Epicurus On The Issue of The Universe Being Infinite In Space

  • Text references:

    Letter to Herodotus:[41] ... Moreover, the universe is boundless. For that which is bounded has an extreme point: and the extreme point is seen against something else. So that as it has no extreme point, it has no limit; and as it has no limit, it must be boundless and not bounded.

    [42] Furthermore, the infinite is boundless both in the number of the bodies and in the extent of the void. For if on the one hand the void were boundless, and the bodies limited in number, the bodies could not stay anywhere, but would be carried about and scattered through the infinite void, not having other bodies to support them and keep them in place by means of collisions. But if, on the other hand, the void were limited, the infinite bodies would not have room wherein to take their place.
    [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.
    Lucretius:Book One:

    [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.

    [1002] The nature of room then and the space of the deep is such that neither could the bright thunderbolts course through it in their career, gliding on through the everlasting tract of time, nor bring it about that there remain a whit less to traverse as they travel; so far on every side spreads out huge room for things, free from limit in all directions everywhere. [

    1008] Nay more, nature ordains that the sum of things may not have power to set a limit to itself, since she constrains body to be bounded by void, and all that is void to be bounded by body, so that thus she makes the universe infinite by their interchange, or else at least one of the two, if the other of them bound it not, yet spreads out immeasurable with nature unmixed. But space I have taught above spreads out without limit. If then the sum of matter were bounded, neither sea nor earth nor the gleaming quarters of heaven nor the race of mortal men, nor the hallowed bodies of the gods could exist for the short space of an hour. For driven apart from its unions the store of matter would be carried all dissolved through the great void, or rather in truth it could never have grown together and given birth to anything, since scattered abroad it could not have been brought to meet.

    For our mind now seeks to reason, since the sum of space is boundless out beyond the walls of this world, what there is far out there, whither the spirit desires always to look forward, and whither the unfettered projection of our mind flies on unchecked.

    [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.

    [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.
  • The idea of the universe as infinite is an interesting one. What is the nature of the universe and what are its limits? If the universe has always existed what are its boundaries? If the universe has a beginning as a big bang what does it expand into? Both are good questions. I bought a copy of the Penguin Latham translation of Lucretius in the 1970s as a science student. I recently came across this chapter by Frederik Bakker on “The End of Epicurean Infinity: Critical Reflections on the Epicurean Infinite Universe”

    The End of Epicurean Infinity: Critical Reflections on the Epicurean Infinite Universe
    In contrast to other ancient philosophers, Epicurus and his followers famously maintained the infinity of matter, and consequently of worlds. This was inferred…

    However the models of classical physics are different to models post Einstein. So I suppose the idea of the universe as infinite has a different meaning depending on the model used? So we have the ideas of Albert Einstein of the relation of space to time. Special Relativity has time as a dimension and so we live in four dimensions. With his General Theory of Relativity the universe does not have an edge and does not expand into anything. Space may be curved. This is discussed well by the physicist Sabine Hossenfelder in her YouTube talk: “What does the universe expand into? Do we expand with it?” With Einstein and the models of modern physics the universe does not expand into anything. It would be interesting to have an imaginary conversation between Albert Einstein, Epicurus and Lucretius in the garden. What would they say?

  • Thank you for posting not only the thoughtful post but because it exposes that the cites supposedly listed in the first post have somehow disappeared! I will work to fix that - thanks!

  • At the risk of seeming frivolous, (comes with age :P ) here's a moment with Woody Allen that may add something to this topic.

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    With Einstein and the models of modern physics the universe does not expand into anything.

    This statement is misleading. As of current models and observations, both the universe and the space in which it exists are in accelerated expansion. The expansion of space seems to add so much that the distances between our galaxy and the most distant still observable galaxies seem to increase with more than the speed of light. The continued dilution of matter on the largest scale, the increase in entropy and the further development of stars will make the universe much different from now.

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    both the universe and the space in which it exists are in accelerated expansion

    This is interesting. The universe has been defined as all existing matter and space considered as a whole, so is there anything outside the universe for it to expand into? If there is something outside the universe what is it?

    There is a great deal of discussion on what does the universe expand into? This is discussed by the physicist Sabine Hossenfelder in her interesting YouTube video “What does the universe expand into? Do we expand with it?”, and also in her 2022 book “Existential Physics: A Scientist’s Guide to Life’s Biggest Questions.”

    Are you possibly referring to the no-boundary proposal which avoids the Big Bang singularity by replacing time with space outside the early universe? Hossenfelder says outside because it makes little sense to use before if there was no time. In the no-boundary proposal, the universe is embedded into space. I find the concept of a space outside the universe for the universe to expand into difficulty to conceive since all space is surely within the universe? Cosmology is very interesting.

  • I find the concept of a space outside the universe for the universe to expand into difficulty to conceive since all space is surely within the universe?

    And to me this is an issue of word-play as much as it is of anything else. If we are defining the "all" as everything, then it seems to me the only way you end up with these seemingly-conflicting positions is by ignoring the definition issue. If, like Lucretius and his javelin, the universe is "expanding" - then whatever it is expanding into would seem to be by definition part of the universe.

    I can't help but being suspicious that there is something more behind these formulations than good-faith science. Every time I have tried to dig deeper into these questions it seems to me I have found that the issue is that those who are postulating some kind of weirdness are fudging that they are considering the universe as a whole to be "what is observable as of now" which is NOT the definition of "the all" traditionally meant as the definition of "the universe."