the Stobaeus/Chrysippus text and in the Stobaeus/Posidonius text) means “known” / “understood” (“saisi par la pensée” and possibly “νοεῖσθαι” in the Stobaeus/Posidonius text). And “broadly” or “in a broad sense” (“en étendue” and perhaps “πλάτος” in the Stobaeus/Posidonius text) means known by perception (“perceptible” or perhaps “πρὸς αἴσθησιν” in the Stobaeus/Posidonius text). The present that Chrysippus says exists is thus a “being of reason”; so, it is quite natural in this sensualist philosophy that such a being as this does not really exist. [The English translation for this part is: “Now and the like are thought of broadly and not exactly. (5) But now is also spoken of with reference to the least perceptible time encompassing the division of the future and the past” (Long and Sedley 1987: I, 305; II, 303-304) / “And the ‘now’ and similar expressions are time understood in a broad sense and not with precision. The ‘now’ and the minimal perceptible time are established around the division between future and past” (Inwood and Gerson 2008: 86-87). The idea here seems to be the following, but I am not sure. No time exists in the exact sense means that in reality, there is no past or future that inheres in the present. But we also have a phenomenological notion of the present as having a certain thickness including a little past that is going away and a little future that is coming to be. Goldschmidt might be saying that we are to understand the present taken in the broad sense to mean the specious present of sense experience, and the present taken in the exact sense to mean the real physical present, which admits of no past or future parts (and thus has no duration).] Thus these incorporeals [the past and the present], which are sayables, only exist in thought.

La thèse : « Aucun temps n’est entièrement présent », est précisée dans la conclusion : « Aucun temps n’est rigoureusement présent, mais on le dit (présent) selon une certaine étendue. » C’est donc au sens « rigoureux », qu’aucun temps n’est « entièrement présent ». Le sens de cette distinction nous est donné dans le texte parallèle de Posidonius. « Rigoureux » signifie : « saisi par la pensée » ; « en étendue » veut dire : « saisi par la sensation »². Le présent dont Chrysippe conteste l’existence, est donc un « être de raison » ; il est très naturel, dans cette philosophie sensualiste, qu’un tel être n’existe pas. C’est le propre de ces incorporels que sont les exprimables, que de n’exister que dans la « pensée »³.

2. Posidonius ap. Ar. Did., 26 (Dox. gr., 461, 19-21) : [See the last two sentences of the following text

Posidonius in Stobaeus 1.105,17-106,4 in Anthologium, vol.1:

(Stobaeus 1884a: 105-106)]

3. Diog. Laërt., VII, 63 (S.V.F., II, 181) : Φασὶ δὲ [τὸ] λεκτὸν εἶναι τὸ κατὰ φαντασίαν λογικὴν ὑφιστάμενον ; cf. p. 18, n. 4-5. Et le texte de Proclus, au sujet du temps : [See the part below beginning : ἕν γὰρ ἦν τῶν παρ᾽ αὐτοῖς and ending φιλαῖς] (in Plat. Tim., 271 d = S.V.F., II, 521).

(SVF II, 521, p.166)

 

 

1.1.3.14.3

 

[The Continuous Divisibility of Corporeality]

 

(pp.37-38: “La preuve de l’inexistence de ce…”)

 

[In sum: The non-existence of the present is based on the Stoic argument against Epicurean atoms. Atoms are small parts of corporeal bodies, and so they are arrived upon by division. As corporeal, they are defined as having extension. And as atomic, they are defined as being indivisible. But anything with extension is divisible, for otherwise it would lack substantiality as a corporeality. Thus atoms are both divisible and indivisible, which is absurd. There are thus no atoms, and corporeal divisibility would have to continue to infinity, never arriving upon an indivisible part.]

 

The proof of the inexistence of the present is based on the infinite divisibility of continua. This particular theory of division is borrowed from Aristotle, and we note that for the Stoics, it has primarily a polemical intention, namely, to show that, contra Epicurus, the division of bodies can continue infinitely without ever arriving upon indivisible elements that are atoms. Under this presentation of the theory, we find that it involves a reduction to absurdity. For, it shows how the atomistic conception, when applied rigorously, destroys the so-called “indivisibles” [or “unbreakables”] and thereby destroys itself. [I am not certain, but the idea might be the following, and this is a guess. Suppose there are indivisible atoms. They would be arrived upon by dividing composites. We also assume that a body is something that has some extension, for otherwise it would have no substantiality in corporeality. But whatever has extension can be divided. So atoms both have and do not have extension, which is absurd. (They have extension because they are corporeal but they do not have extension because they are indivisible.) Thus there are no atoms.]

La preuve de l’inexistence de ce présent s’appuie sur la divisibilité à l’infini des continus. Cette théorie de la division est empruntée à Aristote, et l’on admet que, chez les Stoïciens, elle procède d’une intention surtout polémique : il s’agit de montrer, contre Epicure, que la division des corps peut se poursuivre à l’infini, sans que l’on puisse jamais rencontrer ces éléments « indivisibles » que seraient les atomes⁴. Si telle est bien la prétention de cette théorie, elle enveloppe donc une réduction à l’absurde ; elle fait voir que la conception atomiste, appliquée rigoureusement, dé- | truit les soi-disant insécables derniers et, par là, se détruit elle-même.

4. Voir E. Bréhier, Chrysippe, p.120.

 

 

1.1.3.14.4

 

[The Mathematically Infinite Divisibility of Bodies and Time. The Impossibility of Actual Infinite Divisibility]

 

(p.38: “Cette polémique implique deux idées …”)

 

[In sum: For the Stoics, it is only mentally that we can divide bodies and time infinitely such that we arrive upon indivisibles. But in actuality, such a dividing process can never finish. Thus Chrysippus says that bodies and time are infinitely divisible (mathematically) but in actuality bodies and time are only continuously divisible, never arriving upon an infinity of indivisibles.]

 

This polemic against atomism implies two ideas: {1} that whose non-existence we wish to demonstrate are not the real elements of things but are only those elements which are indivisible and which, for Epicurus and Democritus, and deprived of any sensible quality, making them, in the eyes of the Stoics, no more than “thought” [or mentally conceived] elements. {2} the division to infinity is made using a “dianoetic” [purely intellectual] method of mathematical analyses, which is completely unable to help us grasp the real elements of things. As such, we can apply them without much difficulty to both incorporeals and corporeals, even though in both cases we are only making the divisions in thought without ever making any divisions in real being. This is what Aetius explains (as it is in Stobaeus): “Chrysippus said that bodies are divided to infinity, and likewise things comparable to bodies, such as surface, line, place, void and time. But although these are divided to infinity, a body does not consist of infinitely many bodies, and the same applies to surface, line and place [<and void and time>]” (Long and Sedley 1987: I, 297; II, 296. Bracketed insertions added in accordance with the Long and Sedley II, p.296 footnote and the French text (see the comments following footnote 4 below): “Chrysippe a dit que les corps se divisent à l’infini, de même que les choses qui ressemblent aux corps, comme la surface, la ligne, le lieu, le vide, le temps ; si ces choses se divisent à l’infini, le corps n’est pas (pour autant) composé² de corps infinis, pas plus que la surface³, ni la ligne, ni le lieu < ni le vide, ni le temps”.) [I gather that the idea here is the following, but I am still not entirely sure. For the Stoics, we can divide bodies to infinity only using mathematical methods and by considering them as mental entities. But were we to actually divide bodies or time, that is something that would never be completed, at least in a finite amount of time. So insofar as the presumed smallest parts are only obtained by actual division, we can say that bodies and time can be divided to infinity mathematically but only infinitely divided (continuously but never to completion) in actuality.] [I note something that I find odd at this point. We are saying that in actuality bodies and time are not divisible into an infinity of indivisibles. But we are also saying that the present in reality (or at least in the strict sense) has no parts. I am not confident in my interpretation so far. But I would have thought that we would say that in the mind the present admits of parts but in reality it does not. Perhaps the idea is the following. The present really does not have parts. We can at best obtain a mathematical notion of this, because it is not possible for humans to arrive upon in actuality. However, we should be cautious with this mathematical notion, because it is only a mental construction and it does not give us the real indivisible itself.]

Cette polémique implique deux idées, d’ailleurs solidaires : a) ce dont on veut ainsi démontrer l’inexistence, ce ne sont pas les éléments réels des choses, mais uniquement ces éléments insécables, invisibles et dépourvus, pour Epicure comme pour Démocrite, de toute qualité sensible¹, donc, aux yeux des Stoïciens, des éléments simplement « pensés » ; b) la division à l’infini se fait selon une méthode d’analyse mathémathique, « dianoétique », qui se révèle radicalement impuissante à nous faire saisir les éléments réels des choses. Aussi peut-on l’appliquer sans inconvénient, non seulement aux incorporels, mais encore aux corps : dans les deux cas, on ne divise qu’ « en pensée », sans entamer l’être réel. C’est ce que nous explique Aëtius : « Chrysippe a dit que les corps se divisent à l’infini, de même que les choses qui ressemblent aux corps, comme la surface, la ligne, le lieu, le vide, le temps ; si ces choses se divisent à l’infini, le corps n’est pas (pour autant) composé² de corps infinis, pas plus que la surface³, ni la ligne, ni le lieu < ni le vide, ni le temps >⁴ »⁵.

(38)

Démocrite, in Vors6., 68 A 49 (Galien, de elem. sec. Hipp., I, 2) ; Epicure, Lettre à Hérodote, 54.

2. Cf. Plut., de comm. not., 38, 1079 b-c (S.V.F., II, 483).

3. Il faut comprendre : «  ... n’est composée de surfaces », et de même pour les autres termes de l’énumération.

4. L’addition, due à Heeren, semble s’imposer ; l’hésitation de Diels (« ceterum dubitari potest de vacui et temporis notione corporea ») ne se justifie pas ; la corporéité n’est affirmée, ni du vide, ni du temps, dans ce texte, dont la thèse principale (la divisibilité à l’infini des corps, des lieux et des temps) est corroborée par Sextus, math., X, 142 (S.V.F., II, 491).

5. Aëtius, I, 16, 4 (Dox. gr., 315, 8-15 = S.V.F., II, 482).

(38)

[Regarding note 4, I cannot follow the explanations in Latin, but let me provide them for the record:

(345)

(344)

(344)

(Stobaeus; Heeren 1792: 344-345)

 

(Stobaeus; Diels, Doxographi graeci. 1879: 315)

In Long and Sedley II, the additions are given only in footnote, and in Long and Sedley I, there is no inclusion or footnote.]

 

 

1.1.3.14.5

 

[Chrysippus and the Reality of Time]

 

(pp.38-39: “On ne saurait donc conclure de notre texte …”)

 

[In sum: So Chrysippus is not arguing that time, which is continuously divisible, is divisible in actuality to indivisible parts. Were he to argue such a thing, that would mean that time is composed of durationaless points where there is neither past nor future, but only a cut between them. And such an argument would imply that time is not real. But that cannot be Chrysippus’ argument, because then by the same operation of division bodies would be composed of non-extending parts, and surely Chrysippus is not arguing that bodies are irreal. Rather, these indivisibles are attainable only through mental operations and not in reality.]

 

So even though Chrysippus speaks of the infinite divisibility of time, we should not simply conclude that he was arguing for the irreality of time. For, were he doing so, we would have to conclude that bodies are not real. [I am not certain what is meant here, so I will guess that the idea is the following. Superficially we might note that Chrysippus says that bodies and time are divisible to infinity. That would leave time being composed of parts with no temporality, because these parts at best would be like cuts within the flow from future to past. And an infinity of cuts would not make time. This cannot be right, because if Chrysippus also meant that bodies are divisible into indivisible parts, that would mean that bodies are fundamentally composed of things without extension, which is also absurd.] Later we will ask if the theory of the division of continua for Chrysippus entails a positive counterpart. But for now, we simply note that irreality is affirmed of a time or of a present that we might claim to know by a dianoetic analysis. This is similar to the reasoning Chrysippus used when discussing the parts of a cone, which Democritus criticized. For surely the Stoics did not mean to conclude that the cone does not exist. [See the discussion here. Perhaps the idea is that for Chrysippus, only in the mind would there be an infinity of depthless circles making a cone. In reality, the cone would be made of very many ribbons set at the angle of the cone’s slope.] [The last idea might be: Rather, the present is to a certain extent real, and it is grasped by sensation.] [Note 6 will be important in the next section, so let us take a look at it now:] Recall that we said that irreality is affirmed of a time or of a present that we know by mental, mathematical operations. The time that is divided to infinity is “total time,” which extends infinitely into the past and future. But the division applies also to the present, which is limited, because the division cannot stop at an indivisible instant. [If we take present, understood as having a duration, we can also divide it continuously without arriving upon a durationless instant.] This is implied in our text, and Plutarch says it formally: “this is the result for the Stoics, who do not admit a minimal time or wish the now to be partless but claim that whatever one thinks one has grasped and is considering as present is in part future and in part past.” (Plutarch, On common conceptions 1081C, from Long and Sedley I, p.304. In the French: « Ils ne veulent | pas reconnaitre un instant sans parties ; si l’on croit saisir par la pensée un présent, ils répondent que ce présent est en partie du passé, en partie, du futur ». And in the Greek: “ὅ τι ἄν τις ὡς ἐνεστὼς οἴηται λαβὼν διανοεῖσθαι, τούτου τὸ μὲν μέλλον τὸ δὲ παρῳχημένον εἶναι φάσκουσιν”.)

On ne saurait donc conclure de notre texte que Chrysippe enseignant la divisibilité à l’infini du temps, ait voulu montrer l’irréalité de celui-ci, car une conclusion analogue réduirait également à néant, la réalité des corps. Nous nous demanderons plus loin si la théorie de la division des continus ne comporte pas, chez Chrysippe, une contre-partie positive. Pour l’instant, il suffit de voir que l’irréalité est affirmée d’un temps (ou d’un présent)⁶ que l’on prétendrait saisir par l’analyse dianoétique, de même que sont irréels les | disques innombrables dans lesquels Démocrite avait décomposé le cône¹ ; de quoi, assurément, les Stoïciens n’entendaient pas conclure que le cône même n’existait pas². Est réel, en revanche, le présent d’une certaine étendue et saisi par la sensation.

(38-39)

6. C’est « le temps total » qui, en tant que continu, comporte la division à l’infini (le temps total, qui est infini du côté du passé et du côté de l’avenir). Mais la division, puisqu’elle ne peut s’arrêter à aucun instant indivisible, s’applique également au présent (qui, lui, est limité) ; c’est ce qu’implique notre texte même, et c’est ce que nous dit formellement Plutarque ; « Ils ne veulent | pas reconnaitre un instant sans parties ; si l’on croit saisir par la pensée un présent, ils répondent que ce présent est en partie du passé, en partie, du futur » (ὅ τι ἄν τις ὡς ἐνεστὼς οἴηται λαβὼν διανοεῖσθαι, τούτου τὸ μὲν μέλλον τὸ δὲ παρῳχημένον εἶναι φάσκουσιν), de comm. not., 41, 1081 c (S.V.F, II, 519).

(38-39. Greek text copied from Perseus)

1. Plut., de comm. not., 39, 1079 e (S.V.F, II, 489).

 

 

 

 

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

 

Doxographi graeci. 1879. Edited by Hermann Diels. Berlin: Reimer.

PDF available at:

https://archive.org/details/doxographigraec00dielgoog

 

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.

 

Plutarch. De communibus notitiis contra Stoicos. Taken from:

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A2008.01.0392%3Astephpage%3D1058f

 

Stobaeus. 1792.  Ioannis Stobaei. Eclogarum physicarum et ethicarum. Libri duo. Pars Prima. Physica continens. Edited by Arnold Heeren. Göttingen: Vandenhoeck and Ruprecht.

PDF available at:

https://books.google.com.tr/books?id=61wUAAAAQAAJ&dq=stobaeus+Heeren&source=gbs_navlinks_s

 

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.

PDF at:

https://archive.org/details/adw8682.0001.001.umich.edu

 

SVF. 1964b. Stoicorum veterum fragmenta, vol.2: Chrysippi Fragmenta Logica et Physica. Ed.  Hans von Arnim. Stuttgart: Teubner.

PDF available at:

https://archive.org/details/stoicorumveterum02arniuoft

 

 

 

 

 

 

 

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