Key Citations - The Universe As Infinite In Space - Many Worlds With Life

1. Velleius, in Cicero's On The Nature of The Gods, XIX - Moreover, there is the supremely potent principle of infinity, which claims the closest and most careful study....
2. Epicurus to Herodotus 45 - These brief sayings, if all these points are borne in mind, afford a sufficient outline for our understanding of the nature of existing things. Furthermore, there are infinite worlds both like and unlike this world of ours. For the atoms being infinite in number, as was proved already, are borne on far out into space. For those atoms, which are of such nature that a world could be created out of them or made by them, have not been used up either on one world or on a limited number of worlds, nor again on all the worlds which are alike, or on those which are different from these. So that there nowhere exists an obstacle to the infinite number of the worlds. [46] Moreover, there are images like in shape to the solid bodies, far surpassing perceptible things in their subtlety of texture. For it is not impossible that such emanations should be formed in that which surrounds the objects, nor that there should be opportunities for the formation of such hollow and thin frames, nor that there should be effluences which preserve the respective position and order which they had before in the solid bodies: these images we call idols.
3. Epicurus to Pythocles 117 - All these things, Pythocles, you must bear in mind; for thus you will escape in most things from superstition and will be enabled to understand what is akin to them. And most of all give yourself up to the study of the beginnings and of infinity and of the things akin to them, and also of the criteria of truth and of the feelings, and of the purpose for which we reason out these things. For these points when they are thoroughly studied will most easily enable you to understand the causes of the details. But those who have not thoroughly taken these things to heart could not rightly study them in themselves, nor have they made their own the reason for observing them.
4. Epicurus to Menoeceus - [135] ... Meditate therefore on these things and things akin to them night and day by yourself; and with a companion like to yourself, and never shall you be disturbed waking or asleep, but you shall live like a god among men. For a man who lives among immortal blessings is not like unto a mortal being.
5. Lucretius Book 2, Bailey: [522] And since I have taught this much, I will hasten to link on a truth which holds to it and wins belief from it, that the first-beginnings of things, which are formed with a shape like to one another, are in number infinite. For since the difference of forms is limited, it must needs be that those which are alike are unlimited, or else that the sum of matter is created limited, which I have proved not to be, showing in my verses that the tiny bodies of matter from everlasting always keep up the sum of things, as the team of blows is harnessed on unbroken on every side. [532] For in that you see that certain animals are more rare, and perceive that nature is less fruitful in them, yet in another quarter and spot, in some distant lands, there may be many in that kind, and so the tale is made up; even as in the race of four-footed beasts we see that elephants with their snaky hands come first of all, by whose many thousands India is embattled with a bulwark of ivory, so that no way can be found into its inner parts: so great is the multitude of those beasts, whereof we see but a very few samples. [541] But still, let me grant this too, let there be, if you will, some one thing unique, alone in the body of its birth, to which there is not a fellow in the whole wide world; yet unless there is an unlimited stock of matter, from which it might be conceived and brought to birth, it will not be able to be created, nor, after that, to grow on and be nourished.
6. Lucretius [2:1048] First of all, we find that in every direction everywhere, and on either side, above and below, through all the universe, there is no limit, as I have shown, and indeed the truth cries out for itself and the nature of the deep shines clear. Now in no way must we think it likely, since towards every side is infinite empty space, and seeds in unnumbered numbers in the deep universe fly about in many ways driven on in everlasting motion, that this one world and sky was brought to birth, but that beyond it all those bodies of matter do naught; above all, since this world was so made by nature, as the seeds of things themselves of their own accord, jostling from time to time, were driven together in many ways, rashly, idly, and in vain, and at last those united, which, suddenly cast together, might become ever and anon the beginnings of great things, of earth and sea and sky, and the race of living things. Wherefore, again and again, you must needs confess that there are here and there other gatherings of matter, such as is this, which the ether holds in its greedy grip.
7. Lucretius [2:1067] Moreover, when there is much matter ready to hand, when space is there, and no thing, no cause delays, things must, we may be sure, be carried on and completed. As it is, if there is so great a store of seeds as the whole life of living things could not number, and if the same force and nature abides which could throw together the seeds of things, each into their place in like manner as they are thrown together here, it must needs be that you confess that there are other worlds in other regions, and diverse races of men and tribes of wild beasts.
8. Lucretius Book 2: 1077 - Bailey: [1077] This there is too that in the universe there is nothing single, nothing born unique and growing unique and alone, but it is always of some tribe, and there are many things in the same race. First of all turn your mind to living creatures; you will find that in this wise is begotten the race of wild beasts that haunts the mountains, in this wise the stock of men, in this wise again the dumb herds of scaly fishes, and all the bodies of flying fowls. Wherefore you must confess in the same way that sky and earth and sun, moon, sea, and all else that exists, are not unique, but rather of number numberless; inasmuch as the deep-fixed boundary-stone of life awaits these as surely, and they are just as much of a body that has birth, as every race which is here on earth, abounding in things after its kind.
9. Lucretius Book 3 Bailey - [843] And even if the nature of mind and the power of soul has feeling, after it has been rent asunder from our body, yet it is naught to us, who are made one by the mating and marriage of body and soul. Nor, if time should gather together our substance after our decease and bring it back again as it is now placed, if once more the light of life should be vouchsafed to us, yet, even were that done, it would not concern us at all, when once the remembrance of our former selves were snapped in twain. And even now we care not at all for the selves that we once were, not at all are we touched by any torturing pain for them. For when you look back over all the lapse of immeasurable time that now is gone, and think how manifold are the motions of matter, you could easily believe this too, that these same seeds, whereof we now are made, have often been placed in the same order as they are now; and yet we cannot recall that in our mind’s memory; for in between lies a break in life, and all the motions have wandered everywhere far astray from sense.
10. Diogenes of Oinoanda Letter to Antipater - Fr. 63 So, as I was saying, having had my appetite most keenly whetted by all the advantage of the voyage, I shall try to meet you as soon as winter had ended, sailing first either to Athens or to Chalcis and Boeotia. But, since this is uncertain, both on account of the changeability and inconstancy of our fortunes and on account of my old age besides, I am sending you, in accordance with your request, the arguments concerning an infinite number of worlds. And you have enjoyed good fortune in the matter; for, before your letter arrived, Theodoridas of Lindus, a member of our school not unknown to you, who is still a novice in philosophy, was dealing with the same doctrine. And this doctrine came to be better articulated as a result of being turned over between the two of us face to face; for our agreements and disagreements with one another, and also our questionings, rendered the inquiry into the object of our search more precise. I am therefore sending you that dialogue, Antipater, so that you may be in the same position as if you yourself were present, like Theodoridas, agreeing about some matters and making further inquires in cases where you had doubts. The dialogue began something like this: «Diogenes,» said Theodoridas, «that the [doctrine laid down] by Epicurus on an infinite number of worlds is true [I am confident], ................ ................., as [if] ............. Epicurus .......

I am going through and upgrading the "Infinity' forum to emphasize its importance. For the moment it is renamed "The Universe Is Boundless - Infinity And Its Implications," however we need to greatly expand it in the direction of exploring general implications of infinity, of which "life on other worlds" is just one major subtopic. The implications for "how many things there will be of a kind, given the limited shapes of the atoms" are wide and deep. I feel sure there are many good discussions of this, both in nonfiction and in science fiction literature, that ought to be added in for consideration.

Future visitors here will want to check out Lucretius Today Podcast Episode 237 for our strongest focus on Principles of Infinity to date. Feel free to open new discussions in this forum, because we need to flesh out in full the implications of infinity as explored by Epicurus and others of similar mindset.

One question on my mind at the moment relates to question of whether "nature never makes a single thing of a kind" means that "single things can be and are duplicated exactly an infinite number of times, given the infinite universe" or "kinds will have infinite numbers of examples of their kind over the infinite universe, but the individual examples within the kind are not duplicated. In other words, do the principles of infinity imply that the universe has within it: (1) infinite earth-like plants, or (2) infinite beings which are essentially "human," or (3) infinite numbers of humans who look like Epicurus, or (4) infinite numbers of actual Epicurus clones?

What did Epicurus (and do we now, if different) observe here on earth? Are there in fact never two snowflakes exactly the same, even though within the class of snowflakes there are virtually boundless instances of snowflakes? Is there something in the formation of bodies (perhaps related to irrational numbers / fibonacci / fractal issues) that lead to vast numbers of similars but imply that no two natural objects are ever *exactly* duplicated?

I will also add to the above list of cites those we collected for Episode 237.

Quote from Godfrey

Then there's Nietzche's eternal recurrence. I'm not too familiar with it, but it seems to me that this was just a thought experiment and not a serious proposal of the way things are. But I could be wrong on that.

Yes apparently there is a question as to whether he believed this himself or not. And some quick googling links "eternal recurrence" to the STOICS, of whom he generally disapproved, so that's another mark against it. It seems that the Stoic version may have been based on their ideas of fate/necessity, so they may have seen it as inevitable from that point of view, which Epicurus would reject. We need a lot more detail on both Nietzche's version and the Stoic version.

Quote from kochiekoch

But you might end up with infinite multiverses too, all with different laws of physics, so infinity is the limit!

Whenever I hear "multiverse" my blood runs cold, especially with references to "different laws of physics." Apparently "multiverse" needs closer definition too, and anyone who wants to explore that is welcome, but it's not likely to be me. I am firmly in the camp that "universe" should be taken to mean "all that exists" - and if that's what the word means then fine, but I see no reason to change the traditional meaning of "everything." But the "different laws of physics" is a showstopper too, from an Epicurean perspective, it seems to me. Sure different circumstances lead to different outcomes, but that's different circumstances, not different "laws of physics."

At the moment I am thinking that:

1 - "Infinity on the downside" (infinite divisibility) is a total dead end. That kind of thinking leads to the "it's impossible to walk across the room" which we observe to be nonsense.

At the opposite extreme, on the "up-side":

2 - Infinity meaning "different laws of physics" and "anything goes" and anything is possible" is also a non-starter. By definition this is postulating something that we have never seen, and for which we have no evidence, and you might as well start postulating pink elephants on the other side of the moon, and supernatural gods. All that is a total non-starter in Epicurean terms.

The most interesting questions to me seem to be along the lines stated above, including:

1. Whether infinity means that any combination of atoms which *is* possible does in fact happen,
2. Whether any combination which does happen, happens and infinite number of times.
3. Whether the swerve of the atom, or something like irrational numbers / fractals / fibonacci sequences, should make us expect that "classes" of "like" events will happen an infinite number of times, like snowflakes or grains of sand, but that recurrence in IDENTICAL ways should not be expected.

These are basic questions that would have occurred to Epicurus, and the texts maybe already indicate in fact *did* occur to Epicurus, and which we can use to shed light on how to reconstruct our interpretation of what Epicurus in fact taught.

Quote from kochiekoch

The bottom line is, all this stuff is hypothetical, and may not be real at all, but it's mind blowing to contemplate.

Difficult perhaps, but not for that reason something that we should not do. In fact the "recommendation" or "command" that we do spend our time considering it is probably one of the most clear "recommendations" that Epicurus gives. Lots of the other material ends up being "Choose what makes the most sense in terms of pleasure and pain in your own situation." In this case, he's giving a flat statement to students that this is something we should definitely do. I am on board that this is a much-neglected aspect of Epicurean philosophy that needs to be dramatically elevated in focus.

In fact, I would say that the implication of what Epicurus has stated that we should do - MOST OF ALL -- is that we should study the principles of infinity and take them to be correct. We should not consider them to be "mind-blowing' at all, but they should be second nature and taken to be as obvious and easy to understand as anyone for the past 2000 years has taken the incorrect "In the beginning GOD created the heaven and the earth...":

Quote from Epicurus Letter to Pythocles

All these things, Pythocles, you must bear in mind; for thus you will escape in most things from superstition and will be enabled to understand what is akin to them. And most of all give yourself up to the study of the beginnings and of infinity and of the things akin to them, and also of the criteria of truth and of the feelings, and of the purpose for which we reason out these things. For these points when they are thoroughly studied will most easily enable you to understand the causes of the details. But those who have not thoroughly taken these things to heart could not rightly study them in themselves, nor have they made their own the reason for observing them.

Quote from TauPhi

As of now, infinity of the universe (among other infinities) is neither obvious nor easy to understand (or prove) to humanity.

Probably they were neither obvious or easy in the ancient world either, and that was a large part of the undertaking of studying and applying Epicurean philosophy. I don't recall Epicurus or Lucretius of Diogenes of Oinoanda implying that the philosophy was easy -- the closest I recall in the texts to calling it easy or simply was Cicero making a similar comment, and that's in his own words in a statement I'm happy to consider to be one to take with a grain of salt.

But it makes sense to me that Epicurus would start out personally motivated with an interest in where the universe came from and then continue to the end of his life seeing the importance of that conveying that very same issue to others. If you're going to wrestle people out of the jail of supernatural religion you're going to need to replace "god" with something, and "atoms" is only a part of the picture. The rest of the picture as a whole requires "infinity" to be plausible and persuasive to people of normal intelligence - and 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.

All of the perspectives you've expressed in the last several messages Tau Phi, are fine if they work for you, but as you say and know - they are not Epicurean perspectives. Would that the world were filled with people like you, but it's not. It's filled with "lost" people who are in the grip of supernatural religion, and unable to think their own way out of it, just like they were in the time of Lucretius and the time of Diogenes of Oinoanda, not to mention the time of Epicurus.

Epicurean philosophy was then, and can be today, an organized method of bringing answers to such people. If there are individuals like you who don't need its help, and can do it on your own, then that's all to the better for you, but it does nothing for the large numbers of the "hearts in darkness" that Lucretius was talking about in his poem.

Not everyone has to participate in the kind of organized activity that the ancient Epicureans were engaged in, but at the same time, if some don't, then the same patterns of deception and manipulation will go on and on and on and never be challenged. Maybe you see it differently, but to me it is in the nature of things that lone individuals, especially lone individuals who focus on retreating into their own gardens, can do little or nothing to change that situation. And of course I'm not at all referring to you as retreating into your own garden, but referring to the allusion often applied to the ancient Epicureans, which I will never admit to be true. The ancient Epicureans were part of an organized campaign, not lone rangers.

That's the value Epicurus saw in putting together a team and a community, and the same thing holds true today. People have to work together to accomplish anything, and to accomplish things they have to be aware of the situation around them. Again, I would wish that the world were full of Tau Phi's, but there are far too few of them. The great majority fit the description of the people Diogenes of Oinoanda referenced on his wall. They won't and can't think through a system of philosophy for themselves, and they will forever be at the mercy of the organized manipulators if those who know better don't step up to help them.

i guess we'll just have to agree to disagree on our assessment of the general situation and how to deal with it. No one is ever going to force you to accept any position of Epicurus with which you don't agree, but just like in the ancient world the teachings of Epicurus formed the basis of the "movement," and that's where this forum and our organized activities needs to remain focused.

I am not sure you can square that with the "javelin" example in Lucretius, Don. Can you?

I need to know exactly what Aristotle said, but I could see Epicurus agreeing that the 'concept of infinity" is a mental construct only, while at the same time holding that the number of atoms actually existing is uncountable and extends without limit or boundary out into space "forever."

I see the javelin example as highly useful - it illustrates that the limit is in US, not in the reality of space or atoms, because "if we could live forever" we could go on throwing the javelin outward, and counting atoms, forever and ever.

These would be the key sections from Lucretius (Bailey Edition) supporting the conventional view that Epicurus held that the universe is limitless in size in all directions.

[951] But since I have taught that the most solid bodies of matter fly about for ever unvanquished through the ages, come now, let us unfold, whether there be a certain limit to their full sum or not; and likewise the void that we have discovered, or room or space, in which all things are carried on, let us see clearly whether it is all altogether bounded or spreads out limitless and immeasurably deep.

[958] The whole universe then is bounded in no direction of its ways; for then it would be bound to have an extreme point. Now it is seen that nothing can have an extreme point, unless there be something beyond to bound it, so that there is seen to be a spot further than which the nature of our sense cannot follow it. As it is, since we must admit that there is nothing outside the whole sum, it has not an extreme point, it lacks therefore bound and limit. Nor does it matter in which quarter of it you take your stand; so true is it that, whatever place every man takes up, he leaves the whole boundless just as much on every side.

[968] Moreover, suppose now that all space were created finite, if one were to run on to the end, to its furthest coasts, and throw a flying dart, would you have it that that dart, hurled with might and main, goes on whither it is sped and flies afar, or do you think that something can check and bar its way? For one or the other you must needs admit and choose. Yet both shut off your escape and constrain you to grant that the universe spreads out free from limit. For whether there is something to check it and bring it about that it arrives not whither it was sped, nor plants itself in the goal, or whether it fares forward, it set not forth from the end. In this way I will press on, and wherever you shall set the furthest coasts, I shall ask what then becomes of the dart. It will come to pass that nowhere can a bound be set and room for flight ever prolongs the chance of flight. Lastly, before our eyes one thing is seen to bound another; air is as a wall between the hills, and mountains between tracts of air, land bounds the sea, and again sea bounds all lands; yet the universe in truth there is nothing to limit outside.

[984] Moreover, if all the space in the whole universe were shut in on all sides, and were created with borders determined, and had been bounded, then the store of matter would have flowed together with solid weight from all sides to the bottom, nor could anything be carried on beneath the canopy of the sky, nor would there be sky at all, nor the light of the sun, since in truth all matter would lie idle piled together by sinking down from limitless time. But as it is, no rest, we may be sure, has been granted to the bodies of the first-beginnings, because there is no bottom at all, whither they may, as it were, flow together, and make their resting-place. All things are for ever carried on in ceaseless movement from all sides, and bodies of matter, are even stirred up and supplied from beneath out of limitless space.

*Loeb here has* [998] Lastly, one thing is seen before our eyes to be the limit of another; air separates hills and mountains air, earth bounds sea and contrariwise the sea is the boundary of all lands; the universe, however, has nothing outside to be its limit.

OK maybe I misinterpreted your post above -- I was thinking you meant that the Epicureans did not think that there was no limit to the amount of distance you could travel in any direction.