The Presocratic's Logical Path to Atomism

likely (philosophy)
created: 06 Nov 2010; modified: 08 Mar 2017; status: notes; confidence: log; importance: 3

I noticed a comment on LessWrong once:

Democritus may have had an atomic theory, but his reasons for having it were no better than those for the earth, wind, fire and water theory; i.e., wild conjecture.

I wrote a comment opposed to this, and decided to give a more rigorous explanation. (Another example, slamming Aristotle: http://groups.google.com/group/overcomingbiasnyc/browse_thread/thread/901e3c884867c241.)

The basic point of this essay is that basic logic can get us surprisingly far and our ancestors were not that stupid. Finish with open question: where did the Greeks go wrong that they dead-ended after a few centuries? Similar to the question, why didn’t China have the Industrial Revolution rather than England? Tentative suggestion: no emphasis on empirical refutation - point to how the various ontological theories make clear testable predictions like Anaximenes about breath, but apparently weren’t test. Cavil with observation that the situation might be like that for geocentrism/heliocentrism - they knew the arguments in favor of both but lacked the sophisticated instruments necessary to detect stellar parallax and so made the wrong conclusion.

The Presocratic ontological/physics discussions presuppose a few basic principles which rule out some theories and allow others.

One of the most fundamental is nothing from nothing; nothingness never somehow causes a somethingness. Dew does not spontaneously arise out of nowhere, but is, say, present in the air, or is made by cooling some air. This is basically a demand for causality, that nothings cause nothings and somethings cause somethings. It’s hard to imagine what things would be like if you could do something from nothing. Nothing presumably is the same everywhere, so why did something emerge here and not over there? For that matter, why did a proton suddenly appear rather than Elvis? Even if we suggested that only a very specific something is allowed to acausally emerge from nothing (suppose a lobster), then that leads to further perplexities - clearly some nothings have not been blessed with lobsters while some have, but why are the latter different? Why aren’t lobsters emerging at every possible instant in every possible nothingness? They’re supposed to be the same sort of nothing, by definition. (It would be like if most number 2s were even, but a few rare number 2s are actually odd; even if this makes sense, it begs for further explanation of why same is not the same.)

(In this respect, the Presocratics were more hardcore materialists than LessWrong is, because we happily believe in apparently acausal events like quantum decay or phantom particles emerging out of the vacuum energy. We might try to defend ourselves with many-worlds interpretation - everything possible does emerge from nothing! Just in different world-lines - but we still accept all sorts of weirdly immaterial occult phenomenon like magnetic fields or gravity.)

Milesians

Thales

All quotations are from A Presocratics reader, ed. Patricia Curd, trans. Richard D. McKirahan; ISBN 0-87220-326-3, 1996, Hackett Publishing Company, 126pg

Of those who first pursued philosophy, the majority believed that the only principles of all things are principles in the form of matter. For that of which all existing things are composed and that out of which they originally come into being and that into which they finally perish, the substance persisting but changing in its attributes, this they state is the element and principle of things that are…For there must be one or more than one nature out of which the rest come to be, while it is preserved.

However, not all agree about the number and form of such a principle, but Thales, the founder of this kind of philosophy, declares it to be water. (This is why he indicated that the earth rests on water.) Maybe he got this idea from seeing that the nourishment of all things is moist, and that the hot itself comes to be from this and lives on this (the principle of all things is that from which they come to be) - getting this idea from this consideration and also because the seeds of all things have a moist nature; and water is the principle of the nature of moist things.

Anaximander

This does not have a first principle, but this seems to be the first principle of the rest, and to contain all things and steer all things, as all declare who do not fashion other causes from the infinite…and this is divine. For it is deathless and indestructible, as Anaximander says and most of the natural philosophers.

He declares that what arose from the eternal and is productive of [or capable of giving birth to] hot and cold was separated off at the coming to be of this cosmos, and a kind of sphere of flame from this grew around the dark mist about the earth like bark about a tree. When it was broken off and enclosed in certain circles, the sun, moon, and stars came to be.

Anaximenes

Anaximenes…like Anaximander, declares that the underlying nature is one and boundless, but not indeterminate as Anaximander held, but definite, saying that it is air. It differs in rarity and density according to the substances [it becomes]. Becoming finer it comes to be fire; being condensed it comes to be wind, then cloud, and when still further condensed it becomes water, then earth, then stones, and the rest come to be out of these. He too makes motion eternal and says that change also comes to be through it.

Anaximenes…said that the principle is unlimited [boundless] air, out of which come to be things that are coming to be, things that have come to be, and things that will be, and gods and divine things. The rest come to be out of the products of this. The form of air is the following: when it is most even, it is invisible, but it is revealed by the cold and the hot and the wet, and movement. It is always moving, for all the things that undergo change would not change unless it was moving. For when it becomes condensed and finer, it appears different. For when it is dissolved into what is finer, it comes to be fire, and on the other hand air comes to be winds when it becomes condensed. Cloud results from air through felting [sic], and water when this happens to a greater degree. When condensed still more it becomes earth and when it reaches the absolutely densest stage it becomes stones.

As a result he Anaximenes claimed that it is not said unreasonably that a person releases both hot and cold from his mouth. For the breath becomes cold when compressed and condensed by the lips, and when the mouth is relaxed, the escaping breath becomes warm through the rareness.

Pythagoreans

Pythagoras

At the same time as these [Leucippus and Democritus] and before them, those called Pythagoreans took hold of mathematics and were the first to advance that study, and being brought up in it, they believed that its principles are the principles of all things that are. Since numbers are naturally first among these, and in numbers they thought they observed many likenesses to things that are and that come to be…and since they saw the attributes and ratios of musical scales in numbers, and other things seemed to be made in the likeness of numbers in their entire nature, and numbers seemed to be primary in all nature, they supposed the elements of numbers to be the elements of all things that are.

The elements of number are the even and the odd, and of these the latter is limited and the former unlimited. The One is composed of both of these (for it is both even and odd) and number springs from the One; and numbers, as I have said, constitute the whole universe.

The Pythagoreans similarly posited two principles, but added something peculiar to themselves, not that the limited and the unlimited are distinct natures like fire or earth or something similar, but that the unlimited itself and the One itself are the substance of what they are predicated of. This is why they call number the substance of all things.

Philolaus

Nature in the cosmos was fitted together out of unlimiteds and limiters; both the cosmos as a whole and everything in it.

It is necessary that the things that are be all either limiters or unlimiteds, or both limiters and unlimiteds; but they could not always be unlimiteds only. Since, then, it appears that they are neither from limiters only nor from unlimiteds only, it is thus clear that both the cosmos and the things in it were fitted together from both limiters and unlimiteds. And things in their activities make this clear. For, some of them, from limiters, limited; some, from both limiters and unlimiteds, both limit and do not limit; and others, from unlimiteds, will be clearly unlimited.

And indeed all things that are known have number. For without this nothing whatever could possibly be thought of or known.

Eleatics

Xenophanes

Xenophanes used to say that those who say that the gods are born are just as impious as those who say that they die, since in both ways it follows that there is a time when the gods do not exist.

God is one, greatest among gods and men,  not at all like mortals in body or thought.

All of him [God] sees, all of him thinks, all of him hears.

But without effort he [God] shakes all things by the thought of his mind.

He always remains in the same place, moving not at all  nor is it fitting for him to go to different places at different times.

Parmenides

…But nevertheless you will learn these too - that the things that appear / must genuinely be, being always, indeed, all things….

That which is there to be spoken and thought of must be.  For it is possible for it to be  but not possible for nothing to be. I bid you consider this.  For [I bar] you from this first way of inquiry,  but next from the way on which mortals, knowing nothing,  two-headed, wander. For helplessness  in their breasts guides their wandering mind. But they are carried on  equally deaf and blind, amazed, hordes without judgment,  for whom both to be and not to be are judged the same and  not the same, and the path of all is backward-turning.

…being ungenerated it is also imperishable,  whole and of a single kind and unshaken and complete.  Nor was it ever nor will it be, since it is now, all together  one, continuous. For what birth will you seek for it?….What necessity would have stirred it up  to grow later rather than earlier, beginning from nothing?  Thus it must either fully be or not….How could what is be in the future? How could it come to be?  For if it came into being, it is not, nor if it is ever going to be.  In this way, coming to be has been extinguished and destruction is unheard of….mighty Necessity holds it in the bonds of a limit, which pens it in all round,  since it is right for what is to be not incomplete;  for it is not lacking; if it were, it would lack everything.

Such, unchanging, is that for which as a whole the name is to be.

Melissus

Whatever was, always was and always will be. For if it came to be, it is necessary that before it came to be it was nothing. Now if it was nothing, in no way could anything come to be out of nothing.

Now since it did not come to be, it is and always was and always will be, and does not have a beginning or an end, but is unlimited. For if it had come to be it would have a beginning (for having come to be it would have begun at some time) and an end (for having come to be it would have ended at some time). But since it neither began nor ended, it always was and always will be and does not have a beginning or end. For whatever is not entire cannot always be.

Nothing that has both a beginning and an end is either eternal or unlimited. And so whatever does not have them is unlimited.

For if it is [unlimited], it will be one. For if there were two, they could not be unlimited, but would have limits against each other.

Thus it is eternal and unlimited and one and all alike. And it cannot perish, or become greater, or be rearranged, or feel pain or distress. For if it experienced any of these, it would no longer be one. For if it became different, it is necessary that what is is not alike, but what previously was perishes, and what is not comes to be. Now if it should become different by one hair in ten thousand years, it will all perish in all of time. But it is not possible for it to be rearranged, either. For the arrangement that previously was is not destroyed and an arrangement that is not does not come to be. But when nothing either comes to be in addition or is destroyed or becomes different, how could anything that is be rearranged? For if it became at all different, it would indeed already have been rearranged….Nor is any of it empty. For what is empty is nothing, and of course what is nothing would not be. Nor does it move. For it is not able to give way anywhere, but is full. For if it were empty it would give way into the empty. But since it is not empty, it does not have anywhere to give way….

[That he intends what is to be bodiless he indicated, saying;] Now if it is, it must be one. But being one, it must not have body. But if it had thickness, it would have parts and no longer would be one.

For he himself Melissus proves that what is, is indivisible. For if what is is divided, it moves. But if it moved, it would not be. [But by magnitude he means the greatness of its being.]

Zeno of Elea

For it should be added to something else that exists, it would not make it any bigger. For if it were of no size and was added, it [the thing it is added to] cannot increase in size. And so it follows immediately that what is added is nothing. But if when it is subtracted, the other thing is no smaller, nor is it increased when it is added, clearly the thing being added or subtracted is nothing.

But if it exists, each thing must have some size and thickness, and part of it must be apart from the rest. And the same reasoning holds concerning the part that is in front. For that too will have size and part of it will be in front. Now it is the same thing to say this once and to keep saying it forever. For no such part of it will be last, nor will there be one part [of any such part] not related to one another. Therefore, if there are many things, they must be both small and large; so small as not to have size, but so large as to be unlimited.

If there are many, they must be just as many as they are and neither more nor less than that. But if they are as many as they are, they would be limited. If there are many, things that are are unlimited. For there are always others between the things that are, and again others between those, and so the things that are are unlimited.

Pluralists

Anaxagoras

All things were together, unlimited in both amount and smallness. For the small too were unlimited. And when (or, since) all things were together, nothing was manifest on account of smallness. For air and aither dominated all things, both being unlimited. For these are the largest ingredients in the totality, both in amount and in size.

For both air and aither are being separated off from the surrounding multitude and what surrounds is unlimited in amount.

for of the small there is no smallest, but always a smaller (for what is cannot not be). But also of the large there is always a larger, and it is equal in amount to the small. But in relation to itself, each is both large and small.

The things in the single cosmos are not separate from one another, nor are they split apart with an axe, either the hot from the cold or the cold from the hot.

For how could hair come to be from not hair or flesh from not flesh?

From these things as they are being separated off, earth is being compounded; for water is being separated off out of the clouds, earth out of water, and out of the earth stones are being compounded by the cold, and these [ie. stones] move further out than the water.

The Greeks are wrong to accept coming to be and perishing, for no thing comes to be, nor does it perish, but they are mixed together from things that are and they are separated apart. And so they would be correct to call coming to be being mixed together, and perishing being separated apart.

[Empedocles and Anaxagoras say that] other things come to be from the mixture by separation. They differ from one another in that the former makes a cycle of these separations and the latter [supposes that there is] only one. Anaxagoras makes [the principles] infinite, both the uniform parts and the opposites, but Empedocles makes them only the so-called elements. It seems that Anaxagoras thought the principles were infinite because he accepted as true the common opinion of the physicists that nothing comes to be from not being (for it was on account of this that they say all things were together, and the coming to be of such and such a thing is construed as alteration, though some say it is mixture and separation). [They thought this] also because the opposites come to be from one another; they must then have been present in each other. For if everything that comes to be necessarily comes to be either from being or from not being, and it is impossible that it comes to be from not being (for all the physicists agree in this belief), they thought that the alternative followed necessarily, that things come to be out of things that are, that is, out of things in which they are already present, but they are imperceptible to us on account of the smallness of their bulk. On account of this they say that everything has been mixed in everything, because they saw everything coming to be from everything. But things appear to differ from each other and are called by different names from one another based on what is most predominant in extent in the mixture of the infinitely many [components]. Nothing is purely, or as a whole, pale or dark or sweet or flesh or bone, but whatever each contains the most of is thought to be nature of that thing.

Anaxagoras says the opposite of Empedocles about the elements. For he Empedocles says that fire and earth and the others like them are the elements of bodies and everything else is composed of them; but Anaxagoras says the opposite. For the homoiomerous things (I mean flesh and bone and each of the things of that sort) are elements, but air and fire are mixtures of these and of all the other seeds, for each of them is a conglomeration of invisible [amounts] of all the homoiomerous things.

Anaxagoras…says that the elements are unlimited in number. For he makes the elements homoiomerous things, such as bone and flesh and marrow, and each of the others whose parts have the same name [as the whole].

Empedocles

…For these [the four elements] are all equal and of the same age,  but each rules in its own provinces and possesses its own individual character,  bu they dominate in turn as time revolves.  And nothing is added to them, nor do they leave off,  for if they were perishing continuously, they would no longer be.  But what could increase this totality? And where could it come from?  And how [or, where] could it perish, since nothing is empty of these?  But there are just these very things, and running through one another  at different times they come to be different things and yet are always and continuously the same.

Fools. For their thoughts are not far-reaching,  who expect that there comes to be what previously was not,  or that anything perishes and is completely destroyed.

For it is impossible to come to be from what in no way is,  and it is not to be accomplished and is unheard of that what is perishes absolutely.  For each time it will be where a person thrusts it each time.

I will tell you another thing. There is coming to be of not a single one of all  mortal things, nor is there any end of deadly death,  but only mixture, and separation of what is mixed,  and nature is the name given to them by humans.

Atomists

Democritus/Leucippus

Leucippus and his associate Democritus declare the full and the empty [void] to be the elements, calling the former what is and the other what is not. Of these the one, what is, is full and solid, the other, what is not is empty [void] and rare. (This is why they say that what is is no more than what is not, because the void is no less than body is.) These are the material causes of existing things…They declare that the differences [among these] are the causes of the rest. Moreover, they say that the differences are three: shape, arrangement, and position. For they say that what is differs only in rhythm, touching, and turning - and of these rhythm is shape, touching is arrangement, and turning is position. For A differs from N in shape, AN from NA in arrangement, and Z from N in position. Concerning the origin and manner of motion in existing things, these men too, like the rest, lazily neglected to give an account.

Leucippus…did not follow the same path as Parmenides and Xenophanes concerning things that are, but seemingly the opposite one. For while they made the universe one, ungenerated, and limited, and did not even permit the investigation of what is not, he posited the atoms as unlimited and ever moving elements, and an unlimited multitude of shapes among them on the grounds that they are no more like this than like that, since he observed that coming to be and change are unceasing in things that are. Further, he posited that what is is no more than what is not, and both are equally causes of what comes to be. For supposing the substance of the atoms to be compact and full, he said it is being and that is moves in the void, which he called not-being and which he declares is no less than what is. His associate, Democritus of Abdera, likewise posited the full and the void as principles, of which he calls the former being and the latter not-being. For positing the atoms as matter for the things that are they generate the rest by means of their differences. These are three; rhythm, turning, and touching, ie. shape, position, and arrangement. For like is by nature moved by like, and things of the same kind move towards one another, and each of the shapes produces a different composition when arranged in a different compound. Thus, since the principles are unlimited, they reasonable promised to account for all attributes and substances - how and through what cause anything comes to be. This is why they say that only those who make the elements unlimited account for everything reasonably. They say that the multitude of the shapes among the atoms is unlimited on the grounds that they are no more like this than like that. For they themselves assign this as a cause of the unlimitedness.

Those who abandoned division to infinity on the grounds that we cannot divide to infinity and as a result cannot guarantee that the division cannot end, declared that bodies are composed of indivisible things and are divided into indivisibles. Except that Leucippus and Democritus hold that the cause of the primary bodies’ indivisibility is not only their inability to be affected but also their minute size and lack of parts.

…For there is a difficulty in supposing that there is some body, a magnitude, that is everywhere divisible and that this [the complete division] is possible. For what will there be that escapes the division?…Now since such a body is everywhere divisible, let it be divided. What, then, will be left? A magnitude? But this cannot be. For there will be something that has not been divided, whereas we supposed that it was everywhere divisible. But if there will be no body or magnitude left and yet the division will take place, either [the original body] will consist of points and its components will be without magnitude, or it will be nothing at all, so that it could come to be out of nothing and be composed of nothing, and the whole thing would then be nothing but an appearance. Likewise, if it is imposed of points, it will not be a quantity. For when they were in contact and there was a single magnitude and they coincided, they made the whole thing none the larger. For when it is divided into two or more, the whole is no smaller or larger than before. And so, even if all the points are put together they will not make any magnitude…These problems result from supposing that any body whatever of any size is everywhere divisible…And so, since magnitudes cannot be composed of contacts or points, it is necessary for there to be indivisible bodies and magnitudes.

People mean by void an interval in which there is no perceptible body. Since they believe that everything that is is body, they say that void is that in which there is nothing at all…So it is necessary to prove…that there is no interval different from bodies…which breaks up the whole body so that it is not continuous, as Democritus and Leucippus say, and many other natural philosophers, or anything outside the whole body, which is continuous. They say that there would be no change in place (ie. motion and growth), since motion would not seem to exist if there were no void, since what is full cannot admit anything…Some things are seen to contract and be compressed; for example, they say that the jars hold the wine along with the wineskins, since the compressed body contracts into the voids that are in it. Further all believe that growth takes place through void, since the nourishment is a body and two bodies cannot be together. They also use as evidence what happens with ash, which receives as much water as the empty vessel.

Democritus

Democritus believes that the nature of the eternal things is small beings unlimited in multitude. As a place for these he hypothesizes something else, unlimited in size, and he calls the place by the names void, nothing and unlimited [or, infinite] and he calls each of the substances thing and compact and what is. He holds that the substances are so small that they escape our senses. They have all kinds of forms and shapes and differences in size. Out of these as elements he generates and combines visible and perceptible bodies. [These substances] contend with one another and move in the void on account of their dissimilarity and the other differences I have mentioned, and as they move they strike against one another and become entangled in a way that makes them be in contact and close to one another, but does not make anything out of them that is truly one, for it is quite foolish [to think] that two or more things could ever come to be one. The grounds he gives for why the substances stay together up to a point are that the bodies fit together and hold each other fast. For some of them are rough, some are hooked, others concave and others convex, while yet others have innumerable other differences. So he thinks that they cling to each other and stay together until some stronger necessity comes along from the environment and shakes them and scatters them apart. He describes the generation and its contrary, separation, not only for animals but also for plants, cosmoi, and altogether for all perceptible bodies.

When Democritus said that the atoms are in contact with each other, he did not mean contact strictly speaking…but the condition in which the atoms are near one another and not far apart is what he called concat. For no matter what, they are separated by the void.

…when he Democritus declares that the thing is no more than the nothing, he is calling body thing and void nothing, and declaring that this too [void] has some nature and existence of its own.

Indian

“What motivates an atomistic conception of nature? Nyāya-Vaiśeṣika thinkers offer a two-step argument to establish the existence of atoms. The first step is:

Every visible substance is composed of parts.

Therefore, the smallest visible composite thing—say, the smallest mote seen in a sunbeam—is also composed of parts, as it is visible, like a piece of cloth.

There are two presuppositions of this argument: (1) A part of a whole is always smaller in size than a whole—a thesis of which no counter-instance is available in our world; and (2) the parts of the smallest visible composite thing are imperceptible. The second step of the argument runs as follows:

The imperceptible part of the smallest visible thing must possess parts, if it is a composite thing.

However, this division of composite things into its parts must come to an end; otherwise there will be a vicious infinite regress (anavasthā).

So, there must be partless, indivisible, imperceptible things, things which are defined as atoms.

But why is a process of infinite division inadmissible? Because, reason the Nyāya-Vaiśeṣikas, a mountain and a mustard seed will then be equal in size: both being infinitely divisible, they will have countless parts. One might object that the said division will stop only when there is nothing left to be divided, but that this would imply that the whole world can be created out of nothing; and the idea of creation ex nihilo is not viable. But division is possible only when there is a thing to be divided, something which forms the base (ādhāra) of division. A process of division annulling its base is as absurd a notion as digging a hole in empty space. To avoid these inconsistencies, therefore, indivisible atoms must be admitted."

Naturalism in Classical Indian Philosophy, Amita Chatterjee