Section 42 (first updated 2.12.2021)

Infinitesimal and Continuity

The infinitesimal is not merely a general continuity; rather, it is the infinite continuity within a discrete point of singularity. This means that, on the one hand, there are an infinite number of separate discrete points whose total amount is innumerable—they cannot be counted as individually separate units. This very innumerability constitutes their limitation: any number of different objects that can be counted is inherently finite.

Thus, the infinite is not the countless multitude of discrete objects; rather, it is the set of possible forms or shapes that a single object may assume at any discrete point separable from another object occupying its own discrete point.

All such forms are the infinite shapes that an event may take when disclosed within a discrete measure. The total number of discrete events is finite, but what happens within each individual event is infinite.

Hence,

Infinity = Finite

Peirce points out that the infinite is itself finite.¹ This means that the finite, by definition, assumes uniqueness. But there are infinitely many finites. The infinite is the collective expression of finite things, each of which is unique, yet each expresses the same infinite form: the capacity to differ without limit. Thus, each finite is at the same time an infinite.

This contradiction means:

• each finite, being unique, exists externally to all other unique finites;
• yet all finites share the infinite nature that every finite is infinitely different from every other.

Numbers illustrate this:

1, 2, 3, 4, 5 …

Each number is unique, but each is generated by the infinite form of addition.

3.4 Continuity

Peirce notes that, according to Kant, continuity consists in infinite divisibility—the idea that between any two variables in a series a third can always be found.² Division thus constitutes continuity. However, Peirce argues that although Kant identifies a key feature of continuity (that it is divisible), he fails to address the mathematical and logical difficulties that this definition creates.

In particular, Kant’s definition poses a problem when comparing:

• a series of numbers
• with points on a line

Both are continuous, but in different senses. The entire series of rational fractions ordered by magnitude is an infinite series, but the points of a line are innumerable. Between any two rational fractions, a third can be found, yet the points on a line cannot be treated as merely divisible without destroying the line. The line must be divisible while remaining whole. Thus, in what sense can the points in a line be distinct from the line itself?

Kant’s definition produces a tension between the numerable and the innumerable.

Rational fractions are considered divisible, while line-points are considered continuous, but this explains neither the nature of the rational fractions nor the internal relation of points on a line.

Cantor and Concatenation

Cantor defines a continuous series as “concatenated”—a perfect chain whose parts are linked in such a way that any finite distance between two points can be traversed by a sequence of increments each smaller than that distance.³

In other words, if there is a finite distance between point A and point B, that finite distance contains an even smaller distance, and that smaller distance contains a yet smaller distance, and so on. Continuity here is the idea that a finite interval contains an infinite regress of sub-intervals.

Peirce argues that Cantor’s definition is merely “a definition by negation,” because it does not specify what components make up continuity, only what continuity does not exclude.⁴

Kant’s Gap Problem

Consider:

A……….B   C……….D

Suppose B and C constitute a gap. According to Kant’s definition of continuity, either B or C—or both—must be excluded; otherwise a point between them must exist. If the series contains C, even if it contains all points up to B, it cannot contain B, because then B would be indistinguishable from the points leading to C.⁵

Peirce concludes: if a continuum contains a series approaching a limit, the limit must also be included in the continuum.

Aristotle and the Limit

Consider the infinite decimal series between 0 and 1:

0, 0.1, 0.11, 0.111, … , 1

According to Aristotle, the series between 0 and 1 is continuous; therefore there must be a “least” real number greater than every number in the endless series.⁶ If we abstract a number such as 0.111, that number becomes a limit: it is greater than all previous numbers and less than all subsequent ones.

Yet, because an infinite number of numbers lie between any two decimals, the limit is itself infinitely limiting. For Aristotle, limits are qualitative standards: each limit defines the relation between its neighbors.

Peirce and the Infinitieth

According to Peirce, continuity presupposes infinitesimal quantities. These imply an “infinitieth” place of decimals—an infinity in sequence.⁷

Thus each number presupposes infinitely many decimal points between it and every other number:

1, 1.1, 1.11, 1.111 … → 2,
2, 2.1, 2.11, 2.111 … → 3, etc.

The infinitesimal captures the magnitude of infinity within a sequence.

Apeiron and the Infinite as Limitless Passage

The infinite has always been one of the most challenging concepts in mathematics and metaphysics. The ancient Greek term apeiron (“unbounded”) is defined by Aristotle as:

“A quantity is infinite if we can always take a part outside.”⁸

This is identical to what we mean by the spatial infinite: space is that from which we can always take more, a perfect example of a finite expression of infinity. Space serves as nature’s practical use of infinity: we can always move outside the position we occupy; we can move beyond ourselves indefinitely. Space is therefore both:

• an infinite extension, and
• a finite here, the particular position we now inhabit.

Footnotes

1. C. S. Peirce, “The Law of Mind” (1892), Collected Papers 6.102–6.103: Peirce’s claim that the “infinitesimal is itself finite.”
2. Immanuel Kant, Critique of Pure Reason, A25/B39–A26/B42, on the “composition of the continuum” as infinite divisibility.
3. Georg Cantor, Foundations of a General Theory of Sets (Grundlagen, 1883), §§2–4, on Kettenbildung (concatenation).
4. Peirce, Collected Papers 6.109–6.111.
5. Peirce, Collected Papers 6.112–6.114, illustrations of gaps and limits.
6. Aristotle, Physics III.6 (206a6–206b13), the infinite as “that from which one can always take more.”
7. Peirce, Collected Papers 6.115–6.120, on the “infinitieth” decimal and the infinitesimal.
8. Aristotle, Physics III.6 (206b): apeiron as that which is always further divisible or extendable.

Infinity, Limits, and Continuity

Having a basic grasp of the infinite is necessary for understanding the nature of development in terms of continuity.

The notion of the limit is generally used to “solve” the infinite. The common view is that the infinite is simply the sum total of all finite numbers. For Peirce, however, this is “an irrational prejudice,” because infinity is not a collection of finite units but rather the incommensurable relation that produces numerable results.¹ In other words, infinity is not a heap of discrete quantities scattered like objects in space. That conception stems from sense-perception, which sees objects as isolated and then assumes that their indefinite aggregation yields “the infinite.”

Peirce distinguishes finite from infinite quantities through what he calls the syllogism of transposed quantity.² This method presupposes certain limiting conditions within a series to test whether a conclusion follows. Peirce gives the example: if every young Frenchman claims to have seduced a Frenchwoman, if a woman can be seduced only once, and if the populations of young men and women remain fixed, then every woman must eventually be seduced. The reasoning appears valid until one considers the actual conditions: populations increase, a woman can be seduced more than once, and the average age difference shifts. Once these incommensurable factors enter, the conclusion collapses. The finite presuppositions could not accommodate what is effectively an indefinite situation.

According to Peirce, the syllogism of transposed quantity is not applicable to infinite series. Euclid is therefore mistaken, he claims, in treating the axiom “the whole is greater than the part” as universally valid.³ For infinite quantities, the relation between whole and part breaks down. Any limit imposed upon a series introduces an innumerable range of possibilities in which the limit itself becomes another member within the sequence. The so-called boundary between part and whole becomes arbitrary.

For example, as discussed earlier regarding motion, the part–whole distinction is not a natural separation but an abstraction. A “part” is simply the whole viewed under a restricted set of conditions. A heart, for instance, ceases to function without the whole organism. Likewise, the supposed “part” of a quantity has no independent existence apart from the whole of which it is an abstraction.

The Problem of the Limit

Infinity, when understood purely in terms of scale, is said to be “unlimitedly large.” Mathematics introduces the concept of the limit, especially in calculus, to deal with the infinite by transforming it into a divisible sequence. Yet this approach encounters the same difficulties found in Kant’s account of continuity, which relies on infinite divisibility.⁴

Peirce objects to the term limit because it implies a boundary separating one value from another, suggesting a discontinuity or a “gap.” A genuine continuum, however, does not contain such separations.

To illustrate the arbitrary nature of the limit, Peirce refers to what he calls the Aristotelian principle, which he considers crucial.⁵ Imagine a surface divided into a red region and a blue region, with every point either strictly red or strictly blue. Peirce asks: what is the color of the boundary line separating them?

The answer is that red and blue exist only by being spread continuously over a surface, and the boundary shares the color of its immediate neighborhood. Therefore, the boundary between red and blue is both red and blue, not a third color.⁶ The limit is not something other than the variables; rather, the limit is their continuity.

Thus, red is not the limit of blue, nor blue of red. Instead, their relation—the point of transition—is the limit for both. As Peirce says: “the color of the parts of a surface at any finite distance from a point has nothing to do with its color just at that point.”⁷

Translated: the limit is not defined by either variable individually but by their relation.

The Self-Limiting Nature of Limits

A value that serves as a limit for a sequence also means that the sequence is, in turn, the limit of that value. Whenever something is the limit of all other things, all other things are likewise the limit of that something. Thus, the limit is self-limiting: every limit is bounded by another limit, and so on. The limit is always the point just beyond itself.

Consider the two sequences:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …

The second sequence (even numbers) is derived by doubling the first. Yet the sequence of even numbers appears larger, even though it is generated entirely from the first. If we look only at the finite numbers, a paradox emerges: the set of even numbers seems larger, but is perfectly one-to-one with the whole numbers.⁸

This shows that number series cannot be understood by their members alone; one must understand the relations between members. Each number in the series captures the relations of the previous numbers.

For example, if we select 5 as the interval-limit of the series, then all relations among 1–4 constitute the conditions for 5. Possible combinations include:

• 1+1+1+1+1 = 5
• 2+3 = 5
• 1+1+1+2 = 5
• 4+1 = 5

Similarly, numbers after 5 relate back to 5 by subtraction:

• 12 − 7 = 5
• 14 − 9 = 5

Thus, a limit is the culmination of all possible relations leading to it, and each relation is constrained by the totality of the series up to and beyond it.

Infinitesimals as Magnitudes of Infinity

Peirce prefers the term infinitesimal to “limit,” because the infinitesimal resolves the self-contradictory structure of a limit that is endlessly limiting itself.⁹ In this sense, the infinitesimal measures the magnitude of infinity.

Peirce expresses this idea using the equation:

A + i = A

where A is finite and i is infinite.¹⁰ The equation states that the finite plus the infinite yields the finite—because anything “beyond” the infinite is simply the infinite itself. Infinity, taken in its totality, is a single finite point that is indefinitely self-transcending.

The Limit in Mathematics vs. Logic

In calculus, the limit is a value that a function approaches but never fully attains. The limit is thus an abstract placeholder for the next value—an endless approach, a regulated infinite regress. This infinite regress is essential to derivatives, integrals, and continuous change.

In logic, the relation is inverted. The infinite is the limit. For Aristotle, the infinite taken as a whole is still a kind of finitude: no matter how large or small a magnitude is, it is measurable as a totality, and whatever is measurable as a whole is finite.¹¹

The finite is finite because it is restricted to what it is. But the infinite is finite because it is the totality of all possibilities of finitude. Aristotle describes the infinite as an activity—a continual surpassing of limits—not as a completed object.

Thus, in the domain of thought, reason is the infinite substance expressed through finite forms. Each finite form is an abstraction from the infinite activity that gives structure to thought. Each finite form functions as an interval-limit of the infinite activity: the infinite views itself from each finite point.

Footnotes

1. C. S. Peirce, “The Law of Mind” (1892), Collected Papers 6.538.
2. Ibid., 6.538–6.539.
3. Euclid, Elements, Book I, Common Notion 5; Peirce critiques this in Collected Papers 6.539.
4. Immanuel Kant, Critique of Pure Reason, A25–A30/B39–B45, on infinite divisibility and continuity.
5. Peirce, Collected Papers 6.545.
6. Aristotle discusses similar cases in Physics III and Metaphysics V–X, on continuity and limits.
7. Peirce, Collected Papers 6.546.
8. This is the classical form of Galileo’s paradox and also treated in Cantor’s early set theory.
9. Peirce, Collected Papers 6.545–6.547.
10. Ibid.
11. Aristotle, Physics III.6, 206a–206b, on the infinite as “that from which one can always take more,” and on the infinite as an activity rather than a completed whole.

Infinitesimal

The concept of the infinitesimal describes the magnitude of existence. Magnitude usually refers to size and scale, but both notions ultimately depend on the concept of the infinite. Magnitude concerns the nature of matter: for Kant, matter is essentially divisibility;¹ for Cantor, matter is structured by orders of infinity;² and for Peirce, the infinitesimal resolves the infinite by making it particular—by giving infinity a definite point of determination.

The term infinitesimal presupposes a culmination at the smallest possible degree. The term culmination is not incorrect, but misplaced, because it treats the infinitesimal only as a quantitative measure of being—as if the last point in a series were simply the numerical sum of all preceding points. If this were true, then the “greatest” point in a series would always be greater than itself, violating the law of non-contradiction: a number would be both the greatest and not the greatest at the same time, which would destroy its divisibility.

For example, consider the ordinary series:

1, 2, 3, 4, …

If 4 were merely the quantitative outcome of the preceding numbers, then the sum of the preceding numbers (1+2+3=6) would exceed 4. How, then, does 4 follow 1, 2, and 3? The answer is that 4 is not merely a quantity but a quality: it embodies the real relations which condition its expression. The number 4 expresses the structure of all prior relations:

• 1 + 1 + 1 + 1 = 4
• 2 + 2 = 4
• 3 + 1 = 4

Being as Quality

Being is fundamentally a quality—an essential determination characterized by its activity. In Aristotelian terms, being is an energeia, an activity that takes on form;³ and each form brings with it the efficient cause that sustains it. Peirce interprets this as the level of generality, which refers to laws, tendencies, and persistent relations.⁴

The general state consists of two inverse determinations, each receiving its particular character from its difference from the other. Their difference is precisely the similarity they share: a relation which is more fundamental than either particular alone. The relation is the being of which the particular determinations are attributes.

The general is essential because it discloses the relation between the parts, while the particular is essential because it expresses the general in a determinate form. Thus, to ask what the infinitesimal is as the culmination of being is to question whether being is the result of parts, or whether the parts are expressions of the whole. Logic demonstrates that the latter is true: each particular is an expression of some whole, which is to say that being is substance—that which has an essential nature directing its activity.

Difference Between the Infinitesimal and the Infinite

The infinitesimal and the infinite differ fundamentally. The infinitesimal is an endlessly small magnitude; the infinite is an endlessly large magnitude. In both concepts, an innumerable series of finite points may be selected arbitrarily.

In the series 1, 2, 3, 4, 5,
we may choose any number as a limit.

The infinite allows us to indefinitely extend the series beyond any arbitrary point (e.g., from 5 to 5,000,000). The infinitesimal, by contrast, allows us to choose an arbitrary finite point and treat it as the general point governing all that precedes it. Thus the infinitesimal refers to a limit from below, whereas the infinite refers to a limit from above.

For example, in:

1, 2, 3, 4, 5

5 is the general limit of all preceding numbers (1–4), and also the structural expression of all configurations that sum to it:

• 1+1+1+1+1
• 2+3
• 1+1+1+2

Each number is both a quantity (a unit double or half of others) and a quality: it is greater than all previous numbers and smaller than all that follow. Each number stands in a special relation to its immediate predecessor and successor.

Thus:

• 2 relates uniquely to 1 and 3.
• 3 relates uniquely to 2 and 4.
• 3 is the number after 2 because it is the number before 4.

In this way, 3 is structurally similar to 1 and 2, because each occupies a relational position defined by both what precedes and what succeeds.

Time and the Infinitesimal

The structure of number relations mirrors the structure of time:

• The past requires the future as the aim toward which it tends.
• The future requires the past as the basis from which it proceeds.
• The present requires both: it leaves one behind and enters the other.

From the past we speak only of what has been.
From the future we speak only of what will be.
In both cases, the thing in question is not present.
The present contains both potentialities and both absences.

Reason as the Quanta

Reason is the quanta: the smallest unit that cannot itself be quantified. It is a quantity that is not a particular thing, but every possible kind of thing—infinite in its potential determinations.

Peirce asserts that the infinitesimal exists as a continuity.⁵ This continuity can be understood in two related ways:

(1) The Infinitesimal as Temporal Continuity

At the smallest unit of time, ideas emerge with intensity. Their intense relations generate contradictions—e.g., the idea of a circle and a square immediately conflict. This conflict is pure process. The contradiction generalizes into a higher-order unity: a new form distinct from each term taken alone. This is the general level.

(2) The Infinitesimal as Spatial Continuity

We can also deduce continuity by moving downward from the general to the particular. Between any two distinct objects there is an infinitesimally small quantitative continuity. For example, when you see a chair, there must be a physical continuity between your eyes and the chair: the light that travels from the chair to your retina. Without this continuity, the chair would not be registered as an object.

From these two perspectives, mind—if it constitutes the nature of matter as the unquantifiable quantity—is the continuity of all relations.

Indivisibility as the Ground of Divisibility

An unquantifiable quantity does not mean something unmeasurable, but something infinite. We can measure only finite segments of an infinite magnitude, but the infinite cannot be exhaustively defined as a number. The infinite is therefore indivisible; it cannot be partitioned into isolated parts.

Yet the indivisible can produce divisible parts. Indeed, indivisibility must precede divisibility, because if everything were divisible without limit, no relations could hold together. There would be no unity, no structure, no coherence.

Thus:

• What is divisible must be grounded in what is indivisible.
• What is separate must be grounded in what is continuous.
• What is finite must be grounded in what is infinite.

This indivisibility is thought—reason itself.

Footnotes

1. Immanuel Kant, Critique of Pure Reason, A48–A49/B65–B66, on matter as the “movable in space” and its divisibility.
2. Georg Cantor, Contributions to the Founding of the Theory of Transfinite Numbers (1895–97).
3. Aristotle, Metaphysics, Book Θ (Theta), especially 1046a–1050a.
4. Charles S. Peirce, “The Law of Mind” (1892), Collected Papers 6.10–6.22.
5. Ibid., 6.545–6.547.

Continuity of Time into Consciousness

The infinitesimal is defined by continuity, and continuity is defined by time, and time is defined by consciousness, and consciousness is defined by ideas, and ideas are expressed by feeling. This entire process is demonstrated by mathematics and the logical understanding of infinite numbers in relation to finite. This describes how the infinitesimal is continuity, how that continuity is consciousness in time, and how what is consciousness in time is the spreading of ideas. The law of mind is the infinitesimal.¹

(Find logic and math)

The idea of infinity in mathematics is generally understood by finite numbers, that is, the sum total of all finite numbers is considered the infinite.² (Talk about Gödel’s incomplete theorem)³

Peirce made the abstract concept of infinity concrete by associating it as the infinitesimal.⁴

Infinitesimal Indivisible

The idea of the infinitesimal aims to explain how we can divide an indivisible substance. What it means for a substance to be indivisible just means that the substance is abstract; in other words, the physical representation of it does not comply with ordinary matter of classical physics—analogously its physical make-up is more holographic.⁵ This substance is the infinite complexity of mind bundled up into a warped, undiscerned, and undetermined slab of nature. Plato calls it the Forms; Aristotle describes it as thought; Hegel as reason; Whitehead describes it as a relatum; psychologists like Jung describe it as a complexity and the unconscious; Einstein calls it spacetime—all these are different perspectives of the same infinite fundamental nature.⁶

The infinitesimal concerns how this is divided, that from a certain perspective it appears to be a two-dimensional object in space, but as the observer develops momentum in motion and therefore acceleration toward it, it becomes a three-dimensional object. It begins to transform into particular and specific finite objects that are composited. Consciousness goes at the speed of light in respect to this object, and therefore becomes a particle-state, becomes a finite and specific thing within it.⁷

Let us apply our general ontological scheme to this more definite conception of substance. If we start, let’s say, at the beginning—as furthest back—or the state that is furthest unlike the state we are in at this moment right now, in this state we have an indiscernible state of nature: an infinity, which is the indeterminacy of everything. This fills in the content of the notion that if we begin with nothing, that itself is a something. If we have an infinity that is everything, that itself is still a single thing, or rather an identical conception. However, it is not a single thing in being one thing distinct from another, because in this case we have a multiplicity of separate things, the collection of which constitutes their whole.⁸

When Aristotle proposes the claim that the “whole is greater than the sum of its parts,” this means that the efforts generated by all the parts working together outweigh the maximum effort any single part may have on its own. However, this so-called collective energy is not a result of the parts merely coming together to make it happen; it is rather, according to Aristotle, a potential energy that is at the base, which the parts tap into and access and therefore actualize, or they are the products that realize it.⁹ It is this latter claim that is confusing because we ask where such a potential energy exists. However, as to where it exists is the wrong question in the first place. The conception of infinity as a distinct self-identical thing is none of these.

So how is the conception of infinity—of everything—a distinct thing while not being any single and specific kind of thing? This can be answered by the next ontological claim following the proposition that if nothing is itself a being, then being is technically nothing, or rather no-thing, not a single thing; that is the feature, not a negation. But as we stated, it cannot be the sum total of all single things, since we cannot propose what we are trying to prove. So how can the characteristic of being be nothing and define fundamentally what a thing is?¹⁰

From a purely spatial domain this cannot be true, because when a thing is being it cannot be at the same time nothing. Rather, nothing stands relative to it as what it is not, or rather an other—whether that be the space it maneuvers within or some other object occupying another location. The point is: an object cannot occupy the same position at the same time as some other object within the same space. However, both nothing and being can occupy the same space at the same time as they are opposite substances and are within each other, because one fills in where the other is not.¹¹

If we add the element of time, then it becomes clear how nothing can be the characteristic of a thing, because the characteristic of any particular kind of thing is that it is potentially itself. This means that before even coming to be the kind of thing that it is, it must have been not-that, and must have been potentially that; so that coming to be what it is, is the acting on its potential—it simply conceived its potential into being from nothing.¹² Moreover, in time it is the case that an innumerable number of different things can occupy the same point in time: they share the same year or moment, in other words, they share the same space in which events common to all happen simultaneously.

So if there is an infinity before us, and it is indiscernibly everything, and that is equal with no single thing—nor is it all things at once—then it must be the coming-to-be of one thing at one point in time. In order for everything to exist at once, it must have come to exist at one point in time, even if it was never created or destroyed but occupies the point of time we know as eternity, which is the temporal equivalence of entirety.¹³ It is the full content of the point of time.

But the partial point of time—the finite duration of time—is not a piece of this full point of time, because the eternal point of time is infinitely dense in space; it is indivisible. Therefore the finite point in time becomes distinct and separated from that in space—that which revolves around it, as we see galaxies revolving around the black-hole singularity.¹⁴

The nature of the universe has a very weird and strange physical layout, where things we take to be real things are literally on one side, and things we take to be indiscernible and only abstractly conceivable, like black holes or dark matter, are on the other side. In other words, light may only enter the black hole but cannot escape. In space these two sides are separated from each other but maintained gravitationally by their separation, while in time—[sentence breaks off but is preserved].¹⁵

How can a thing be nothing so that it can be any single thing at all? This is the only way everything can be any one thing at all: because everything is in a state of nothing, or rather an abstract state. This means that it can penetrate through things, navigate through them; it is, as Hegel calls it, spirit, which goes through things, and its going through them is at the same time the very becoming of them. Its penetration through them is their very creation.¹⁶

Footnotes

1. Peirce, “The Law of Mind,” The Monist (1892).
2. Standard mathematical definition of ℵ₀ and ordinal/limit concepts.
3. Gödel’s incompleteness theorem shows that no finite formal system can complete itself from within.
4. Peirce identifies infinitesimals with true continuity (“true continua contain infinitesimals”).
5. Analogy to the holographic principle (’t Hooft, Susskind).
6. Comparative metaphysics across major thinkers.
7. Rough analogy to relativistic frames and Planck-scale discreteness.
8. Infinite = indeterminate; cf. Aristotle Physics III.
9. Aristotle Metaphysics Θ (potentiality and actuality).
10. Hegel, Science of Logic, Doctrine of Being (“Being is Nothing”).
11. Dialectical complementarity.
12. Aristotle’s doctrine of potential being (dynamis).
13. Eternal vs. temporal: Boethius, Hegel, Peirce.
14. Modern GR description of singularities.
15. Black hole information structure; causal separation.
16. Hegel’s Phenomenology of Spirit (“Spirit is this movement”).

Moments

Whitehead, in The Concept of Nature, discusses the senses and “moments.” A moment is a state; it is not a passing incident. This means that a moment is the experience of itself for its own development. Moments in time become structures— they become concrete. A moment, in relation to time, takes on density. And it is this state that we call existence qua existence.^1 Our subjective experience conceives this process as a flowing stream of events constituted by a set of unrelated passing periods; once an event occurs, it no longer exists. Thus the past becomes merely a memory of the present, and the future possesses no reality yet. When we ask what past and future are, they are usually reduced to mere hypotheses. But potentiality is the future— the ability of the present to continue.^2

What we see as moments external to one another is in fact the experience of existence itself. This is what Einstein sought in the idea of the space–time continuum. However, he did not make the further connection between this fact about space and time and the fact that Reason is the experience of itself.^3 In this latter sense spacetime exists as concrete density. What he also did not further develop—quite understandably, since this truth lies beyond the subject matter of physics— is that spacetime is not merely a set of contingencies. Rather, space and time bear a qualitative relation to one another: the relation of the object. Space and time are different experiences of Reason and therefore the same reality in different states. The object, in this sense, bears a new external reality pressing against space and time. The object becomes the particular in tension with the universal. This tension determines the qualitative process of nature, culminating in the process of evolution— the development of self-realization. But before we consider this, we must understand how Reason functions as the entity of spacetime.

Planck length may be interpreted here as describing the “density” of Reason— the minimal grain or threshold of actualization.^4

Nature is the site in which such experience takes place. In nature the Idea takes on a concrete form: the object in nature is the manifestation of Reason as Idea. The Idea is the set of logical relations that constitute Reason. If we assume that Reason is merely the sum of such logical relations, our immediate intuition is that these ideas must exist in an abstract realm, scattered from each other, and only through this scattering do we obtain the random association of logical propositions; or, in materialist terms, the random process of external relations.^5 But such a view conceives Reason as abstract, belonging to nothing but itself. This abstract understanding does not reveal the ground from which Reason arises— namely, its organic development. Reason is organism. The organic, in the ontological sense, presupposes the inorganic as its antithesis. Any organic existence presupposes a whole in which it can operate as a living system. Reason, accordingly, must be understood as inseparable from the living entity. With this realization, the notion that Reason is merely the scattering of ideas in an abstract realm does not hold.

What does this realization imply? It implies that there exists an entity in which Reason lies as a whole. We may identify this entity as God. The term God, however, is so burdened by historical semantics that invoking it often obscures the concrete truth it is meant to indicate. Setting semantics aside, it is a fact— within this framework— that there exists some Being in which the whole resides: a Being that expresses Reason. This Being must be organic, meaning alive, not merely a mathematical algorithm. A purely mathematical system would have no necessity to self-actualize; it would already be pure actuality without potentiality.^6 This is what Whitehead means by fatigue, in contrast with Reason: fatigue is contentment with mere being. But the existence of space and time presupposes an immediacy to become what they are potentially. Their mathematical character is merely the skeleton of the process, only one variable within the organism.

Scientific materialism interprets the expansion of the universe as an infinite set of external relations between objects: each object multiplies, forming a surplus of additions. This view implies an infinite regress of material objects, each relative only to others. The ontological understanding of the universe, properly accounting for quantum states, indicates instead that the universe operates through internal relations. The universe is the inner self-reflection of itself. Its expansion is the inward multiplication of itself— the process of self-activity and the actualization of self-movement. Such terms are ordinarily associated with the notion of God, for only a being capable of free self-movement could set nature in motion through its own internal activity.

Footnotes

1. Whitehead, The Concept of Nature. Whitehead argues that nature is composed of “events,” not substance, and that events possess temporal thickness or “duration.”
2. This aligns with Whitehead’s distinction between actuality (present) and potentiality (future), later elaborated in Process and Reality.
3. The contrast between Einstein’s geometric spacetime and process-philosophical accounts of experiential becoming is a recurring theme in the secondary literature.
4. In physics, Planck length is the smallest meaningful scale; here you are employing it metaphorically or metaphysically as a density of experiential or rational actualization.
5. This section describes the contrast between external relations (Hume, Russell, classical materialism) and internal relations (Hegel, Bradley, process philosophy).
6. In classical metaphysics, a being lacking potentiality is termed pure act (actus purus). You argue that the universe’s dynamism implies a different, organic ground.

The Word “God”

According to Hegel, the notion of “God” is largely a matter of semantics apart from its meaning. He explains:

“In a proposition of that kind we begin with the word God. By itself this is a meaningless sound, a mere name; the predicate says afterwards what it is, gives it content and meaning: the empty beginning becomes real knowledge only when we thus get to the end of the statement. So far as that goes, why not speak alone of the eternal, of the moral order of the world, etc., or, like the ancients, of pure conceptions such as being, the one, etc., i.e. of what gives the meaning without adding the meaningless sound at all?”¹

The belief that nature is the product of God’s free will does not by itself indicate what is meant by the universe as self-activity. The universe operates according to the laws of Reason and is identified as self-activity only through these laws. But the term “law” should not be misunderstood as implying something fixed or static. The term merely clarifies that self-movement or self-activity—however one may describe it—is neither arbitrary nor outside the domain of Logic. The inquiry into how the universe operates as self-movement is the true task of quantum mechanics, for it is in quantum theory that each moment of self-movement becomes a systematic predisposition. Stage by stage, quantum mechanics seeks to identify the whole behind what presently appear only as fragments of Reason in the world.²

— Plato’s Timaeus

In the Timaeus, the attempt to describe the formation of the universe is a metaphysical account rather than a merely cosmological one. It is metaphysical in that it outlines the essential coming-to-be of the universe rather than its natural order—though the latter is implied by the former. The concept of “God” is introduced as the cause of the universe. Two possible interpretations of this “God” appear in the Timaeus.³

1. The Traditional (Theistic) Interpretation

On the first interpretation, God is understood in the traditional, monotheistic sense. The universe is created in accordance with God’s will; God is a conscious being who determines the world. This reading allows one to trace certain monotheistic notions back to Plato. Plato writes, for example, that the world is unique: “For this world is truly one, and there is not, nor ever will be, another like it.”⁴

2. The Rational or Impersonal Interpretation

On the second interpretation, God is the universal force directing the universe through the laws of Reason. The universe is Reason because God actualizes the Good in the world. The difference between the two interpretations is this:

• In the first, the Good depends on God’s will—Good is good because God wills it.
• In the second, God wills the Good because it is good—the Good is rational, and God is the activity of Reason itself.

This second interpretation is more consistent with Plato’s claim that the cosmos is crafted “as far as possible” to be good,⁵ suggesting that nature is produced in universal perfection, even though its particular parts undergo degeneration or death as required by the whole. Matter assumes form according to the virtues appropriate to each phenomenon; the material structure of objects embodies goodness insofar as it is mathematical in nature.⁶

Objection and Reply

A potential critique of the second interpretation is that Timaeus merely projects his own rational capacities onto the cosmos—e.g., when he describes the demiurge dividing the world (“he took away one part of the whole, and then separated a second part…”⁷). The argument is that Timaeus describes the world mathematically because he thinks mathematically, not because the world is mathematical.

However, this critique fails once we ask: Where does Timaeus’ Reason come from, if not the world? Or when does his Reason cease to be merely his own? When does his Reason extend beyond the man himself—beyond his particular circumstances and relations—and become universal Reason? Can a person tap into a Reason that transcends the individual? And if this universal Reason speaks through him, how are we to understand it? Timaeus understood it mathematically.

If Reason is derived from nature, then projecting Reason onto the cosmos is simply projecting nature onto itself. Whether his account is correct or not, it presupposes that human Reason originates in the world. The true projection in Timaeus is not Reason but anthropomorphic emotion—when he calls God “the father,” who “rejoiced” and “in his joy determined to make a copy.”⁸ These projections do not describe Reason itself.

But the characteristics of Reason—how Reason manifests through a human being—cannot be separated from the person himself. Man and Reason are synonymous; we cannot truly understand one without the other, except in abstraction. To describe a “pure Reason” beyond man is likewise only an abstraction of a more fundamental principle already within him. As we observe, the human being always embodies Reason, and Reason is expressed through him.

How we distinguish his emotions from the deeper workings of Reason is a further question—one that belongs to philosophy, and more specifically to psychology, which is the branch of philosophy concerned with epistemology.

Particle Physics and the Universal

In particle physics, the concept of a particle is often inherited from classical physics; however, modern quantum theory shows that matter and energy behave very differently from what ordinary experience suggests. Every particular object contains within it a universal process—its capacity for anything and everything. Implicit in the world of objects are the ideas conceived in the mind; both distinctions reflect the same underlying reality.⁹

Classical physics investigates general, observable objects. But inquiry into the universal nature of objects reveals a structure different from the relations described by general relativity. Subatomic inquiry shows that there is no essential distinction between the universal state of the particle and the quantum state. The quantum state is the universal state.

Whether one “zooms in” to the subatomic or “zooms out” to the cosmic scale, quantum laws appear operative. Direction is irrelevant; the quantum state is universal. Every object is a particular modulation of the universal, a moderated self-actualization of universal movement. Wave-particle duality expresses this: light operates as both particle and wave, revealing the universal process of matter. The uncertainty principle expresses the infinite potentiality implicit in particles. Each concept derived from quantum behavior is an instance of the operation of Reason.¹⁰

The Infinitesimal and the Infinite

The quantum particle is the atomic unity of space-in-time—a point where space assumes the form of an idea. The infinitesimal is the concrete expression of the infinite. (1) In the infinitesimal, the infinite takes on a particular, finite form—bounded and limited. This seems contradictory: how can the infinite have bounds? The contradiction arises only if we assume that the infinite has no form. But what if the form of the infinite is precisely the form that can assume all forms?

It is often claimed that the infinite has no form because it cannot exist in only one direction. But if the infinite exists in every direction, its very activity presupposes some ground enabling such determination. Consider the circle: it extends equally in every direction from its center, including into itself. Our habitual limitation of the infinite to locomotion—movement in space—prevents us from understanding its deeper nature. The infinite must be understood as capable of every kind of determination, including self-determination or becoming. (2) A particular form may thus still bear the nature of the infinite by expressing universal structure.¹¹

At the infinitesimal level the universal is specialized into a particular; but that particular contains within itself the means of extending itself universally. The idea at the infinitesimal becomes both a particular material form and a general form capable of taking on any further form. The infinite relates to itself through this contradiction between its universality and its particularization—squaring the circle. This contradiction is concrete and unresolved for a reason.¹²

Ideas, Minds, and Feeling

The notion of the “idea” is not limited to relations between separate minds. Rather, there is an infinitesimal relation implicit between minds—a material continuity at the infinitesimal level. The link between separate minds is feeling. Feelings take on quantitative, even material, form—Peirce identifies protoplasm as the medium of such “cells of feeling.”¹³ Feeling functions as a kind of attraction and repulsion, forming the basis for the “law of mind.”

This continuity is Consciousness: the continuity of ideas at the infinitesimal level. Here ideas bear immediate relations constituted by intensity. They contain contradictions harmonized into a unified whole. This whole expresses the abstract infinite, propagated as distinct energy states, each embodying an idea associated with Reason. The idea embodies the abstract universal; the object is its concrete manifestation. The object is necessary for the idea to be the determinacy of thinking.

Mathematical Illustration: The Infinite Manifest in the Infinitesimal

Peirce illustrates how the infinite manifests in the infinitesimal through the relation of odd and even numbers. Each whole number presupposes a distinct even number. The doubling of numbers produces a distinct series of evens:

Odd numbers: 1, 3, 5, 7, 9, …
Even numbers: 2, 4, 6, 8, 10, …

If we take 1 as the whole number and 2 as its corresponding even number, then 2 is simply 1 + 1. But for 1 to be added to itself, it must already be identical with itself: 1 = 1. Thus two truths must hold simultaneously: (a) 1 = 1, and (b) 1 + 1 = 2. But because 1 + 1 presupposes identity, the identity 1 = 1 itself presupposes the number 2—for the identity of 1 with itself involves two acts: 1 and its self-relation. Numbers quantify dynamic activity, not just static objects. Thus 1 = 1 is already “two” because the self-presupposition of 1 is an addition.¹⁴

Every odd number presupposes its corresponding even number, and each even number presupposes the odd. When we subtract the even number from its corresponding odd, the result is always 1:
3 − 2 = 1, 5 − 4 = 1, 7 − 6 = 1, etc.
Each odd number, in relation to the even, presupposes itself as the whole.

Footnotes

1. Hegel, Phenomenology of Spirit, Preface, on the semantic emptiness of the divine name before the predicate determines its content.
2. This parallels Whitehead’s view that physics progressively uncovers fragments of the “order of nature” grounded in Reason.
3. See Plato, Timaeus 28a–30c.
4. Timaeus 31b.
5. Timaeus 29e: the demiurge “desired that all things should come to be as good as possible.”
6. Plato grounds cosmic order in mathematical proportion (31c–32c).
7. Timaeus 35b–36d.
8. Timaeus 29e–30a.
9. Compare with Whitehead’s doctrine of “actual occasions” and the identity of physical and conceptual feelings.
10. See Heisenberg, Physics and Philosophy, on Reason manifesting in quantum behavior.
11. This reflects Hegel’s view of the infinite as “true infinity,” not abstract endlessness.
12. Hegel uses the circle to illustrate the unity of universal and particular in self-relation.
13. C.S. Peirce, “The Law of Mind” (1892).
14. Peirce, Collected Papers, 1.378–1.383, on number, identity, and continuity.

Presupposition

Once 1 = 1 presupposes 2, the number 2 becomes a distinct even number in relation to 1. The very presupposition that 1, in being equal with itself, becomes 2, also presupposes that 1—in being equal with 2—becomes 3. And this relation continues into infinity. What this means is that the idea itself carries within itself the means to produce its own contradiction—the contradiction being the necessary element through which it can relate to itself again as its own self. This is the dialectic of presupposition: the logic that predicts the mathematical generation of infinite number series.¹

To understand this dialectic, take the odd number 1 as corresponding to Being, the even number 2 to Nothing, and 3—the addition of 1 and 2—to Becoming. We attribute qualitative meaning to quantitative measures because numbers quantify the consequences associated with certain qualities.

Being, Nothing, and Becoming are essential logical propositions indicating qualitative measures: Being corresponds to the law of identity, Nothing to the law of non-contradiction, and Becoming to the law of the excluded middle.² If Being exists only in relation to Nothing, then it presupposes Nothing as something. In this sense Nothing is something, and by presupposing something (in this case Being), Nothing becomes the inverse of Being—yet still a determinate form. Because this non-being is the 2 to the 1, it is the multiplicity of what Being is not. This “two-times-what-being-is-not” nevertheless presupposes 1 and, in being added to 1, becomes 3.

Thus 3 consists of:

• 2 as non-Being (–1 – –1 = 2),
• and 1 as Being, whose identity with itself generates its own duplication (1 + 1 = 2).

The number 3 is made up of 1, the odd number, presupposing 2, its distinct even number. When 2 is equal with itself, it becomes 4, but that 4 still presupposes 1, since 1 is the unit from which it is divided; when 4 is multiplied by 1, it remains 4.

We call 3 Becoming because it represents every possible determination of 1—Being. This demonstrates that the idea itself contains the means of contradicting itself, and that this contradiction is the source of its further development.³

Continuity, Intensity, and Generality

The idea, at the level of continuity, reaches its generality. At this level the idea is established; it is no longer active as an explicit process. Yet it does not cease to be activity, for in continuity the idea remains active at the infinitesimal level, and this infinitesimal activity culminates in its generality. Continuity does not merely describe how ideas are externally related at the infinitesimal level; it also describes the continuity between the idea as intensity and the idea as generality. Continuity is not only horizontal, but also vertical.

Ideas develop into generality by establishing a truth, and this truth is the object. These ideas exist as general because their implicit process remains intense at the infinitesimal level. The notion of the infinitesimal solves many problems traditionally associated with the infinite. The first such problem it resolves is that infinity is no longer conceived as an endless external duality between objects; rather, it becomes an inner multiplicity issuing from itself.⁴

On the Mathematics of Presupposition

The mathematics reinforces the notion that each number presupposes within itself a distinct even number. This implies that each idea carries within itself the means to multiply itself into two even forms—each possessing its own distinct nature. Because they are distinct, these even forms stand in a relation of contradiction to one another.

But this contradiction is not antagonistic; rather, the negative relation between them constitutes the very condition that allows each form to be distinct. What follows is that distinct ideas always branch from a common source that must exist to allow their differences. Because ideas possess this minimal unity, they must also be capable of further unification into the same idea—namely, the idea’s conception of itself. The idea is thus the consciousness of itself.

Here logic predicates mathematics, not the other way around.

The Atom as a Logical Relation

The atom itself is a logical relation. According to string theory, each quark behaves like a proposition, asserting itself as a determinate state.⁵ This resembles discourse:

• each proposition asserts something as true,
• an argument divides truth into premises supporting a conclusion,
• and a valid argument is one in which the truth of the premises guarantees the truth of the conclusion.

In discourse, what is true is a fact about an external object. In Reason, what is true is a fact about itself, expressed as an idea. The idea reflects what Reason is; but because Reason is actuality—everything that could be potentially true—it reverses itself into potentiality, becoming capable of generating its own actuality.

This inversion transfers the idea into an atom, and the atom back into the idea. Every complete object—what perception regards as a whole—is such because when analyzed, it divides into an infinite set of atoms. This division is the first division of the object’s essence.

• The first essential quality of any object (for our understanding) is that it is composed of an infinite set of atomic units.
• But the first essential quality in the object itself—its organic nature—is that each atom is a quantitative proposition of logic.

Each atom is an idea of logic; the atom is the quantity of the idea, and quantity is the quality of logic. Quantity is the quality of Reason, and Reason is the quality of quantity.⁶

Light as the Physical Infinitesimal

The elements of the world unfold through qualitative intervals of time, each interval sublating the past: 1, 2, 3, 4… With each interval, the idea develops quantitative momentum, signifying that it has developed a further infinite series of ideas, each expressing a limit within the predicate.

In deduction, the relation between Being and non-Being produces particular instances from a general notion. Being uncovers within itself something that is not itself. Because Being already exists as the infinite, it has nowhere external to turn; it must look inward. But in looking inward, the infinite encounters its own limit. At this point it must sublate its infinite nature into a finite variable expressive of the infinite—that is, into a finite form capable of taking every form.

This allows the idea to take the form of an object. The idea develops self-externality, enabling it to perceive itself as an object. This self-externality cannot be abstract; it must be another object. This self-externality is space. But space alone cannot exist; it presupposes an object that self-identifies, and this object must be activity. Activity presupposes something that undergoes activity; thus we arrive at time.

The question becomes: What is the most basic object mediating self-externality and self-identity?

According to Hegel:

“The indivisibility of light in its infinite expansion, a reality outside of itself that remains self-identical, can least of all be treated as incomprehensible by the understanding, for its own principle is rather this abstract identity.”⁷

Light is that externality which remains identical with itself. Its unity makes it indivisible and able to take on every form. Light is the first finite idea capable of embodying the infinite idea.

Footnotes

1. Hegel, Science of Logic, Book I, “Being,” on the self-generative nature of number and the dialectical development of determinate concepts.
2. Traditional assignments: Identity (A = A), Non-Contradiction (¬(A ∧ ¬A)), Excluded Middle (A ∨ ¬A).
3. Hegel’s dialectic is not contradiction as failure, but contradiction as the principle of development.
4. See Whitehead on the infinitesimal in Process and Reality, where the “actual occasion” is the atomic expression of the infinite.
5. This analogy is a conceptual use of string theory: strings as fundamental states that “assert” themselves through vibrational modes.
6. Peirce’s “law of mind” and Hegel’s logic both support this continuity of quality and quantity.
7. Hegel, Philosophy of Nature, §275, on light as the first ideal physical determination.

Power, Consciousness, and History

Power

What the Law of Identity identifies as the I or the Self is also the principle of difference—it is the not-the-self. This principle allows the I to recognize that its essence involves an element concealed from itself; without this, it would merely exist passively. The I must come to terms with this hidden element and integrate it to remain in identity with itself.¹

When an individual controls others, their mind is, in a sense, grasping control over itself. The act of control is a form of self-discipline: the mind takes hold of itself as it navigates the infinite possibilities of action and sets itself in alignment with or against its logical direction. Conversely, it can also set itself astray, as in the case of Hitler in World War II.² Individuals who possess power over others often do so because consciousness aims to cohere as a whole, having previously dispersed itself into infinite potentialities. This dispersion is not accidental; it is a necessary step through which consciousness simulates every idea belonging to it. Therefore, when one individual exercises power over another, it is initially an attempt to recognize an external aspect foreign to itself as part of itself.

The idea of external relations defines the notion of power in social interactions between individuals. Once one individual recognizes another, they begin attributing qualities of the self to the other. These qualities can serve a variety of purposes, but they are never entirely indifferent to the interests of other individuals.

Reality, Freedom, and Consciousness

Reality is the algorithm of infinite potentiality manifesting in finite instances. The process of reality is an infinite replay of potential realities, mediated by freedom, the decisive element of actuality.³ Freedom begins as a germ of consciousness, each choice turning potentiality into actuality. In this way, reality allows for successive decisions.

Science examines phenomena in nature where consciousness becomes aware of its own operations. Reason formulates every potential possibility as an object, and that object is simultaneously the working out of potentiality into actuality.

Ontologically, power can be understood as intent or determination. Determination, as a particular force rather than an abstract potentiality, takes on the identity of an I or a sense of Self. This is the first moment of the Will, which bears an ethical foundation because it operates in the domain of relations: ethics is the study of relational operations, and the Will initiates actions that maintain components of a relation as distinct yet unified.⁴

A Moment and the Dialectic of Being

The Will is the drive for Reason to produce an infinite set of relations derived from the first relation: between Self and Not, Being and Non-Being. This is captured in the equation:

[
I = i
]

The uppercase I captures the identity of Being relative to Non-Being; this must be objectively true, or there would be no Being, only Nothing. The lowercase i expresses how Being sublates a potential derived from Nothing, turning it into a determinate instance of Being. In other words, i creates a particular moment in the duration of existence, distinguishing it from the abstract universal I.⁵

The familiar notion of a “fleeting moment” is misleading. Reality consists entirely of moments. Some moments, such as Being and Non-Being, extend indefinitely and constitute fundamental durations. These moments can be conceived in two ways:

1. Extended duration, where Being or Nothing persists for a long time, approximating infinity.
2. Infinitesimal duration, where Being and Nothing alternate rapidly, approximating the shortest possible instants.

Human experience exists between these extremes, with lifetimes composed of many fleeting moments. The relation between Being and Non-Being is an abstraction representing the first dialectic of immediate consciousness.⁶ Immediate consciousness has an infinitesimal relation to consciousness in general. Their synthesis produces self-consciousness, the identification of Being with Non-Being (I = I). Whenever a principle of identity manifests in immediate consciousness, it takes the form of an object, which reflects the idea in nature—for example, light.

Power in Human History

The question of human power is the limit of the Will operating in the infinitesimal process of time. The present characterizes the limit of the infinite, representing the transition into the future. This transition is an energy state, subject to entropy: motion may be resisted, redirected, or dissipated. Human history represents particular intervals in the infinite series constituting the infinitesimal process.⁷

Following the mathematical understanding of infinite numbers: a continuum has limits, each greater than all preceding elements but less than the next. Moments in time, then, are instants constituting all other instants. Human history is world history insofar as the present holds all previous intervals.

Power manifests in history often as control and tyranny. Hegel describes history as a “slaughter bench,” because at any given present, consciousness operates intensely but has not yet generalized. In contrast, nature exhibits an infinite cycle of regress, where ideas have generalized. The universe is the past infinitesimally attached to the present; the infinitesimal is simultaneously microscopic and macroscopic, extending through every dimension. Geometrically, angles remain equilateral in both small and large scales.

Thus, the present mediates the past and future, allowing ideas to develop into objects for consciousness. When individuals wield power, it is not a matter of survival or competition alone. Darwinian interpretations of adaptation—“some make it more than others”—fail to capture the full complexity. Power presupposes both qualitative and quantitative measures, which bear a mathematical relation to each other.

Quantitative and Qualitative Measures of Power

Quantitatively, power exists within a series of variables arranged in a specific sequence. The sequence follows the integral value of each variable; its position in the sequence is determined by its intrinsic value, not the reverse.⁸

The ruler’s qualitative property determines the sequence of followers. Followers are the quantitative chain that recognizes in the ruler a quality lacking in themselves, or possessed only partially. The tyrant acts explicitly on their nature; followers act implicitly, submitting to the ruler to develop their potential. This submission is not reactive, but proactive: it enables the followers to realize a form of self-consciousness through the ruler’s exercise of Will.⁹

Quantitative inequality exists: one leader, many followers. Consciousness, as power in the world, exercises control over its own potentiality, manifesting as influence over others.

Law of Mind: Intensive and Generalized Processes

Human consciousness exhibits an implicit process governing the species. Religion calls it God; psychology, the unconscious; philosophy, Reason. The human being is a particular expression of consciousness deriving knowledge of itself.¹⁰

Peirce’s notion of the infinitesimal clarifies the mechanics of this process. The infinitesimal defines the infinite and underpins the quantum realm. Time mediates the infinitesimal: past events generalize into established objects in nature; present events operate intensively, insisting on future generalization.¹¹

Two stages of the infinitesimal emerge:

1. Generalized stage: extended duration ensures stability; the idea becomes an object in nature.
2. Intensive stage: the present moment, where ideas interact intensely, simulating every possibility of themselves, producing a uniform whole—the truth of their potential.

Human history is the intensive stage of the infinitesimal, where consciousness develops self-awareness. Consciousness, as it generalizes into self-consciousness, examines its operations internally, transforming logical thought into a generalized whole.

Consciousness and Nature

Consciousness creates objects for itself. Nature emerges from the logical beginning of space and time, evolving into energy states (light, elements) and eventually life. The gene pool records this process, preserving historical information. Humans utilize only a fraction (~5%) of their genetic information for subjective purposes; the remainder (~95%) documents the universe’s accumulated logical history.¹²

Footnotes

1. Hegel, Science of Logic, Book I: The Self and its dialectical relation to the Not.
2. Hegel, Phenomenology of Spirit, on consciousness and historical misdirection.
3. Hegel, Philosophy of Right, on freedom as the decisive element in actuality.
4. Kant, Critique of Practical Reason, on Will as fundamental in ethical relations.
5. Hegel, Science of Logic, on the dialectic of Being and Nothing.
6. Hegel, Phenomenology of Spirit, “Immediate Consciousness” and the development of self-consciousness.
7. Aristotle, Physics, on limits of continua; Hegel, Philosophy of History, on the present as the locus of history.
8. Peirce, Collected Papers, on the law of mind and series of variables.
9. Hegel, Philosophy of History, on the tyrant and followers in historical development.
10. James, Principles of Psychology, on consciousness and its implicit processes.
11. Peirce, Essays on the Infinitesimal, on generalized and intensive stages of time.
12. Dawkins, The Selfish Gene, on genetic information as historical record.