But there are many Beings, not just one, which are separated from another by nothing, i. Zeno had argued that, if magnitudes can be divided to infinity, it would be impossible for motion to occur. The problem seems to be that a body moving would have to traverse an infinite number of spaces in a finite time.
By supposing that the atoms form the lowest limit to division, the atomists escape from this dilemma: a total space traversed has only a finite number of parts. As it is unclear whether the earliest atomists understood the atoms to be physically or theoretically indivisible, they may not have made the distinction. The changes in the world of macroscopic objects are caused by rearrangements of the atomic clusters.
Atoms can differ in size, shape, order and position the way they are turned ; they move about in the void, and—depending on their shape—some can temporarily bond with one another by means of tiny hooks and barbs on their surfaces. Thus the shape of individual atoms affects the macroscopic texture of clusters of atoms, which may be fluid and yielding or firm and resistant, depending on the amount of void space between and the coalescence of the atomic shapes.
The texture of surfaces and the relative density and fragility of different materials are also accounted for by the same means. The atomists accounted for perception by means of films of atoms sloughed off from their surfaces by external objects, and entering and impacting the sense organs. Democritus was taken by Aristotle to have considered thought to be a material process involving the local rearrangement of bodies, just as much as is perception.
However, he apparently recognized an epistemological problem for an empiricist philosophy that nonetheless regards the objects of sense as unreal. In another famous quotation, the senses accuse the mind of overthrowing them, although mind is dependent on the senses. The accusation is that, by developing an atomist theory that undermines the basis for confidence in sense perception, thought has in effect undercut its own foundation on knowledge gained through the senses.
Democritus sometimes seems to doubt or deny the possibility of knowledge. The early atomists try to account for the formation of the natural world by means of their simple ontology of atoms and void alone. Leucippus held that there are an infinite number of atoms moving for all time in an infinite void, and that these can form into cosmic systems or kosmoi by means of a whirling motion which randomly establishes itself in a large enough cluster of atoms. It is controversial whether atoms are thought to have weight as an intrinsic property, causing them all to fall in some given direction, or whether weight is simply a tendency for atoms which otherwise move in any and every direction, except when struck to move towards the centre of a system, created by the whirling of the cosmic vortices.
When a vortex is formed, it creates a membrane of atoms at its outer edge, and the outer band of atoms catches fire, forming a sun and stars. These kosmoi are impermanent, and are not accounted for by purpose or design. The earth is described as a flat cylindrical drum at the center of our cosmos.
Species are not regarded as permanent abstract forms, but as the result of chance combinations of atoms. Organisms are thought to reproduce by means of seed: Democritus seems to have held that both parents produce seeds composed of fragments from each organ of their body. Whichever of the parts drawn from the relevant organ of the parents predominates in the new mixture determines which characteristics are inherited by the offspring.
Democritus is reported to have given an account of the origin of human beings from the earth. He is also said to be the founder of a kind of cultural anthropology, since his account of the origin of the cosmos includes an account of the origin of human institutions, including language and social and political organization.
The dialogue elaborates an account of the world wherein the four different basic kinds of matter—earth, air, fire, and water—are regular solids composed from plane figures: isoceles and scalene right-angled triangles. Because the same triangles can form into different regular solids, the theory thus explains how some of the elements can transform into one another, as was widely believed.
In this theory, it is the elemental triangles composing the solids that are regarded as indivisible, not the solids themselves.
It has been suggested that Plato accepted time atoms, i. Simplicius credits the Pythagoreans as well as Plato with a theory composing bodies from plane surfaces. Simplicius also compares Pythagorean views to Democritean atomism, inasmuch as both theories posit a cause for hot and cold, rather than taking these to be fundamental principles, as the Aristotelians do.
A treatise in the Aristotelian corpus probably not by Aristotle himself On Indivisible Lines addresses and refutes a number of arguments offered for the existence of indivisible lines, without naming their author. One of the arguments attacked addresses a Zenonian problem about traversing or touching in succession an infinite series of parts.
The idea that there are indivisible lines offers an alternative to the view that any extended magnitude must be divisible to infinity. Another argument concerns Platonic Forms, and would only apply to those who accepted their existence. It argues that the Form of a triangle presupposes the existence of a Form of a line, and adds that this ideal line cannot have parts, presumably because parts are taken to be prior to the whole they compose and Forms need to have a kind of primacy to be explanatory.
A distinct argument also depends on the idea of priority: it is argued that if the physical elements composing a body are regarded as the ultimate parts prior to a whole, they cannot be further divisible. Although this does not argue for indivisible lines per se , it is used to suggest that the objects of sense as well as those of thought must include things without parts.
It is then concluded that there must be a magnitude without parts, apparently so that it is not further divisible and thus composed of an infinite number of parts. The last argument depends on the idea that mathematicians talk of commensurable lines, and posit a single unit of measurement: this would not be possible if the unit were divisible, because the parts of the unit, if measured, would be measured by the unit measure and it would then turn out to contain multiple units within itself.
An argument in Aristotle Physics 1. Aristotle writes that there is a smallest size of material substrate on which it is possible for the form of a given natural tissue to occur. Blood and bone, say, are all materially composed of given proportions of earth, air, fire, and water: there needs to be a certain minimal amount of these material components present before the form of blood or bone can occur.
This doctrine, while it is surely compatible with the view that the material components are nonetheless infinitely divisible, is sometimes read, by some Neoplatonist commentators and later sources interested in atomist theory, as evidence that Aristotle endorsed the existence of minimal physical parts.
Diodorus Cronus late 4th c. BCE , a member of the supposed Dialectical School, is reported to have offered new arguments that there must be partless bodies or magnitudes. Most reports suggest that his focus was on logical arguments rather than on physical theory: he used arguments that depend on positing mutually exhaustive alternatives. His argument begins from the idea that there is a difference in size between the smallest size at which a given object is visible—presumably from a given distance—and the largest size at which it is invisible.
Unless we concede that, at some magnitude, a body is both invisible and visible or neither , there cannot be any other magnitude intermediate between these two magnitudes. Magnitudes must increase by discrete units. Sextus Empiricus AM It also denies the existence of moving bodies, insisting that bodies move neither when they are in the place where they are, nor when they are in the place where they are not.
Since these alternatives are presented as exhaustive, the conclusion must be that bodies are never moving. However, rather than assert that everything is static, Diodorus took the view that bodies must have moved without ever being in motion: they are simply at one place at one moment, and at another place at another moment. As well as postulating the existence of indivisible smallest bodies and magnitudes, Diodorus seems to have supposed that there are indivisible smallest units of time.
The argument about motion does not quite make it explicit that this is what he is committed to, but it is a reasonable inference: given his insistence that bodies are always at one place or another at any given time, he might well suppose that infinite divisibility of time would open up the threatening possibility of indeterminacy as to whether the change of place has taken place. For those who posit indivisibles as a way to escape paradoxes about infinite divisibility, parallel arguments might equally well have been applied to the problem of completing tasks in an infinitely divisible time.
Sextus Empiricus reports that the Aristotelian Strato of Lampsacus d. Sorabji suggests that Strato merely countenanced the possibility that time could be discrete while space and motion are continuous, without endorsing this position. The Epicureans formed more of a closed community than other schools, and promoted a philosophy of a simple, pleasant life lived with friends.
The community included women, and some of its members raised children. The works of the founder were revered and some of them were memorized, a practice that may have discouraged philosophical innovation by later members of the school. Epicurus takes to heart a problem Democritus himself recognized see 2.
Reasoning to truths about things that are not apparent—like the existence of atoms—depends on the evidence of the senses, which is always true in that it consists of impacts from actually existing films. For particular phenomena, like meteorological events, Epicurus endorses the existence of multiple valid explanations, acknowledging that we may have no evidence for preferring one explanation over another.
It may be that Epicurus was less troubled by any such epistemological uncertainties because of his emphasis on the value of atomist theory for teaching us how to live the untroubled and tranquil life. Denying any divine sanction for morality, and holding that the experience of pleasure and pain are the source of all value, Epicurus thought we can learn from atomist philosophy that pursuing natural and necessary pleasures—rather than the misleading desires inculcated by society—will make pleasure readily attainable.
At the same time, we will avoid the pains brought on by pursuing unnatural and unnecessary pleasures. Understanding, on the basis of the atomist theory, that our fears of the gods and of death are groundless will free us from our chief mental pains. It seems that Democritus did not properly distinguish between the thesis of the physical uncuttability of atoms and that of their conceptual indivisibility: this raises a problem about how atoms can have parts, as evidenced by their variations in shape or their ability to compose a magnitude, touching one another in a series on different sides.
Epicurus distinguished the two, holding that uncuttable atoms did have conceptually distinct parts, but that there was a lowest limit to these. Rather than talking of a motion towards the center of a given cosmos, possibly created by the cosmic vortex, Epicurus grants to atoms an innate tendency to downward motion through the infinite cosmos. The downward direction is simply the original direction of atomic fall.
This may be in response to Aristotelian criticisms that Democritus does not show why atomic motion exists, merely saying that it is eternal and that it is perpetuated by collisions. Moreover, although this is not attested in the surviving writings of Epicurus, authoritative later sources attribute to him the idea that it belongs to the nature of atoms occasionally to exhibit a slight, otherwise uncaused swerve from their downward path.
These responses to Parmenides suppose that there are multiple unchanging material principles, which persist and merely rearrange themselves to form the changing world of appearances. In the atomist version, these unchanging material principles are indivisible particles, the atoms: the atomists are often thought to have taken the idea that there is a lower limit to divisibility to answer Zeno's paradoxes about the impossibility of traversing infinitely divisible magnitudes Hasper Reconstructions offered by Wardy and Sedley argue, instead, that atomism was developed as a response to Parmenidean arguments.
The atomists held that there are two fundamentally different kinds of realities composing the natural world, atoms and void. They move about in an infinite void, repelling one another when they collide or combining into clusters by means of tiny hooks and barbs on their surfaces, which become entangled. Other than changing place, they are unchangeable, ungenerated and indestructible.
All changes in the visible objects of the world of appearance are brought about by relocations of these atoms: in Aristotelian terms, the atomists reduce all change to change of place. Macroscopic objects in the world that we experience are really clusters of these atoms; changes in the objects we see—qualitative changes or growth, say—are caused by rearrangements or additions to the atoms composing them.
While the atoms are eternal, the objects compounded out of them are not. Clusters of atoms moving in the infinite void come to form kosmoi or worlds as a result of a circular motion that gathers atoms up into a whirl, creating clusters within it DK 68B ; these kosmoi are impermanent.
Our world and the species within it have arisen from the collision of atoms moving about in such a whirl, and will likewise disintegrate in time.
Schofield argues that this particular phrase originated with Democritus and not his teacher Leucippus. By putting the full or solid and the void ontologically on a par, the atomists were apparently denying the impossibility of void. Void they considered to be a necessary condition for local motion: if there were no unoccupied places, where could bodies move into? Melissus had argued from the impossibility of void to the impossibility of motion; the atomists apparently reasoned in reverse, arguing from the fact that motion exists to the necessity for void space to exist DK 67A7.
It has been suggested that Democritus' conception of void is that of the temporarily unfilled regions between atoms rather than a concept of absolute space Sedley Some controversy surrounds the properties of the atoms. They vary in size: one report—which some scholars question—suggests that atoms could, in principle, be as large as a cosmos, although at least in this cosmos they all seem to be too small to perceive DK 68A Many kinds of atoms can interlock with one another because of their irregular shapes and hooks at their surface, accounting for the cohesiveness of some compounds.
It is not clear whether the early atomists regarded atoms as conceptually indivisible or merely physically indivisible Furley The idea that there is a smallest possible magnitude seems to suggest that this is the lower limit of size for atoms, although notions like being in contact or having shape seem to entail that even the smallest atoms have parts in some sense, if only mathematically or conceptually.
There are conflicting reports on whether atoms move in a particular direction as a result of their weight: a number of scholars have tried to reconcile these by supposing that weight is not intrinsic to the atoms, but is a result of the centripetal tendencies set up in the cosmic whirl cf. O'Brien ; Furley , pp. Atoms may have an inherent tendency to a kind of vibratory motion, although the evidence for this is uncertain McDiarmid However, their primary movement seems to result from collision with other atoms, wherein their mutual resistance or antitupia causes them to move away from one another when struck.
Democritus is criticized by Aristotle for supposing that the sequence of colliding atoms has no beginning, and thus for not offering an explanation of the existence of atomic motion per se , even though the prior collision with another atom can account for the direction of each individual atomic motion see O'Keefe According to different reports, Democritus ascribed the causes of things to necessity, and also to chance. Democritus apparently recognized a need to account for the fact that the disorderly motion of individual distinct atoms could produce an orderly cosmos in which atoms are not just randomly scattered, but cluster to form masses of distinct types.
He compares this to the winnowing of grains in a sieve, or the sorting of pebbles riffled by the tide: it is as if there were a kind of attraction of like to like DK 68B Although this claim has been interpreted differently e. Taylor b p.
No attractive forces or purposes need be introduced to explain the sorting by the tide or in the sieve: it is probable that this is an attempt to show how apparently orderly effects can be produced without goal-directioned forces or purpose. Democritus regards the properties of atoms in combination as sufficient to account for the multitude of differences among the objects in the world that appears to us. These terms are Aristotle's interpretation of Democritus' own terminology, which has a more dynamic sense Mourelatos This passage omits differences of size, perhaps because it is focused on the analogy to letters of the alphabet: it is quite clear from other texts that Democritus thinks that atoms also differ in size.
Taylor a. The contrast here is intended to be that between real and unreal properties Furley ; cf. Barnes , pp. One report indeed attributes to Democritus a denial that two things could become one, or vice versa DK 68A42 , thus suggesting that combinations are regarded as conventional.
Commentators differ as to the authenticity of Plutarch's report. However, Furley concedes that Plutarch at least understands the earliest atomists to be committed to the view that all combinations of atoms, as much as sensible qualities, should be understood as conventional rather than real Furley pp. This would suggest that everything at the macroscopic level—or, strictly, everything available to perception—is regarded as unreal.
The ontological status of arrangement or combination of atoms for Democritus is a vexed question, that affects our understanding of his metaphysics, his historical relationship to Melissus, and the similarity of his views to the modern primary-secondary quality distinction Wardy ; Curd ; Lee ; Mourelatos ; Pasnau Later atomists cite as evidence for this the gradual erosion of bodies over time.
These films of atoms shrink and expand; only those that shrink sufficiently can enter the eye. It is the impact of these on our sense organs that enables us to perceive. Visible properties of macroscopic objects, like their size and shape, are conveyed to us by these films, which tend to be distorted as they pass through greater distances in the air, since they are subject to more collisions with air atoms.
The properties perceived by other senses are also conveyed by contact of some kind. Democritus' theory of taste, for example, shows how different taste sensations are regularly produced by contact with different shapes of atoms: some atoms are jagged and tear the tongue, creating bitter sensations, or are smooth and thus roll easily over the tongue, causing sensations of sweetness. Theophrastus, who gives us the most thorough report of Democritus' theory, criticizes it for raising the expectation that the same kinds of atoms would always cause similar appearances.
However, it may be that most explanations are directed towards the normal case of a typical observer, and that a different account is given as to the perceptions of a nontypical observer, such as someone who is ill. Democritus' account why honey sometimes tastes bitter to people who are ill depends on two factors, neither of which undercut the notion that certain atomic shapes regularly affect us in a given way. One is that a given substance like honey is not quite homogeneous, but contains atoms of different shapes.
While it takes its normal character from the predominant type of atom present, there are other atom-types present within. The other is that our sense-organs need to be suitably harmonized to admit a given atom-type, and the disposition of our passageways can be affected by illness or other conditions.
Thus someone who is ill may become unusually receptive to an atom-type that is only a small part of honey's overall constitution. Other observed effects, however, require a theory whereby the same atoms can produce different effects without supposing that the observer has changed.
The change must then occur in the object seen. Aristotle gives this as the reason why color is not ascribed to the atoms themselves.
Lucretius' account of why color cannot belong to atoms may help clarify the point here. We are told that if the sea's atoms were really blue, they could not undergo some change and look white DRN 2.
This seems to assume that, while an appearance of a property P can be produced by something that is neither P nor not-P, nonetheless something P cannot appear not-P. Since atoms do not change their intrinsic properties, it seems that change in a relational property, such as the relative position of atoms, is most likely to be the cause of differing perceptions.
In the shifting surface of the sea or the flutter of the pigeon with its irridescent neck, it is evident that the parts of the object are moving and shifting in their positional relations. By ascribing the causes of sensible qualities to relational properties of atoms, Democritus forfeits the prima facie plausibility of claiming that things seem P because they are P.
Much of Theophrastus' report seems to focus on the need to make it plausible that a composite can produce an appearance of properties it does not have. Democritus is flying in the face of at least one strand of commonsense when he claims that textures produce the appearance of hot or cold, impacts cause colour sensations. The lists of examples offered, drawing on commonsense associations or anecdotal experience, are attempts to make such claims persuasive. Each atom, according to Jaina philosophy, has one kind of taste , one smell , one color , and two kinds of touch , and can exist in one of two states , "subtle" in which case they can fit in infinitesimally small spaces and "gross" in which case they have extension and occupy a finite space.
Aristotle explicitly credited Leucippus with the invention of Atomism, although no fragments of his writings survive, and we have only a few fragments of the writing of Democritus and most of that second-hand.
Democritus and Leucippus taught that the hidden substance in all physical objects consists of different arrangements of atoms and void. Both atoms and the void were never created , and they will be never ending. The void is infinite and provides the space in which the atoms can pack or scatter differently.
The different possible packings and scatterings within the void make up the shifting outlines and bulk of the objects that we feel, see, eat, hear, smell, and taste. While we may feel hot or cold, "hot" and "cold" actually have no real existence , but are simply sensations produced in us by the different packings and scatterings of the atoms in the void that compose the object.
Plato objected to the mechanistic purposelessness of the Atomism of Democritus , arguing that atoms just crashing into other atoms could never produce the beauty and form of the world.
For Plato , the four simple bodies fire, air, water and earth were geometric solids , the faces of which were, in turn, made up of triangles. Since the simple bodies could be decomposed into triangles, the triangles could be reassembled into atoms of different elements and substances. Aristotle asserted that the elements of fire, air, earth, and water were not made of atoms, but were continuous.
He considered the existence of a void , which was required by atomic theories, to violate physical principles , and speculated that change took place not by the rearrangement of atoms to make new structures, but by transformation of matter from what it was in potential to a new actuality. Aristotle represented the first important movement away from Atomism.
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