Episode 010 - The Void And Its Nature
Date: 03/22/20
Link: https://www.epicureanfriends.com/thread/1472-episode-ten-the-void-and-its-nature/
Summary
Section titled “Summary”Episode 010 is a special “coronavirus edition” featuring only Cassius and Martin, as the other panelists were unavailable. The episode introduces the second fundamental building block of Epicurean physics: void. Martin reads the opening passage from Book 1 of Lucretius in Daniel Brown’s 1743 translation, asserting that not all things are formed of close and solid matter — there is void, and understanding this will preserve the inquiring mind from doubt. Cassius compares this to Bailey’s translation and to Epicurus’s own statement in the Letter to Herodotus, where Epicurus insists that bodies and space together constitute the universe, and that without void, motion would be impossible.
The philosophical backdrop is the ancient battle between Epicurus and the Eleatics. Parmenides and his school rejected sense experience entirely, insisting that reality is a single, unchanging unity of being and that all apparent motion and change are illusions. The Stoics replaced Epicurean void with God — positing matter and God rather than matter and void. Cassius and Martin work through Zeno’s famous paradoxes — Achilles and the tortoise, the arrow paradox, and the paradox of place — showing that these were not mere mathematical puzzles but weapons intended to destroy confidence in the senses and in the reality of motion. Martin explains that the Greeks lacked the mathematical tools to resolve these paradoxes, and that Newton and Leibniz’s invention of calculus — the ability to sum an infinite series to a finite result — later provided a formal resolution.
The episode closes with Cassius reading the concluding passage from the Torquatus section of Cicero’s On Ends, in which Epicurus is defended as the true educator: one who taught what actually matters — happiness — rather than wasting time on geometry, astronomy, and music that contribute nothing to the good life. The practical upshot for the ordinary person confronted with a Zenonian logical paradox is, in Martin’s words: either study logic and mathematics deeply enough to expose the flawed premises, or trust the Epicurean canon and simply refuse to play the opponent’s game.
Transcript
Section titled “Transcript”Cassius: Welcome to Episode 10 of Lucretius Today. This is a podcast dedicated to the poet Lucretius, who lived in the age of Julius Caesar and wrote On the Nature of Things, the only complete presentation of Epicurean philosophy left to us from the ancient world. I’m your host Cassius, and together with my panelists from the EpicureanFriends.com forum, we’ll walk you through the six books of Lucretius’ poem and discuss how Epicurean philosophy can apply to you today. Be aware that none of us are professional philosophers, and everyone here is a self-taught Epicurean. We encourage you to study Epicurus for yourself, and we suggest the best place to start is the book Epicurus and His Philosophy by Canadian professor Norman DeWitt.
Today’s episode is the first to be significantly impacted by the coronavirus, so we’ll be more brief than normal, and Martin and I will be carrying the full show while we await several of our normal panelists to return hopefully next week. Today, Martin and I will begin the discussion of the void, mainly by introducing the topic and the implications of it. And then in the next episode, we’ll dive more deeply into the details of the text. So with that, Martin, please read the next section for us from Book One.
Martin: [reads Daniel Brown’s 1743 translation]
And yet all beings are not formed of close and solid parts. In things there is a void, which in your searches into nature will be of use to know. This will preserve your wandering mind from doubt, prevent your constant toil by judging right of nature’s laws, and make my words believed. Wherefore there is a place we call a void, an empty space intangible, or else no bodies could be moved or stir. The quality all bodies have to stop and to oppose does never fail, so that to move would be in vain to try. No body first by yielding would give way. But now we see before our eyes that things move various ways in seas, in earth and in the heaven above. But where there is no void, they would not be deprived of that activity of motion only, but would not be at all, for matter wedged and crowded close on every side had ever been at rest.
Cassius: Thanks, Martin, for reading that. This is going to be our special coronavirus edition of the podcast because it’s only Martin and I. Before we go further than in the reading, what I’m thinking would make the most sense would be to talk in general about why we’re now going to talk about the void. There’s a lot of detail that is going to come out in the passages that follow what Martin just read, not only in this episode, but in some following episodes as we talk about the various theories of matter and void. But before we get into the details of what Lucretius is going to present, it would be helpful, I think, to discuss why this is such an important topic.
And to do that, we can compare what Martin just read — “and yet all beings are not formed of close and solid parts” — we can compare that maybe to what the Bailey translation says. Let me read that one very quickly: “And yet all things are not close pressed on every side by the nature of body, for there is void in things. To have learned this will be of profit to you in dealing with many things. It will save you from wandering in doubt and always questioning about the sum of things and distrusting my words.”
So what Martin has read there is that Lucretius is saying that this is a very important topic that is going to have a lot of application. And we can compare that to a similar statement from the Letter to Herodotus, where Epicurus himself said:
Moreover, the universe is bodies and space, for the bodies exist, sense itself witnesses in the experience of all men. And in accordance with the evidence of sense, we must of necessity judge of the imperceptible by reasoning, as I’ve already said. And if there were not that which we term void and place and intangible existence, bodies would have nowhere to exist and nothing through which to move as they are seen to move. And besides these two, nothing can even be thought of either by conception or by the analogy of things conceivable, such as could be grasped as whole existences and not spoken of as the accidents or properties of such existences.
The significance of this issue is probably much more than we could go into in one podcast, but there was already in Epicurus’ time a lot of controversy about the nature of void. There’s a Wikipedia article on void in philosophy, which says: “Western philosophers have discussed the existence and nature of void since Parmenides suggested it did not exist and used this to argue for the non-existence of change, motion, differentiation, among other things. In response to Parmenides, Democritus described the universe as only being composed of atoms and void.” And this section also says that Aristotle in Book Four of the Physics denied the existence of the void with rejection of finite entities.
So clearly at Epicurus’ time, there was a well-established tradition against Democritus that the void does not exist, which basically means that everything is one. Before we move on to more detail about Parmenides, we could contrast their position to what the Stoics believed. And for that purpose, we can look to David Sedley’s book, Lucretius and the Transformation of Greek Wisdom. And in that book, it says that Diogenes of Oinoanda had listed a series of philosophers and the positions that they had taken on the void. The Stoics believed that the universe was composed of matter and God — not matter and void, but matter and God.
Again, how does that translate into practical reality? Parmenides was the leader of the Eleatic school, and the Wikipedia article on Eleatic philosophy says this. The Eleatics rejected the epistemological validity of sense experience, and instead took logical standards of clarity and necessity to be the criteria of truth. That’s obviously something that we’ll find over and over that Epicurus rejected, because Epicurus upheld the validity of sense experience and did not include logical standards in his criteria of truth. Then the article continues: “The main doctrines of the Eleatics were evolved in opposition to the theories of the early physicalist philosophers who explained all existence in terms of primary matter, and to the theory of Heraclitus, which declared that all existence may be summed up as perpetual change. The Eleatics maintained that the true explanation of things lies in the concept of a universal unity of being. According to their doctrine, the senses cannot cognize this unity because their reports are inconsistent. It is by thought alone that we can pass beyond the false appearances of sense and arrive at the knowledge of being.”
Martin, you jump in there. Would you agree with me that that’s about as contradictory to Epicurus as you could possibly be?
Martin: Yeah, yes.
Cassius: And then a little further on, what Parmenides himself said — in the Wikipedia article on Parmenides — it is stated: “Parmenides claimed there is no truth in the opinion of the mortals. Genesis and destruction, as Parmenides emphasizes, is a false opinion, because to be means to be completely, once and for all. What exists can in no way not exist.” And the quote, a passage from Parmenides, is saying: “For this view, that that which is not exists, can never predominate. You must debar your thought from this way of search, nor let ordinary experience in its variety force you along this way — namely that of allowing the eye, sightless as it is, and the ear full of sound, and the tongue, to rule. But you must judge by means of the reason, logos, the much contested proof which is expounded by me.”
Again, Parmenides, in rejecting the void, is saying everything is one, and the senses cannot be trusted, so you must follow reason and logic to find what is really the truth. And then this is a commentary that’s in that Wikipedia article on Parmenides: “The traditional interpretation of Parmenides’ work is that he argued that the everyday perception of reality of the physical world, as described in Doxa, is mistaken, and that the reality of the world is ‘one being,’ an unchanging, ungenerated, indestructible whole. Under the way of opinion, Parmenides set out a contrasting but more conventional view of the world, thereby becoming an early exponent of the duality of appearance and reality. For him and his pupils, the phenomena of movement and change are simply appearances of a changeless, eternal reality.”
And if those statements are not clear enough about how the Eleatics and Parmenides were arguing for a doctrine that Epicurus rejected, we have the well-known Zeno’s paradoxes. Again, the Wikipedia article on Zeno’s paradoxes says: “Zeno’s paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea to support Parmenides’ doctrine that, contrary to the evidence of one’s senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.”
And examples of these paradoxes are — one is Achilles and the tortoise, which is described by Aristotle in his Physics this way: “In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursuit started, so that the slower must always hold a lead.” And that’s pretty similar to the arrow paradox, which goes this way, again as recounted by Aristotle in Book Six of his Physics: “If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.”
And so Zeno’s paradoxes, in one of its most famous applications, was intended to be a logical proof that motion is impossible. Martin, comment — or do you know what the responses to that were, or what the practical answer to that is?
Martin: I believe some of the more well-known responses involve people who just walk across the room to display motion. Yeah, of course it can be done like this, but it can also be done by describing this from a higher-level model, which then shows what this paradox expresses and how it can easily be overcome. So for example, the Achilles and the tortoise paradox limits itself to the time before Achilles reaches the tortoise. So this whole paradox is set up so that you don’t get to that point — but if you say that time goes by anyway, and calculate simply when Achilles will pass the tortoise, then you see where this paradox comes from. Or put the other way around: the remaining distance Achilles has to run to catch up with the tortoise takes less and less time to fulfill, and this series of smaller and smaller pieces of time then adds up to a finite time — the time that Achilles reaches the tortoise — if he takes a limit to infinity. This is the thing the Greeks didn’t know how to do. So this is something where Newton and Leibniz are credited. And before that, mankind just didn’t know how to do that.
Cassius: Are you able to explain that in more detail? When you say that the Greeks did not know how to do that — what is that?
Martin: Doing calculus. The Greeks were very close to inventing calculus, but they stopped short of it because they didn’t know how to sum up an infinite sum of members.
Cassius: Where you’re going with that is that there were refinements in mathematical theory over time, which produced a method for accounting for this. And that’s what calculus is.
Martin: It’s related to these fundamental problems which the Greeks already were aware of — how to calculate the space under a curve, so to say, or how to determine the slope of a curve. And this one can be done by infinite-series theory.
Cassius: So in my less mathematically inclined analysis, I would see this as an illustration of the big problem, which is that logic and reason — which abstracts out reality and does not account for the whole of reality — is going to lead you to absurd conclusions. If not erroneous, certainly erroneous, and in many cases absurd conclusions, such as that motion is impossible. Which when you say that the Greeks did not know how to do this, they certainly were confident that motion was possible because they saw it in their own lives. And yet when confronted with a logical mathematical argument by someone who was very well versed in mathematical theory, it’s very difficult or impossible within the limits of a particular theory at a particular time to know what the right answer is under the terms of that theory. And what you’re saying is that the calculus that was developed later on extended the mathematical model to be able to account for that.
Martin: Yes, account for that within the terms of this artificially reduced scope of Achilles and the tortoise.
Cassius: The ancient Greeks had other methods to overcome this. Do you know what those were?
Martin: Like you said — you just see Achilles is passing by the tortoise.
Cassius: Right. And ultimately, in many cases, I think that’s where we end up again: this conflict between what happens when a logical deduction appears to be consistent within itself, and yet it’s inconsistent with what we observe in reality outside of that logical construction. And in the Epicurean view of the universe, we go with the reality that we see through the senses, and we don’t let a logical paradox cause us to dissolve into jellyfish and question existence and question everything. We have to have confidence in dealing with attacks like this, because really that’s what these people arguing Achilles and the tortoise had a purpose. It wasn’t just for purposes of mathematical theory. They were arguing towards a goal, which includes arguing that the senses are not reliable — that you have to go by logic above and contrary to the senses. Ultimately that’s the issue here: you can have self-contained, self-consistent systems which produce absurd results.
You can take within a mathematical system and say “let one equal two, let two equal three” — and in that case what is one plus two? Equal five? That would be a self-consistent statement within those premises, but it would be wrong in the way we apply mathematics to the real world. What would you say about an illustration like that, Martin? What is that an example of? Is that just an invalid illustration or does it help anything?
Martin: No, this one is not consistent — that’s why it’s not really a valid example.
Cassius: It’s not consistent with reality to say “let one equal two,” but how do you know that one doesn’t equal two? What are “one” and “two”? Are they not just symbols? And in order to decide “one of anything” you have to go to the particular — you have to say one apple or one orange, one of what you’re talking about — in order to have anything specific to talk about. Is there a word for that in number theory?
Martin: Yeah, algebra — this is covered by algebra. And the way the mathematicians do it, they define an algebraic structure with these particular properties, and this can be done without referring to actual numbers. But in order to make the connection to reality and to make it relevant, then you can identify elements of that algebraic structure as numbers. And it turns out this accurately describes how we do simple calculation. But it’s all a matter of definition — you have a set of axioms, you make some definitions, and everything else then follows by logic out of it. And in order to demonstrate that this whole thing works, what the mathematicians do is they prove that the system is self-consistent — that it doesn’t produce contradictions in itself — and that the set of axioms is minimal.
Cassius: Well, now I know that the Greeks were supposedly into geometry — were they also into algebra?
Martin: Probably, but they did it differently than us. The thing is there’s a connection between geometry and algebra, and even until Newton’s time, Newton himself typically used geometric proofs rather than algebraic proofs.
Cassius: Okay, just looking up Wikipedia under algebra: “Algebra is the study of mathematical symbols and the rules for manipulating these symbols.” This is a very simplistic example of algebra.
The next Zeno paradox was the paradox of place, and Aristotle recorded it as: “If everything that exists has a place, place too will have a place, and so on ad infinitum.” Do you know what that is intended to mean, Martin?
Martin: Yeah, I mean it confounds something material with the void. The void doesn’t need anything — it’s just there as a void, and that makes it different from the bodies. So the mistake done here is that they assign properties which bodies have to the void.
Cassius: Are you saying that that is the assertion of the paradox or is that the answer to the paradox?
Martin: That is how the paradox works — it makes a wrong assignment, that void is like a body, and it’s not.
Cassius: Okay, and just to try to be as clear as possible about that: the paradox of place argument was the Eleatic argument that it’s invalid to say void must exist just because everything has to have a place — because that argument means nothing, since place too would have to have a place. Is that the argument?
Martin: Yeah, that is the argument. And the thing is, if you have a void and then you create something like a void on top of it, it doesn’t matter — you can draw two coordinates on top of each other, it doesn’t matter. And that’s the same thing. The thing is, this whole distinction between body and void is a very simplistic hard-body model, so that at the elementary level these elementary particles do not occupy the same space.
Cassius: Why don’t we try to conclude back on what I think is probably the original point: that the issue of void and place and intangible existence are very important to Epicurus because he was confronting, in his own time, philosophers who were arguing that because void does not exist, things like motion are impossible. And if you follow arguments like that to their logical conclusion, you reach absurd results that are not consistent with reality — which means that as a philosopher you’re going to have to reconcile logic and reality and discuss how they fit together. And if you find an inconsistency, you’re going to have to decide what to do with that inconsistency.
And these philosophers are very good at coming up with games such as Zeno’s paradoxes, which are very confusing to regular people — normal people who are not experts in mathematical argument. And so it’s necessary to have, as part of your philosophy of life, a way to incorporate these paradoxes and understandings into your own day-to-day life. In the sense that you’ve got to live day-to-day — you cannot constantly be like a deer staring into headlights, amazed by the logical intricacy of an argument that appears to tell you that your life is impossible because it tells you that motion is impossible. So therefore what do you do, and how do you deal with something like that? That would be, I think, for some people every bit as fear-inducing or confidence-destroying as any religion or fear of death could be, if they are confronted with the argument that motion is impossible and they can’t figure their way out of that argument. What is your advice to such a person, Martin? What is your advice to a person who reads Zeno’s paradox that motion is impossible and is confused by it?
Martin: If he does not have the mathematical or physical knowledge, he should just follow Epicurus’ advice: don’t play around with logical fallacies. Just ignore them — don’t play the game of the opponent, just refuse to discuss that nonsense.
Cassius: And the last word that you’ve just used is “nonsense.” How does the regular person know that Zeno’s paradox is nonsense?
Martin: This is the one good thing — I mean, normally I don’t particularly like it that Epicurus puts down logic so much, but if you think about it that most people cannot really handle it properly, it’s the best advice. So if someone comes up with logical arguments, just ignore it.
Cassius: All right, I’m trying to bore in on that. How are they to have confidence that they should ignore it? Are they to have confidence because they think Epicurus was a smart guy and they’re just going to rely on Epicurus, or is there some other argument?
Martin: Of course they use the Epicurean canon — so they rely on the senses. Of course, they may then apply whatever logic they can master to be aware that an impression we have from a particular sense input may be misleading. So it’s not that we can necessarily draw every conclusion we would immediately make from the sensory input. But that is the thing: whatever logic comes up with has to match what we perceive through the senses, and if it doesn’t, logic has to explain how our senses come to an apparently different result.
Cassius: But why is the burden on logic, Martin? Isn’t man the rational animal? Isn’t reason and logic an unchallengeable and unchallenged standard of all human life?
Martin: We have a very weird problem with this logic. If we want to have some logical system that is complete and free of contradiction, that simply doesn’t exist. So that means we have to choose: either our modeling is incomplete, or it will lead to contradictions. A logical model can be self-consistent and without contradiction within itself —
Cassius: Yeah, it can be —
Martin: — but at the expense of not being complete. So there will always be possible propositions which are in principle possible within that system of logic but they lead to contradictions. So in order to avoid this contradiction, certain types of statements have to be excluded.
Cassius: Martin, a moment ago you said that the problem with that situation was that the logic would not be complete. Why would you presume that the senses must be incorporated within logic? Doesn’t logic itself have such overriding importance and significance that aren’t all things ultimately logically reconcilable? Why would we allow a sensation to contradict what logic tells us?
Martin: Because the logic has to make some assumptions of course to be applied, and they can be wrong.
Cassius: You know where I’m going, and you know that I’m playing — not exactly a game, but I’m trying to follow this to its logical conclusion. Is it valid for a human being to trust his own senses and to say that he’s going to go with his senses and not with logic? How does the normal person — who is easily mesmerized, I think — later on, not very far in Lucretius, we’ll find that he criticizes Heraclitus for using a lot of dark terminology, and he says that people are easily tickled by things that appear to be intricate formulations, which can tickle their fancy and in a sense mesmerize them very easily, so that they are fooled by things that really don’t make any sense. But what’s ultimately the standard of making sense?
While you’re thinking — let me say this. What came to my mind while I was listening to you think is that these principles are basically the kind of things that the Epicureans were saying should be taught to children. They were saying that they were so basic that everyone should understand them. Let me go back to the ending of the Torquatus section of Cicero’s On Ends, where it says — and let me quote the last couple paragraphs:
If then the doctrine I have set forth is clearer and more luminous than daylight itself, if it is derived entirely from nature’s source, if my whole discourse relies throughout for confirmation on the unbiased and unimpeachable evidence of the senses; if lisping infants, nay even dumb animals, prompted by nature’s teaching almost find voice to proclaim that there is no welfare but pleasure, no hardship but pain — and their judgment in these matters is neither sophisticated nor biased — ought we not feel the greatest gratitude to him who taught this utterance of nature’s voice, and grasps its import so firmly and so fully that he has guided all sane-minded men into the paths of peace and happiness, calmness and repose? You are pleased to think him uneducated. The reason is that he refused to consider any education worth the name that did not help to school us in happiness. Was he to spend his time, as you encourage Triarius and me to do, in perusing poets who give us nothing solid and useful but merely childish amusement? Was he to occupy himself like Plato with music and geometry, arithmetic and astronomy, which, starting from false premises, cannot be true, and which moreover, if they were true, would contribute nothing to make our lives pleasanter and therefore better? Was he, I say, to study arts like these and neglect the master art, so difficult and correspondingly so fruitful — the art of living? No, Epicurus was not uneducated. The real philistines are those who ask us to go on studying till old age the subjects we ought to be ashamed not to have learned in boyhood.
So Martin, what would we tell our boys is the way to deal with a philosopher who walks up to them and says “motion is impossible,” and gives them a logical proof that seems to actually prove that motion is impossible?
Martin: Yeah, the boy has two choices. Either he has some talent with logic and some interest in figuring it out — so then he should study logic and mathematics and scientific modeling, and then he will figure out that these paradoxes are invalid. Or if he doesn’t want to do that, then he needs to stick to the canon and rely on his senses. And if whoever comes by and talks logic which doesn’t match the senses — and without even explaining why his senses contradict the logic — he can ignore this.
Cassius: And in answering that you said something to the effect of invalidating the logic. How do you invalidate logic?
Martin: By analyzing the premises and pointing out where the premise is wrong, or where the scope to which this logic applies is exceeded when drawing the conclusion.
Cassius: Yeah, that’s your “incomplete” word again — where the logic is incomplete and fails to account for each of the particulars that we do observe. All of which just leads us constantly back to the senses as the standard of ultimate reality.
Martin: Yes.
Cassius: And we can probably come to a conclusion for today. But where we’re about to launch into is that Epicurus held that the existence of void was an important part of the analysis that allows us to ultimately invalidate arguments such as that motion is impossible — it’s impossible to walk across a room. And having an understanding of space, empty space and void as the companion to the elements goes a long way to addressing those issues in Epicurus’ philosophy anyway. Anything else come to your mind, Martin?
Martin: No.
Cassius: Okay. Maybe I’ll just include the sentence that you read from as we started: “In things there is a void, which in your searches into nature will be of use to know. This will preserve your wandering mind from doubt, prevent your constant toil by judging right of nature’s laws, and make my words believed.”
So even though we’ll be discussing a lot of detail that might not seem to be all that exciting, the ultimate issue is very, very important. Martin, well thank you for tolerating this day without the fun of having Julie and Elaine and Charles too with us. And I should have plenty of time to edit if the world shuts down from coronavirus in the meantime.
Martin: Yeah, thanks for keeping it going. So it was an enjoyable discussion. Plus, I got the opportunity that I could say something before someone else.
Cassius: That’s exactly right, Martin. Your contributions — especially through the physics part, but all the rest of it too — are very valuable to this. And I know we don’t hear enough of you every week. So always feel free to chime in. And with that, I guess we’ll close. Thanks, then. Thank you, Martin. Talk to you soon. Bye.
Martin: Bye.