HI there! 
Here, as promised on the chat, is the link I mentioned with Stephen Hawkings views, before he died, on the infinite universe. Enjoy!
Key Citations - The Universe As Infinite In Space - Many Worlds With Life
-
-
Okay, as promised, here's a start to Epicurus's mention of "infinity, infinite" specifically using the term απειρον / απειρος. Below are only the mentions in the Letter to Herodotus with both Greek and English for comparison. One idiosyncrasy I noticed is that the translator likes to use "ad infinitum" where Epicurus uses εἰς ἄπειρον "to infinity". Granted, the Latin means the same as the Greek but it obscures Epicurus's use of the word he says we need to study:
Epicurus, Letter to Herodotus
37
Πρῶτον μὲν οὖν τὰ ὑποτεταγμένα τοῖς φθόγγοις, ὦ Ἡρόδοτε, δεῖ εἰληφέναι, ὅπως ἂν τὰ δοξαζόμενα ἢ ζητούμενα ἢ ἀπορούμενα ἔχωμεν εἰς ταῦτα ἀνάγοντες ἐπικρίνειν, καὶ μὴ ἄκριτα πάντα ἡμῖν <ἴῃ>42 εἰς ἄπειρον ἀποδεικνύουσιν ἢ κενοὺς φθόγγους ἔχωμεν.
"In the first place, Herodotus, you must understand what it is that words denote, in order that by reference to this we may be in a position to test opinions, inquiries, or problems, so that our proofs may not run on untested ad infinitum, nor the terms we use be empty of meaning.41-43
"Ἀλλὰ μὴν καὶ τὸ πᾶν ἄπειρόν ἐστι. τὸ γὰρ πεπερασμένον ἄκρον ἔχει: τὸ δὲ ἄκρον παρ᾽ ἕτερόν τι θεωρεῖται: <τὸ δὲ πᾶν οὐ παρ᾽ ἕτερόν τι θεωρεῖται:>51 ὥστε οὐκ ἔχον ἄκρον πέρας οὐκ ἔχει: πέρας δὲ οὐκ ἔχον ἄπειρον ἂν εἴη καὶ οὐ πεπερασμένον."Καὶ μὴν καὶ τῷ πλήθει τῶν σωμάτων ἄπειρόν ἐστι τὸ πᾶν καὶ τῷ μεγέθει τοῦ κενοῦ. [42] εἴ τε γὰρ ἦν τὸ κενὸν ἄπειρον, τὰ δὲ σώματα ὡρισμένα, οὐθαμοῦ ἂν ἔμενε τὰ σώματα, ἀλλ᾽ ἐφέρετο κατὰ τὸ ἄπειρον κενὸν διεσπαρμένα, οὐκ ἔχοντα τὰ ὑπερείδοντα καὶ στέλλοντα κατὰ τὰς ἀνακοπάς: εἴ τε τὸ κενὸν ἦν ὡρισμένον, οὐκ ἂν εἶχε τὰ ἄπειρα σώματα ὅπου ἐνέστη.
"Πρός τε τούτοις τὰ ἄτομα τῶν σωμάτων καὶ μεστά, ἐξ ὧν καὶ αἱ συγκρίσεις γίνονται καὶ εἰς ἃ διαλύονται, ἀπερίληπτά ἐστι ταῖς διαφοραῖς τῶν σχημάτων: οὐ γὰρ δυνατὸν γενέσθαι τὰς τοσαύτας διαφορὰς ἐκ τῶν αὐτῶν σχημάτων περιειλημμένων. καὶ καθ᾽ ἑκάστην δὲ σχημάτισιν ἁπλῶς ἄπειροί εἰσιν αἱ ὅμοιαι, ταῖς δὲ διαφοραῖς οὐχ ἁπλῶς 53 [43] ἄπειροι ἀλλὰ μόνον ἀπερίληπτοι, [οὐδὲ γάρ φησιν ἐνδοτέρω εἰς ἄπειρον τὴν τομὴν τυγχάνειν. λέγει δέ, ἐπειδὴ αἱ ποιότητες μεταβάλλονται, εἰ μέλλει τις μὴ καὶ τοῖς μεγέθεσιν ἁπλῶς εἰς ἄπειρον αὐτὰς ἐκβάλλειν].
"Again, the sum of things (The All, τὸ πᾶν) is infinite (ἄπειρόν). For what is finite has an extremity, and the extremity of anything is discerned only by comparison with something else. (Now the sum of things is not discerned by comparison with anything else :64) hence, since it has no extremity, it has no limit ; and, since it has no limit, it must be unlimited or infinite (ἄπειρον).
"Moreover, the sum of things (The All, τὸ πᾶν) is unlimited (ἄπειρόν) both by reason of the multitude of the atoms and the extent of the void. [42] For if the void were infinite (ἄπειρον) and bodies finite, the bodies would not have stayed anywhere but would have been dispersed in their course through the infinite (ἄπειρον) void, not having any supports or counter- checks to send them back on their upward rebound. Again, if the void were finite, the infinity (ἄπειρα) of bodies would not have anywhere to be.
"Furthermore, the atoms, which have no void in them--out of which composite bodies arise and into which they are dissolved--vary indefinitely in their shapes ; for so many varieties of things as we see could never have arisen out of a recurrence of a definite number of the same shapes. The like atoms of each shape are absolutely infinite (ἄπειροί); but the variety of shapes, though indefinitely large, is not absolutely infinite. [43] [For neither does the divisibility go on "ad infinitum," he says below; but he adds, since the qualities change, unless one is prepared to keep enlarging their magnitudes also simply "ad infinitum." (ἄπειρον)]
45
"Ἀλλὰ μὴν καὶ κόσμοι ἄπειροί εἰσιν, οἵ θ᾽ ὅμοιοι τούτῳ καὶ ἀνόμοιοι. αἵ τε γὰρ ἄτομοι ἄπειροι οὖσαι, ὡς ἄρτι ἀπεδείχθη, φέρονται καὶ πορρωτάτω. οὐ γὰρ κατανήλωνται αἱ τοιαῦται ἄτομοι, ἐξ ὧν ἂν γένοιτο κόσμος ἢ ὑφ᾽ ὧν ἂν ποιηθείη, οὔτ᾽ εἰς ἕνα οὔτ᾽ εἰς πεπερασμένους, οὔθ᾽ ὅσοι τοιοῦτοι οὔθ᾽ ὅσοι διάφοροι τούτοις. ὥστε οὐδὲν τὸ ἐμποδοστατῆσόν ἐστι πρὸς τὴν ἀπειρίαν τῶν κόσμων."Moreover, there is an infinite number of worlds (κόσμοι ἄπειροί kosmoi apeiroi), some like this world, others unlike it. For the atoms being infinite (ἄτομοι ἄπειροι) in number, as has just been proved, are borne ever further in their course. For the atoms out of which a world might arise, or by which a world might be formed, have not all been expended on one world or a finite number of worlds, whether like or unlike this one. Hence there will be nothing to hinder an infinity of worlds (τὴν ἀπειρίαν τῶν κόσμων).
47
[47] "Οὐ μὴν οὐδ᾽ ἅμα κατὰ τοὺς διὰ λόγου θεωρητοὺς χρόνους αὐτὸ τὸ φερόμενον σῶμα ἐπὶ τοὺς πλείους τόπους ἀφικνεῖται -- ἀδιανόητον γάρ,-- καὶ τοῦτο συναφικνούμενον ἐν αἰσθητῷ χρόνῳ ὅθεν δήποθεν τοῦ ἀπείρου οὐκ ἐξ οὗ ἂν περιλάβωμεν τὴν φορὰν τόπου ἔσται ἀφιστάμενον: ἀντικοπῇ γὰρ ὅμοιον ἔσται, κἂν μέχρι τοσούτου τὸ τάχος τῆς φορᾶς μὴ ἀντικόπτον καταλίπωμεν. χρήσιμον δὴ καὶ τοῦτο κατασχεῖν τὸ στοιχεῖον. εἶθ᾽ ὅτι τὰ εἴδωλα ταῖς λεπτότησιν ἀνυπερβλήτοις κέχρηται, οὐθὲν ἀντιμαρτυρεῖ τῶν φαινομένων: ὅθεν καὶ τάχη ἀνυπέρβλητα ἔχει, πάντα πόρον σύμμετρον ἔχοντα πρὸς τῷ <τῷ>61 ἀπείρῳ αὐτῶν μηθὲν ἀντικόπτειν ἢ ὀλίγα ἀντικόπτειν, πολλαῖς δὲ καὶ ἀπείροις εὐθὺς ἀντικόπτειν τι.[47] "Not that, if we consider the minute times perceptible by reason alone,69 the moving body itself arrives at more than one place simultaneously (for this too is inconceivable), although in time perceptible to sense it does arrive simultaneously, however different the point of departure from that conceived by us (...from the infinite). For if it changed its direction, that would be equivalent to its meeting with resistance, even if up to that point we allow nothing to impede the rate of its flight. This is an elementary fact which in itself is well worth bearing in mind. In the next place the exceeding thinness of the images is contradicted by none of the facts under our observation. Hence also their velocities are enormous, since they always find a void passage to fit them. Besides, their incessant (ἀπείρῳ) effluence meets with no resistance, or very little, although many atoms, not to say an unlimited number (ἀπείροις) , do at once encounter resistance.
56-57
"Πρὸς δὲ τούτοις οὐ δεῖ νομίζειν ἐν τῷ ὡρισμένῳ σώματι ἀπείρους ὄγκους εἶναι οὐδ᾽ ὁπηλίκους οὖν. ὥστε οὐ μόνον τὴν εἰς ἄπειρον τομὴν ἐπὶ τοὔλαττον ἀναιρετέον, ἵνα μὴ πάντα ἀσθενῆ ποιῶμεν κἀν ταῖς περιλήψεσι τῶν ἀθρόων εἰς τὸ μὴ ὂν ἀναγκαζώμεθα τὰ ὄντα θλίβοντες καταναλίσκειν, ἀλλὰ καὶ τὴν μετάβασιν μὴ νομιστέον γίνεσθαι ἐν τοῖς ὡρισμένοις εἰς ἄπειρον μηδ᾽ ἐπὶ τοὔλαττον.[57] "Οὔτε γὰρ ὅπως, ἐπειδὰν ἅπαξ τις εἴπῃ ὅτι ἄπειροι ὄγκοι ἔν τινι ὑπάρχουσιν ἢ ὁπηλίκοι οὖν, ἔστι νοῆσαι ὅπως78 ἂν ἔτι τοῦτο πεπερασμένον εἴη τὸ μέγεθος. πηλίκοι γάρ τινες δῆλον ὡς οἱ ἄπειροί εἰσιν ὄγκοι: καὶ οὗτοι ὁπηλίκοι ἄν ποτε ὦσιν, ἄπειρον ἂν ἦν καὶ τὸ μέγεθος. ἄκρον τε ἔχοντος τοῦ πεπερασμένου διαληπτόν, εἰ μὴ καὶ καθ᾽ ἑαυτὸ θεωρητόν, οὐκ ἔστι μὴ οὐ καὶ τὸ ἑξῆς τούτου τοιοῦτον νοεῖν καὶ οὕτω κατὰ τὸ ἑξῆς εἰς τοὔμπροσθεν βαδίζοντα εἰς τὸ ἄπειρον ὑπάρχειν καὶ τὸ τοιοῦτον ἀφικνεῖσθαι τῇ ἐννοίᾳ.
"Besides, you must not suppose that there are parts unlimited (ἀπείρους) in number, be they ever so small, in any finite body. Hence not only must we reject as impossible subdivision ad infinitum (εἰς ἄπειρον) into smaller and smaller parts, lest we make all things too weak and, in our conceptions of the aggregates, be driven to pulverize the things that exist, i.e. the atoms, and annihilate87 them ; but in dealing with finite things we must also reject as impossible the progression ad infinitum (εἰς ἄπειρον) by less and less increments.
[57] "For when once we have said that an infinite (ἄπειροι) number of particles, however small, are contained in anything, it is not possible to conceive how it could any longer be limited or finite in size. For clearly our infinite (οἱ ἄπειροί) number of particles must have some size ; and then, of whatever size they were, the aggregate they made would be infinite (ἄπειρον). And, in the next place, since what is finite has an extremity which is distinguishable, even if it is not by itself observable, it is not possible to avoid thinking of another such extremity next to this. Nor can we help thinking that in this way, by proceeding forward from one to the next in order, it is possible by such a progression to arrive in thought at infinity (εἰς τὸ ἄπειρον).
60
[60] "Καὶ84 μὴν καὶ τοῦ ἀπείρου ὡς μὲν ἀνωτάτω καὶ κατώτατω οὐ δεῖ κατηγορεῖν τὸ ἄνω ἢ κάτω. ἴσμεν μέντοι τὸ ὑπὲρ κεφαλῆς, ὅθεν ἂν στῶμεν, εἰς ἄπειρον ἄγειν ὄν, μηδέποτε φανεῖσθαι τοῦτο ἡμῖν, ἢ τὸ ὑποκάτω τοῦ νοηθέντος εἰς ἄπειρον, ἅμα ἄνω τε εἶναι καὶ κάτω πρὸς τὸ αὐτό: τοῦτο γὰρ ἀδύνατον διανοηθῆναι. ὥστε ἔστι μίαν λαβεῖν φορὰν τὴν ἄνω νοουμένην εἰς ἄπειρον καὶ μίαν τὴν κάτω, ἂν καὶ μυριάκις πρὸς τοὺς πόδας τῶν ἐπάνω τὸ παρ᾽ ἡμῶν φερόμενον εἰς τοὺς ὑπὲρ κεφαλῆς ἡμῶν τόπους ἀφικνῆται ἢ ἐπὶ τὴν κεφαλὴν τῶν ὑποκάτω τὸ παρ᾽ ἡμῶν κάτω φερόμενον: ἡ γὰρ ὅλη φορὰ οὐθὲν ἧττον ἑκατέρα ἑκατέρᾳ ἀντικειμένη ἐπ᾽ ἄπειρον νοεῖται.[60] "Further, we must not assert `up' or `down' of that which is unlimited (ἀπείρου), as if there were a zenith or nadir. As to the space overhead, however, if it be possible to draw a line to infinity (εἰς ἄπειρον) from the point where we stand, we know that never will this space --or, for that matter, the space below the supposed standpoint if produced to infinity (εἰς ἄπειρον) --appear to us to be at the same time `up' and `down' with reference to the same point ; for this is inconceivable. Hence it is possible to assume one direction of motion, which we conceive as extending upwards ad infinitum (εἰς ἄπειρον), and another downwards, even if it should happen ten thousand times that what moves from us to the spaces above our heads reaches the feet of those above us, or that which moves downwards from us the heads of those below us. None the less is it true that the whole of the motion in the respective cases is conceived as extending in opposite directions ad infinitum (εἰς ἄπειρον).
73
"Ἐπί τε τοῖς προειρημένοις τοὺς κόσμους δεῖ καὶ πᾶσαν σύγκρισιν πεπερασμένην τὸ ὁμοειδὲς τοῖς θεωρουμένοις πυκνῶς ἔχουσαν νομίζειν γεγονέναι ἀπὸ τοῦ ἀπείρου,"After the foregoing we have next to consider that the worlds and every finite aggregate which bears a strong resemblance to things we commonly see have arisen out of the infinite (ἀπὸ τοῦ ἀπείρου).
74 in a scholia
[ἀλλὰ καὶ διαφόρους αὐτοὺς ἐν τῇ ιβ᾽ Περὶ φύσεως αὐτός φησιν: οὓς μὲν γὰρ σφαιροειδεῖς, καὶ ᾠοειδεῖς ἄλλους, καὶ ἀλλοιοσχήμονας ἑτέρους: οὐ μέντοι πᾶν σχῆμα ἔχειν. οὐδὲ ζῷα εἶναι ἀποκριθέντα ἀπὸ τοῦ ἀπείρου.]
[On the contrary, in the twelfth book "On Nature" he himself says that the shapes of the worlds differ, some being spherical, some oval, others again of shapes different from these. They do not, however, admit of every shape. Nor are they living beings which have been separated from the infinite (ἀπὸ τοῦ ἀπείρου).] -
Mentions of ἄπειρόν (infinity) in Principal Doctrines: These are a little more hidden by translations that the Herodotus references. The etymology of the word is important to point out: From ἀ- (a-, “not”) + πεῖραρ (peîrar), πέρας (péras, “end, limit”).
[χιιι.] Οὐθὲν ὄφελος ἦν τὴν κατ᾽ ἀνθρώπους ἀσφάλειαν κατασκευάζεσθαι τῶν ἄνωθεν ὑπόπτων καθεστώτων καὶ τῶν ὑπὸ γῆς καὶ ἁπλῶς τῶν *ἐν τῷ ἀπείρῳ.*
13. It is useless to be safe from other people while retaining suspicions about what is above and below the earth and in general *about the infinite unknown*. (Saint-Andre)
13. There would be no advantage in providing security against our fellow-men, so long as we were alarmed by occurrences over our heads or beneath the earth or in general by whatever happens *in the boundless universe* (ἐν τῷ ἀπείρῳ). (Hicks)[χϝ.] Ὁ τῆς φύσεως πλοῦτος καὶ ὥρισται καὶ εὐπόριστός ἐστιν: ὁ δὲ τῶν κενῶν δοξῶν *εἰς ἄπειρον* ἐκπίπτει.
15. Natural wealth is both limited and easy to acquire, but the riches incited by groundless opinion *have no end.* (Saint-Andre)
15. Nature's wealth at once has its bounds and is easy to procure ; but the wealth of vain fancies recedes *to an infinite distance*. (Hicks)
[χιχ.] Ὁ ἄπειρος χρόνος ἴσην ἔχει τὴν ἡδονὴν καὶ ὁ πεπερασμένος, ἐάν τις αὐτῆς τὰ πέρατα καταμετρήσῃ τῷ λογισμῷ.
19. Finite time and infinite time (Ὁ ἄπειρος χρόνος) contain the same amount of joy, if its limits are measured out through reasoning. (Saint-Andre)
19. Unlimited time (Ὁ ἄπειρος χρόνος) and limited time afford an equal amount of pleasure, if we measure the limits of that pleasure by reason. (Hicks)
[χχ.] Ἡ μὲν σὰρξ ἀπέλαβε τὰ πέρατα τῆς ἡδονῆς ἄπειρα, καὶ ἄπειρος αὐτὴν χρόνος παρεσκεύασεν. ἡ δὲ διάνοια τοῦ τῆς σαρκὸς τέλους καὶ πέρατος λαβοῦσα τὸν ἐπιλογισμὸν καὶ τοὺς ὑπὲρ τοῦ αἰῶνος φόβους ἐκλύσασα τὸν παντελῆ βίον παρεσκεύασεν, καὶ οὐθὲν ἔτι τοῦ ἀπείρου χρόνου προσεδεήθη: <οὐ> μὴν ἀλλ᾽ οὔτε ἔφυγε τὴν ἡδονήν, οὐθ᾽ ἡνίκα τὴν ἐξαγωγὴν ἐκ τοῦ ζῆν τὰ πράγματα παρεσκεύαζεν, ὡς ἐλλείπουσά τι τοῦ ἀρίστου βίου κατέστρεφεν.
20. The flesh assumes that the limits of joy are infinite (τῆς ἡδονῆς ἄπειρα), and that infinite joy can be produced only through infinite (ἄπειρος) time. But the mind, thinking through the goal and limits of the flesh and dissolving fears about eternity, produces a complete way of life and therefore has no need of infinite time (τοῦ ἀπείρου χρόνου); yet the mind does not flee from joy, nor when events cause it to exit from life does it look back as if it has missed any aspect of the best life. (Saint-Andre)
20. The flesh receives as unlimited (ἄπειρα) the limits of pleasure ; and to provide it requires unlimited (ἄπειρος) time. But the mind, grasping in thought what the end and limit of the flesh is, and banishing the terrors of futurity, procures a complete and perfect life, and has no longer any need of unlimited time (τοῦ ἀπείρου χρόνου). Nevertheless it does not shun pleasure, and even in the hour of death, when ushered out of existence by circumstances, the mind does not lack enjoyment of the best life. (Hicks) -
people of normal intelligence shouldn't be asked to accept "trust the scientists" or "trust the mathematicians" any more than they accept "trust the priests" as an explanation.
Yes, as we know, authorities and what they say may or may not be helpful, but they are certainly not our measure of truth. Sensation is our measure of truth.
infinite number of worlds (κόσμοι ἄπειροί kosmoi apeiroi)
I agree we should not "update" or add ideas when translating -- but do we have any good arguments or objections to using "galaxies" for "kosmoi"? (We all know the difficulty with the English "world," which now means only one planet).
-
I agree we should not "update" or add ideas when translating -- but do we have any good arguments or objections to using "galaxies" for "kosmoi"? (We all know the difficulty with the English "world," which now means only one planet).
I agree "world" is problematic, but using "galaxy" obscures the ancient Greek understanding of what a kosmos was. I prefer "world-system" or something like that. Kosmos is not directly translated into a modern idiom.
-
Using "galaxy" obscures the ancient Greek understanding of what a kosmos was.
This is certainly true and I do agree. But then of course Epicurus would have a different view of the meaning of the word compared to his predecessors. LSJ often accommodates Epicurus' variance, but it does so unevenly, as you know. I see that galaxy is too much, and that "world-system" is correct, but I do wish for a more elegant solution. I only want one unnamed thing (that 4th part) and this feels like adding to that list. Perhaps, just cosmos.
-
" is correct, but I do wish for a more elegant solution.
LOL Completely agree, although to quote the philosopher Mick Jagger "You can't always get what you want..."
-
Galaxy is too much for me, too. Solar system appears to be the modern term closest to what Epicurus called a cosmos.
-
From the whole surface of the Earth there are less than 10,000 stars visible to the naked eye--out of something like 100 billion stars in our galaxy.
-
I know I've brought this up ad nauseum at this point and in this thread already, but Lucretius' talk about Epicurus going beyond the "fiery ramparts" of the "mundus" ("world") tells me their concept of the structure of their "world-system" included a fiery "shell or dome" through which Epicurus was able to think beyond and to imagine other such world-systems throughout The All, the entirety of the whole universe. There really is no applicable analogy in modern cosmology unless, in my opinion, one wants to go down the "bubble universe" track. We can assert that "other worlds" is like Star Trek's "strange new worlds" in other solar systems, but I don't believe that was Epicurus's or Lucretius's image of a κοσμος/mundus. Now, could the ancient Epicureans be made to understand the modern concept of solar system, galaxy, etc.? Sure. Given enough evidence, they could probably accept or at least entertain the ideas that modern cosmology provides. But trying to map κοσμος/mundus onto modern concepts is going to be fraught with complications and requiring an ancient culture to adhere to our modern ideas. I think that does a disservice to them and us.
IF we want to think of "other kosmoi" as other planets in other solar systems, that's fine IF we're honest and acknowledge that's most likely not how Epicurus nor Lucretius nor Diogenes of Oenoanda nor the other ancient Epicureans conceived of it.
-
There really is no applicable analogy in modern cosmology
Yes, given our inability to translate it, I suppose we can take refuge in "cosmos" and "cosmoi."
I fully agree using terms from other schools confuses the issue and should probably be avoided... to the extent that cosmos means different things to different people, this will be ground that must be defended, and we will have to educate them about the correct meaning!
(As we know, Epicurus uses "atomos" and translating that as "atom" means we use the word that is not the same as modern science. But, I think you would agree, not using "atom" when translating him certainly gives up too much ground. We can use "atom" in our school, and use in its proper and true meaning. )
-
(As we know, Epicurus uses "atomos" and translating that as "atom" means we use the word that is not the same as modern science. But, I think you would agree, not using "atom" when translating him certainly gives up too much ground. We can use "atom" in our school, and use in its proper and true meaning. )
Oh, I fully agree with using "atom" to translate atomos is fine. Even though they aren't completely analogous from ancient to modern ideas, they are closer, in my opinion, than world and kosmos. Both atomos and atom get at minute particles of matter that make up compound bodies and, for us, molecules. Yeah, I'm not getting on a soapbox over those. (Is that a collective sigh of relief I hear?)
-
Okay, so this is about as close as I could find of κόσμος = modern cosmology. There's even some "fiery ramparts"...
CIRCULAR MAP OF THE UNIVERSE ALL VERSIONS - Pablo Carlos Budassiother languages / other versionspablocarlosbudassi.comSee also: https://bigthink.com/starts-with-a-…-view-universe/
