1.53 Ancient Atomism

Section 53 (first updated 2.14.2021)

The Atom as Void: The Void of Non-Void

“The atom as void is the void of non-void—nothing as something.”
—Alan Watts¹

To speak of the atom as void is not to deny void, but to dissolve the opposition between atom and void altogether. The phrase “the void of voidness” means precisely the dismissal of void as mere absence. Void is not a negation standing outside being; it is the internal condition that allows being to appear at all. In this sense, nothing is not the opposite of something, but the condition under which something can be determined.

Pre-Socratic Atomism and Aristotle’s Engagement

It is easy to say that Aristotle simply rejects atomism, but his engagement with it is far more intricate. Aristotle recognizes that atomism captures something essential about ontological principles, even if it fails to synthesize them adequately. Atomism is incomplete, but incompleteness is not the same as error. This is similar to how Anaximenes is not wrong in identifying air as an element, yet mistaken in treating it as the ultimate substance of the universe.

The true ontological difficulty is not analysis, but synthesis: how to reunite analytically separated principles so that their relation exhibits the same unity they possessed prior to conceptual distinction. Atomism catalogues nature into fundamental abstractions—atom and void—without fully explaining how these abstractions together form a single, unified conception of reality.

The very word substance points toward this problem. Sub-stance means that which “stands under” or supports.² Atomists understood substance as an underlayment of nature, but they conceived this underlayment too literally, as though it were a passive ground upon which change occurs—like the earth supporting one’s feet.

This view resembles what George Berkeley later critiques in material realism: the idea that matter functions as a kind of inert ground beneath experience, rather than as something inseparable from activity and perception.³ When substance is treated merely as a support, it becomes detached from causation itself.

Substance, Causation, and Activity

This misunderstanding extends to causation. Cause and effect are often conceived as two separate things, one producing the other from outside—my hand causes the ball to move, but my hand is not the ball. Atomism attempts to resolve this by saying both are ultimately composed of the same atomic material. But this answer only relocates the problem; it does not explain how substance itself is active.

Substance loses its character as an active principle when it is reduced to a static bedrock. Atomism identifies substance but fails to articulate how it is an agent of change. As Alan Watts frequently notes, causation is not the pushing of one thing by another, but a single event seen from two perspectives.⁴

Aristotle on Atom and Void

Aristotle summarizes atomist doctrine as follows:

“Leucippus and his associate Democritus declare the full and the empty [void] to be the elements, calling the former ‘what-is’ (to on) and the latter ‘what-is-not’ (to mē on). … 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.”
(Metaphysics 1.4, 985b4–19 = DK 67A6)

Here, Aristotle acknowledges that atomists grasped something profound: being and non-being are equally necessary. The void is “no less” than body. The material cause refers not simply to matter as stuff, but to whatever fulfills the function of making something what it is.

However, Aristotle reverses the atomists’ explanatory order. For him, Being and Nothing are not abstractions derived from material arrangements; rather, they are logical principles that function as efficient causes of material determination. Atomism, by contrast, treats Being and Nothing as names given after material arrangements are conceived, thereby obscuring the causal role of form and negation.

Atom, Void, and Indivisibility

The Greek word atomos means “uncuttable” or “indivisible.” The atom represents the principle of fixity: what remains what-is. Yet the void also expresses indivisibility, because it cannot be divided into parts without becoming something. This is why the atomists claim that “what-is is no more than what-is-not.”

The void (kenon), meaning “empty” or “rare,” is not antithetical to the atom. As McKirahan notes, the atom and the void are equally real as material principles.⁵ Aristotle himself observes:

“They also use as evidence what happens with ash: it takes no less water to fill a jar that contains ashes than it does to fill the same jar when it is empty.”
(Physics 4.6, 213a27–b22 = DK 67A19)

This example shows that “emptiness” is not the absence of reality, but a different mode of occupation.

Difference of Form, Not Matter

The atom and the void do not differ in material, but in form and function. Difference in form does not imply separate substances. To differ in material would mean that the same activity is divided into distinct entities. Instead, atom and void are inverse determinations of the same activity.

The atom is “full” and “compact” because its function is to remain what-is—to hold, fix, and stabilize activity. The void is “empty” and “rare” because its function is to be what-is-not—to allow activity to move, differentiate, and transform. Both are the same matter operating under opposing determinations.

Thus, atom and void are not two things standing side by side. They are the dual expressions of a single ontological process: fixation and release, presence and absence, being and becoming.

Footnotes

1. Alan Watts, lecture on Buddhism and the nature of nothingness (timestamp approx. 14:02:45).
2. Alan Watts, The Nature of God, lecture series.
3. George Berkeley, A Treatise Concerning the Principles of Human Knowledge (1710).
4. Alan Watts, lectures on causation and non-duality.
5. Richard McKirahan, Philosophy Before Socrates, p. 306.

Atoms not perceptible

Atomism, Imperceptibility, and the Problem of Qualitative Emergence

Fundamental to atomic theory is the claim that all atoms are made of the same paraphernalia, yet the so-called “stuff” of which atoms are composed possesses no perceptible qualities. The atom is not, in the first instance, hard or soft, hot or cold, wet or dry. These are properties of macroscopic, perceptible compounds of atoms and depend on atomic arrangement rather than on the nature of the atom as a component.

This raises the central difficulty: how does the atom, as an imperceptible component, constitute a perceptible compound?

Closely related is a second question: What is the atom itself made of? Atomists appeal to shape, size, position, and arrangement, yet these are already differentiated qualities. What, then, is the substance that underlies these determinations and makes them the “stuff” of atoms at all?

This section exposes the failure of atomism to explain how perceptible qualities arise from an imperceptible basis. The reason for this failure is not merely empirical, but conceptual. Atomists did not take mind—or intelligibility—as the basis for the emergence of the perceptible. Instead, they abstracted external relations between things as they appear to perception (concave/convex, hooked/smooth, large/small) and treated these abstractions as fundamental explanatory principles. In doing so, they inverted the order of explanation: perceptual relations were made prior to perceptibility itself.

Aristotle summarizes Democritus’ position as follows:

“They have all kinds of forms and shapes and differences in size. Out of these as elements he generates and forms visible and perceptible bodies. These substances are at odds with one another and move in the void because of their dissimilarity and the other differences mentioned. As they move, they strike 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 are that the bodies fit together and hold each other fast: some are rough, some hooked, others concave or convex, and others have innumerable differences. Thus they cling together until some stronger necessity from the environment scatters them apart.”¹

Here, generation and corruption are explained entirely through mechanical fitting, yet Aristotle objects that mere contact cannot yield true unity. A compound produced this way is only an aggregate, not a genuinely unified being.

Whitehead: Discernible and Indiscernible Time

This difficulty can be clarified through Whitehead’s distinction between the discernible and the indiscernible.² The atom exhibits the activity of hing—a holding-together, a fixation—and is therefore definite and discernible. Atomists thus associated atomic activity with physical minuteness and determinacy.

The void, however, was associated with infinity and indeterminacy, making it difficult to classify. Because void was identified with what-is-not, it was treated as passive, merely the condition for motion rather than an active principle. This asymmetry led atomists to assume that determination flows from atom to void, rather than recognizing both as co-constitutive processes.

Simplicius reports:

“While the Eleatics made the universe one, immovable, ungenerated, and limited, and did not permit investigation of what-is-not, Democritus posited atoms as infinite and ever-moving elements, with an infinite number of shapes, on the grounds that they are no more like this than like that, and because coming-to-be and change are unceasing.”³

The atom is thus the form of a relation as component, but as substratum it remains eternal and without perceptible qualities. Perceptibility belongs not to the atom, but to its relational expression.

Intelligibility over Perceptibility

This conclusion was already recognized in antiquity. Sextus Empiricus writes:

“Plato and Democritus supposed that only intelligible things are true. Democritus held this view because there is by nature no perceptible substrate, since the atoms, which combine to form all things, have a nature deprived of every perceptible quality.”⁴

The ultimate nature of atom and void is therefore intelligible, not perceptible. The perceptual character of atoms arises only at the level of compounds—as a result of relations, not as intrinsic features.

The claim that there is an infinite number of atoms follows from the claim that there is an infinite number of shapes. Shapes themselves are relations, and number is the abstraction that assigns these relations determinacy. Aristotle observes:

“Since the bodies differ in shape, and the shapes are infinite, they declare the simple bodies to be infinite too. But they did not determine further what the shape of each element is, beyond assigning a spherical shape to fire, and distinguishing air and water by largeness and smallness.”⁵

This brings us to the most essential ontological question: How can something without quality bear qualities?

Quality, Change, and the Limits of Atomism

Atomists were compelled to deny perceptible qualities to atoms in order to explain qualitative change at the macroscopic level. Iron, for instance, changes from gray to red when heated. If iron were composed of gray atoms, this change would be inexplicable. By denying color to atoms, atomists could explain color as a function of atomic structure and motion.

In this sense, the quality-less atom functions as a standard of invariance that allows qualitative change to be intelligible. Yet atomism never explains how this invariant basis actively participates in the generation of qualities rather than merely permitting their rearrangement.

The failure lies in separating the subjective constitution of phenomena from the universal principles implicit in that constitution. Perception and intelligibility are not separable domains. Attempting to explain perceptibility without reference to mind—or intelligibility—results in an explanatory gap that atomism cannot bridge.

Footnotes

1. Aristotle, On Democritus, quoted by Simplicius, Commentary on Aristotle’s On the Heavens 295.1–22 = DK 68A37.
2. Alfred North Whitehead, Process and Reality, esp. on discernible vs. indiscernible actuality.
3. Simplicius, Commentary on Aristotle’s Physics 28.4–26 = DK 67A8, 68A38.
4. Sextus Empiricus, Against the Mathematicians 8.6 = DK 68A59.
5. Aristotle, On the Heavens 3.4, 303a11–15 = DK 67A15.

Atomism and the Problem of Qualitative Emergence

Democritus and Leucippus base their account of alteration and coming-to-be on separation and combination: coming-to-be and perishing occur through separation and combination, while alteration occurs through arrangement and position. Because they held that truth lies in appearance—and because appearances are opposite and infinite—they posited an infinite number of shapes. This allowed them to explain why, through changes in composition, the same thing appears opposite to different people, why it changes when a small amount is added, and why it appears completely different when a single element shifts position. Aristotle illustrates this by noting that tragedy and comedy are composed of the same letters.¹

In this way, the atomists grasped that change is fundamental in determining perceptual qualities. They investigated change not merely as accidental motion, but as the activity through which objects appear as they do. From this investigation, they identified at least three fundamental modes of change.

Aristotle reports:

“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.”²

Objects of appearance are therefore in constant motion and relation with one another. The atomists agree that relations determine perceptual qualities, and that the way objects appear depends on the nature of their changes. However, when attempting to identify the fundamental relations of change that determine appearances, atomism encounters serious conceptual difficulties.

Simplicius summarizes their position:

“For positing the atoms as matter for existing things, they generate the rest by means of their differences—rhythm, turning, and touching, that is, shape, position, and arrangement. For by nature like is moved by like, and things of the same kind move toward one another, and each shape produces a different condition when arranged in a different combination. Since the principles are infinite, they reasonably promised to account for all attributes and substances. This is why they say that only those who make the elements infinite account for everything reasonably.”³

This raises a central problem: How can atoms, which fundamentally lack perceptible qualities, nevertheless constitute the physical qualities of perceptible objects?

The atomists appear to advance a logically consistent claim: activities themselves do not possess perceptible qualities. An atom, understood fundamentally, is an activity, and only when activities form compounds do perceptible qualities emerge. The activity itself must remain without specific quality, because possessing a quality would already make it a determinate compound. In order to remain pure activity, the atom must be quality-less while simultaneously serving as the source of qualities.

However, atomism reverses the logical order of explanation. It treats activity as a consequence of the atomic unit rather than recognizing the unit as a fixation of activity. Activity is thus seen as coming after the unit, instead of the unit being a stabilized moment within activity itself.

Size and shape, for example, govern the kinds of compounds in which an atom can participate, determining which configurations are possible.⁴ Yet size and shape are already relational abstractions, not explanatory ultimates.

Indivisibility is meant to explain how process can be physical without dissolving into nothingness. The atom remains indivisible so that activity may persist as determinate rather than collapsing into indefinite flux. Nevertheless, atomism does not explain why indivisibility itself should generate determinate qualities, rather than merely preserving motion.

The unresolved tension remains: how an imperceptible, quality-less principle can actively generate perceptible qualities without already presupposing intelligibility or form as primary. This is the point at which atomism gestures toward, but does not yet articulate, a process-based or mind-involving ontology.

Footnotes

1. Aristotle, On Generation and Corruption 1.1, 315b6–15 = DK 67A97.
2. Aristotle, Metaphysics 1.4, 985b4–19 = DK 67A6.
3. Simplicius, Commentary on Aristotle’s Physics 28.4–26 = DK 67A8, 68A38.
4. Cf. Aristotle’s discussion of atomic size and shape in Metaphysics and On the Heavens.

Determinacy and necessity are often conflated, yet they name fundamentally different modes of explanation. Necessity refers to what must be the case given a set of conditions or laws; it expresses constraint, compulsion, or inevitability. Determinacy, by contrast, refers to what is the case in a definite manner, without implying that it could not have been otherwise. Something can be fully determinate—having a specific form, structure, or outcome—without being necessary in the strong sense of logical or metaphysical compulsion. Determinacy concerns how something is actual; necessity concerns why it could not be otherwise.

In classical metaphysics, especially in atomism and later mechanistic physics, determinacy is frequently treated as a consequence of necessity. Events are thought to be determinate because they are governed by necessary laws; outcomes are fixed because causes compel effects. Yet this reverses the deeper ontological order. Determinacy does not arise because nature is necessary; rather, necessity is an abstraction derived from patterns of determinacy observed across repeated processes. Laws do not produce determinacy; laws summarize it. What appears as necessity is the stabilization of determinacy across many instances.

This distinction becomes clear when considering change. A particular event—such as an atom occupying a position, a molecule binding, or a cell dividing—is determinate: it happens in one way rather than another. But this does not mean it was necessary in the sense that no other outcome was possible. Prior to its occurrence, multiple possibilities were open; after its occurrence, one possibility has been actualized. Determinacy is therefore retrospective, while necessity is projective. Necessity speaks from the standpoint of completed explanation; determinacy belongs to the moment of becoming.

In process-oriented ontologies, such as those suggested by Aristotle, Whitehead, and implicitly by modern physics, determinacy emerges from a field of indeterminacy. The actual is carved out of the possible, not compelled by it. This is why determinacy always bears the trace of contingency: it is precise, but not logically forced. The world is determinate without being rigid; structured without being closed. Necessity, by contrast, belongs primarily to relations among abstractions—definitions, logical implications, mathematical identities—rather than to concrete events themselves.

This distinction also clarifies the status of physical law. A law of nature expresses necessity only insofar as it describes invariant relations under specified conditions. But the conditions themselves are not necessary; they are given. The law does not dictate that this particle must exist, or this event must occur, but rather that if such an event occurs, it will do so in a determinate way. Necessity governs form; determinacy governs existence. Confusing the two leads to the false conclusion that the universe is a closed system of inevitabilities rather than an open system of structured becoming.

At the epistemological level, determinacy corresponds to what can be known as this rather than that, while necessity corresponds to what must be known if something is to count as knowledge at all. A fact can be determinate without being necessary for understanding; conversely, a necessary principle may be entirely indeterminate with respect to concrete outcomes. This is why epistemology proceeds from the unknown to the known: determinacy arises first in experience, while necessity is inferred afterward as a rational constraint on explanation.

In ethical and existential contexts, the difference is equally crucial. Human actions are determinate—we act in specific ways at specific times—but they are not strictly necessary. To reduce action to necessity is to deny responsibility; to deny determinacy is to deny intelligibility. Freedom, properly understood, lies not in the absence of determinacy but in the absence of necessity. One acts freely when one’s action is fully determinate yet not compelled.

Finally, the distinction between determinacy and necessity mirrors the deeper ontological contrast between being and nothing that runs throughout your work. Determinacy is the mark of being—something is this rather than that. Necessity, however, belongs to the void-like structure of reason itself, which excludes alternatives by definition. Being emerges as determinate against the background of nothing; necessity emerges as the logical shadow cast by repeated determinations. The universe, therefore, is not necessary—but it is intelligible. It does not have to be this way—but having become this way, it is precise, structured, and knowable.

Infinity and Indivisibility

Leucippus held that atoms are exceedingly small—indeed, “invisible because of the minuteness of their size.” Democritus, by contrast, maintained that atoms could in principle be of any size whatsoever, while nonetheless insisting, like Leucippus, that atoms are imperceptible to the senses. This dual claim gives rise to a striking tension in atomist thought: if atoms admit of all possible differences in size, then some atoms must be massive, even cosmically so. Indeed, Democritus explicitly allows that there could be an atom the size of a kosmos itself.¹ How, then, can the atom be in principle the largest conceivable magnitude and yet remain too small to be seen?

The difficulty arises because the size of the atom is not a merely empirical question but is fundamentally informed by the concept of infinity. For Democritus, the eternal constituents of reality are “small substances” (ousiai) infinite in number, existing within something else that is itself infinite in extent, namely the void. He calls this place “the void,” “nothing” (ouden), and “the unlimited” or “the infinite,” while each substance is called “hing” (den), “the compact,” and “what-is.”² Although the substances are said to be imperceptible due to their smallness, this smallness is not a simple quantitative magnitude but an ontological determination: atoms escape the senses not because they are merely tiny bodies, but because they lack the perceptible qualities that would make them sensible objects.

The indivisibility of atoms is therefore not a trivial claim and was a subject of debate even in antiquity. According to Simplicius, those who rejected infinite divisibility did so because division to infinity could not be completed and thus could not guarantee the coherence of bodies. Leucippus and Democritus, however, argued that the primary bodies are indivisible not merely because of their minuteness, but because they are incapable of being affected and therefore lack internal parts.³ Indivisibility, in this sense, is not only physical but causal: what has no parts cannot be altered internally.

This account, however, appears circular. Atoms are said to be indivisible because they have no parts, yet we know they have no parts only because they are said to be indivisible. The paradox sharpens when we consider the atomist claim that bodies are composed of indivisible things and are divided into indivisibles. How can extended bodies be composed of entities that themselves have no divisible extension?

Zeno of Elea had already exposed the difficulty underlying infinite divisibility in his “Argument from Large and Small.”⁴ If a finite-sized object is infinitely divisible, then either its ultimate parts have no size or they have some positive size. If they have no size, no amount of recombination can yield a magnitude; if they have positive size, then an infinite number of such parts would generate an infinite magnitude rather than a finite one. Either alternative undermines the coherence of finite bodies. The atomists avoided this dilemma by rejecting the hypothesis on which it depends—namely, that what-is is infinitely divisible.

Aristotle notes that “some gave in to [Zeno’s arguments] by positing atomic magnitudes.”⁵ If this refers to the fifth-century atomists, then their concession is not a logical failure but a strategic insight: they acknowledged the force of Zeno’s reasoning and resolved the paradox by denying infinite divisibility at the level of physical being. Bodies are divisible only down to indivisible units; beyond that point, division ceases not as a matter of convenience, but as a matter of principle.

To understand how bodies can nevertheless be infinitely divisible in one sense, it is necessary to distinguish between physical divisibility and logical divisibility. Infinite divisibility is itself an indivisible relation. That is, the form of divisibility—the rule or principle governing division—is indivisible and immutable, even though its application yields indefinitely many divisions. Indivisibility here does not mean spatial minimality but logical necessity. It designates what cannot be otherwise if division is to occur at all.

In this sense, indivisibility is the form of divisibility: indivisibility is the activity, while divisibility is the physical result. The indivisible is not simply that into which a thing cannot be divided, but rather that through which division is intelligible. Atoms are indivisible not because they are the smallest bits of matter in a quantitative sense, but because they express a limit-condition of physical determination. Their indivisibility explains why they cannot be perceived directly, since perception itself depends on qualitative differentiation, which arises only at the level of composite relations.

The atomists did not prove the existence of atoms in a demonstrative sense. Rather, they assumed atoms in the absence of a conclusive reason to deny them. Yet this assumption is philosophically significant: by hypothesizing atoms, they demonstrated the possibility of physically indivisible bodies and thereby provided a coherent response to the paradoxes of infinite division. In doing so, they uncovered a fundamental ontological insight—namely, that infinity and indivisibility are not opposites, but mutually implicating principles. Infinity expresses itself not only through endless divisibility, but also through the necessity of indivisible form.

Footnotes

1. Democritus, fragment DK 68A21; see also discussion in Jonathan Barnes, The Presocratic Philosophers, vol. 2, pp. 316–318.
2. Simplicius, Commentary on Aristotle’s Physics 28.4–26 = DK 67A8, 68A38.
3. Simplicius, Commentary on Aristotle’s Physics 925.10–15 = DK 67A13.
4. Zeno’s “Argument from Large and Small,” discussed in Aristotle, Physics 1.3; see also DK 29B1–B4.
5. Aristotle, Physics 1.3, 187a1–3 = DK 29A22.

Indivisible Units Everywhere Divisibility

Fundamental to any coherent account of quantity in nature is the assumption that there exists some indivisible unit by means of which any two quantities can, at least in principle, be compared. Without such a unit, measurement would collapse into indeterminacy. This does not mean that such an indivisible must be empirically observable, but rather that comparison presupposes a minimal standard that is not itself decomposed further in the act of comparison.

A crucial distinction must therefore be drawn between what Aristotle calls being everywhere divisible and what later discussions often conflate as being infinitely divisible. A body can be everywhere divisible even if it is not actually divided everywhere. This distinction lies at the heart of Aristotle’s critique of certain assumptions about magnitude and division.

In On Generation and Corruption, Aristotle formulates the difficulty as follows. If a body is everywhere divisible and that complete division is actually carried out, then nothing can remain undivided. Yet if something remains, then the original supposition—that the body was everywhere divisible—has been violated. But if nothing remains, then the body must either be composed of points, which have no magnitude, or be composed of nothing at all, in which case it is merely an appearance. However, points cannot compose a magnitude, since no aggregation of non-extended entities can produce extension. Hence Aristotle concludes that magnitudes cannot be composed of points or mere contacts, and that it is therefore necessary to posit indivisible bodies and magnitudes.¹

This argument does not target infinite divisibility as such, but rather the stronger claim that a body can be actually divided at every place. Infinite divisibility in the weaker sense means that division can proceed without limit, but always yields parts with positive magnitude. Everywhere divisibility, by contrast, implies a division so thorough that no extended remainder survives. It is this latter claim that atomism must reject, and Aristotle’s argument is therefore well-directed against it.

To illustrate the distinction: dividing a one-meter rod successively in half—first into two halves, then one half into quarters, and so on—yields an infinite series of divisions, yet every resulting part has positive size. This is infinite divisibility. By contrast, dividing the rod everywhere—dividing all parts simultaneously at every point—would leave no part of positive size at all. It is this latter notion that leads to paradox.² A body may be everywhere divisible in principle without being everywhere divided in actuality.

By positing atoms—even without a demonstrative proof of their existence—the atomists avoided the Scylla and Charybdis of Zeno’s “Argument from Large and Small.” They showed that physically indivisible bodies are at least possible, even if this does not dissolve all of Zeno’s paradoxes. For physical indivisibility does not guarantee geometric indivisibility. Atoms have shapes and sizes, and shapes involve spatial extension. A spherical atom, however small, can be divided in thought even if not with a knife. Once this conceptual division is admitted, Zeno’s Dichotomy and Achilles paradoxes reassert themselves: to traverse an atom, one would first have to cross half of it, then half of the remainder, and so on ad infinitum.³

This reveals that the deepest problem of indivisibility is not primarily physical but conceptual. The atomists focused on division as it appears to sensation—cutting with a knife—while the more radical difficulty concerns division in thought. In thought, we can distinguish one part of an indivisible whole from another, just as we can distinguish hemispheres of a sphere. What the atomists did not fully recognize is that the thinking activity that performs this distinction is itself indivisible as an act, even though it is everywhere divisible in its content. Thought is one act that can generate indefinitely many distinctions.

Here the relation between atom and void becomes clearer. The atom corresponds to the determination of the many: it fixes activity into definite being. The void corresponds to the determination of the one: it is that which allows all distinctions by being itself undetermined. In mathematical terms, zero is present implicitly in every number, just as one immediately follows zero as the first determination. Every quantitative differentiation presupposes an underlying unity that is not itself one quantity among others. The void is everywhere divisible because it stimulates the indivisible into many differentiations; the atom is indivisible because it is the fixation of that differentiation into determinate being.

Like Melissus’ One, each atom is ungenerated and imperishable, and therefore eternal. It is continuous and indivisible, and unchanging in quality—indeed, it has no qualities at all.⁴ This is why atoms are imperceptible: perception requires qualitative difference, and atoms precede quality. Infinity, in this context, does not primarily name an immense size, but the process of size itself—the activity by which magnitude becomes determinate.

The atomists’ attempt to explain how size results from infinity is arguably incomplete, but this incompleteness arises from the profundity of the problem rather than from confusion. Aristotle himself acknowledges the systematic power of their theory. Against the Eleatics, who denied motion and plurality because they denied the void, Leucippus and Democritus asserted the existence of void as what-is-not in order to preserve coming-to-be, perishing, motion, and plurality.⁵ Motion is impossible without void, because without void there is nothing to differentiate one body from another, no interval, no room for displacement.

Yet this raises a final and subtle difficulty. If void is what-is-not, and the atom is what-is, then in what sense can the atom be said to be one thing? If it were simply one thing, it would resemble nothing, for nothing is precisely one thing in the sense of being no thing at all. To avoid collapsing into the unity of nothing, the atom must be many. It must be “things infinite in number,” always differing in shape, size, and arrangement, so that it is never reducible to the undifferentiated oneness of non-being. The atom is thus the “nothing of what-is-not”: it is being precisely by being endlessly something else.

In this way, atom and void are not opposites but reciprocal determinations. Void is the unity that makes plurality possible; atoms are the plurality that prevents unity from collapsing into nothingness. Infinity is not merely endless extension, but the dynamic relation between indivisible unity and inexhaustible differentiation.

Footnotes

1. Aristotle, On Generation and Corruption 1.2, 316a13–b16 = DK 68A48b.
2. See discussion in Jonathan Barnes, The Presocratic Philosophers, vol. 2, pp. 309–311.
3. Zeno’s Dichotomy and Achilles paradoxes, Aristotle, Physics 6; DK 29B1–B4.
4. Melissus, DK 30B7; Aristotle, Physics 1.3.
5. Aristotle, On Generation and Corruption 1.8, 324b35–325a36 = DK 67A7.

Zero as the Implicit One-in-All

Every number implicitly contains both 1 and 0. The 1 expresses the identity of the number—that it is this number and not another. The 0, by contrast, expresses the possibility of alteration: addition, subtraction, increase, decrease. Zero is not merely another number placed alongside others; it is the condition that allows any number to enter into relation at all.

A number is one because it is itself, but it is determinable only because zero accompanies it as the lack of determinate value. Zero has no value of its own, and precisely for that reason it must always be attached to value. It cannot appear independently as a positive or negative magnitude, yet it is present everywhere by default. Its presence consists in its absence: it bears no quantity, and thus allows quantity to remain what it is while also being capable of becoming other than it is.

Zero is therefore neither a positive number nor a negative number. It is not the negation of number, but the suspension of numerical determination. Because zero lacks value, it does not compete with the value of the number; instead, it preserves that value by allowing it to stand as itself. The number remains what it is because zero does not interfere with it. Yet without zero, the number could not maintain its identity. If zero were not implicitly present, the number would be incapable of being distinguished from nothing, from its opposite, or from any replacement whatsoever. Zero is what makes the number capable of not-being without ceasing to be.

In this sense, zero is attached to every number as an invariant background. It is the universal condition of arithmetic identity. A number without zero would be frozen, unable to enter into any operation, unable to be compared, transformed, or even affirmed as this number rather than another. Zero ensures that a number can be something rather than nothing, while also remaining capable of becoming something else.

This mirrors the ontological relation between atom and void. The atom corresponds to the one—the determinate identity of being. The void corresponds to zero—the lack of determination that allows being to move, combine, separate, and transform. Just as zero is present in every number without itself being a number in the same way, the void is present in every being without itself being a being. It is the non-being that makes being possible.

Mathematically, this is why zero is implicit in every numerical operation. Ontologically, this is why the void is implicit in every object. Zero is the possibility of difference; one is the actuality of identity. Every number is therefore a unity of identity (1) and indeterminacy (0). Likewise, every being is a unity of form and void. Identity without zero would collapse into immobility; zero without identity would collapse into nothingness. Their inseparability is the logic of number, just as it is the logic of being.

In this way, zero is not an absence that negates number, but the silent condition that allows number to exist as number. It is everywhere present precisely because it has no presence of its own.

The relationship between atom and void presents a fundamental ontological difficulty, because motion—understood here not merely as spatial displacement but as generation itself—depends on the void. To say that atoms move is already to say that something comes to be, changes, or transforms. Yet atomism defines the atom as what-is (to on) and the void as what-is-not (to mē on). This immediately raises a paradox: how can what-is arise, change, or become through what-is-not? If the void is nothing, how can it be the condition for motion, and therefore for being itself?

The problem deepens when the Atomists insist that what-is is not one thing but infinitely many things. Aristotle notes that they “declare that their nature is but one, as if each one were a separate piece of gold”¹—meaning that while each atom is internally identical, being itself appears only as plurality. If what-is were simply one, it would collapse into immobility, like the Eleatic One. If it were simply nothing, it could not appear at all. The solution implied—but not fully articulated—by atomism is that what-is exists only as many, while its unity is supplied negatively by what-is-not.

This is why the void cannot be understood as a container, like air surrounding ash in a jar. The void is not outside beings; it is that within which beings appear as distinct at all. What we perceive as external reality—space, separation, distance, extension—is not a positive substance but a field of absence that allows differentiation. We do not exist in the void the way objects sit in a box; rather, the void exists through us as the condition of perception itself. Sensation is already structured by void, by spacing, by the possibility of distinction.

This can be illustrated visually by imagining a black sphere—symbolizing void or nothingness—appearing at multiple scales: first within the human head (as consciousness), then within animals, then within the solar system, and finally within the universe as a whole. The same “nothing” is present at every level, not as a thing, but as the structural unity that holds multiplicity together. The void is thus the one in every many. It is not a substance among substances, but the indivisible background that allows any division to occur.

A helpful metaphor here is not ash in a jar, but a fishnet. The fishnet is not what you see when you look at the fish; yet without the net, there would be no pattern, no capture, no structure. Likewise, the void is not what appears in sensation, but it is what holds appearances in relation. The knots of the net correspond to atoms—definite, determinate, “hing” (den)—while the empty spaces correspond to void. The form emerges only through their unity.

The linguistic distinction preserved in Greek reinforces this point. The atom is called den (“hing”), derived from ouden(“nothing”) minus ou (“not”)². The atom is thus not opposed to nothing, but is nothing with negation removed—a first positive determination emerging from indeterminacy. The atom is the void made definite. Conversely, the void is not sheer negation, but the activity of negation itself, the ongoing capacity for change, separation, and recombination.

Thus, the atom is the first fixed relation—a component—while the void is the transformative negation that allows that component to become something else. Motion is not something added to atoms afterward; it is the ontological tensionbetween atom and void. Generation occurs because the void is never merely absent—it is the active condition through which being differentiates itself.

In this sense, the void is not opposed to being but is the unity of being across all scales. Consciousness, organism, solar system, and cosmos are not separate domains filled with different substances; they are different expressions of the same underlying relation between determinacy and indeterminacy. The nothing is not nowhere—it is everywhere, precisely because it is no thing.

Below is a visual representation of this idea.

The void is shown as structural, not external.

A black sphere (void / nothingness) appears:

inside the head of a human

echoed within animals

echoed within the solar system

echoed within the entire universe

The background uses a fishnet / lattice structure, symbolizing void as relational space rather than container.

• he black sphere represents void / nothingness — not as absence, but as the indivisible condition of relation.
• It appears at every scale:
  • inside the human head (as consciousness / interiority),
  • within animals (as organic self-relation),
  • within the solar system (as spacing and motion),
  • and within the universe as a whole (as cosmological unity).
• The repetition is intentional: it shows that the same nothing is present everywhere, not multiplied, but expressed through many forms.

The fishnet-like lattice symbolizes what you emphasized:
we are not in the void like ash in a jar, but rather what we experience as external reality is already held together by void. The net is not the fish, yet without it there is no structure, no pattern, no capture. Likewise, void is not what appears in sensation, but what makes appearance possible at all.

The atom is the first positive determination of void. It is void fixed, void negated, void given edge. The void, in contrast, is the negation that never settles, the spacing that allows atoms to move, combine, and dissolve. Motion—understood as generation—is nothing other than this oscillation between determination and indeterminacy.

Thus, the void is not opposed to being; it is the unity of being across difference. The atom is “hing” (den): nothing without negation. The void is not nothingness as lack, but nothingness as relational openness. Together they form a single ontological structure, just as the image shows one black sphere mirrored through many domains.

Nothing as Being: The Materiality of Negation

“Nothing is also being” means that nothing is material.

To say that nothing is also being is to say that nothing is material, though not as a bearer of determinate qualities. Nothing is material insofar as it functions as substrate—that which allows relation, motion, and change to occur at all.

Concerning the relationship between activity and physical result, the Atomists argue that activity requires a substrate and that this substrate constitutes the physical result. From this perspective, the material cause appears to govern formal activity, since activity must initiate from something already given. This stands as the logical inverse of the more familiar claim that the form of activity governs the material substrate. Although this inversion introduces a conceptual tension, it nevertheless reveals something logically invariable: activity itself must be quality-less if it is to generate qualities.

However, it is important to correct the attribution here. The Atomists do not explicitly formulate the claim that activity is quality-less while yet productive of quality. Rather, they implicitly recognize that the atom is something—a positive determination—while failing to fully attribute physical reality to the void as an equally constitutive principle. This limitation becomes evident when we examine their account of atomic motion.

They insinuate that the quality-less nature of the atom, as the fundamental principle of compounds, nevertheless possesses physical form. Something without any perceptible quality is still somehow physical. The principle of nothing is therefore inherently physical, precisely because it functions as a substrate for relations while remaining itself quality-less.

The atoms are described as impassive, incapable of being affected or acted upon:

“These men [Leucippus, Democritus, and Epicurus] said that the principles are infinite in multitude, and they believed them to be atoms and indivisible and incapable of being affected because they are compact and have no share of void. (For they claimed that division occurs where there is void in bodies.)”¹

Because atoms are quality-less, they cannot undergo qualitative change. Nor can they change quantitatively by becoming more or fewer, which would imply generation or destruction, or by growing or shrinking. As Simplicius elsewhere reports, “on account of their hardness the atoms are not acted upon and do not change.”²

The only sort of change attributable to atoms concerns their spatial relations—size, shape, position, and arrangement. Yet even these are limited by the absence of internal void, which prevents atoms from bending, breaking, or being internally altered.

The claim that atoms are also incapable of acting must be understood in this restricted sense: they cannot cause change in other atoms as atoms. The contrary claim that “they act and are acted upon whenever they happen to be in contact”³ refers not to atoms in isolation, but to atoms as components of compounds.

This introduces a deeper difficulty. A compound, being a relation, is itself treated as something individual—but individual in contrast to what? Another relation? Yet the separation of relations would amount to non-relation, that is, void. But void itself is already a relation—the relation of separation. Thus, relations cannot be cleanly opposed to non-relations without contradiction.

The implication of all this is that the atom in itself is nothing, and yet it somehow serves as the material basis of all change. The atom, insofar as it stands in relation to the void, constitutes the first physical differentiation. Although the Atomists explicitly claim that atoms interact in the void, it is not clear that atom and void should be understood as separate physical forces. Rather, they may be understood as two abstractions of the same process.

If the atom is what-is and the void is what-is-not, then the atom cannot simply be opposed to the void as one thing opposed to another. Instead, atom and void express two poles of a single relation. The contradiction between what-is and what-is-not is not accidental; it is the very structure of physicality.

Matter, therefore, is not a static substance but an eternal activity: the continual passing from what-is to what-is-not and from what-is-not to what-is. This movement is not secondary to matter—it is what matter means. Physical being endures not by remaining identical, but by persisting as the relation that survives change itself.

Footnotes

1. Simplicius, Commentary on Aristotle’s On the Heavens 242.18–21 = DK 67A14.
2. Simplicius, DK 68A40 / 16.33 (standard Atomist testimonia).
3. Aristotle, On Generation and Corruption 1.8 324b35–325a36 = DK 67A7.

To say that the atom is the first void—or rather, that the void is the first atom—means that we have assigned “nothing” a certain character, an instance of being. This being might, for visualization, resemble a sphere of dark matter or an infinitesimally dense point: it is the “first” of any item, the primordial instance of existence. Importantly, at this stage, the atom or void is not yet physical in the usual sense: it does not necessarily possess perceptible traits. It is abstract; it exists as an identity or a principle first, then acquires bare traits, and only subsequently manifests specific qualities.

The pressing question then arises: if the atom begins as nothing—or as pure potential—where do its qualities come from? Where does the combinatory information that allows atoms to form structures originate? The classical Atomists give an incomplete answer. They claim that the arrangement of atoms is a matter of chance or accident, or that physical forces such as attraction or reposition dictate the formation of compounds. Yet even in positing motion or force, they do not explain the ultimate origin of these motions. There is always an assumption of some being—or at least some “activity”—underlying the system. Unlike strict materialists, who reduce everything to matter in motion, the Atomists implicitly presuppose a kind of being capable of “doing,” a principle of activity beyond mere mechanical motion.

In this sense, the atom begins as a spherical void, pure nothingness. Yet in its being as a distinct entity, it is differentiated from other atoms, and this differentiation is infinite. From this difference-within-itself emerges an infinite number of distinct and differentiated spheres, each sprouting from another in space and time. These spheres are infinite in number. However, this alone does not explain how the atoms combine to constitute observable objects, qualities, or functions. The mere formation of structures does not automatically yield perception, function, or life; structures themselves are secondary to the relation between atoms and the principles that organize them.

The question of whether form precedes the combination of objects was raised by several Presocratic thinkers. Anaxagoras, for instance, posited that nous (mind) organizes the infinite seeds of things according to form, implying that the intelligible principle comes first, and matter is shaped according to it. Plato, later, argued similarly that forms (ideas) exist prior to their instantiations in matter: the form is ontologically primary, while the perceptible object is secondary. A similar position can be seen in Empedocles, who suggested that fundamental qualities (love and strife) act as organizing principles for the otherwise undifferentiated material elements. These thinkers emphasize that the perceptible and functional characteristics of objects cannot be explained purely by the mechanical arrangement of particles; rather, form or principle must exist prior to and guide the combination of matter.

Thus, the Atomists face a critical gap: while they can describe how structures might arise from the interaction of atoms, they do not account for the principle that governs the emergence of qualities or functions. Their “chance” explanations or mechanical interactions remain insufficient to explain the ordered complexity of observable phenomena. The problem is not merely the combination of atoms but the origination of form, which allows these combinations to produce coherent objects, perceptual qualities, and functional reality.

Footnotes / References:

1. Aristotle, On Generation and Corruption 1.8 324b35–325a36 = DK 67A7.
2. Simplicius, Commentary on Aristotle’s Physics 28.4–26 = DK 67A8, 68A38.
3. Anaxagoras, DK 59B1–B5 (Nous organizing matter).
4. Plato, Timaeus 30b–31c (forms precede material instantiation).
5. Empedocles, DK 31B1–B2 (Love and Strife as principles organizing matter).

The first atom is the void; the void is the first atom.

The point becomes the line, and the line becomes the circle. The point, being nowhere, extends itself into everywhere as the line, which represents the relation—a series of all possibilities of the point. This line then connects back into itself as the totality of possibilities, forming the circle. The circle represents the connection of all possibilities into a single possibility, encompassing the initial reality: nothing. The point, the origin of being, occupies the area of the circle, while the circle itself represents the process of the point.

Being in two different places at the same time manifests as the wave, and because it is still somewhere at the same time, it remains connected to itself. Waves, therefore, connect to form the sphere, representing the continuity and unity of the process.

What is behind your eyes—the perceiver—is the point encapsulated by the world, reflecting back to the perceiver. Imagine the perceiver at one point on the circle, while the circle itself represents the world. Analogously, the baby in the womb serves as a prototype for the universal form of reality; in the universal form, the womb is the mind, containing and nurturing all potentialities.

We will later explain why the fundamental relation is spherical; the form of the atom itself is spherical.

The same relation that the atom and the void constitute as the principle of matter is infinity and indivisibility. Understanding the connection between infinity and indivisibility is essential for comprehending how the atom and the void are the same relation, together constituting the principle of matter.

Footnotes:

1. Alan Watts, The Nature of God, YouTube, 14:02:45.
2. Aristotle, Metaphysics 1.4 985b4–19 = DK 67A6.
3. Simplicius, Commentary on Aristotle’s Physics 28.4–26 = DK 67A8, 68A38.
4. McKirahan, Philosophy Before Socrates, p. 306.
5. Sextus Empiricus, Against the Mathematicians 8.6 = DK 68A59.

Principle of Sufficient Reason

The Atomists held the existence of the void on the grounds of the Principle of Sufficient Reason (16.3, 16.4, and 16.5¹⁹).

Democritus states:

“There is no more reason for the ‘hing’ to be than the nothing.” (DK 68B156²)

The Principle of Sufficient Reason states that everything that exists or happens must have a reason, cause, or explanation for why it is so rather than otherwise. In other words, nothing occurs without a sufficient explanation for its existence or properties. There is no need for an explanation in order for something to occur. However, this is a logical principle, and as such, it is based on presupposition—the whole truth of it is presupposed. Correctly understood, if nothing existed, there would be no need for a reason for being to exist, because nothingness does not demand explanation; asking why nothing does not exist or whether it exists is meaningless, since nonexistence is simply the absence of presence. By contrast, the presence of being provides reasons for why it exists, in the sense that it appears in a certain way, moves in a certain way, and can be explained in terms of what makes it distinct from other, unlike things. As to the question of why being exists rather than nothing—why there is being instead of nothing—the answer is derived from the Principle of Sufficient Reason. This principle is sufficient because being requires no further explanation beyond itself in order to exist.

The Atomists argued that “motion is impossible without a separate void, nor can there be many things without something to keep them apart” (16.5³). The void enables atoms to move, and it also maintains the identity of the atom. Leucippus and Democritus held that the void separates atoms: “division occurs where there is void in bodies”; otherwise, there would only be a single, infinitely large, indivisible mass of matter. The question arises whether the void has an active or passive role in enabling and maintaining the motion of atoms.

Aristotle presents four reasons for believing in the void, all of which he regards as inconclusive:

“By ‘void’ people mean 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. … It is necessary to prove that there is no interval different from bodies which breaks up the totality of body so that it is not continuous, as Democritus, Leucippus, and many other natural philosophers say, or that there is anything outside the totality of body, supposing that it is continuous. They say that (1) there would be no change in place (that is, motion and growth), since it does not seem that there would be motion unless there were void, because what is full cannot admit anything else; (2) some things are seen to contract and be compressed, for example, jars hold the wine along with the wineskins, since the compressed body contracts into the empty places within it; and (3) all believe that growth takes place through void, since nourishment is a body and two bodies cannot coincide.” (Aristotle, Physics 4.6 213a27–b22 = DK 67A19⁴)

Democritus calls the void “nothing,” and for him, the existence of nothing is a necessary condition for the fact that everything that-is is body, because “both [what-is and what-is-not] are equally causes of things that come to be” (16.4⁵). Void is crucial for the becoming of bodies because:
A) the totality of body can be broken into intervals, and
B) there is something outside the totality of the body, allowing it to be continuous.

Void is distinct from air, whose corporeal nature is emphasized by the early Anaximenes. It is also not identical to space. The Atomists did not clearly distinguish the nature of void from other objects. It is unclear whether void is more fundamental than space or air. In one sense, the Atomists suggest that atoms and void both occupy space and have locations. Atoms move through the void, and both are situated in space, yet neither should be confused with space itself. Distinguishing void from objects is important because void classifies “nothing” as a principle rather than a mere absence.

This raises the problem posed by Parmenides: if “nothing is not,” then how can atoms be separate if there is nothing between them (11.6 line 2)? The Atomists argue that nothing is the gap between atoms—a region devoid of matter. The term “nothing” denotes a gap, because a gap has no material existence. Yet the mere fact that void is nothing material does not explain why atoms move.

Parmenides further argues that what-is-not cannot be known or declared (11.2 lines 7–8) and forbids inquiry into what-is-not (11.2 lines 5–6). According to him, nothing cannot exist as a physical principle; therefore, it cannot exist in the same way as “hing” (the atom). Parmenides asserts that being and non-being cannot coexist:

“Not at all more in any respect … or at all inferior… It is right for what-is to be not incomplete; for it is not lacking; otherwise, what-is would be in want of everything… For it is right for it to be not in any way greater or any lesser than in another; nor is there any way in which what-is would be in one way more than what-is and in another way less.” (11.8 lines 23–48⁶)

This argument connects to the idea in subjective idealism that Socrates expresses in saying he knows that he knows nothing: knowledge of “nothing” is in itself a form of awareness.

The Atomists counter Parmenides by asserting that what-is-not is on par with what-is in terms of being. Void and atoms both exist fully, though the fullness of void is “empty.” Melissus, in contrast, argues:

“Nor is any of it empty. For what is empty is nothing, and of course what is nothing cannot be.” (15.9 section 7⁷)

The Atomists preserve the premise that what is empty is nothing but maintain that what is nothing (the void) still exists. In other words, against Parmenides, the Atomists declare that “what-is-not is.” Parmenides argues that nothing cannot be thought or spoken of (11.2 lines 7–8), but the void can clearly be thought and spoken of: it is the negation of body, empty as opposed to full.

Footnotes:

1. Principle of Sufficient Reason references: DK 68B156, DK 67A19.
2. Democritus, DK 68B156, in Kirk, Raven, and Schofield, The Presocratic Philosophers.
3. Aristotle, Physics 1.4–1.5.
4. Aristotle, Physics 4.6 213a27–b22 = DK 67A19.
5. Democritus, DK 68B156.
6. Parmenides, DK 28B8 (lines 23–48).
7. Melissus, DK 30B7, On Being.

Void as Mind: The Link to Subjective Idealism

In subjective idealism, the foundational insight is that reality, as experienced, is inseparable from the mind that perceives it. Socrates’ famous claim, “I know that I know nothing,” reflects the recognition that knowledge—and indeed all experience—arises from the mind itself. This principle can be connected to the atomist notion of void in a profound way: just as the mind is the condition for perception, the void can be understood as the substrate that allows atoms and matter to manifest. In this view, the void is not merely empty space but the very form of mind itself—the observer of all physical events.

The void, as the observer, is where “real” matter-events occur, while objects as we perceive them—their colors, textures, and motions—exist only as secondary qualities within the mind. Atoms, moving and combining in the void, constitute the potentialities of matter, but it is the void itself that provides the framework for distinction, relation, and motion. In this sense, the void limits and differentiates objects from one another: it creates the space in which atoms can exist as distinct entities and in which motion and interaction become possible. Without the void, atoms would be indistinguishable, collapsing into a singular, undifferentiated mass, much like the unperceived “being” of Parmenides.

Furthermore, the void as mind provides a principle of lawfulness or rational order. The motions of atoms, whether determined by chance, physical forces, or necessity, are experienced as coherent by the observer because the void—like consciousness—establishes the condition in which laws and regularities can be apprehended. In other words, the laws of motion and combination are not just external realities; they are necessarily experienced within the framework provided by the void. The observer, as the void, is both the limit of what can be distinguished and the condition that allows relations, movement, and combinations to exist.

Thus, the void is the missing link in atomist materialism. Classical atomists recognized atoms and the void as coexisting principles of reality, but they failed to account for the role of perception or consciousness in giving structure and intelligibility to atomic motion. By understanding the void as mind—or as the observer itself—we bridge the gap between the purely material and the experiential. The void is simultaneously nothing in a material sense and everything in a perceptual sense: it is the invisible medium that makes the differentiation of atoms, the motion of matter, and the experience of objects possible. Reality, therefore, is not simply a collection of atoms in empty space; it is the interaction of potentialities within the void, where the void itself functions as the perceiving mind that structures and realizes the possibilities of being.

In this sense, the void is not inert or passive; it is the principle of relationality, perception, and limitation. Atoms move and combine within it, but they are made manifest only through the condition the void provides. As such, the void is the ontological basis of subjective experience, the first principle that allows the atomist universe to be intelligible. It is the observer, the medium of differentiation, and the source of law-like regularities—a conception that unites atomist materialism with the insights of subjective idealism.

Tangibility of Void

The tangibility of the void remains a major problem for Atomism.

The Atomists struggled to understand how the void could characterize negation because, like Parmenides and Melissus, they took what-is as their point of departure, while what-is-not appeared only as a reaction to it. Non-being was thus always secondary, defined in relation to being rather than possessing any intelligibility of its own.

Yet what-is-not plays a crucial role in atomic theory. The presence of void is necessary to account for the qualities of compounds, as well as for the separation, arrangement, and motion of atoms. Although void is indispensable for the structuring of compounds, Atomism can describe compounds only in terms of the structures exhibited by atoms themselves. The void, for the Atomists, is knowable and describable only by contrast with atoms and in relation to them. In this way, the function of the void is treated as passive: it becomes merely a substrate or background—the canvas upon which the atomic “artwork” appears. We perceive only the outline of dark figures against a white surface, while the void itself remains an abstraction. This results in an incomplete understanding of the role of void in the very being of atoms.

The only feature the void possesses in its own right is infinite extension. It has no shape or size of its own and no determinate spatial qualities. Atoms themselves are quality-less, yet they possess spatial determinations—such as shape, arrangement, and position—made possible by the void.¹ The void can therefore be characterized in terms of its rules for occupying space and enabling atomic motion. Nevertheless, Atomists tend to describe the void negatively, as simply that which atoms are not.

This negative characterization rests on the assumption that the negative is merely what is missing from the positive, such that the positive determines the negative. Wherever something positive exists, the negative appears only as its absence. When we observe the structure of a compound, we assume that structure to be primary, while the void between atoms is understood simply as the place where atoms are not. This approach, however, overlooks the way in which the negative determines the positive. The negative is not merely the absence of being, but the negation through which the positive comes to be in the first place. At the most fundamental level, the nature of the positive cannot be taken for granted; it must be explained in terms of the negation that makes its determination possible.

The negative is itself positive insofar as it is that which is not. Whenever it becomes a positive determination, it is immediately negated by what it is not—by its own potentiality. The positive is eternal only insofar as it continuously comes to be positive through this first negation, in which what-is-not is, in itself, what-is. Atomism lacks a developed dialectical framework for understanding this relation between being and non-being. Aristotle’s concepts of actuality and potentiality represent the first systematic logical articulation of such a dialectic.

For Aristotle, the negative corresponds to potentiality: even if nothing positive is present, the negation of that absence is itself positive—namely, that there could be something.²

Footnotes

1. Aristotle reports that atoms differ only by rhythmos (shape), taxis (arrangement), and thesis (position). See Aristotle, Metaphysics A.4, 985b4–20; De Generatione et Corruptione I.2, 315b6–15.
2. Aristotle, Metaphysics Θ.1–5; Physics III.1–3. Potentiality (dynamis) is not mere non-being but a determinate mode of being oriented toward actuality (energeia).

Atomic Motion

Atoms move and encounter other atoms, whether of the same kind or of different kinds. When atoms collide, they either rebound from one another or combine to form compounds. Aristotle criticizes this account of motion on the grounds that it merely assumes the external movements of atoms without explaining the cause of those movements or the relations that arise from them.

This is why Aristotle insists that Leucippus and Democritus—who maintain that the primary bodies are always moving in the void, that is, in the infinite—must specify what kind of motion the atoms possess and what their natural motion is.¹ Motion cannot be treated as a brute fact if it is to serve as an explanatory principle.

The motion involved in the generation of things is essential for explaining the kinds of movements things exhibit in relation to one another. Yet Aristotle repeatedly accuses the Atomists of neglecting precisely this issue:

“Concerning the origin and manner of motion in existing things, these men too, like the rest, lazily neglected to give an account.”²

The Atomists argue that because atoms and void are eternal, motion itself has no beginning. Since motion has always existed, they claim that there is no need to posit an initial cause of motion. However, this response fails to satisfy Aristotle’s requirement for a complete explanation of motion:

“For they say that there is always motion. But why it is and what motion it is, they do not state, nor do they give the cause of its being of one sort rather than another.”³

The eternity of motion does not explain why particular kinds of things come into being rather than others. By claiming that motion simply always exists, the Atomists avoid the deeper ontological problem of becoming. Instead, they maintain that an atom’s motion is determined solely by its most recent interactions with other atoms. There is no original motion; at any given moment, an atom’s motion is determined entirely by its immediately preceding state. If atoms are in motion, they will never cease moving unless acted upon, and if they are currently moving, they must always have been moving.

Simplicius reports that Leucippus and Democritus held that atoms are always moving in the infinite void by compulsion.⁴ Compulsion thus becomes the explanatory category for atomic motion. The Atomists use this appeal to compulsion to exclude any need for an original source of motion: atoms are causes of motion for one another. Yet they fail to address whether there is a more fundamental kind of motion that makes atoms capable of acting as causes for one another in the first place.

This difficulty becomes especially clear in Democritus’ claim that atoms are by nature motionless and move only “by a blow.”⁵ Such motion, however, is precisely what Aristotle classifies as compelled rather than natural motion. Compelled motion, for Aristotle, presupposes natural motion and is therefore ontologically posterior to it.

As Alexander of Aphrodisias explains:

“These men say that the atoms move by hitting and striking against each other, but they do not specify the source of their natural motion. For the motion of striking each other is compelled and not natural, and compelled motion is posterior to natural motion.”⁶

Atomism thus reduces atomic motion to compulsion, but the meaning of this compulsion remains unclear. Even if atoms move only as the result of striking one another, and even if there is no first collision, this still requires an explanation of why collisions occur at all. The Atomists deny that atoms have natural motion because they lack any inherent tendency either toward rest or toward motion in a particular direction or place. Yet the absence of a determinate tendency does not necessarily exclude the possibility that atoms possess an inherent principle of motion—one that produces determinate tendencies only through interaction.

Indeed, the Atomists tacitly assume that atoms possess at least the form by which they are capable of striking one another, without explaining the basis of this form. Why do atoms strike each other at all? This cannot be explained solely by the physical structure of atoms, since the formation of that structure itself requires explanation in terms of the activity that produced it.

Compelled motion, for Aristotle, is defined by its external origin, whereas natural motion proceeds from an internal principle. The Atomists respond to this problem by appealing to necessity rather than purpose, but they do not examine why necessity itself should be necessary. By treating necessity as self-explanatory, they assume that the concept requires no further qualification. This reveals a broader difficulty within early natural science: explanatory terms are often taken as ultimate simply because they name a regularity, rather than because their grounding has been adequately accounted for.

Footnotes

1. Aristotle, On the Heavens III.2, 300b8–11 = DK 67A16.
2. Aristotle, Metaphysics I.4, 985b19–20 = DK 67A6.
3. Aristotle, Metaphysics XII.6, 1071b33–35 = DK 67A18.
4. Simplicius, Commentary on Aristotle’s On the Heavens 583.18–20 = DK 67A16.
5. Simplicius, Commentary on Aristotle’s Physics 42.10–11 = DK 68A47.
6. Alexander of Aphrodisias, Commentary on Aristotle’s Metaphysics 36.21–25 = DK 67A6.

Necessity

Atomism entails a rigid form of determinism, since motion is reduced to the mechanical interaction of atoms in the void. Leucippus expresses this determinism in his well-known claim concerning causality:

“No thing happens at random, but all things as a result of a reason and by necessity.”¹

This statement must be understood within the framework of atomic ontology. For the Atomists, “nothing happens at random” does not imply that events occur for a purpose, nor does “all things as a result of a reason” suggest that the universe is governed by a conscious intelligence. The Atomist would explicitly reject a conception such as Heraclitus’ rational logos. Within atomic theory there is no place for rational design or teleology. The decisive term in the fragment is therefore necessity.

In this context, necessity is blind rather than purposive. It is opposed not only to conscious intention but to any form of planning whatsoever. According to Leucippus, the movements and relations of atoms in the void occur by necessity: given the nature of atoms and void, together with their positions and motions, events cannot occur otherwise.

Special attention must be paid to the use of the word given. The nature of atoms and void is simply posited, without any account of how they come to be or why they possess the determinations attributed to them. Atomism thus provides an ironic justification for the claim that nothing happens by chance. The reason that everything happens necessarily is not because the world is governed by mind, but because every phenomenon has an explanation in terms of atomic interactions. The question then becomes: what produces this explanation, if not some governing principle? And is the mind that formulates the explanation not already implicated in the conception of the phenomena it seeks to explain?

Democritus elaborates Leucippus’ position by asserting that “the knocking against each other, the collisions, and the blows of matter” are the causes of all perceptible events, explicitly rejecting chance and purpose as genuine explanatory principles.² Aristotle summarizes this view by noting that Democritus “leaves aside purpose and refers all things which nature employs to necessity.”³

Democritus argues against chance in the following way:

“Democritus seemed to employ chance in his cosmogony, but in his detailed discussions he declares that chance is the cause of nothing, and he refers to other causes.”⁴

For Democritus, chance is an appearance that arises from events that lie beyond human perception and therefore beyond prediction. He assumes that there is nothing prior to the interactions of atoms themselves; consequently, neither chance nor purpose can serve as legitimate causes of what happens. Atomic collisions appear accidental only because there is no purpose governing them.

This becomes particularly clear in the case of cosmic formation. The vast number of atomic motions required to produce a cosmic vortex (kosmos) exceeds our capacity to apprehend them. Atomism therefore treats the resulting kosmos as unrelated to any purpose in the interactions that produced it. Because the number and complexity of atomic interactions exceed human understanding, the outcome is interpreted as purposeless.

Democritus thus excludes purpose from atomic interactions and, in doing so, must also exclude chance, since chance would render collisions arbitrary. Necessity becomes the sole explanatory principle.

There is something correct in the claim that necessity describes what cannot be otherwise, but not in the manner proposed by the Atomists. There is also something correct in the idea that chance is an appearance arising from limited understanding, yet this does not follow from the absence of purpose. Properly understood, chance does not exclude purpose but rather presupposes it as the horizon within which deviations and unpredictability occur.

Atomism mistakes a limitation of method for a fact about reality. Because it presupposes the nature of atoms and void, as well as the external relations of compounds, as already given, it concludes that necessity in nature is blind. This blindness, however, follows from the method itself, which refuses to inquire into the causes and coming-to-be of its first principles. By treating its explanatory starting points as self-evident, Atomism renders itself incapable of recognizing any intelligibility in nature beyond mechanical interaction and thereby mistakes methodological abstraction for ontological truth.

Footnotes

1. Leucippus, DK 67B2.
2. Aëtius, Placita 1.26.2 = DK 68A66.
3. Aristotle, Generation of Animals V.8, 789b2–4 = DK 68A66.
4. Simplicius, Commentary on Aristotle’s Physics 330.14–17 = DK 68A68.

Chance

There is something philosophically significant in the claim that “chance is the cause of nothing.” If this assertion is taken literally, and if nothing is understood as no-thing—a state that nonetheless has physical significance—then a proper account of chance may illuminate the function of the void itself.

If chance results from the limitation of perception, then it exists precisely as that limit. If consciousness, even in a universal form, produces the world in a way that confirms its own truth, this activity still belongs to knowledge. Knowledge is not merely the acquisition of something previously absent; remembering, recognizing, and sustaining what is already known are also modes of knowing. Atomism, however, treats chance as a non-rational principle because it is associated with ignorance or lack of knowledge. Yet if nature is governed entirely by necessity—even in the strict sense of rigid determinism—the world nonetheless exhibits order, and order is itself a rational principle.

We cannot simply dismiss chance on the grounds that it signifies ignorance. How could we know that chance is a principle of not-knowing unless we already possess some knowledge of what chance is? To claim that chance is ignorance is itself a form of knowledge about ignorance. Logically, the concept of not-knowing presupposes knowing as its predicate. The difficulty, therefore, is not whether chance involves ignorance, but whether it can be grasped correctly in its rational role within the order of nature. It is thus reasonable to begin from the presupposition that chance fulfills a rational function in that order.

In its most basic sense, chance as a noun signifies possibility—the opportunity for something to occur. As a verb, to chance means to happen accidentally or without apparent design. These linguistic uses already suggest that chance is not sheer nothingness, but a mode of possibility that becomes intelligible only in relation to actuality.¹

The void may therefore be understood as the physical manifestation of potentiality.² It is only from the standpoint of particular beings that something is defined as other than itself. Yet any particular thing existing in the void is merely a part within a whole that expresses it. Chance corresponds to the void beyond the particular—not “outside” it, since that would imply simple opposition—but rather as that in which the particular both is and is not. In the void, the particular exists as what it is and as what it is not. This duality constitutes the differentiation by which one thing is one way and another thing another way. What I am not is simply someone else who is not me; otherwise, we would be identical.

The logic underlying the concept of chance thus explains why there is multiplicity in the world rather than a single, undifferentiated being. When we say that an atom both is and is not at the same time, the claim becomes intelligible if what-is-not is understood as what the atom potentially is—namely, something other. What I am not is someone else, and yet both of us contain aspects that are potentially the other. What a thing is not does not negate what it is; rather, it is the variant of what it is as something else for itself.

Within the void, chance appears as probability—the range of possible happenings. We interpret this as randomness because the same underlying principle bears inverse properties simultaneously, and this apparent contradiction is taken to signify disorder. Yet the possibilities present in the void correspond to actual objects and actual relations, all governed by the logical determinacy that gave rise to them. Chance, properly understood, is not the absence of order, but the expression of potentiality within an ordered whole.

Footnotes

1. Aristotle distinguishes chance (tychē) from spontaneity (automaton) while still treating both as intelligible within the causal order; see Physics II.4–6.
2. Aristotle, Metaphysics Θ.1–5, on potentiality (dynamis) as a mode of being; compare the Atomist conception of void as that which allows for differentiation and motion (DK 67A16).
3. For the Atomist rejection of chance as a real cause, see Simplicius, Commentary on Aristotle’s Physics 330.14–17 = DK 68A68.

Void as Natural Motion

The void may be understood as implicit chance within the atom—the condition that allows the atom to possibly become something other than what it presently is.

According to Aristotle, natural motion is prior to compelled motion because it explains the cause of form. Natural motion concerns the generation of the object that is capable of compelled motion. What is natural to a thing is the form that denotes the activity of a concept realized in matter. Thus, the earth moves toward the center because such motion is the actualization of the abstract principle that defines what it means for earth to move toward the center.¹

Aristotle calls the relation between the abstract principle and the concrete object natural because there is no rigidity or external imposition involved, but rather a harmony between form and manifestation. To be natural is for the material realization to follow invariably from the abstract form.² In this sense, natural motion expresses the inner intelligibility of a thing.

The void, however, is postulated as an abstract principle, since it cannot be directly perceived in itself. Yet the void, insofar as it stands in relation to atoms, conditions the very way atoms are conceived. To what extent the void is the cause of atoms remains ambiguous within atomic theory. The Atomists assert that motion occurs because of the void, but they do not clarify whether the void is merely a condition of motion or its source.

Aristotle reports:

“They say that motion occurs because of the void. For they too say that nature undergoes motion in respect of place.”³

Atomism thus treats the void as a necessary condition for motion, but not as a cause in the sense of originating motion. This raises a crucial question: to what degree is original motion related to compelled motion, and in what sense is the void a cause of motion at all? Clarifying this relationship reveals the special role of the void in the nature of the atom, particularly in relation to the concept of weight. A correct understanding of weight leads directly to an account of how natural motion grounds compelled motion.

Aristotle discusses this problem explicitly:

“Those who call the primary bodies solid can say that the larger ones are heavier. But since compounds do not appear to behave in this way—for we see many that are smaller in bulk but heavier, as bronze is heavier than wood—some think and say that the cause is different, namely that the void enclosed within makes bodies light and sometimes makes larger things lighter, since they contain more void… But those who make these distinctions must add not only that something contains more void if it is lighter, but also that it contains less solid.”⁴

This passage is especially important for understanding the relationship between void and atom in the constitution of weight. The void is not merely the absence of atoms, such that more void simply means less atom and therefore less weight. Rather, weight is understood by contrast with the void. The void, as the negative, is not merely the place where the atom is not, but functions as the negation through which the atom’s weight is determined. In this sense, the void does not subtract weight mechanically; it defines weight relationally.

Weight is therefore central to the question of motion. Yet the Atomists found the attribution of weight to atoms deeply problematic. Atoms appear both to possess weight and not to possess it as a primary property. This difficulty arises because the atoms are composed of a uniform material whose determinacy becomes apparent only through the void. The void constitutes the condition under which atoms both have and do not yet have weight.

In this sense, the void is the context in which the weight of the atom remains undetermined. This undetermined activity—prior to the specification of heaviness or lightness—is the same uniform “stuff” of which atoms are composed. The void thus does not merely separate atoms; it articulates the potentiality through which atomic properties, including weight and motion, become determinate.

Footnotes

1. Aristotle, On the Heavens I.8, 276a22–277b10; Physics IV.8.
2. Aristotle, On the Heavens I.8; see also Physics II.1 on nature (physis) as an internal principle of motion and rest.
3. Aristotle, Physics VIII.9, 265b24–25 = DK 68A58.
4. Aristotle, On the Heavens IV.2, 309a1–14 = DK 68A60.

Weight and the Void

Weight can be understood in several distinct ways. The Greek word translated as “weight” is the noun derived from the adjective meaning “heavy.” While weight has a technical meaning in modern physics—mass multiplied by gravitational acceleration—ancient discussions conflate several related but distinct notions.

First, weight may be understood as mass, that is, as the persistence of a body regardless of its motion. In this sense, the atom possesses mass insofar as it exists in a state of indeterminacy: it is something that can move, but is not yet determined to move in any particular way. This corresponds roughly to the modern concept of mass as resistance to acceleration.

Second, weight may be understood as a tendency to move in certain ways under certain conditions, but differently under different conditions, without a universal tendency toward any single direction. This sense of weight again approximates our modern understanding of mass rather than gravitational weight.

Third, weight may be understood as a determinate tendency to move in a particular direction. For Aristotle, this direction is toward the center of the cosmos; for Epicurus, it is downward.¹

The void, understood as the undetermined state of the atom, corresponds most fundamentally to the first sense: it is the capacity to be affected by force, the condition under which motion is possible at all. Indeterminacy does not mean absence, but the possession of potentiality for motion. To say that a state is indeterminate is simply to say that it contains the capacity for certain motions without yet being specified.

The void outlines the material of the atom. The atom’s form is conceivable only because of the void. This form includes the size and shape of the atom, determining how much matter it contains, which in turn determines its weight.² In this sense, mass—understood as the absence of a determinate tendency to move—is determined by the motion implicit in form.

The Atomists hold that an atom’s motion is determined solely by its previous collisions with other atoms. However, this account of compelled motion makes no appeal to any immaterial force such as gravity. Gravity, by contrast, is explained as natural motion, since it induces a universal form of motion applicable to all bodies.

Simplicius reports:

“Democritus and later Epicurus said that all the atoms have the same nature and possess weight, but since some are heavier, when these sink down the lighter ones are squeezed out and move upward, and in this way they say that some things appear light and others heavy.”³

Atomism thus offers a mechanistic basis for attraction and repulsion: heavier bodies sink, lighter bodies rise, like atoms move toward like, and heavier atoms move toward the center in the formation of a cosmic vortex. Yet Democritus also makes a distinctive claim concerning indivisibles:

“Each of the indivisibles is heavier according as its quantity is greater.”⁴

This raises a provocative question: does this suggest an early intuition of something akin to singularity—that increasing quantity leads to increasing weight without limit, as in the modern conception of black holes? While such a comparison must remain speculative, it suggests that Democritus grasped a deep connection between quantity and weight that exceeds simple mechanical explanation.

The void may thus be understood as the abstract principle of the atom, while the atom is the manifestation of the void. This does not mean that they are numerically identical, but that they express the same underlying potentiality. The atom is not a static substance but the determination of possibility.

Aristotle identifies void as the place of atoms, not as empty space, and his conception of place supports this interpretation. He notes that proponents of the void conceive it as “a place in which there is no body.”⁵ Since Aristotle defines place as “the innermost motionless boundary of what contains it,” or more generally as “that which contains the thing whose place it is and is no part of that thing,” the void becomes a potential container of bodies rather than an independent spatial expanse.⁶ Place, on this account, is not a location but another body that contains the thing—just as an egg carton is the place of an egg.

Natural motion explains the atom as the context for motion. For Aristotle, this place is motionless, while in compelled motion the motion is external to the thing. In natural motion, the atom is the context within which motion is determined; in compelled motion, the atom is merely an object acted upon.

This distinction mirrors the philosophical difference between conceiving and being conceived. As Alan Watts observes, to conceive is to begin from a source that is itself nothing—not an object, but that which observes. Objects are always what is conceived, never what is conceiving. Other people are objects of my conception, just as I am an object of theirs, but the act of conceiving itself is never an object. It is analogous to the concave rather than the convex: a self-stimulating emptiness rather than a thing.⁷

In this way, Atomism ultimately maintains the atom as an empty abstraction. The atom becomes a rule for explaining appearances while avoiding deeper questions of substance. Explanation is confined to external relations and sensory effects, and determination is stripped from the atom itself. The atom is reduced to a unit in a vulgar determinism, incapable of being understood as a kind of motion in its own right.

Aristotle recognizes that the true nature of the atom—or of any basic entity—must be explained through motion. An atom must be understood as the context for the determination of motion, not as something that merely participates in a presupposed motion. Only by grounding motion in form and potentiality can the atom be understood as more than a mechanical placeholder.

Footnotes

1. Aristotle, On the Heavens I.8; Epicurus, Letter to Herodotus 61–63.
2. Aristotle, On Generation and Corruption I.8, 326a9–10 = DK 68A60.
3. Simplicius, Commentary on Aristotle’s On the Heavens 569.5–9 = DK 68A61.
4. Aristotle, On Generation and Corruption I.8, 326a9–10 = DK 68A60.
5. Aristotle, Physics IV.7, 213b33.
6. Aristotle, Physics IV.4, 210b34–211a1; 212a20–21.
7. Alan Watts, The Book: On the Taboo Against Knowing Who You Are, esp. chs. 1–2 (conceptual parallel, not historical source).

Compounds

The idea that atoms are discrete units separated by void is a more complex notion than it initially appears. What it means for atoms to be “in contact” is not that they literally touch, but that their spatial extensions are perfectly aligned. The question then arises: what exactly is being aligned? This alignment is not merely physical adjacency, but a continuity of form or idea.

Atomism misconstrues the philosophical notions of activity and relation by restricting them to external relations. For the Atomists, all activity—even at the most fundamental level—is understood as an interaction between externally distinct entities whose forms are already presupposed prior to any activity. On this view, relations arise only between entities that are fully formed in advance, and activity consists in the compulsion of one entity by another.

By contrast, activity understood as an internal relation does not presuppose the pre-existence of the entity whose activity it is. Rather, the activity itself constitutes the form of the entity. In an internal relation, there is no independently existing thing that subsequently acts; instead, the activity that generates the entity is the entity. The relation is internal because it originates from itself and takes its own origination as its being. This conception challenges our ordinary sense of what it means for something to be physical, since physicality is no longer grounded in static objects but in self-generating activity.

Weight provides a clear example of this difficulty. Heaviness is always relative: for something to be heavier, it must be heavier than something else. Nothing is heavy or light in itself, but potentially both, depending on the context. Weight is therefore not an object with structure, but a concept—an activity whose form is its own operation. It is experienced, not possessed.

Atomism fails to address the fundamental relationship between the physical nature of the atom and its rational conception. The existence of atoms, for the Atomists, is not established through perception but through rational deduction. This raises a crucial question that Atomism leaves unanswered: in what sense is rational conception related to physical composition? The theory relies on rational abstraction to posit atoms, yet refuses to integrate rationality into the ontology of nature itself.

This problem reappears in modern philosophy and science in the question of whether the existence of objects requires an observer. Quantum physics has given renewed force to this issue. In certain interpretations, the observer plays a constitutive role in determining physical outcomes. John Archibald Wheeler famously argued that the universe is a “self-excited circuit,” in which observers are not incidental but essential to the universe’s existence.¹ Perception itself is not passive: the eye, for example, produces photons in order to see.

If properties such as heaviness, hardness, or softness are relational—hardness being felt only by something soft, such as skin—then it becomes plausible to ask whether abstract concepts are physically real for the mind that conceives them. If consciousness conceives the idea of a circle, in what sense is the circle physical? The mind that apprehends pure concepts experiences them as real, no less than the body experiences weight as real. Quantum science, in this respect, does not merely study nature theoretically; it reveals a genuinely theoretical dimension within nature itself.

Time illustrates this clearly. Time is an abstraction derived from activity. The future, stripped of activity, is empty. It has no content apart from the processes that generate it.

Thought and the external world are therefore continuous. Their apparent division is a differentiation within continuity, not a separation of substances. Practices such as meditation make this continuity experientially evident: when the interpretive activity of the understanding quiets, and consciousness attends directly to what is happening, the distinction between mental events and external events dissolves. Quantum mechanics encounters peculiarity precisely because it investigates nature at the infinitesimal level, where abstraction and physicality coincide. The very act of observation reveals the theoretical dimension of reality.²

Democritus himself acknowledges the abstraction involved in atomic theory:

“Democritus says that the primary bodies do not possess weight but move by striking against one another in the infinite, and that there can be an atom the size of a kosmos.”³

Calling the void “nothing” is, in part, a strategic response to Zeno’s argument from the limited and the unlimited. Zeno claimed that if there are many things, then between any two there must always be others, and thus reality is infinitely divisible.⁴ The Atomists reply that between atoms there is not another thing, but nothing—the void. By denying that the void is a thing, they block Zeno’s infinite regress.

Yet this solution comes at a cost. By reducing the void to nothing, Atomism avoids paradox at the expense of ontological depth. The void becomes an empty placeholder rather than a productive principle.

If we instead think of the void as the point of pure indeterminacy—the singularity—then a different picture emerges. The smallest point is not merely minimal, but universal. As we zoom inward, we encounter not fragmentation but generality. Consciousness itself can be understood as such a point: the smallest in relation, yet infinite in scope. From the standpoint of the cosmological principle, consciousness occupies no privileged location, yet it is the point through which the universe reflects upon itself.

In this sense, the universe is a self-exciting circuit. The expansion of the universe may be conceived not only outwardly but inwardly—toward the singularity of present awareness. The smallest point contains the largest achievement, because everything that has come to be is contained within the capacity that actualized it. Consciousness is the one in relation to the many, yet contains the many insofar as it is the condition of their disclosure. This is not metaphorical inflation, but a logical consequence of understanding activity, relation, and form as internally rather than externally grounded.

Footnotes

1. John Archibald Wheeler, “Law Without Law,” in Quantum Theory and Measurement, eds. Wheeler and Zurek (Princeton University Press, 1983).
2. For discussion of observation and measurement, see Niels Bohr, Atomic Physics and Human Knowledge.
3. Aëtius 1.12.6 = DK 68A47.
4. Zeno of Elea, fragment 12 (DK), as reported by Simplicius.

The reason intelligible concepts are able to describe physical properties is that the intelligible corresponds with the physical at the most fundamental level of being. Atomism does not adopt this view. Instead, it offers a confused inversion of it.

The Atomists argue, roughly, that because appearances are infinitely various, the shapes of atoms must also be infinite. In this way, the intelligible is derived from the perceptible. Shape becomes nothing more than an abstraction from appearance. Yet this position is unstable, and it is not even clear that the Atomists consistently held it, which is precisely why the theory becomes conceptually confused.

The core problem is a confusion between method and fact. Atomism treats the way truth is derived as indistinguishable from the way truth is. In other words, the epistemological method of arriving at knowledge is mistaken for the ontological structure of reality itself. This is analogous to claiming that the act of performing heart surgery is identical with the heart. In ordinary contexts, such a mistake is obvious, but in complex metaphysical discussions it often goes unnoticed. To say that the cause is known through the effect does not mean that the effect is the cause.

The Atomists begin with relations between perceptible objects—objects that already possess preconceived qualities—and abstract those relations. They then treat the abstracted relations as determining the qualities of compounds. External relations are taken as primary, and internal relations are either ignored or reduced to them. Yet internal relations have no perceptual qualities; they are intelligible structures that condition perception itself.

Atomism is among the earliest materialist doctrines to invert the ontology of reason. It takes the ultimate nature of reality to be the particle—the part-icle, the particular—and from the differences among these particulars it derives relations, which in turn constitute compounds. The ontology of reason proceeds in the opposite direction. Relation is primary and indivisible, while particulars are derivative determinations within relational structure. A compound is a particular, but its substance consists in relations. The atom, therefore, is not an individual thing but a relation. When we perceive it as a particle, we are apprehending only a partial expression of that relation.

The Atomists themselves state that atoms differ by shape, arrangement, and position. These are relations, not self-subsistent properties. Yet they treat these relations as caused by the atom, while leaving unanswered the question of what the atom is apart from its relations. What is an atom, if stripped of all relational determination?

In attempting to explain the intelligible by the perceptible, Atomism comes to treat relations as properties of objects rather than understanding objects as configurations of relations. This reversal obscures the rational structure of being.

As reported by Aëtius:

“Democritus specified two basic properties of atoms: size and shape; and Epicurus added weight as a third.”¹

Concepts are distinct, and it is precisely in their difference—that is, in their relation—that they are maintained as what they are. Identity is preserved only through difference. This continuity of contradiction is what allows concepts to be determinate rather than collapsing into indifference.

The void, by contrast, is no-thing. As such, it cannot contain inherent differences. This is why it is described as “empty” or “rare,” and why it becomes associated with the unlimited or the infinite. The contradiction between atom and void arises because the void’s lack of difference—its pure self-identity—is the very condition for the atom’s differences. The atom exhibits determinate differences because the void is free from all difference. The void is not itself a difference; it is different from difference.

This also explains why Atomism entails an infinite void in which atoms move, even though we possess no explicit argument from the Atomists demonstrating that the void must be infinite. The infinity follows implicitly from the requirement that atoms not be constrained by any determinate boundary.

As Aristotle reports:

“They are no more like this than like that; therefore there is an infinite multitude of shapes.”²

This argument depends on a version of the Principle of Sufficient Reason already encountered in Anaximander and Parmenides: if there is no reason for one determination rather than another, all determinations must be equally possible.

However, the infinite should be understood not as an amount, but as activity. An infinite amount would itself be determinate and therefore finite. Infinity properly understood is the absence of limitation in the activity of determination.

Atom and void are thus not two fundamentally different substances, but two forms of the same underlying reality. They are forms of thought. The void functions as the principle of identity, while the atom functions as the principle of contradiction. The void maintains the atom by excluding difference; the atom realizes difference within that exclusion.

On this view, the excluded middle is not violated but structured: the void is the form of the atom, while the atom is the content of the void. The atom is not an individual thing, but a relational determination.

The familiar Atomist formulation summarizes the theory as follows: atoms are building blocks too small to be seen, moving in the void and combining to form compounds, some of which are large enough to be perceived, differing only in their spatial properties—size, shape, and arrangement.³ Yet this formulation already presupposes what it claims to explain. It treats relational determinations as secondary to individuals, whereas in truth the individual is nothing apart from its relations.

Footnotes

Aristotle, Metaphysics A.4; Physics IV.6–9.

Aëtius, Placita 1.3.18 = DK 68A47.

Aristotle, Metaphysics A.4, 985b4–20 = DK 67A6; cf. DK 16.4

Exploration of Natural Consciousness

We are all in the void, the void is in all, and this is how all is in the void.

Spherical images of experience—such as planets, bodies, or events—illustrate how infinity physically constitutes particular occurrences. This infinity is not the same as space understood as a container in which particular things can be isolated and enumerated. When we say that the void is different from space, we mean that it is not an abstract coordinate system but the lived actuality of a particular event. The void is one with experience, just as the atom is one with the object.

One might object that such images are merely particular conceptions—limited representations that fail to capture the infinite detail of what they depict. While this is true, it misses the deeper point. The point is that the very consciousness capable of perceiving a particular form is itself the form of that particular event. The nature of consciousness that apprehends particulars is not itself particular. It is universally no-thing. It is the one void present in every atom.

The relation between atom and void—more fundamental than either taken alone—corresponds to the relation between thought and object. This does not mean that the void is thought and the atom is the object, but rather that the void–atom relation is the thought–object relation. Language struggles to express this, because each word tends to fix meaning by opposition: void against atom, thought against object. Our understanding thus instinctively assigns void to thought and atom to object, reproducing the same abstraction it seeks to overcome. This is analogous to mistaking a photograph of a planet for the planet itself, forgetting that the planet includes landscapes, materials, atmospheres—each requiring its own conception.

The question then arises: can the complexity of nature as a whole be grasped in a single act by an ultimate form of consciousness? And what would it mean for each event to be conceived simultaneously in its particularity? This is the problem of temporality and process explored by Whitehead, for whom reality is not composed of static substances but of interrelated events unfolding in time.¹

The most advanced material form is also the most particular point. As a species, human beings are physically small and biologically limited, yet in consciousness they are maximally universal. Consciousness contains the culmination of the world in recollection, representation, and understanding. The smallest point thus becomes the largest, not spatially but in scope.

Sensation operates through exclusion. It bears a negativity in relation to reason insofar as it functions by not admitting what is not presently sensed. Sensation produces artificial exclusivity: when I perceive one object, I necessarily do not perceive another. For sensation, the presence of one thing excludes the presence of others. Although sensation relies on shared grounds—space, continuity, order—it simultaneously excludes those grounds from explicit awareness. This produces what may be called a fallacy of exclusion: the mistake of taking the exclusions produced by sensation as ontologically fundamental.

This fallacy is prominent in empiricist philosophy, particularly in Berkeley and Hume. Berkeley, for example, denies the reality of abstract ideas such as geometrical space, reducing them to collections of sensible impressions, while nonetheless presupposing spatial relations in perception itself.² Geometry is excluded as an abstraction even though it is required for the intelligibility of visual experience. Hume similarly treats causality and necessity as habits of association rather than as features of reality, despite relying on them to describe experience coherently.³

Russell articulates a related distinction when he notes that real space is a universal, abstract concept, whereas apparent space, as given in sensation, consists of particular positions and perspectives within that space.⁴ Sensation delivers localized appearances; reason apprehends the universal structure that makes those appearances intelligible.

Yet we must be cautious. The particular is not merely a product of sensation. The objective world itself exhibits particularity. Sensation is itself a particular event, one that selects particulars from a field of particulars. Reason, by contrast, apprehends the particular as universal, or the universal in the particular. It reveals the particular not as isolated, but as an expression of a universal phenomenon.

In this way, void and atom, thought and object, sensation and reason are not opposites but differentiated moments within a single continuous reality. The void is not elsewhere; it is the openness through which every particular becomes what it is.

Footnotes

1. Alfred North Whitehead, Process and Reality, esp. Part II, on actual occasions and temporality.
2. George Berkeley, An Essay Towards a New Theory of Vision; Principles of Human Knowledge, §§10–15.
3. David Hume, An Enquiry Concerning Human Understanding, Sections IV–VII.
4. Bertrand Russell, The Problems of Philosophy, ch. 3; see also lectures on space and perception (cf. public lecture references).

General Space

We cannot begin to specify what different sensations we derive from a given object under varying circumstances unless we regard both the object and our perception of it as situated within one general space. This is not only a physical requirement but also a logical one. Sensation always begins from a relative position in space, and it is for this reason that it yields particular conceptions of the object—what we ordinarily call appearances. The relativity of position between objects and our perception of them presupposes a single, universal, all-embracing physical space. It is this universal space that allows my particular perception of an object to be objectively confirmed by other senses and by other observers.¹

In the case of pure reason, however, the principle of exclusion does not apply. Objects are not given as mutually exclusive appearances but as substrata—landscapes of interrelated qualities rather than isolated sensory contents.

The senses can derive conceptions of different objects simultaneously, while the objects they derive remain, in an important sense, the same for those senses—though this sameness is not absolute but structured by perspective and condition. Sensory plurality does not imply ontological plurality in the object itself.

Ordinarily, we think that the senses are governed by the brain in order to perceive objects. This is only partially true. There must be something in the object itself that corresponds to the mind’s capacity to synchronize the senses. Just as the mind unifies sensory inputs, there must be something in the object that makes such unification possible. The brain, however, is itself another object with a limited function. Yet this does not mean that what the brain embodies—namely, consciousness—is limited to the organ’s biological role.

This raises a difficult technical question concerning form and matter. If void and atom are so indivisible as to constitute the same reality at the level of infinitesimal processes, why does consciousness arise in such a way that it can mediate between them and distinguish them? Why does there exist a standpoint from which void and atom can appear as differentiated at all?

Ordinarily, consciousness is understood as the function that distinguishes thought from object: either it thinks about an object that is not immediately present, or it perceives an object directly and derives content for thought. In both cases, however, consciousness cannot be reduced to either activity alone. Fundamentally, consciousness is the binding relation between thought and object—it is what constitutes their unity as a relation. When the object does not exist for thought, consciousness produces thought as the object. When the object exists independently of thought, consciousness produces the necessity of thought for the object.

This is not limited to sensation. Thought itself operates as a substance in this sense: an object not immediately present to thought exists as a potential object. Consciousness mediates between actuality and potentiality, not merely between sensation and reflection.

There is, in this mediation, a kind of void between things—and it is precisely in this void that thought occurs. Thought and object are separated as distinct substances, yet their difference is itself their relation. Their relation consists in remaining distinct, for this distinction is what enables consciousness to function at all. Consciousness stands as the mediation whereby thought becomes object and object becomes thought, without collapsing either into the other.

The Atomists argue that atoms are physical forces that directly stimulate the organs of sensation, like pieces of a puzzle fitting together. Yet they do not explain why this correspondence holds. As a result, they treat the connection between object and mind as mechanically driven in the same way that one object comes into contact with another. Modern physics, however, complicates this picture. At the atomic level, matter is structured in ways reminiscent of a solar system, yet unlike planetary systems, atoms are only theoretically stable and are in fact far more dynamic. Their behavior is probabilistic, relational, and governed by fields rather than by direct contact.²

In this respect, the operation of the atom resembles the operation of thought more than it resembles the way sensation presents macroscopic objects to perception. Atomic processes are abstract, relational, and inferential; they are not directly given but are known through theoretical mediation.

Atoms, then, are not simply constituents of objects that mechanically stimulate the senses. Rather, they are what is implicit in the object that allows the senses to be synchronized in the first place. Contrary to traditional atomism, atoms do not originate purely from the object but function as properties of mind as well. They are extensions of mind into nature—principles through which nature becomes intelligible to itself. Atoms are thus the medium of the mind’s self-realization in the object.

Footnotes

1. Bertrand Russell, The Problems of Philosophy, chs. 2–3; see also Kant, Critique of Pure Reason, Transcendental Aesthetic, on space as a condition of possible experience.
2. See standard quantum mechanics accounts of atomic structure; e.g., Werner Heisenberg, Physics and Philosophy, ch. 3; also modern discussions of atomic indeterminacy and field dynamics.

Parmenides (Philosophy Before Socrates)

Parmenides distinguishes between two “routes of investigation,” which are the only ones capable of being thought: the path of what can be known and the path of what cannot be known. He argues that “Truth” is accompanied by a “path of Persuasion,” keeping in mind that for him, truth and persuasion are inseparable: one cannot truly know what is not persuasive to reason.¹

Regarding what is, Parmenides writes that “the One, the Truth, is both that it ‘is’ and that it is not the case that it ‘is not’” (DK 28B2.11.2).² This asserts the principle of existence: being is, and non-being is impossible to conceive. Conversely, the “track entirely unable to be investigated” is “the Other, both that it ‘is not’ and that it ‘is not’ is right.” One cannot know what-is-not, for it cannot exist, nor can one declare it; non-being has no reality and therefore no possibility of thought or speech.³

Parmenides emphasizes the identity of thought and being: “for the same thing both can be thought of and can be” (DK 28B2.11.3). In other words, thinking and being are inseparable: to think of something is for it, in some sense, to exist. He reinforces this in 11.4: “You cannot exclude what-is from the point of view of what-is.” Being cannot be negated from itself; existence is self-evident and indivisible.

The text continues: “Where you begin is where I will arrive back again” (DK 28B2.11.5), indicating the circularity of reasoning in metaphysical inquiry. All thought that starts with what-is returns to what-is; there is no escape from the unity of being. Likewise, “it is right both to say and to think that it is what-is: for it is the case that it is” (DK 28B2.11.6). The principle of being is not merely intellectual—it is ontologically necessary.

Parmenides explicitly rejects the possibility of non-being. “Nothing is not”; it cannot be thought or spoken. He argues that it is mortal and wrong thinking to suppose that what-is can be both the same and not the same.⁴ Ironically, the very act of reasoning that identifies the “mortal” is itself the demonstration of the unity and necessity of being.

He further denies potentiality: “from what is not: for ‘is not’ is not to be said or thought of” (DK 28B2.11.8). Anything that is to come into being must already, in some sense, be, because non-being cannot produce being.⁵ This anticipates later idealist positions, such as Berkeley’s: the unknown, the non-existent, simply cannot exist.

From these arguments, Parmenides denies motion, change, and void. He believes that all existence is a single, indivisible, unchanging mass, a concept known as monism. Change and motion, therefore, are mere illusions of the senses. While this reasoning may seem counterintuitive from an empirical perspective, Parmenides explicitly rejects sensory experience as a path to knowledge, instead relying solely on abstract, logical reasoning.⁶

Specifically, he denies the existence of void, equating it with non-being: “if the void is, then it is not nothing; therefore it is not the void.”⁷ Without void, motion is impossible, because there is no “space” into which anything could move. Furthermore, he maintains that all that exists must be an indivisible unity: if being were manifold, it would require void to separate it, which he rejects. Finally, the all-encompassing Unity is unchanging, for it already contains all that is and all that can be.⁸

Footnotes

1. Parmenides, Fragment 2, in Diels-Kranz, Die Fragmente der Vorsokratiker, 28B2.
2. DK 28B2.11.2: Principle of being; the One is, non-being is impossible.
3. DK 28B2.11.2–11.3: The “track of the Other” is inaccessible; non-being cannot be known or spoken.
4. DK 28B2.11.6–11.7: On the impossibility of what-is being both the same and not the same; distinction between mortal thought and necessary being.
5. DK 28B2.11.8: Argument against potentiality; anything coming to be must already be in some sense.
6. Kirk, G. S., Raven, J. E., & Schofield, M., The Presocratic Philosophers, 2nd ed., Cambridge University Press, 1983, pp. 146–148.
7. Guthrie, W. K. C., A History of Greek Philosophy, Vol. I: The Earlier Presocratics and the Pythagoreans, Cambridge University Press, 1962, pp. 110–115.
8. Ibid.

Parmenides “what cannot be known“

Parmenides distinguishes between two “routes of investigation,” which are the only ones capable of being thought: the path of what can be known and the path of what cannot be known. He argues that “Truth” is accompanied by a “path of Persuasion,” keeping in mind that for him, truth is inseparable from what persuades rational thought.¹

The first path—the path of Truth—asserts that “what-is” is, and that it is not the case that “what-is not” (DK 28B2.11.2). The second path—the path that cannot be investigated—is that of the “other,” which is entirely inaccessible: both that “what-is not” and that “what-is not is right” are beyond human cognition. One cannot know what-is-not, for it cannot be accomplished, nor can it be declared.¹

Parmenides further asserts that thinking and being are the same: the same thing can be both thought and is, for what can be thought must exist in some sense (DK 28B2.11.3–11.4). From this, he concludes that one cannot exclude what-is from the point of view of what-is (DK 28B2.11.4). Every inquiry begins and ends in what-is; there is a circularity of reasoning where one returns to the starting point (DK 28B2.11.5).

It is therefore correct both to say and to think that what-is is, for it is indeed the case that it is (DK 28B2.11.6). Nothing, in contrast, is not; it cannot be spoken of or thought. Parmenides criticizes the idea that what-is can simultaneously be and not be as “mortal and wrong thinking” (DK 28B2.11.6–11.7).

He explicitly rejects the reality of potentiality: anything that is “going to be” derives from non-being, which is impossible. In other words, if something comes to be, it must already “is,” since non-being cannot produce being (DK 28B2.11.8). In this sense, his view resembles Berkeley’s idealism: what cannot be conceived or perceived does not exist.²

Parmenides’ metaphysics leads to the denial of motion, change, and void. He believed all existence to be a single, indivisible, unchanging unity (monism). Change and motion are therefore mere illusions. Since void is non-being, it cannot exist; without void, motion is impossible, as there is no “space” into which anything could move.³

He concludes that all existence is an all-encompassing Unity, which is unchanging because it already encompasses all that is and all that can be. For Parmenides, multiplicity and differentiation are illusory, since if being were manifold, it would require void to divide it—which he denies.⁴

Footnotes

1. Parmenides, Fragment 2, in Diels-Kranz, Die Fragmente der Vorsokratiker, 28B2.
2. Berkeley, G., Principles of Human Knowledge, §1–2; note the parallel in the denial of non-being.
3. Kirk, G. S., Raven, J. E., & Schofield, M., The Presocratic Philosophers, 2nd ed., Cambridge University Press, 1983, pp. 146–148.
4. Guthrie, W. K. C., A History of Greek Philosophy, Vol. I: The Earlier Presocratics and the Pythagoreans, Cambridge University Press, 1962, pp. 110–115.

Atoms and Reciprocal Void

In each atom there exists a reciprocal void, which is simultaneously its observation and its potential. This void is not an object in the same way that space is an object; rather, it is the relation of the atom to itself and to other atoms. In other words, the void is the thought or awareness of the object, the potential for motion, interaction, and combination. It is the medium through which atoms relate, rather than a separate container or substance.

At a cosmological extreme, the concept of the Schwarzschild radius provides a modern analogy: just as a black hole defines a boundary in spacetime where all mass is concentrated, the reciprocal void of an atom defines the “extent” of its relational potential. The atom itself cannot be observed outside of this void; it is the combination of atom and void that constitutes physical reality and relational capacity.¹

The atomist natural philosophy regards the fundamental level of the universe as composed of physical “atoms” (atomos), which literally means “uncuttable” in the language of the Ancients.² The ontological doctrine of atomism does not provide an account of the ultimate cause of nature; rather, it explains natural phenomena purely in terms of material interactions of bodies, and it accounts for the perceived properties of macroscopic objects as the effects of these same atomic interactions.³

Leucippus and Democritus theorized that the two fundamental and oppositely characterized constituents of the natural world are atoms and void. The void is described simply as nothing, the negation of body. Atoms, by contrast, are intrinsically unchangeable: they move through the void, combine into clusters, and collide with one another, but their essential nature remains constant. Because atoms are separated by void, they cannot fuse; collisions are bounces rather than mergers.⁴

Since all macroscopic objects are aggregates of atoms, everything in the macroscopic world is transitory, as the relative positions of atoms shift or disperse. While the atoms themselves persist eternally, the forms they compose are impermanent.⁵

The atomists, however, do not explain the nature of the void itself. This leaves open the question of what causes atoms to collide or combine in particular ways, a question that Parmenides raised in a different form. Although Parmenides’ own attempt to account for the void is ultimately unsuccessful, he highlights an important ontological issue: the nature of non-being as the condition for motion and change, a question that the atomists largely leave unexamined. This question remains relevant even in contemporary physics, as the “space” between particles—whether in quantum fields or in cosmological voids—continues to be a subject of deep inquiry.⁶

Footnotes

1. Schwarzschild radius: the radius defining the event horizon of a black hole, beyond which no information escapes; used here metaphorically to describe the relational boundary of an atom.
2. Plato Stanford Encyclopedia of Philosophy, “Atomism: Ancient,” https://plato.stanford.edu/entries/atomism-ancient.
3. Kirk, G. S., Raven, J. E., & Schofield, M., The Presocratic Philosophers, 2nd ed., Cambridge University Press, 1983, pp. 303–305.
4. Ibid., pp. 303–304; Leucippus and Democritus, DK 68A1–A4.
5. Ibid., pp. 304–305.
6. Guthrie, W. K. C., A History of Greek Philosophy, Vol. I: The Earlier Presocratics and the Pythagoreans, Cambridge University Press, 1962, pp. 110–115.

The atomists do show that there is a necessary relation between atoms and void, and they also show what the relation consists of, but they do not explain the actual nature of the relation. They ultimately hold that atom and void are the same thing, though in different manifestations.

Void and atom can be understood as depictions of internal and external relations. Externally, the void allows atoms to exist infinitely in shape and position, with atoms taking on individual and particular arrangements. Internally, within the atoms themselves, there is void, also infinite, yet it is nothing—it is precisely this “nothing” that directs the motion and configuration of the atoms. In this sense: the many are each one, and the one is many.¹

Outside of my thought, there is one matter taking on many forms; inside my thought, there are many ideas, which together form one coherent structure. Inside the one, there is the many; inside my thought is the whole world, though not each individual object; outside my thought is each individual object, though not the whole. This can be illustrated using the concepts of inscribed and circumscribed circles: inside each object is the one circle, and every object exists within the one circle.² [A diagram showing multiple objects within a larger encompassing circle could visually represent this.]

The orbit of the planets around the sun provides a concrete demonstration of this principle. Each planet has a particular motion around the sun, and it is the motion—its speed and distance in relation to the sun—that influences the planet’s composition, whether gas or rock. The asteroid belt separates the inner from the outer planets, yet all are governed by the circular motion of the solar system. Even though each planet exhibits a distinct orbit, the overall motion encompasses all the planets collectively. The gravity of the sun relative to each planet maintains the system’s coherence: each planet is physically encompassed by the circular motion, yet the motion is expressed individually for each planet.³

Externally, there are many ones, or the one manifests as many: each object takes on an individual form. Internally, the one is many: the same thought transforms itself into every idea. The meditation between the one and the many, void and atom, constitutes their very relation. Outside my thought, each idea takes on one form; inside my thought, the one form—my thinking—takes on many ideas. Externally, matter is where my ideas exist individually; internally, thought unites them.⁴

The atomists confused the “indivisible” with the nature of matter instead of thought. Matter is always divisible, indeed infinitely divisible; what they called “indivisible” refers not to matter itself but to the activity of division, which is indivisible in its process.⁵

This leads to the problem of infinite regress, often considered a difficulty in philosophy. However, infinite regress is not a problem but a feature of the infinite. Regress is commonly misconstrued as a return to a less developed or primitive state. In truth, the so-called “former state” may represent the most advanced state, and development consists not in moving beyond it, but in the actualization of its inherent potential.⁶

Footnotes

1. Kirk, G. S., Raven, J. E., & Schofield, M., The Presocratic Philosophers, 2nd ed., Cambridge University Press, 1983, pp. 303–305.
2. Visualization of inscribed and circumscribed circles as metaphors for internal and external relations of thought and matter can be found in Plato, Timaeus 50d–51c, and in modern interpretations of geometric metaphysics.
3. Newtonian astronomy and orbital mechanics illustrate this principle; see Newton, Principia Mathematica, Book I, Proposition 6.
4. Whitehead, A. N., Process and Reality, 1978, pp. 29–32; on the internal-external relations of events.
5. Plato, Parmenides, 132a–c; discussion on the indivisibility of forms versus matter.
6. Infinite regress discussed in Aristotle, Metaphysics 1045b15–25; the return to a “prior state” is part of actualization rather than a deficiency.

Plato (c. 427 – c. 347 B.C.E.), had he been familiar with the atomism of Democritus, would likely have objected to its mechanistic materialism. He argued that atoms merely colliding with one another could never account for the order, beauty, and harmony of the cosmos. In his dialogue Timaeus (28B–29A), the character Timaeus asserts that the cosmos is not eternal but created by a divine craftsman, who shaped it according to an eternal and unchanging model. This model was mathematical in nature, reflecting Plato’s conviction that geometry and proportion underlie the structure of reality.

Within this framework, Plato described the four classical elements—fire, air, water, and earth—not as indivisible corpuscles, but as composed of geometric forms, which themselves were built from triangles. These “simple bodies” were regular polyhedra, later known as the Platonic solids. The cube, with its stable square faces, was assigned to earth, symbolizing solidity and immobility; the tetrahedron, with its sharp points and penetrating edges, was assigned to fire, reflecting its agility and capacity for motion. The octahedron and icosahedron, possessing blunter points, were assigned to air and water respectively, as they were less mobile than fire but more fluid than earth. Each face of these solids was composed of right-angled triangles: the cube’s square faces contained four isosceles right triangles, while the triangular faces of the tetrahedron, octahedron, and icosahedron contained six right-angled triangles each.

Plato’s geometric model provided a rational explanation for the transformations among the elements, as the triangles could be reassembled to form different polyhedra, which in turn corresponded to different elements. In this way, changes in material substance were not random or purely mechanical, as the atomists suggested, but regulated by a deeper, mathematical order, reflecting his belief in the intelligibility and harmony of the cosmos.⁸⁹

On a deeper level, it seems that the atomists and Plato were observing different dimensions of the same objects. Plato focused on the rational, abstract nature of things, while the atomists concentrated on the material or structural aspects of those forms. The Platonic solids, for instance, are idealized geometrical forms that exist perfectly in the realm of abstract mathematics. Yet these geometric structures themselves can be seen as composed of further, indivisible forms—analogous to atoms, which are the rare, simple bodies that constitute the material structure of everything. However, the atoms are not the ultimate substance; rather, they compile and express the higher-level Forms.

Instead of treating these theories as inconsistent with one another—a position that can lead to dead-end reasoning, or, in Hegel’s terms, the negation of reason—we can view them as complementary perspectives on the same objects. In this sense, the Forms are abstract, perfect, and incorruptible, existing as incorporeal ideals, whereas atoms are physical structures that mediate the connection between objects and the observer, providing the tangible basis from which perception and experience arise. The Forms and atoms thus represent two dimensions of reality: one ideal and intelligible, the other material and perceptible, yet both interdependent in constituting the fullness of being.¹⁰¹¹

Footnotes

8. Plato, Timaeus, 28B–29A. On the creation of the cosmos according to an eternal model.
9. Cornford, F. M., Plato’s Cosmology, Routledge, 1937, pp. 65–72; discussion of the geometric structure of elements and Platonic solids.
10. Plato, Timaeus, 28B–29A; discussion of the abstract geometric Forms underlying physical reality.
11. Hegel, G. W. F., Phenomenology of Spirit, 1807; discussion of reason, negation, and the reconciliation of apparent contradictions in philosophy.

The Rejection of Atoms

Sometime before 330 B.C.E., Aristotle asserted that the classical elements of fire, air, earth, and water were continuous rather than composed of indivisible atoms. He argued that the existence of a void, as required by atomic theories, violated physical principles. Change, in Aristotle’s view, did not occur by the rearrangement of atoms to form new structures, but rather by the transformation of matter from potentiality to actuality. For instance, a piece of wet clay, when acted upon by a potter, fulfills its potential by becoming an actual drinking mug. Aristotle has often been criticized for rejecting atomism, but in ancient Greece, the atomic theories of Democritus were considered “pure speculations, incapable of being put to any experimental test.”¹ Granted that atomism would eventually prove more fruitful than any qualitative theory of matter, in the short term, Aristotle’s theory would have seemed more promising.²

The senses, Aristotle argued, require a synchronization to achieve complete knowledge of objects. Atomists attempted to account for perception by positing films of atoms sloughed off from the surfaces of external objects, which then impacted the sense organs. All sense perceptions were explained as resulting from the contact of these atomic films with the atoms of the observer’s sensory organs. Color, for instance, was said to depend on the orientation or “turning” of the atoms; tastes were determined by the texture of atoms on the tongue (e.g., bitter tastes resulted from sharp atoms tearing the tongue); and sensations of heat were attributed to atomic friction. Democritus, Aristotle claimed, even considered thought to be a material process, involving the rearrangement of bodily atoms, just as perception was.³

Connecting Geometry with Atoms

Plato’s Timaeus provides a complementary approach to the atomists’ material focus. The geometrical simple bodies—the cube, tetrahedron, octahedron, and icosahedron—represent the elemental structure of reality, with each solid composed of triangular faces. For example, water, as an icosahedron, has 20 faces, each subdivided into 120 triangles.⁴ While the atomists emphasize the material and structural arrangement of atoms, Plato focuses on the abstract geometric order that underlies all matter. The two perspectives can be reconciled: atoms correspond to the building blocks of the geometrical forms, while the Forms themselves represent the perfect, intelligible structures that the atoms instantiate.⁵

It is difficult to conceive of an object without the senses, yet the senses themselves only capture the object in a particular way: a distant object seems smaller, a close object larger. Sensation selects a relative perspective, but the essence of the object remains the same. Pure thought, in contrast, apprehends the object as it is in itself, independent of the distortions of perception. Sensation, then, is a specific mode of apprehending the object, while intellect abstracts the universal concept. For example, when observing a tree, we experience it phenomenologically as a completed individuality, yet our mind apprehends the underlying notion of “tree-ness” through pure thought.⁶

Conceiving a tree by pure thought generates the idea of a chair, as well as other notions, by attributing properties such as size, shape, color, and function. These are not mere aggregates but are perceived as wholes through sensation; yet they correspond to the conceptual ideas in the mind of the observer. In this sense, the mind projects its idea outward, akin to a holographic image projected through a lens: the external world is the primordial matter, a quantity of mind made manifest as space. Sensation perceives the externalized idea, while the harmony between the quality (idea) and quantity (external form) constitutes the principle of reality. As Langan argues, nothing exists outside reality; any perception or idea is already a part of the universal principle of being.⁷

What appears as a whole object is in fact a particular, and the details that constitute it are themselves general principles, realized in the structure of the whole. This reflects a logical inversion: the premise is general, while the conclusion appears particular. For example, if X is a mammal, then X is an animal; the conclusion appears general in form but is particular in content, while the premise appears particular in structure but is general in form. Similarly, when we perceive objects through sensation, we often mistake the specific sensory apprehension for the object’s true universal nature.⁸

The concept of the externalization of ideas does not imply an “outside” in a spatial sense. The idea of an outside only arises when two things are contained within a relation; in the universal container of reality, what appears as external is already internal to the structure of the whole. Thus, the atomist’s focus on external structures and Plato’s focus on abstract Forms are complementary, capturing the material and intelligible dimensions of the same underlying reality.

Footnotes

1. Aristotle, Physics, Book IV, 209b–210a; discussion of matter, potentiality, and actuality.
2. Cornford, F. M., From Religion to Philosophy: A Study in the Origins of Western Speculation, 1932, pp. 45–47.
3. Aristotle, De Anima, II.5–7; Democritus’ material theory of thought and perception.
4. Plato, Timaeus, 53–55, 28B–29A; geometric structure of the four elements.
5. Langan, C., The Philosophy of Knowledge and Reality, 2012, ch. 4; comparison of atoms and Forms.
6. Husserl, E., Ideas: General Introduction to Pure Phenomenology, 1913; phenomenological perception versus intellectual conception.
7. Langan, C., The Philosophy of Knowledge and Reality, 2012; principle of reality and the externalization of ideas.
8. Russell, B., The Analysis of Matter, 1927, ch. 2; logical relations between premise and conclusion in perception.

The Spherical Hole and the Externalized Idea

The spherical hole may be considered as the form of the idea externalized. Quality presupposes its own quantization as the measure of its activity. The quantity of quality indicates a standard characteristic and thereby constitutes the standard for its own production, underlying the drive for creation beyond the given. The process of continuous production is quantitative in that it is analytic, and thus quality requires itself to maintain and extend its activity. This function of quantity, in turn, demands from quality the maintenance of its integrity; the quantitative aspect ensures that quality is refined and sustained.

This dynamic can be observed by comparing the totality of perceived objects against the experiences of individual perceivers. Each individual life form will inevitably die, and with it, their unique perception of the world will cease. Yet, species as a whole persist; the genus persists even if particular species die out. Whereas individual consciousness is finite, the collective or universal aspect of perception remains, revealing that life is fundamentally indivisible from the object of perception.ⁱ Langan illustrates this with the principle of the holographic nature of reality, in which the whole is reflected in each part and each part contains the whole externally, mirroring the continuity of perception across individual life forms.ⁱⁱ

At 41:07 in his lectures, Langan notes that when we judge something to be a circle or a square, we are identifying a real shape, which is intrinsic to the object and not merely its apparent shape. Real shapes, which concern science, must exist within a real space, distinct from the relative space of individual participants. Russell also emphasizes that geometric shapes cannot be perceived directly in the way physical objects are; a line, for instance, is not “seen” as an object but is understood through relations between points or objects.ⁱⁱⁱ For example, during an eclipse, we may say that the sun, moon, and Earth form a straight line—but the line itself is not perceived; it exists as a relational property. This does not negate its reality or the possibility of direct conception.

Direct conception is achieved not through sensation but through abstraction. Abstract forms, such as lines or circles, exist independently of perception because they are quantum in nature. Quantum properties dissolve the classical distinction between mind and nature: abstract forms exist both in nature and in the mind, and our faculty of reason allows us direct knowledge of these forms.ⁱⁱⁱⁱ In other words, quantum mechanics provides a bridge between sensory experience and rational abstraction. While we cannot always perceive abstract forms directly through the senses, their existence in the physical and conceptual realms is real, as demonstrated by the patterns and symmetries observable in quantum phenomena.

At 43:01, Langan further explains that the relative position of objects to the perceiver determines the shape derived through sensation. From one angle, an object may appear oval; from another, circular. The true circle, which we may not perceive directly, exists independently of our observation. This highlights the distinction between apparent shapes (sensation-dependent) and real shapes (existence-independent).

Finally, time indicates the occurrence of events: it is the measure of change and process, capturing the continuous unfolding of reality. In the Whiteheadian sense, time is not merely a container but a record of occurrences, of actual events as they come into being.ⁱⁱⁱⁱⁱ

Footnotes

i. Langan, C., The Philosophy of Knowledge and Reality, 2012, ch. 4; holographic principle of perception and continuity of species.
ii. Langan, C., Lecture 41:07, discussion of real geometric forms versus apparent shapes.
iii. Russell, B., The Analysis of Matter, 1927, pp. 45–50; the distinction between perceived objects and abstract geometrical relations.
iv. Langan, C., The Philosophy of Knowledge and Reality, 2012; quantum nature of abstract forms bridging mind and nature.
v. Whitehead, A. N., Process and Reality, 1929, ch. 2; concept of time as the measure of actual occasions or events.

Atmosphere as Atom Sphere

The atmosphere of perception can be thought of as an atom sphere. In this analogy, the Earth itself can be considered an atom. From a close viewpoint, the Earth appears as a complex mass, teeming with processes, interactions, and observable qualities. Mountains, oceans, weather systems, and ecosystems are all revealed in detail when observed at close range. From a farther perspective, however, the Earth is perceived more simply, as a singular unit—an atom in a conceptual sense. Atoms, then, can be understood as perceptions of objects stripped of their qualitative detail, capturing only their fundamental existence. In a way, the closest perspective and the most distant perspective are united: the atom represents the object at its minimal resolution, while close observation reveals maximal differentiation.ⁱ

The perspective of an object, such as a planet, influences the amount of detail perceived. When an object is near to the observer’s conceptual focus, its details and qualities are more fully revealed. Conversely, the atom represents the object in its least resolved form, the most fundamental level of its being, appearing small or distant not in physical terms but in terms of conceptual abstraction. Here, distance functions as a measure of resolution: it defines the degree to which an observer extracts and apprehends the object’s qualities. The more quality the observer perceives, the more fully the object’s reality manifests externally; the less the detail perceived, the more the object is seen as an atom—a fundamental, universal, and relatively undifferentiated unit.ⁱⁱ

Seeing an atom is, in essence, perceiving the object in its least conceived and most fundamental state, independent of external observation. This can be illustrated through an analogy with organic development. The human embryo, for example, is less differentiated, less aesthetic, and simpler in form than the fully developed adult. Yet the embryo contains all the potential for the adult human body: arms, legs, hair, mind, and consciousness. Similarly, an atom is the potential of the fully developed object, capturing its essential, underlying reality, while the fully observed object is the expression of its potential through the manifestation of detailed qualities.ⁱⁱⁱ

In this sense, the atom is both minimal and foundational: it represents the object in a state that is conceptually simple, yet ontologically fundamental. Just as the embryo contains the full potential of the adult, the atom contains the full potential of the object, albeit in a form that is stripped of particular qualities and observable details. The atom is therefore the bridge between potentiality and manifestation, between the abstract conception of an object and its detailed appearance in the world.ⁱⁱⁱⁱ

Footnotes

i. Langan, C., The Philosophy of Knowledge and Reality, 2012; discussion of perception and resolution of objects.
ii. Whitehead, A. N., Process and Reality, 1929, ch. 2; concept of potentiality and actualization in relation to perception.
iii. Plato, Timaeus, 28B–29A; conceptual analogy between forms, elements, and minimal representations of objects.
iv. Democritus, in Simplicius, On Aristotle’s Physics, 24–30; atom as the potential of macroscopic objects and carrier of fundamental reality.

last updated 1.4.2026