section 15 (first updated 12.23.2020)

Quality and Quantity

Hegel simply defines quality ins this manner, he says:

“What I mean by Quality is simple determinateness.”¹

When something possesses quality, it possesses determination—that is, the quality of quality, or rather what a quality is.²

Quality can only be the measure of the one, while the measure of quantity is the many. Quality denotes the conception of something as it is, a determination picked out over other things. Quantity, on the other hand, belongs to a pool of potential others—the amount of which becomes the quality that forms some definite measure beyond the general substrate of which each individual variable is part.³

Hegel writes:

“In the ordinary way, quality and quantity count as a pair of determinations standing independently side by side; and we say, therefore, that things are not only qualitatively, but also quantitatively, determined. We make no further inquiry as to where these determinations come from, or what relationship they have to one another. We have seen, however, that quantity is nothing but sublated quality, and it is through the dialectic of quality considered here that this sublation comes about.” (Science of Logic, Miller trans., 1969, p. 218–219).⁴

Hegel is addressing how philosophy (and common thought) typically treats quality and quantity as separate propertiesof things:

• Quality = what something is in its determinacy. (e.g. “red,” “sweet,” “triangular”)
• Quantity = how much or how little, a numerical measure. (e.g. “3 liters,” “5 meters”)

In “ordinary thought,” we say things are determined both qualitatively and quantitatively, as if these are just two distinct dimensions.

But for Hegel, that’s incomplete. He argues instead that:

1. Quality inherently transforms into quantity.
   Quality pushed to its extreme leads to a change in kind. For instance: heating water (a quantitative increase in temperature) leads to a qualitative change (from liquid to vapor).
2. Quantity is “sublated quality.”
   “Sublation” (Aufhebung) means simultaneously to cancel and to preserve. Quantity is not an independent determination but the result of quality’s own dialectical self-development.
   In other words, quantity is quality that has passed beyond its immediate determinacy into a more abstract form of determinateness.

Against abstraction: Hegel resists the idea that “quality” and “quantity” are external categories arbitrarily applied to things. He insists they are internally related moments of Being itself.

Dialectical movement: Quality leads to quantity through internal contradiction. Quality limits something, but when you stretch the limit (quantitative increase), the “being” undergoes a fundamental transformation.

Unity of opposites: Thus, quality and quantity aren’t just “side by side.” Quantity is the “truth” of quality, and eventually, their unity culminates in the category of Measure, where qualitative and quantitative determinations are inseparably united.

Heat and water:
Water is liquid at ordinary temperature. Raise the quantity of heat → water boils. The qualitative nature of the water changes into gas. Thus, the quantitative change (heat) produces a qualitative leap (phase change).

Weight & strength:
A rope can hold a weight of up to 100kg. Add just 1kg more — quantitatively a small addition — and it snaps. The quality of the rope (its being able to hold) is negated.

concepts are not static but dynamic. Ordinary logic would say: “Things have quality and also quantity.” Hegel says: “Quantity is quality transformed; they are not external but intrinsically related.”

This is a step beyond Aristotelian categories, where quality and quantity were distinct categories of being. Hegel shows their internal necessity.

Hegel’s Doctrine of Being: The passage is in the Science of Logic (Book I, Section 3). Miller translation, p. 218–219.

Aufhebung: Sublation preserves the essence of quality within quantity. It is not a negation that erases, but a transformation.

Measure: Later in the Logic, Hegel introduces “Measure” as the category that unites quantity and quality, showing that every determinate being has a specific measure where quantitative changes produce qualitative thresholds.

Relation to Nature and Science: This dialectic foreshadows scientific laws like phase transitions, thresholds, and nonlinear changes — places where quantity leads to a qualitative leap. Engels later popularized this in dialectical materialism (the “law of the transformation of quantity into quality”).

Atomism and Its Limits

Atomism discovers that at the most minute level, matter exhibits the form of the atom. But according to Hegel, this theory is ontologically deficient, because it merely posits the atom as a basis for calculation without explaining what the atom is as a principle of reason. He writes:

“In physics, where a distinction in specific gravity, for instance, is explained by saying that a body whose specific gravity is twice that of another contains within the same space twice as many material parts (atoms) as the other. It would be the same with heat and light, if the various degrees of temperature and brightness were to be explained in terms of a greater or lesser number of heat or light particles (or molecules).”⁵

This quote originates from Hegel’s Encyclopedia of the Philosophical Sciences, specifically in the Science of Logic, §130 (and related sections), under the heading “Note on the Porosity of Matter.” This passage critiques atomistic explanations of physical phenomena—such as differences in specific gravity—by pointing out their conceptual inadequacy. Engels underscores this in his notes, where he references Hegel’s objection to the view that:

“a body whose specific gravity is twice that of another contains within the same space twice as many material parts (atoms) as the other.”
That the same logic would be applied to heat and light, attributing their differences to greater or lesser numbers of corresponding particles, is similarly rejected.^1

Hegel challenges the atomist perspective by arguing that it explains differences in physical properties solely through quantitative accumulation—i.e., more atoms meaning greater mass—without addressing the qualitative essenceunderlying these properties.

From Hegel’s standpoint, an atom is not an independent substance that exists apart from its relations; rather, it is a quantitative abstraction that fails to capture the unity of continuity and differentiation necessary for explaining matter’s true nature. Stipulating that the difference in specific gravity results from more or fewer atoms neglects the ontological relations constitutive of matter itself.^2

Furthermore, Hegel is critical of explanations that are pragmatically useful in physics but metaphysically superficial. The use of atoms as convenient “units” obscures the dialectical interplay between quantity and quality, and often leads to reifying abstractions rather than understanding the deeper principles at work.^3

• Qualitative Limits of Quantitative Explanations
  Hegel’s point underscores that quantity alone cannot account for differences in physical reality. Atoms may account for weight, but not for why matter behaves differently—why oxygen forms ozone under certain conditions, for example.^4
• Avoidance of Infinite Regress
  By exposing that atoms serve as placeholders rather than explanatory principles, Hegel aims to avoid the infinite regress of asking “What’s under the atom?” Without addressing the internal relations of matter, every explanation defaults to more unseen “particles.”
• Dialectical Insight
  The critique points toward Hegel’s larger project: reconciling the one and the many, unity and multiplicity. Matter is not just a collection of atoms—it is a dynamic, internally related whole. Problems like density, cohesion, and elasticity must be understood in this holistic, relational context.^5

Summary Table

Atomist Explanation	Hegel’s Critique
Twice the density = twice as many atoms	Quantitative difference treated as counting, ignoring quality
Heat/light explained by more particles	Reduces complex properties to particle counts without principle
Atoms as fundamental substances	Atoms are abstractions, not ontological explanations
Physics uses atoms pragmatically	Such metaphysics lacks depth and essential foundation

For Hegel, the notion of the “atom” is a purely quantitative unit of measure used to disclose a quality within a confined measure of space. But when quality is defined as a set of relations, the problem arises: what are the “components” that constitute the atom? This generates an infinite regress, where one always asks what lies beneath the most basic unit of measure. Thus, the atom, as a merely quantitative determination, fails as an ontological theory unless it also entails the qualitative principle of Being itself.

Quality and Quantity in the Quantum

At the level of quantum, quality and quantity collapse into one another. Their negation is indifference. From this indifference arises the result—the unity of quality and quantity. This unity constitutes what Hegel might call the general realm, which is not a specific determination but the substrate of all determination.⁶

Matter, in this sense, is the “quantity of quality.” It is not an independent thing but the point where quality assumes quantitative form. Matter is not a substance separable from qualities but is the very capacity of qualities to become determinate, measurable, and distinct. Aristotle described this as hylē (matter) being pure potentiality,⁷ while actuality (energeia) is what makes matter a specific form. Hegel reformulates this by identifying reason as the true actuality that gives determination to matter.⁸

Thus, matter and reason are inseparable. Reason makes matter a definite kind of thing, and matter provides the substrate by which reason can appear concretely. This insight anticipates the modern notion of quanta—from quantitas, “quantity”—which refers to the indivisible units of energy or matter, the infinitesimals that make up physical reality.⁹

Footnotes

1. G.W.F. Hegel, Science of Logic, trans. A.V. Miller (London: Allen & Unwin, 1969), 85.
2. Ibid.
3. Hegel, Phenomenology of Spirit, trans. A.V. Miller (Oxford: Oxford University Press, 1977), §91.
4. Hegel, Science of Logic, 237.
5. Ibid., 103.
6. See Hegel’s discussion of measure in Science of Logic, 368–390.
7. Aristotle, Metaphysics, Book Z, esp. 1029a–1032b.
8. Hegel, Encyclopedia of the Philosophical Sciences, Part I, §151.
9. Werner Heisenberg, Physics and Philosophy (Harper, 1958), 59–61.

Quanta

Quanta is the smallest possible amount. It is the unit that cannot be further divided, and so it is the indivisible foundation of being. This can be understood by reference to Peirce’s equation concerning the infinitesimal, where he argues that “infinity = finite.” The limit that infinity reaches is itself, so that beyond the infinite there is nothing further. Because there is nothing beyond the infinite, the infinite is, paradoxically, finite—namely, a finite that is infinitely determined. By understanding infinity as finite, the notion of the infinite becomes concrete, existing “here and now.”

This means that the form in which the infinite manifests is a finite form that is infinitely determined. The infinite exists “there and now,” and this presence makes it finite. Yet what is finite is still the infinite, which simply means that the finite is a variable capable of taking on infinite determinations. Every determinate object we encounter is a finite entity that nevertheless has the infinite as its essential nature.

The infinitesimal, as stated earlier, defines the concept of matter—and matter is defined by reason. The infinitesimal is therefore the finite variable with infinite potential, which is none other than reason itself. But before fully exploring this identification, it is necessary to distinguish the infinite from the infinitesimal.

Measure

The relation of infinitesimal determinacy to qualitative being can be clarified through Hegel’s concept of measure. Measure is the unity of quantity and quality; it is the principle that governs how changes in magnitude (quantitative shifts) can affect or transform the very nature of a thing (qualitative shifts).

Hegel explains:

“As for the occurrence of measure in the world of objects, we find first that in nature things exist whose essential content is measure. This is especially the case with the solar system, which we have to regard generally as the realm of free measure. As we advance further in the consideration of inorganic nature, measure retreats into the background, so to speak, because the qualitative and quantitative determinations that we have here prove to be largely indifferent to one another. For example, the qualitative character of a rock or a river is not bound up with a determinate magnitude. Still, a closer study shows that even objects like these are not utterly without measure, since chemical investigation reveals that the water in a river, and the single constituents of a rock, are again qualities that are conditioned by quantitative ratios between the substances they contain. But then, measure emerges again in organic nature, falling now more decisively into the domain of immediate intuition. The various kinds of plants and animals have a certain measure, both as a whole and also in their single parts. We should notice here that the more imperfect organic formations, those that stand closer to inorganic nature, are distinguished in part from the higher organisms through the greater indeterminacy of their measure. Thus, we find among fossils, for example, some so-called ammonites, of which we are cognizant only through the microscope, and others which reach the size of a coach wheel. The same indeterminacy of measure is also shown by many plants which stand on a lower stage of organic development. This is the case with ferns, for example.”¹

And further:

“Insofar as in measure quality and quantity are only in immediate unity, their distinction shows itself in them in an equally immediate way. Under this aspect the specific quantum is in some cases mere quantum, and what is there is capable of increase and decrease without the sublation of measure, which to that extent is a rule; but in other cases the alteration of the quantum is also an alteration of the quality. In this way, on the one hand, quantitative determinations of what is there can be altered, without its quality being affected thereby; but, on the other, this indifferent increase and decrease also has a limit, the transgression of which alters the quality. Thus, for instance, the temperature of water is, up to a point, indifferent in relation to its liquid state; but there comes a point in the increasing or decreasing of the temperature of liquid water where this state of cohesion changes qualitatively, and the water is transformed into steam, on the one hand, and ice, on the other. When a quantitative alteration takes place it appears, to start with, to be something quite innocent; but something quite different lurks behind it, and this seemingly innocent alteration of the quantitative is like a ruse with which to catch the qualitative.”²

What Hegel emphasizes is not that quality is the mere result of quantitative change, but that quantitative change is the empirical indication of the emergence of a qualitative threshold. This leaves open the deeper question of how a quantitative alteration itself arises from qualitative determination. In other words, the relation is not one-sided; quality and quantity are mutually implicative, and their unity is precisely what Hegel means by measure.

Footnotes

1. G. W. F. Hegel, Science of Logic, trans. A. V. Miller (Atlantic Highlands, NJ: Humanities Press, 1969), p. 367–368.
2. Ibid., p. 368–369.
3. On the dialectical unity of quality and quantity in measure, see Stephen Houlgate, The Opening of Hegel’s Logic(West Lafayette: Purdue University Press, 2006), p. 196–202.
4. On the notion that infinitesimals represent the finite as infinitely determined, compare Charles S. Peirce, Collected Papers, Vol. 1, ed. C. Hartshorne and P. Weiss (Cambridge, MA: Harvard University Press, 1931), §1.176.

Heap

Hegel elaborates the contradictions found in our notion of measurements by referring to the ancient paradox of when does a “heap become a heap”? he says;

“The antinomy of measure that is involved here was already depicted by the Greeks under many guises. They raised the question, for instance, [of] whether one grain of wheat can make a heap of wheat, or whether the plucking of one hair from the tail of a horse makes it a bald-tail. Regarding the nature of quantity as an indifferent and external determinacy of being, we are, at first, inclined to answer those questions in the negative. Nevertheless, we must soon concede that this indifferent increasing or decreasing also has a limit, and that a point in the process is finally reached where, through the continued adding of just one grain of wheat at a time, a heap of wheat results, and through the continued plucking of just one hair at a time we have a bald-tail […] It would be very wrong to treat considerations of this sort as idle academic twaddle, for in fact we are dealing with thoughts that it is also very important to be familiar with in our practical and especially in our ethical life.”¹

When we perceive a series of particular objects forming an order, that order is really an abstraction of one particular within it. The arbitrary principle is not that things are ordered randomly—because they are clearly not, since there is always an exact reason and function for the order. Rather, the arbitrary principle concerns which particular the whole derives reference from. That is: what particular thing in the relation of things serves as the basis from which the whole is derived? This arbitrariness is not a blunder, but a utility.

At the macroscopic level, this arbitrariness is not always obvious, because the structures formed—such as a flock of birds—are implicit expressions of internal structures. Yet it is evident that the bird must possess the genetic aptitude to form aerodynamic flocking patterns: a group of snails, for example, cannot. The flock together expresses the principle latent in each one. Each single form results from the continuous adding and subtracting of singular units, a process which constitutes a sequence that yields the unified form.

Here Hegel’s analysis of measure clarifies the dynamic:

“Insofar as in measure quality and quantity are only in immediate unity, their distinction shows itself in them in an equally immediate way. […] In this way, on the one hand, quantitative determinations of what is there can be altered, without its quality being affected thereby, but, on the other, this indifferent increase and decrease also has a limit, the transgression of which alters the quality.”²

The transformation of quality through quantitative change demonstrates that what appears as arbitrary addition and subtraction in fact conceals necessity. Seemingly innocent alterations of magnitude are “a ruse with which to catch the qualitative.”³

Sensation induces a fiat continuity, because it makes immediate contact the most primary function of consciousness. By contact here, we mean touch—the enclosure of one body by another. This has an evolutionary rationale: animals must adapt to maneuver within the specifications of their habitat. Monkeys grasp branches, birds master the airflow of wings, fish learn to swim. Life-forms are born only potentially with the genetic aptitude ordered by nature; they maintain and actualize it only through constant practice.

Thus, the paramount focus on contact with the environment—“hands-on” engagement—often distracts awareness from the abstract qualities embedded in the interaction. Yet continuity is not exhausted by physical touch. In physics, contact is passage—such as electrical current flowing from one conductor to another. What is transmitted is not merely the point of touch, but the enclosure of continuity itself, disclosed in the passage.

In this sense, the event experienced by a particular being is the “idea” in the mind that is passed down as continuity into the next event. The external advances into the internal, only to return again to the external; vice versa, the internal externalizes itself only to reconnect back within.

Conventionally, the macroscopic is thought to derive from the microscopic, as though the macro is simply the scaled accumulation of micro-parts. But this overlooks a deeper point: the macroscopic and microscopic form an equilibrium, co-determining each other rather than unfolding in a one-directional expansion. They are different expressions of the same unity of quality and quantity.

Footnotes

1. G.W.F. Hegel, Science of Logic, trans. A.V. Miller (London: George Allen & Unwin, 1969), 370–71.
2. Hegel, Science of Logic, 368–69.
3. Ibid., 369.

Macro and Microscopic

The macroscopic is not a static state, just as the microscopic is not a static state. The microscopic is associated with the infinitesimal, and is therefore an indefinite extension: whenever we reach a certain decrease in magnitude, the microscopic is the simultaneous passage of this transition. The macroscopic, on the other hand, is often seen as opposed to the microscopic because it is understood as the maintenance of a general and fixed condition. The macroscopic relates to the general analysis of large-scale conceptions, which is why it is associated with what is visible to the naked eye. The problem, however, is that when we reduce the magnitude of a macroscopic conception to a microscopic one, we do not escape perceiving that reduction itself as a generality.

The macroscopic is a balancing force, like a magnetic radiation completing the duration of the passage into an extended point away from the original conception. Magnitude is magnetic in this sense, because extension is always held in place by continuity away from its original position, moving forward. The reason the macroscopic is perceived as an “upward ascension” from the microscopic dimension is that it is conceived inversely to the microscopic: the macroscopic is deduced as the expansion of the microscopic. Yet the microscopic does not merely sustain the macroscopic from the inside out; the macroscopic also descends from the outside inwards as a passage. The two are reciprocal determinations of one process.¹

A quality is likewise not an object or a static thing, as when we say “a house” or “a dog.” These terms are quantitative designations of a quality. The quality, by contrast, concerns what the object does or how it functions: a dog barks, eats, and plays. A quality is therefore a moving continuity disclosed across macroscopic and microscopic ranges. An object is precisely the relation between micro and macro, a dimension disclosed through a macroscopic passage into microscopic range. This notion is quantitative insofar as the quality itself is multiplied into infinite variability, disclosed by the inverse degree of range in the same thing.²

Aristotle: Privation

Aristotle gives several senses of privation (sterēsis): (1) the absence of a quality, and (2) the absence of a quality in something that could naturally have it—for instance, a thing losing a quality it is proper to have.³

Potency and Act

Potency (dunamis) and actuality (energeia or entelecheia) must also be understood in relation to privation. All potencies of the same type are originative sources of some kind, referred back to a primary potency, which is either (a) an originative source of change in another thing, or (b) an originative source of change in the thing itself qua other. One kind of potency is the capacity for being acted upon—i.e., the originative source within the thing itself of its being passively changed by another thing (or by itself, in a different respect). Another kind is the state of insusceptibility to change for the worse, again either by another thing or by the thing itself acting in another respect.⁴

In one sense, the potencies of acting and being acted upon are one, since the same thing may simultaneously act on something else and be acted upon by it. Yet the potencies are also different, since acting and being acted upon are distinct originative sources.⁵

Form and Matter

If we say that one element is matter and the other is form, and that one is potential while the other is actual, the cause of their unity becomes a problem: what unites “bronze” and “roundness” to make a bronze sphere? Aristotle resolves this difficulty by saying that one is form and the other is matter, and there is no further cause beyond this. The potential sphere becomes an actual sphere precisely because this transition is its essence. The essence (to ti ên einai) is thus the cause.⁶

The one is the relation, and the many are the individuals. Each thing is a unity in which the potential and actual are somehow one.⁷

Unity and Definition

Aristotle further asks: what gives unity to a definition? What causes the unity of numbers and definitions? A definition is a set of words which is one not by mere connection, but by referring to one object. What makes an object one thing and not many? Why am I one man? Why is “man” both animal and biped, and not each separately, when there is “animal itself” and “biped itself”? Why are these forms not themselves the man, such that men would exist by participating not in one form, but in two—animal and biped?

The question is why “animal” and “biped” participate in “man,” rather than “man” shifting between them. What causes “man” to be the unity of animal and biped, rather than both separately? The answer points to being as the most real principle, for everything is some kind of being, whether as one form or as many.⁸

Matter and Contraries

There is difficulty in the question of how matter relates to contrary states. If the body is potentially healthy, and disease is contrary to health, is the body potentially both healthy and diseased? Is water potentially wine, and vinegar? This challenges the notion of potentiality: in what sense does matter maintain itself if it can be the very opposite structure? Aristotle answers that matter is the basis of one state by virtue of its positive form, and of its contrary by virtue of privation and corruption. It is harder, however, to say why wine is not the matter of vinegar, even though vinegar is produced from wine, or why a living man is said to be “potentially dead.”⁹

Oneness and Measure

The question of “what sort of things are said to be one” is distinct from the question “what it is to be one” and the definition of oneness. “One” has many meanings, and whatever has one of these kinds of unity is said to be “one.” To be one can mean:

• to be indivisible,
• to be a “this,” capable of being isolated in place, form, or thought,
• to be a whole and indivisible, or
• most strictly, to be the first measure of a kind.

The last is primary, for measure is that by which quantity is known. Quantity qua quantity is known either by a “one” or by a number, and all number is known by the one. Thus, the one is the starting-point of number.¹⁰

Footnotes

1. Cf. Hegel, Science of Logic, Book I, Doctrine of Being, on Quantity and Measure.
2. Ibid., on the transition from quality to quantity.
3. Aristotle, Metaphysics V.22 (1022b23–32).
4. Aristotle, Metaphysics IX.1 (1046a9–22).
5. Ibid., IX.1 (1046a25–35).
6. Aristotle, Metaphysics VIII.6 (1045a8–28).
7. Ibid.
8. Aristotle, Metaphysics VIII.6 (1045a30–b7).
9. Aristotle, Metaphysics IX.7 (1049a5–20).
10. Aristotle, Metaphysics X.1 (1052a15–34).

Quantity as Measure

Aristotle opens Metaphysics Book X with the insight that the essence of the unit is to be a measure of quality and quantity.¹ In this respect, “one” (hen) is not merely a number but a principle of intelligibility and order. There are related meanings to the concept of “one”:

1. The continuous by nature or in general—not by mere contact or by being tied together. Among these, that whose movement is indivisible and simple.
2. That which is a whole and has a definite form or shape, especially that which arises from nature itself, not by external compulsion such as glue or nails, but insofar as it contains within itself the cause of its continuity.²

Hence, to be “one” means to be indivisible and determinate: a this. To be essentially one is to be isolatable either in place, in form, or in thought. It also means “to be whole and indivisible.” But most especially it means “to be the first measure of a kind,” and most strictly of quantity. For it is from this quantitative meaning that the term “measure” (metron) is extended to the other categories. Measure is that by which quantity is known; and quantity qua quantity is known either by “one” or by a number, and all number is known by reference to the “one.” Therefore, all quantity qua quantity is known by the one, and that by which quantities are primarily known is the one itself. The one is thus the starting-point of number qua number.³

For example, speed has any amount of movement; weight has any amount of gravity. But both concepts also admit degrees: excess of movement or gravity. Thus even the slow has a certain speed, and even the light has a certain weight. The measure is always homogeneous with the thing measured: length is measured by length, breadth by breadth, sound by sound, weight by weight, unit by unit. It is improper to say that “the measure of numbers is numbers,” for number is already a plurality of units. The true measure is the one.⁴

This is why Protagoras could claim, “Man is the measure of all things.”⁵ Aristotle interprets this to mean “the man who knows” or “the man who perceives.” Knowledge and perception function as measures because we know objects through them. Yet in reality, they are measured rather than measure other things. To say that knowledge measures is like saying that a cubit-stick measures us, when in truth it is we who apply the cubit-stick to ourselves. Thus the Protagorean claim is only apparently profound. The Protagorean claim refers to the famous assertion by the ancient Greek sophist Protagoras of Abdera, who stated:

“Man is the measure of all things, of the things that are, that they are, and of the things that are not, that they are not.”
(Greek: Πάντων χρημάτων μέτρον ἐστὶν ἄνθρωπος…)

This is known as Protagoras’ relativist thesis, and it’s one of the foundational ideas in epistemological relativism. Truth and knowledge are relative to the individual. There is no objective standard of truth or reality that exists independently of human perception or judgment. Each person’s perception, opinion, or experience is equally valid in determining what is true for them. If one person says, “The wind is cold,” and another says, “The wind is not cold,” both statements are true for each individual. There is no objective “coldness” apart from human sensation. In matters of ethics or aesthetics, this means no universal standard of good, just, or beautiful can exist—only individual or cultural perspectives. Socrates (via Plato) heavily criticizes this view, especially in Plato’s dialogue Theaetetus. Socrates argues that if all beliefs are equally true, then the belief that “relativism is false” must also be true—leading to self-refutation.

Even to be fair to the Protagorean claim, its misinterpretation is a modern blunder—our own misplacement of what we think the ancients said with what we believe today. We project our own error onto the ancient word. The reality is that even the Protagorean claim is objective. The genius of it lies in the fact that it subtly finds the objective within the subjective—or rather, it reveals that a feature of the objective is that it necessarily involves the subjective. “Man is the measure of all things” is objectively true because every object, in order to be known as true, must be related to human conception. Without this relation, it is not true, and even this is objectively true.

Hegel on Measure

Hegel reformulates the Ancient principle of measure. From a spectrum of infinite possibilities, how is a particular form derived? Consider a class of trees: all share the same qualitative essence of being one species, yet among them are infinite quantitative variations in height, shape, and color. These particularities are what Hegel calls the “measures” in nature.

“As the unity of quality and quantity, measure is thus also completed being. When we speak of being, it appears initially to be what is entirely abstract and lacking all determination; but being is essentially what determines itself, and it reaches its completed determinacy in measure. We can also consider measure as a definition of the Absolute, and it has been said accordingly that God is the measure of all things.”⁶

Hegel continues: the ancients intuited this principle in religion. Hebrew psalms glorify God by proclaiming that he has set limits for sea, land, rivers, mountains, plants, and animals. Greek religion personified it in Nemesis, the goddess of measure, who punished excess. To transgress the proper measure of wealth, power, joy, or sorrow leads to ruin.

Thus, measure is not a static unit but the living unity of quality and quantity, whereby a being is concretely determined.

God as Ultimate Measure

Here we reach the delicate question of God. Descartes is often criticized for invoking “God” as the ultimate solution to philosophical questions. The criticism is not that God is false as an answer, but that the answer is too vague to satisfy scientific explanation. Descartes, the father of modern descriptive science, sought clarity and method. Yet “God” remains an ever-correct but empty placeholder.

Technically, any complex question can be answered with the term “God”: What is the meaning of life? God. What is the cause of the universe? God. What is love? God. What is matter? Ultimately, God. But this correctness is deceptive, because the answer does not disclose how or why. It suspends explanation rather than providing one. For example, when pressed on controversial questions of prophetic biography, some Islamic scholars have responded: “We do not know the mysterious ways of God.” This shifts the question away from rational inquiry into ineffable mystery. While reverent, such an answer evades explanation. A better response would ground the practice historically and culturally.

The term “God” defines the absolute and ultimate nature that discloses every finite component within it. For this reason, it can be used as the correct answer to any question. Yet because it can mean everything, it risks meaning nothing. To invoke God without determination leaves thought suspended in indeterminacy.

Time, Measure, and Potentiality

If measure is the unity of quality and quantity, then time is the unity of continuity and determination. Time is the totality of each being imposing its particular duration upon every other, a disjointed entanglement of intersecting timelines forming a cosmic puzzle.

Why is a particular tree this height, this color, this form, rather than another? It cannot be by its own will, for like man, it did not bring itself into being. We explain this by reference to time: its past causes—its parents, its soil, its climate. Yet when asked why it must be so, we often fall back on tautology: “that is the way things are.” This is unsatisfying, for nature reveals teleology everywhere. Every natural element functions in relation to another.

Thus the future plays as much a role in causality as the past. Potentiality shapes actuality. A house is built not only from past conditions but for the future purpose of dwelling. The true problem of time is therefore not simply: How does the past cause the present? but rather: How does the future cause the past to cause the present?

Footnotes

G.W.F. Hegel, Science of Logic, trans. George di Giovanni (Cambridge: CUP, 2010), 107. ↩

Aristotle, Metaphysics, Book X, Ch. 1, 1052b. ↩

Ibid., 1052a–b. ↩

Ibid., 1053a. ↩

Ibid., 1053b. ↩

Protagoras, fragment DK 80B1; Aristotle, Metaphysics X, 1053a. ↩

23# – The Present is the Point of Relation Between Lesser and Greater

The lesser and greater is the ratio of quality in relation to quantity.
The past is quantity, and the future is quality. Quality is mind; quantity is matter. Mind is both quality because it gives meaning to objects, and the actual form of the object because that is rational, receivable by mind. Mind is the quality of the future because it represents the quality necessary for the quantity, meaning that the mind sets a quality into the realm of spacetime, and eventually matter tends toward forming that quality into the present moment. Quantity predicates quantity, meaning that there is always matter before matter and matter after matter, but quality predicates quantity because quality is the idea—it must first be the form before the physical appearance represents that in an intelligible object. In this way, the first principle of the concrete is actually the mind—meaning form—whereas quantity is abstract because it essentially doesn’t mean anything without mind conceiving its form. Yet the mind in excitation, in concrete reality, is abstract; it gives the form first without the matter, while the matter, having taken the form, is concrete for the mind, referring to the properties of the content and the details of the form.

The idea from mind takes on form, which produces the potential to be actualized. This potential is the necessity for the actual to be continuous.

Mind=body unity

There is a mind-body unity. What is unique about the evolution of mind is that it resides in the particular. The particular is merely the external reflection of mind, such that the nature of the body is primarily a reflection of the Reason in mind. When mind conceives an idea, that idea takes on form that insists on change within the continuous sequence of the infinitesimal. In other words, when the mind thinks an idea, that idea literally possesses form that alters the physical nature of the body, and with it, the environment.

The notion of mind according to the Greeks was not limited to the brain residing in each individual body. Mind, for the Greeks, involves the collective reasoning between all particular minds¹. The relation between any two minds is held in sequence by a logical continuity. When two individual minds think, their ideas take on form that become physically entangled together².

Quantum means a quantity that cannot be defined or counted—in other words, an indivisible quantity. This quantity is mind. Quantum can only be defined in a finite sense.

Consciousness and the Limit

Along with the particular, there is simultaneously set up the beyond, as in spatial intuition—beside what is limited. Consciousness, therefore, suffers violence at its own hands; it destroys its own limited satisfaction³.

It is crucial to distinguish between reason in the mind and reason in the world. Equally important is recognizing when one conceives of the other at a particular moment.

Consciousness, however, is to itself its own notion; thus, it immediately transcends what is limited. And since this limitation belongs to it, consciousness transcends its own self. In this way, consciousness becomes unconscious—it becomes something unnatural to itself, something that does not move by its own accord: this is matter. But in coming into opposition with itself, it does not lose itself. All negations are just parts of itself. It merely adds these as aspects of itself; it now has the material to work with.

Matter is substratum—it is the content molded into form by thought. The relation between potentiality and actualityare the forces of thought as its own object⁴.

The Genesis of Quality from Quantity

At the onset of the Big Bang, matter reached its limit by becoming the infinite. This infinite, however, is the first qualitative move consciousness applies in relation to matter. It is the initial premise of reason: matter multiplies itself into infinity, the first move of quality—namely, the infinity of quantity⁵.

From this point on, quality begins to take on shape. The infinite quantities relate with each other in the form of shape. The square is the most basic quantitative shape, or more accurately, the only kind of form that assumes shape at the minimal relation between quantities. These basic relations between quantities result in the square, triangle, circle, etc.

With the emergence of these primary shapes, these very relations begin to relate with one another, giving rise to more complex forms—what are essentially combinations of primary relations. For example, the Kepler triangle illustrates the inevitable relations between basic geometric forms⁶.

Up to this point, it might seem that the relations between quantity that form shapes possess no other quality than the shape itself. This conception is derived from geometry alone and is unavoidable without ontological insight. Geometry, however, is the task of deriving abstractions from the kind of relation quantity assumes with itself, and is not concerned beyond such abstractions.

This alone represents merely a stage in the working of quality. What is missed is the fact that shape itself takes on form that portrays function. Function again reinstates the becoming of quality. At this point, it is the task of the reader to intuitively synthesize the terms through deduction.

It is evident thus far that the working of Reason takes on the form of quality in the world. When shapes form relations that produce greater form than their primary form, they begin to function as laws. Recalling the first principles of Reason—space, time, and motion—such shapes begin to take on a particular motion governed by the kind of form assumed in their relation. This characterizes the concept of Law: quantitative quality in motion; motion itself being the universal quality⁷.

The black hole is the limit in calculus⁸.

Final Notions

Quality is more fundamental than quantity. After all, a quantity is itself a quality. Quantity serves as the square root of quality. In this sense, quantity is the negative concept, whereas quality is the positive. In unity, quantity works in negation to quality to form the concept of the other. Although there is no necessary chronological order to whether quality exists prior to quantity, there must be some conception of quality for the quantitative form to exist.

Chemism is an example of how quality formulates quantity⁹. The elements serve as examples where the quantitative form is determined by quality. Water and air possess peculiar quantity because of their quality. If one argues that the quality of air, for example, is transparency due to its quantity, then why is there a difference in each quantitative form? Why are some things solid and others liquid?

Such qualities cannot be merely given by virtue of quantity, for quantity is equally a substratum. The difference in quantity is derived from the kind of internal relation that possesses quantity and formulates its quality. Water, for instance, possesses the chemical relation of H₂O; air is made of various gases, and so on. It is the relation itself that formulates the quality of the specific quantity.

Footnotes

Hegel’s Science of Logic, particularly the section on “Chemism” where objects reveal themselves in dynamic relationality, not isolation. ↩

See Anaxagoras and Nous in Pre-Socratic philosophy; also referenced in Plato’s Timaeus and Aristotle’s De Anima. ↩

A concept loosely reflected in quantum entanglement, where particles become interdependent regardless of distance. ↩

Hegel’s Phenomenology of Spirit, particularly the section on “Self-Consciousness” and “Reason.” ↩

Aristotle, Metaphysics, Book Θ (Theta) – “The actuality is prior in substance to potentiality.” ↩

Georg Cantor’s work on the infinity of numbers and its metaphysical implications may be loosely tied to this premise. ↩

The Kepler triangle is a right triangle with side lengths in geometric progression, associated with the golden ratio (φ), which emerges in natural and aesthetic proportions. ↩

See Kant’s Critique of Pure Reason on the a priori intuitions of space and time, and Hegel’s Science of Logic on motion as the synthesis of being and nothing. ↩

This refers to the mathematical concept of a limit—used in calculus—and how black holes represent physical boundary conditions where traditional laws of physics collapse. ↩

Quality as Reason in the Object

Quality is the Reason in the object, which serves as its purpose.

Informal logic is the very system that does not belong to any particular system but is rather the system of systems. Logic is called informal when it is speculative. Hegel characterizes this form as philosophy—the thinking about thinking¹.

The dialectic is the organic form of Reason, implanted in the particular as the universalization of itself. It is the discourse of its own course. This is the ontological notion of epistemology, rightly understood and applied. Every intellectual discourse is ontological from its very predisposition.

Understanding and Reason: The Dialectical Unity

The dualism between Understanding and Reason is, moreover, a concrete difference between mind and Nature—a difference between the inconceived, as conceived by consciousness, and its own unconsciousness.

The difference between Understanding and Reason is really their similarity—where one is conceived by the other, in the conception of the other. This is the process of self-consciousness.

The very notion of self-consciousness is universalized in the particular, and with this universalization comes the unity of the Understanding with Reason, as the process of ultimate reality between matter and quantum.

Quantum is mind in Nature, prior to self-consciousness².

Physics and Ontology: Space, Time, and Matter

The fundamental principles of the universe, derived through modern physics, indicate that Space, Time, and Matterare inherently related in the constitution of thermodynamics, electromagnetism, and dynamics.

All subsets of motion cannot be understood without recognizing that space, time, and matter are internal relations of one another. Special Relativity conceives of this relation in the formulation of general graviton—that is, gravity³.

This modern understanding of the fundamental principles of the universe is appropriated from ontology. The latter elucidates the notion that the concept is not only derived from the concrete but that the concept itself gives rise to the concrete. The ontological position is the conception of being as the sole end of itself⁴.

Hegel states this explicitly in his Philosophy of Nature:

“The concept of nature begins with the notion that being is not other than itself, but external to itself”⁵.

Space and Quantity: Abstract Generality and Real Existence

The concept of Space is the abstract generality of nature as its self-externality. It is the ideal that is real because it is pure indifference to difference, and thus, eternally continuous. It is, by definition, mere existence⁶.

Space possesses no difference within itself by virtue of its externality, and is thus the concept in general. Space is the positive concept in nature because its indifference to difference constitutes quantity.

Quantity exists as the difference to its own indifference. It is, by definition, space. Space is spatially unlimited as quantity, but it is also limited as quantity; thus, space and quantity are only understood as relations.

Quantity is the limit of space as itself, but the limit of quantity is its inversion: quality. Quality, for example, determines what is meant by space being empty or full. The quality of density, for instance, characterizes difference in the indifference of quantity.

While the quality of space is quantity, quantity is quality in space. This conceptual analysis of space is, in fact, its concrete reality.

On Geometry and the Evolution of Form

Geometry is the evolution within evolution, especially as discussed in the context of light (see Section: Light in Nature).

Hegel notes in Philosophy of Nature §225:

“The elements are not equally distributed; their determination arises from the totality of the system of nature”⁷.

The proportionality between Being and Non-Being is not equally distributive. This is one of those theoretical insights that has found its place in our understanding of truth.

Quantity can be divided equally—and indeed, this is so—but when it comes to quality, it does not take the same distributive course in relation to its quantitative development. Quality in relation to quantity is the very opposite of a middle ground; it is, by nature, an extreme relation.

This is a logical stage in Reason. The quality of an idea can be divided depending on the nature of the idea. In human history, knowledge is an example of this unevenness, which, though appearing unjust, makes complete logical sense.

The History of Consciousness and Knowledge

In the history of knowledge, if knowledge is concerned with truth, then it develops with one Idea that is true—and every other idea serves as its antithesis.

Each idea, as an antithesis, is a certain elaboration of the truth in its own unique way—each carrying its own contradictions, while simultaneously being a contradiction to the general source, i.e., truth.

As history develops knowledge—and as knowledge is the development of consciousness, the knowledge of self—the antitheses of truth derive greater immediacy and intensity.

The process of consciousness, once it develops the generality of its idea, takes on an inverse role: generality becomes intensity, and intensity generates generality. This force of the Idea is a spectrum collapsing into itself.

In our time, truth is overwhelmed by its antitheses, yet it is still working to resolve them.

Philosophy of Nature and the Concept in Science

The distinctive movement of matter and consciousness in unity presents itself to us as Nature. The philosophy of science takes as its subject-matter the concept of Nature, or more precisely, the concept in Nature.

The concept of nature begins with the examination of matter in motion. This examination is undertaken by mathematics, but because mathematics is not an immanent science, it requires the object as its subject-matter.

Mathematics is the quantitative determination of the object—it is the abstraction of the finite as the infinite. The science of Nature, however, is understood by the notion of quality in the object—that the object is quality.

However, the quality of the object cannot be abstracted away from it, as doing so would render the object no longer itself. To abstract quality away from the object is to annihilate the object.

Mathematics requires that the object remain as itself in order to make its abstractions. The application of mathematics in theoretical physics, to understand the universe, involves taking the quality of the object as the subject-matter in order to derive quantitative abstractions.

Remove the quality, and mathematics no longer applies to nature.

Thus, the concept of Nature, to be understood by science, must begin with the quality that is Nature. However, Nature, unlike consciousness, begins with quantity, because it is a being external to, and other than, itself⁸.

Footnotes

Hegel, Philosophy of Nature, §197–199: Nature begins in indifference, or quantity, whereas Spirit begins in self-relation or quality. ↩

G.W.F. Hegel, Science of Logic and Phenomenology of Spirit. Informal or speculative logic is discussed as the structure of thinking, rather than formal symbolic logic. ↩

This view reflects a metaphysical interpretation of quantum theory, aligned with idealist readings, especially those of Hegel or Bohm. ↩

Einstein’s theory of general relativity shows how space-time curvature relates to gravity. The reference to “graviton” reflects a blend of relativity with quantum field theory. ↩

See Hegel’s Science of Logic on the Concept (“Begriff”) as self-developing and self-determining. ↩

Hegel, Philosophy of Nature, §202–203. ↩

Hegel, Philosophy of Nature, §197, on space as the first immediate existence of Nature and pure self-externality. ↩

Hegel, Philosophy of Nature, §225: the distribution of elements, a precursor to modern notions of symmetry breaking and differentiation in physical systems. ↩