Notes by Gena Kozak on Hegel's, "The Science of Logic", 2013
Volume One: The Objective Logic
Preface to the First Edition, 1812
Metaphysics of the former times has lost its ground. Replaced by “the spirit of practicality”.
Philosophers disappeared from the world: “there vanished from the world those solitary souls who were sacrificed by their people and exiled from the world to the end that the eternal should be contemplated and served by lives devoted solely thereto – not for any practical gain but for the sake of blessedness”
Picture below: Rembrandt, “Philosopher”
The sister of metaphysics is logic. This was retained in university programs for logic was supposed to teach how to think. However, logic that was retained belonged to the older culture: “once the substantial form of the spirit has inwardly reconstituted itself, all attempts to preserve the forms of an earlier culture are utterly in vain; like withered leaves they are pushed off by the new buds already growing at their roots”.
Hence, what we need is a new logic that would be a reflection of the new culture around us in XXI century.
A fresh start had to be made with this logic.
A new scientific procedure is involved. Whereas previously philosophy borrowed its method from mathematics (i.e. assertions and proofs, as in geometry), here “it can be only the nature of the content itself which spontaneously develops itself in a scientific method of knowing”, i.e. the immanent development of “the Notion”.
The content develops through “dialectical reason”. This is the “absolute method of knowing”, i.e. reason determining the content of any one subject by “digging” through it, as a mole.
The System of Science, which Hegel intended to write, was to consist of:
1. The Phenomenology of Spirit – showing development of consciousness (notice: not any one consciousness, but either of an individual, or of the human civilization)
3. Philosophy of Nature – achievements of natural sciences
4. Philosophy of Spirit – the human society and the state; art, etc.
Preface to the Second Edition, 1831
The book was edited again and again, over a number of years, as no comparable work existed previously.
The subject is “the realm of thought”. The forms of thought are first stored in the language. Everything expressed in a language contains a category.
Often, words in a language express several meanings, and sometimes even opposite meanings. E.g. “Yeah, yeah” of Morgenbesser, as a remark to a statement of a philosopher that two negatives don’t make a positive.
A large step forward in development of culture has been made when forms of thought have become an object of thinking. This was first done by Plato and Aristotle. This was done after what was necessary for human comfort was obtained by a limited class of people, e.g. the priestly caste in Egypt.
In everyday life, categories of thinking play a subservient role to our practical interests. However, we are what we desire, or will. We are likely to follow our feelings, or impulses, but not our thoughts.
The task here is to focus on logical nature which is immanently present in everything. Logic will clarify the categories of our thinking.
The object and aim of logic is “the truth”. Truth is not only a formal relation, but has content. What is needed is an empirical investigation into the nature of modern logic, through a cross-section look at different spheres of the Universe and life.
How does thought develop? Naturally, this depends on the object of thinking, but suppose also has some universal aspects.
An exposition of this course of thinking needs to be “plastic”, not rigid.
“Form” and “content” of thinking are inseparable from each other. It is not possible to have “formal” thoughts without a content, and visa versa: not possible to think concrete content without certain categories, or forms.
General notion of logic
Logic is not only about the form of thinking, but also about the content of thinking. These two are inseparable.
This is a question of relation of thought to object, or object to thought.
True nature of objects, or things, can only be obtained through thinking them.
Thinking an object consists in taking it as a whole, splitting up into its elements, i.e. analyzing the object, and then connecting these elements into a new whole.
Logic has substantial content.
Logic which is presented today as “formal logic” is really dead (for it lacks content, as grammar which is not about anything). We need first to examine various achievements of knowledge and previous doctrines of logic, before sketching new dialectics. Logic is what is contained (essential) in the new knowledge. Logic is a summary of new knowledge as a whole.
Laws of thought are the laws of the objective world, and visa versa. Hence, when we investigate the laws of the objective world, as we understand them in modernity, we’re formulating the laws of thinking.
Logic stands in need of a complete reconstruction because of the new developments in science and conscious life in general. Achievements in various departments of knowledge are far ahead of logic.
Reason for the dullness of logic: 1) it is presented without a content, 2) it is thought determinations of knowledge long past outdated.
The method of a science is development of the subject matter internally: “the inwardness of the content, the dialectic which it possesses within itself, which is the mainspring of its advance”.
1) logic and content are presented together, united without our consciousness of it;
2) we discuss the relationship between one and the other.
Dialectical thinking is grasping opposites in their unity. Dialectic implies a classless society, for there would be no classes, but any one person would be able to perform different, opposite kinds of functions, be both “the top” and “the bottom”. (This idea is very modern considering such advances in theory as quantum theory and theory of relativity.)
Grammar is the logic of language. Grammar proper would examine the development of language through time. Similarly for dialectic: it examines the development of knowledge through time.
Logic must be studied alongside other sciences, for thus it is revealed as a “universal which embraces within itself the wealth of the particular”.
Dialectical logic appears as another word for a unified theory.
General division of Logic
In logic, the opposition between the object being investigated and the knowing subject is overcome, for they are both one: thought.
“Logic” is divided into 1) logic of being, i.e. objective logic, 2) logic of notion, i.e. subjective logic. Between these, there is 3) the doctrine of the essence, which mediates the relation of the logic of being to the logic of notion.
BOOK I: THE DOCTRINE OF BEING
With what must the science begin?
The beginning of knowledge must be an objective one, “the beginning of everything”. By this, today we understand “the Big Bang”.
As Hegel sees the question of beginning as one of “immediacy” or something “mediated” – immature categories, when seen from modern perspective – he writes: “there is nothing, nothing in heaven or in nature or mind or anywhere else which does not equally contain both immediacy and mediation, so that these two determinations reveal themselves to be unseparated and inseparable and the opposition between them to be a nullity”. This is correct in the sense that everything is a unity of opposites, e.g. a person is a result of the union of a man and a woman, a project is a result of a union of theory and practical activity, even a matter consists of opposite elements (electrons & protons, etc.)
Logic is a result of development of consciousness towards science. Thus, this book is preceded by phenomenology of spirit. Logic is concerned with the entire range of knowledge in its development. In this sense, it is a grand unified theory.
Beginning of knowledge is with “being in general, without any further specification and filling”.
The Universe, the human society (social Revolution) and knowledge – all have the same shape of development – a vortex with spiral arms (not a circle, as Hegel says). This implies that all these 3 develop according to the same law. Approaches which are made to finding this law:
· Aesthetics – a theory of beauty
· “Larry Gonick’s Cartoon History of the Universe”
· A. Bogdanov’s “Tectology”
· General Systems theory
· “A theory of everything” in physics: symmetry theories
· In mathematics: Godel’s incompleteness theorem, fractals, Wolfram’s mathematics
· Attempts at mapping knowledge: IT
· Systems of logic, dialectic
· “Interdisciplinary approach” at universities
The beginning is a unity of being and nothingness.
The beginning Hegel also understands as “God”. So, the “Big Bang” is “God” to Hegel.
(Beginning of knowledge must be made with the beginning of the Universe, for in the beginning there is no difference between one and the other.)
General division of being
Being is defined as: 1) quality, 2) quantity, 3) measure (“a qualitatively determined quantity”).
Section One: Determinateness (Quality)
Chapter 1: Being
First, there is indeterminate being. Indeterminate being is the same as nothingness. Indeterminate being and nothingness, on the one hand, are the same, but are also distinct. Transition from the one to the other forms the category of “becoming”. All is becoming, in the sense that Heraclitus held it: “all flows”. “All that exists has the germ of death in its very birth, … death, on the other hand, is the entrance into new life, (this) expresses at the bottom the same union of being and nothing”. In other words: “life” and “death”, “the beginning” (of the Universe, of a human being, etc.), and “the end” (death of a person, collapse of a Universe, etc.) are the first categories. They resolve themselves into “becoming”, “development”, “transition”, as the category mediating the two extremes.
· “birth”, “beginning”, “the Big Bang”, “revolution”
· “death”, “the end”, “collapse”, “destruction”
· “becoming”, “development”, “transition”, “evolution”
The principle of conservation (of matter, energy, space-time, etc.) was expressed in metaphysics by a phrase: “Ex nihilo nihil fit”, from nothing nothing comes.
In everything that exists, there are the categories of “being” and “nothing”, united. For example, electricity is a transition of electrical current from positive pole (“being”) to negative pole (“nothingness”).
A determinate being is a being that stands in relation to another content, and hence to the whole world. Thus, when we touch something, we really touch upon everything.
Being and nothing are the same, yet different. Their relationship to one another constitutes “becoming”.
Transition is the same as becoming. We need to be aware that in transition, from “A” to “B”, “A” and “B” do not remain in rest, but are constantly developing, perhaps towards each other, and perhaps away from each other. Hence, a transition from “capitalism” to “communism” today is transition from today’s capitalism to today’s, or tomorrow’s “communism”, and is not a matter of yesterday. Thus, the matter becomes: “what is today’s capitalism?” & “what is today’s, or tomorrow’s communism?” Moreover, as the transition has already been in large part effected in XX century, we have a number of bureaucratic states now in the process of Restoration of capitalism (the former USSR, the former Yugoslavia, etc.), or in the process of transition towards Restoration (China, Vietnam, Cuba, etc.) And hence, there is the need to characterize these states, as they are today. So, the problem of transition is really characterizing the whole of the global situation.
In the beginning, it is necessary to grasp the problem as a whole, because going into the details immediately, one can loose the sight, and hence the meaning, of the whole problem.
In the beginning there is indeterminate being. Process of development consists of its self-determination.
(A large part of Hegel’s “Logic” is metaphysics of scholasticism, and has been outdated, for example, by modern conceptions of space-time, matter-energy, etc. However, no overall synthesis of knowledge has yet been made, to replace that of Hegel. This is what I’ll attempt to do.)
Becoming is a double determination: 1) from nothing to being, i.e. coming-to-be; 2) from being to nothing, i.e. ceasing-to-be. These two moments interpenetrate each other.
“Becoming (transition) is an unstable unrest which settles into a stable result”. Becoming settles into “determinate being”. Thus, we’ve proceeded from indeterminate being to determinate one.
That which is sublated (снято) is not “nothing”, but is a result from which it has came, has in itself the determinateness from which it originated. Communism today is the result of the negative experience with it we’ve had in XX century.
Word “to sublate” has 2 meanings: 1) to preserve, to maintain, 2) to cause to cease, to put an end to. Thus, language is dialectical, as in the same word it displays 2 opposite meanings.
(Hegel’s “Logic” a good deal depends on achievements of mathematics of his time. So I better learn it.)
Chapter 2: Determinate being
“Determinate being” means considering a thing as a quality.
God is defined as the sum-total of all realities. That is what all knowledge is striving after, in one way or another, e.g. “the Big History” project.
“Determinateness is negation posited as affirmative”, Spinoza: “omnis determinatio est negatio” – all that is determined is negation.
Determinate being is something.
(cont. “Finitude”. Reading of Hegel is mostly empty, yesterday’s metaphysics. I am surprised that in spite of that there is still so much content and respect assigned to the book.)
(I don't think that knowledge of everything is possible at the present, or at all, but it is certainly possible to do better than Hegel in generalizing all that we know. «(мир) может быть постижимым, но все таки бесконечным». Бродский)
Opposite moments are present in every determination.
One moment is meaningless without the other, as “cause” and meaningless without an “effect”.
(This helps to explain why revolution comes in the wake of a war.)
Physical exercise and mental work are tied together. Here, again, we see 2 opposites “united” together in the sense that they are necessary for each other: physical exercise is necessary for productive mental work, as war is necessary for revolution, as man is necessary to a woman, and visa versa.
Order and chaos (disorder) – again, these two opposites are tied together. Looking for one leads one to discovering the other.
In general, the Universe consists of a kind of union of opposites. This union is not that the opposites “go together”, as spoon comes with a fork, but in the sense that one conditions and begets the other, gives meaning to the other.
Disharmony, dissonance is the sound present in every family, as for example between Humbart and his wife (“Lolita”). This disharmony points to the death knell of this type of arrangement, i.e. a family, “an American dream”.
Being fixed in one spot is a limitation for a modern person. One must live traveling, moving, as for example on a boat.
Infinity is the negation of the finite.
There is a “true infinity” vs. “spurious infinity”. The true infinity, it seems, includes and sublates the finite: “in the very act of keeping the infinite pure and aloof from the finite, the infinite is only made finite”. True infinite is that which includes finite.
The infinite is what makes the mind happy: “At the name of the infinite, the mind and the heart light up, for in the infinite the spirit is not merely abstractly present to itself, but rises to its own self, to the light of thinking, of its universality, of its freedom”.
Finite being determines itself as finite and transcends this limitation. “It is the very nature of the finite to transcend itself, to negate its negation and to become infinite”.
At first, the infinite is also limited, for it does not include the finite as a part of itself. Thus, it is not the true infinite. Hegel calls this “non-finite”.
What is interesting here is to see how the two opposites are tied to one another: the finite is what it is only in relation to what it ought to be, i.e. the infinite; and the infinite is infinite only to relation to the finite. They are inseparable and mutually related.
The true infinity is the unity of infinity and finite. “Unity” is not the proper word for the relation, for the right word is “becoming”. In this process of becoming of the finite and infinite, each of the two moments is further determined, is also becoming, developing. Thus, the process is a constantly changing unity of the finite and infinite, a universe swirling consisting of these moments, and each has many instances and concrete expressions.
From “infinity” a transition is made to the category of “being-for-self”.
Again, on the relation of the opposites:
1. the (finite) and (infinite) are a single unity;
2. they are different and opposed to each other;
3. they are inseparable, the determination of each lies in the other.
“What is untrue is incomprehensible”. Thus, what is true must be easily understood, easily expressed.
Idealism in philosophy, according to Hegel, is recognizing that the finite has no veritable being. What really subsists are thoughts. But these subsist where? In “finite” beings.
Chapter 3: Being-for-self
Being-for-self means transcending otherness. An object is taken in an ideal form into consciousness, and at the same time preserved as an external reality.
Ancient proposition: one is many, and many is one.
Repulsion and attraction are forces, and they mutually condition each other. Time for philosophy is truly the morning, when the birds are singing, the dogs barking.
Section 2: Magnitude (Quantity)
Quantity is a determination which is indifferent to what is being determined, e.g. apples or oranges.
Chapter I: Quantity
Quantity is a unity of continuity and discreteness.
On the basis of this “contradiction”, Kant has built “Antinomy of the indivisibility and infinite divisibility of Time, Space, Matter”. However, as in all dialectics, one opposing moment must be asserted as much as the other, continuity as much as discreteness.
Any notion, any idea is a unity of opposed moments. Expressed in another way: “two opposed determinations which belong necessarily to one and the same Notion cannot be valid each on its own in its one-sidedness; on the contrary, they are true only as sublated, only in the unity of their Notion”.
Quantity is both a continuous magnitude and a discrete magnitude.
Chapter 2: Quantum
This is mostly empty scholasticism. Much better use of time would be to study history of mathematics.
Two basic aspects of mathematics are arithmetic, or the study of a number, and geometry, or the study of shapes.
Education in mathematics is a good preparation for knowledge in general.
There are two kinds of infinity: “the infinite of reason” and “the irrational infinite”
Chapter 3: the quantitative relation or quantitative measure
Before thought reaches the stage at which it can grasp Notions in themselves, it designates numbers with specific properties of a Notion. Hence, both in history, and in development of individual human consciousness, first mathematics develop, then there is a transition to grasping abstract ideas in themselves. But development of mathematics is a prerequisite: “it was not until after Pythagoras that thought determinations themselves were discovered, i.e. became on their own account objects for consciousness”.
Section 3: Measure
In measure, quality and quantity are united.
Measure, in its more developed form, is necessity, “fate”.
The next category after measure is essence.
Chapter I: Specific Quantity
“all that exists has a measure. Everything that exists has a magnitude and this magnitude belongs to the nature of the something itself; it constitutes its specific nature… an alteration of the magnitude would alter the quality of the something”
Alteration of quantity is at the same time a transition from one quality into another. E.g. a heap ceases to be a heap is a grain is removed, continuously. This points to the danger of corruption for our states, i.e. behind a certain point a qualitative change will become necessary, via a civil war. The state pushes the society towards the civil war. E.g. conversation with the doctor from “Serafima”. On the one hand, the state doesn’t give money for medicine. On the other hand, people demand medicine, and clean hospitals, with working toilets, etc. Hence, the doctors are forced into taking money from people. Part of it goes towards their profits (doctor was driving “Citroen”), and part towards books, equipment, supplies, etc. There is a dichotomy which the doctors don’t like: “free medicine” and the need to extort money. They want some decision: either free medicine, which within the given state of affairs with corrupt and capitalism-oriented bureaucracy is impossible, or “laissez-faire”, so they can practice capitalist relations without looking back over their shoulder at the Attorney General.
We never see a “quantum” as such in the world. We always see a specific quantity, e.g. 5 kg of apples, 2 grams of salt, etc. A quantum is always qualitatively determined. Hence, plain mathematics makes no sense by itself. It’s only an instrument, a preparation for dealing with real problems involving quanta.
Some quantities are derivative of others, such as velocity is a derivative of time and space. These basic determinations are what’s to be studied and understood as the essence of the Universe.
Laws discovered explain a whole compass of phenomena which correspond to them.
Chapter 2: real measure
A measure is a relation of measures which constitute the quality of something.
(A large part of Hegel is outdated, as he talks for example about chemistry on ideas before the discovery of the periodic table).
A progress from one quality to another is gradual.
“Natura non facit saltum” – nature does not make leaps.
A change in general is a transition from one quantity into another, but also of a quantity into a quality, and vice versa.
“The attempt to explain coming-to-be or ceasing-to-be on the basis of the gradualness of the alteration is tedious like any tautology; what comes to be or ceases to be is assumed as already complete and in existence beforehand and the alteration is turned into a mere change of an external difference, with the result that the explanation is in fact a mere tautology. The intellectual difficulty attendant on such an attempted explanation comes from the qualitative transition from something into its other in general, and then into its opposite”
Same logic applies to states and moral behavior. A mere frivolity may turn into a crime. A corruption leads to a disappearance of one state and a period of transition into another.
Chapter 3: the becoming of essence
Book 2: The Doctrine of essence
A transition is made from being to essence.
At first, the absolute was being, now it is “essence”.
In the process of knowing, the absolute constantly shifts.
Essence is in the middle between being and notion.
Section One: Essence as Reflection within itself
What is “essence”?
1. It is not “absolute”, but relative to circumstances
2. It is that which defines the moment, its most important characteristic
3. Remember my motto from the 8th grade: “know the essence». The meaning here is that which remains while all else passes. But that which remains also develops and leads to something greater, to light.
Essence is a reflection. A reflection is that which subsumes (or tries to subsume) a particular under a universal. A person who can do this well is said to have a good judgment.
Chapter 1: Illusory being
Essential vs. unessential. Being is an illusion, the unessential.
Chapter 2: the essentialities or deteterminations of reflection
First law of thought is “A” = “A”, the law of identity. Identity is different from difference. Thus, difference is a part of identity. The unity of identity and difference is the truth.
Difference is only in relation to identity, i.e. in order to posit the idea of a “difference”, we must first have an idea of an identity, e.g. “A” is “A” and “A is not “A”. Thus, difference, like identity, contains both moments, i.e. difference and identity.
Positive and negative make sense only in relation to each other. This is true for all opposites.
All identity passes into difference, and difference into opposition.
Everything is inherently contradictory. “Contradiction is the root of all movement and vitality”
Chapter 3: Ground (основание)
“Ground” is a medieval concept, it corresponds with the category of a “cause”, e.g. the ground for this or that statement, i.e. the reason, the basis for the statement.
Here, we have an interesting opposition of “form” and “essence”, “form” and “matter”, and “form and “content”. All these categories mutually condition each other, for example, Hegel writes “form determines matter, and matter is determined by form”, and “only their unity is the truth”, for none of these moments by itself makes sense.
A logical mistake often made is pre-supposing that which is to be explained. This stems from lack of understanding of the deeper ground which underlie a phenomenon.
“The fact is, before it exists”. The fact first exists in a number of conditions that are necessary for its appearance.
Section two: appearance
Chapter 1: Existence
The main preposition of the section called “ground” is that “whatever is has a ground”; similarly, the main preposition of the section called “existence” is “whatever is, exists”.
Proof in general is a mediated cognition. That means that essence of everything must appear, must be present in our cognition. A proof is thinking about that which appears.
Every thing is essentially its properties.
Many things stand in reciprocal action to one another through interaction of their properties.
Chapter 2: Appearance
The world of appearance vs. the world of essence
The first may be seen as “sensuous world” and the later as “super sensuous world”
A law, manifested in the world of appearance, is an essential relation, i.e. belongs to the later world.
Chapter 3: The essential relation
The truth of appearance is the essential relation, i.e. the law of the phenomena.
The law is the notion of the phenomenon, it is formulation of the notion in mathematical, logical way.
The law shows the relation of the whole (of the phenomenon) and its parts. What is interesting about this relation is that, on the one hand, the whole is equal to the parts. On the other hand, the whole is greater than the parts, it has new properties which were not present in the parts. Thus, for example, H2O has different properties from H2 and O. This is called “emergence”.
Section three: Actuality
Actuality is the unity of essence and existence.
Chapter I: The Absolute
In oriental philosophy, the absolute is the light, which illuminates itself.
In Spinoza’s philosophy, the absolute is “the substance”, which is “a cause of itself”, “substance is that whose essence includes existence”.
In Leibniz’s philosophy, the absolute is the monad, “it is the totality of the content of the world”.
For Hegel, the absolute is the unity of being (external existence) and essence (internal existence). The absolute is “the identity of being and essence, or the identity of inner and outer”. In Hegel’s philosophy, the same idea is repeated again and again, as “the Absolute” is almost the same as “the Idea”. Hence, his work is interesting to read in the beginning, but boring at the end.
For materialists, the absolute is “the matter”. Lenin is here.
For dialectical materialists (which is the camp I am in), the absolute is the unity, and constant transition, of matter and thinking.
Chapter 2: Actuality
“What is actual is possible”, but the other way around this does not work: what is possible is not necessary actual.
Chapter 3: The Absolute Relation
The absolute relation, or “a law” of something, is the notion of that thing, or a process, “a concept”.
The absolute relation is the relationship of “cause” and “effect”. This relationship has several forms:
1. Simple one-way relationship, i.e. “A” is the cause of “B”. “A” -> “B”
2. Two-way relationship, “A” is the cause of “B”, but “B” also influences “A”. Thus, “A” continually influences “B” and “B” continually influences “A”, and hence there is an infinite reciprocal action. This is the law of “action” and “reaction”. “A” and “B” cause each other
P.S. Under this heading we find “the law of boomerang”, i.e. our own action (or inaction!) upon a second person comes back to us in another form, through an action of a third person.
3. Each “cause” has a cause of itself. Thus, in effect, each cause is also an effect of another cause.
4. In a “field” type of relationships not only “A” and “B” mutually determine each other, but also determine and are determined by “third” entities, which form “the field”. These are “vectors” or forces acting in other directions, e.g. sideways, up and down, diagonally.
Hence, the concept of a “cause” and “effect” leads us to a wider, more realistic picture of the world as “a field”. But this was already past Hegel’s view of science, and he didn’t work with his hands to understand the picture from own experience.
Logic is the sum total of knowledge of a given epoch.
Volume Two: The Subjective Logic
The Notion in general
The subject matter is “the Truth”. The truth is the identity of the notion and the thing of which it is the notion.
“Notion” is the synthesis of “being” and “essence”, or “reflection”. However, it appears that there is another category in Hegel’s system, “the Idea”, which is the synthesis of “the Notion” and reality. It seems to me just a repetition of “the Notion”.
Refutation of any system consists in adopting its standpoint of view and going through its own dialectic to raise to something higher. Refutation is trying an idea in practice, seeing its faults and problems, and attempting to understand them, and hence overcoming them, in practice again.
Notion is the unity of being and essence
Subjective notion, objective notion, the Idea.
Section 1: subjectivity
Chapter 1: the Notion
Universal notion, particular notion, the individual
Chapter 2: the Judgement
Chapter 3: the syllogism
Everything rational is a syllogism
A syllogism consists of a major premise, a minor premise, and a conclusion
e.g. “all men are mortal”, “Socrates is a man”, therefore, “Socrates is mortal”
There is also a mathematical syllogism: e.g. if 2 things are equal to a third, then they’re equal to each other.
The above are examples of deduction. There is also an induction: reasoning from individual to universal, e.g. the sun has risen yesterday, today, hence, it will always rise. This is not true. Reasoning by induction is problematic.
There is also reasoning by analogy. It is equally problematic. E.g. This planet is inhabited. Mars is a planet. Therefore, Mars is inhabited.
Section 2: objectivity
This section will discuss logic in the objective world: in the mechanics, chemistry, biology, and finally in psychology.
Section 3: the Idea
The idea is the unity of notion and objectivity.
The absolute idea is the identity of the practical and theoretical idea.