Science of Logic
Encyclopedia
Hegel's work The Science of Logic (Wissenschaft der Logik) outlined his vision of logic
, which is an ontology that incorporates the traditional Aristotelian syllogism
as a sub-component rather than a basis. For Hegel, the most important achievement of German Idealism
, starting with Kant
and culminating in his own philosophy, was the demonstration that reality is shaped through and through by mind and, when properly understood, is mind. Thus ultimately the structures of thought and reality, subject and object, are identical. And since for Hegel the underlying structure of all of reality is ultimately rational, logic is not merely about reasoning or argument but rather is also the rational, structural core of all of reality and every dimension of it. Thus Hegel's Science of Logic includes among other things analyses of being, nothingness, becoming, existence, reality, essence, reflection, concept, and method. As developed, it included the fullest description of his dialectic
. Hegel considered it one of his major works and therefore kept it up to date through revision. The Science of Logic is sometimes referred to as the Greater Logic to distinguish it from the condensed version of it he presented in what is called the Lesser Logic, namely the Logic section of his Encyclopedia of the Philosophical Sciences.
and while he was in Nuremberg
working at a secondary school and courting his fiancé. It was published in a number of volumes. The first, ‘The Objective Logic’, has two parts (the Doctrines of Being and Essence) and each part was published in 1812 and 1813 respectively. The second volume, ‘The Subjective Logic’ was published in 1816 the same year he became a professor of philosophy at Heidelberg
. The Science of Logic is too advanced for undergraduate students so Hegel wrote an Encyclopaedic version of the logic which was published in 1817.
In 1826 the book went out of stock. Instead of reprinting, as requested, Hegel undertook some revisions. By 1831 Hegel completed a greatly revised and expanded version of the ‘Doctrine of Being’, but had no time to revise the rest of the book. The Preface to the second edition is dated 7 November 1831, just before his death on 14 November 1831. This edition appeared in 1832, and again in 1834–5 in the posthumous Works. Only the second edition of Science of Logic is translated into English.
1. In his Categories, Aristotle
tried to list and define the most general types of predicates applicable to an entity: substance (ousia), quality, quantity, relation. Plato had attempted a similar task, especially in the Sophist, Hegel's favourite Platonic dialogue.
2. In his De Interpretatione, Aristotle considered the structure and constituents of the proposition or judgement. Plato had again explored this matter, especially in the Theaetetus and Sophist.
3. Aristotle's Prior Analytics
deals with the nature and validity of inferences or syllogisms, while his Posterior Analytics deals with proof or demonstration and with demonstrative science. 'Analutika' is Aristotle's word for 'logic'. Logiki (techne) ('(the art of) logic', from logos, 'word, reason', etc.) was first used by the stoics.
These and other logical works of Aristotle were later called the Organon
, the 'instrument' of correct thought. (Works entitled 'New Organon', such as Bacon's and Lambert's, are attempts to outdo, or update, Aristotle.)
4. In his Metaphysics, Aristotle attempted to justify the law of non contradiction and of the excluded middle. He considered them to be metaphysics or 'first philosophy', since they apply to all entities. By Hegel's time the 'laws of thought' also included the law of identity and, since Leibniz and Enlightenment, the principle of sufficient reason or ground.
5. Hegel also says that the Science of Logic incorporates the material of the 'old' metaphysics, which derives from Aristotle and Plato
, but also embraces Leibniz, Spinoza, Wolff, etc. Many of the concepts he examined, especially in the 'Doctrine of Essence', were employed by metaphysicians.
6. In the first main section of Kant's Critique of Pure Reason
, the 'Transcendental Doctrine of Elements', Kant
defines 'transcendental' logic as the science which, in contrast to formal logic, 'determines the origin, range and objective validity of a priori cognitions' (Critique of Pure Reason, A57, B8I). Transcendental logic falls into two parts: (a) the logic of truth (transcendental analytic), and (b) the logic of illusion (Schein) (transcendental dialectic). In (a) he attempts to systematize and justify the categories (e.g. causality) presupposed by objective judgements and experience. In (b) he attempts to curb the speculative
use of reason, arguing, e.g., that it leads to antinomies. Many of the concepts considered in (a) and (b) reappear. But Hegel combines analytic and dialectic at every stage, arguing that every concept (except the absolute idea, which even so is instantiated in these proliferating contradictions) gives rise to antinomies or contradictions. The second main section of Kant's book, the 'Transcendental Doctrine of Method', which determines the 'formal conditions of a complete system of pure reason' (A708, B735), is also relevant, especially to Hegel's concern for system. Hegel's knowledge of, and indebtedness to, Kant were great. But the extent to which his fundamental motivations and procedures are Kantian is still a matter of controversy.
7. Hegel also explores concepts such as force
, polarity or opposition and infinity
, which figured not only in metaphysics and theology
, but also in the natural science and mathematics
of the day.
(2), (3), (4) and, in part, (1) made up the subject-matter of the 'formal', 'classical' or 'traditional' logic of Hegel's day. Hegel, like Kant, held that this had made no important advance since Aristotle. This underrates the medieval and stoic
contributions to logic, as well as the mathematical logic
that began with Leibniz's 'universal characteristic', and which Hegel argued against.
's ideas of judgement and categorical classification, more or less wholesale copied from the Critique of Pure Reason
and adapted into his system. In the end of the book Hegel wraps all of reality into a single Absolute
. This absolute covers basically everything which can happen, has happened, and all viewpoints rolled into one. Importantly Hegel then links this final absolute idea with his ordinary concept of being which he introduced in the start of the book. Hence the Science of Logic is actually a circle and there is no starting point, no sequence, but rather a totality.
thinking permeates all the Science of Logic under one heading or another.
If reality were static there wouldn't be much to explain, but reality is a continual oscillation from being to nothing, from quality to quality, from something to other. Hegel identifies "becoming" as the substrate upon which changes takes place.
Most of reality is like that to some extent . A person is alive—but will be dead. When you look at a person you know death is only sublated. Death is still there. The important point to Hegel is that reality is not simply a set of discrete states akin to a computer state machine . Hegel notes that "there is nothing on heaven and earth which does not contain within itself both being and nothing." By this he means that being is continually changing from something to nothing and back, and "becoming" is the substrate upon which change takes place. In order to process reality we need to take the totality of an object's states into consideration, not just the present determinate being.
But, to Hegel, however, this transition to the infinite is a fallacy. There is no such infinite. What results from one finite state is always just a new finite state. Even if we take an enormous number of different qualities, this is still finite, although too large even to perhaps be counted. We can still add one to the enormous number and we still have another finite enormous number of qualities for as long as it pleases us. Because a new finite always results, no matter how large, Hegel states that this "infinite" is in fact the "spurious infinite." We are fooled into the belief of a truly objective infinite, but we will always just have another finite.
Regardless of this seeming contradition of infinites, reality nevertheless presents itself to all persons as a single unified whole. Hegel introduces the concepts of "Being-For-Self" and "Being-For-One" to describe this state of affairs. Due to this system of presenting one single unified whole to any person, the concept of quantity emerges directly out of Being-For-One. If we have Being-For-One we definitely have a quantity of one to start off with. No matter how infinite reality appears to us, it is still one single reality for one person to us. One reality, one person, and there is no mistaking the concept of one and quantity is easy to envision. Hegel uses this as his springboard from quality to quantity.
Does that mean there is no true infinite? According to Hegel the true infinite appears as thought itself.
Hegel groups attraction and repulsion together. Attraction simply means that a set of ones can be grouped together resulting in a new one. For example, a group of students is one. Repulsion is the reverse: we take a group and split it into subcomponents. Now we have a set of ones.
Intensive magnitude refers to the numerical size of some object, for example the intensive magnitude of a person may be five and a half feet tall. Extensive magnitude refers to the effect that this intensive magnitude has on everything else.
Continuous and discrete are straightforward. An example would be a line painted on a highway that is continuous, alternatively the same line could have been discrete (split into sections).
Number to Hegel is basically a determinate quantum like 35. Note however that this 35 is still "one," i.e., it is one 35 and not other numbers like 34 and 36; it is limited at 35. That a thing (here a quantity) is limited and is not something else is of great importance to Hegel and a recurring theme of the work. Amount refers to a set of ones within the number 35. Unit is the standard understanding—for example force
may be expressed in newtons. So we may for example have one "number" equal to 35 newtons, one "amount" referring to the set of newtons, and finally individually 35 of one unit. Note that we are continuing down a kind of hierarchy of ones.
Hegel's "direct ratio" is the ordinary ratio, such as 2/3. We can alter the arguments in keeping with the ratio, such as 40/60 but the result (which Hegel curiously calls the "exponent" throughout the discussion) remains the same. The "inverse ratio" refers to the basic mathematical relationship in which the product of two arguments stays the same while the arguments vary in an inverse fashion to each other. For example, 20 = 10 * 2, but if we change 10 to 5 we are obliged to change 2 to 4, yielding 20 = 5 * 4. The result is the same as the arguments depend upon each other.
The upshot of Hegel's discussion is that within the realm of ratio, the arguments are bound to each other so much so that each argument "is" the other, not existing in isolation. By the time Hegel's reaches his last ratio, the so-called "ratio of powers," he begins a shift back from quantity to quality because we attach a quality to ratios.
Hegel specifies two forms of measure: "Specifying Measure" and "Real Measure."
Specifying measure can rely on a rule established beforehand by taking an instance of measure as the reference point. Let us use average car as a reference point. Here we have a general idea of the size in terms of quantity of dimensions, for example in meters. We assign to this quantity of the dimensions of the car the quality average. Now suppose we see somebody driving a little 1960s VW Bug: we utilize our specifying measure and assign the value small car to this instance because the quantity in terms of dimensions of the VW is much smaller than our average reference. Now somebody drives by in a roomy 1975 Buick sedan. In relation to our average car measure, the quantity of roominess in the Buick held in relation to our average car dimensions results in the quality "big." It is important to note that by this time in Hegel's system we are utilizing elements of ratio as above expressly for quantitative comparison for qualitative reasons.
By the time Hegel reaches his "Real Measure" he has begun to compound relations between measures. For example, establishing a measure that is the contrast of two previous measures, such as a measure that shows an overall increase or decrease. For example suppose we see a succession of persons based upon increasing age. Each person could have a specific measure in terms of quantity (age) and quality (young, middle age, old). Yet, we could establish a secondary, overall measure that indicates increasing age in succession. As another point he discusses the importance of realizing all the qualities that a specific measure is not, such as obviously a young person is not an old person. What something is not is just as relevant as what something is to Hegel. Hegel also mentions that just because quantity changes, it does not immediately signal a change of quality. Usually a couple of years will not immediately change a young person to middle aged for example.
In previous sections, Hegel established that being can shift from some determinate something to another determinate other, and becoming was the substrate upon which these transitions took place. For example your shoes might be off or they might be on, and that is all there is to it. However, now we have to deal in things that are naturally not in a single discrete state but have some imprecise value on a continuum.
So at this stage Hegel takes his idea of sublation a bit further and introduces "absolute indifference." He claims absolute indifference is the substrate upon which a thing can basically be in two states at once to different varying degrees. Some things in reality are never completely in one discrete state or another (this is an idea akin to fuzzy logic
) yet we seem to be able to handle this situation easily. For example suppose we may have a partly cloudy, partly sunny day and we desire to state some objective measurement of the weather conditions to a friend. It is up to us to mediate multiple, non-discrete states, yet still arrive at a single "posited reflection." To continue the example we could say that "the weather today is fair," being neither totally cloudy nor totally clear.
for Hegel seems to take as its starting point the traditional conception of essence descended down from the ancient Greeks.
Hegel points out that the object of our attention may contain the unessential as well as the essential. Later on he will note that all of appearance contains the essential and unessential. A horse might be brown or black, but in any case it is still a horse. It is not essential the horse be black to be a horse. When we experience something, we consider its essential features, but at the same time are also able to "throw out" unessential features and ultimately arrive at a true objective essential conception. This process he terms reflection: a wholly "illusory" process which filters the essential from the unessential and ultimately results in some determinate conception which Hegel calls "illusory being." Yet illusory being, the mediation of essential and unessential, Hegel terms an outright mind dependent "nullity" when considered in contrast to the more
stable and simpler qualities above.
Let us take for an example "happy group of people" as our object. It is essential that the people be smiling, laughing, and so forth, but unessential as to location and dress. They may be in an elevator or walking on a sidewalk dressed in suits or shorts. It makes no difference. We reflect on the situation and hold the essential (smiling, laughing, etc.) together with the unessential (location, dress, etc.), and the result is an "illusory being" -- nothing more than a "nullity" that arises as a result of our mediation of essential and unessential. We are able to determine, by reflection, the essence of our group of observed people as a "happy group of people."
Hegel claims there are three general types of reflection: "positing reflection," in which one forms a reflection internally (i.e., completely within one's mind); "external reflection," in which one reflects upon two objects external to oneself; and finally "determining reflection," in which one draws a relation between an internal representation and something external. The result of a completed reflection is "already in propositional form."
" that has "no content." If someone declares that the book in front of him is the book in front of him it leads nowhere, in the same way that a person claiming that "God is--God" is wasting our time. These are "boring and tedious" statements utilizing the "pure law of identity" which merely "reiterate the same thing" in Hegel's view.
As soon as "A is..." completes (is predicated by something), says Hegel, difference emerges. Thus he claims broadly that "everything is inherently contradictory." Taking "the camera is black" as our example, a camera is not the same thing as the color black, yet it is what it is (a black camera) through this resolved contradiction.
Hegel identifies three types of difference. "Absolute difference" is the most general and abstract (mental reflection) sense. "Diversity" includes the "otherness of reflection" meaning that we essentially think of how "A" is different from all other possible cases. Finally, "Opposition" is the "completion of determinate difference" with "moments that are different in one identity."
Regarding diversity, let's assume there is some American person "A" who is overweight. In considering the obesity of "A" in our mental reflection we at the same time consider all the potential and possible weights that "A" is not along some continuum. "A" is not thin nor of normal weight either and this needs to be taken into consideration. Hegel says that things are different through unlikeness: this is the so-called "Law of Diversity."
Hegel considers form to be the focal point of "absolute ground," saying that form is the "completed whole of reflection." Broken into components, form taken together with essence gives us "a substrate for the ground relation" (Hegel seems to mean relation in a quasi-universal sense). When we combine form with matter the result is "determinate matter." Hegel thinks that matter itself "cannot be seen": only a determination of matter resulting from a specific form can be seen. Thus the only way to see matter is by combining matter with form (given a literal reading of his text). Finally, content is the unity of form and determinate matter. Content is what we perceive.
"Determinate ground" consists of "formal ground," "real ground," and "complete ground." Remember with Hegel that when we classify something as determinate we are not referring to absolute abstractions (as in absolute ground, above) but now (with determinate ground) have some values attached to some variables—or to put it in Hegel's terminology, ground is now "posited and derived" with "determinate content."
In formal ground Hegel seems to be referring to those causal explanations of some phenomena that make it what it is. In a (uncharacteristically) readable three paragraph remark, Hegel criticizes the misuse of formal grounds, claiming that the sciences are basically built upon empty tautologies. Centrifugal force, Hegel states as one of several examples drawn from the physical sciences,
may be given as prime grounds (i.e. "explanation of") some phenomena, but we may later find upon critical examination that this phenomenon supposedly explained by centrifugal force is actually used to infer centrifugal force in the first place. Hegel characterizes this sort of reasoning as a "witch's circle" in which "phenomena and phantoms run riot."
Real ground is external and made up of two substrates, both directly applicable to content (which evidently is what we seem to perceive). The first is the relation between the ground and the grounded and the second substrate handles the diversity of content. As an example Hegel says that an official may hold an office for a variety of reasons—suitable connections, made an appearance on such and such occasion, and so forth. These various factors are the grounds for his holding office. It is real ground that serves to firstly make the connection between holding office and these reasons, and secondly to bind the various reasons, i.e. diverse content, together. Hegel points out that "the door is wide open" to infinite determinations that are external to the thing itself (recall that real ground is external). Potentially any set of reasons could be given for an official to be holding office.
In complete ground Hegel brings together formal and real ground, now saying that formal ground presupposes real ground and vice versa. Complete ground Hegel says is the "total ground-relation."
(In progress)
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, which is an ontology that incorporates the traditional Aristotelian syllogism
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
as a sub-component rather than a basis. For Hegel, the most important achievement of German Idealism
German idealism
German idealism was a philosophical movement that emerged in Germany in the late 18th and early 19th centuries. It developed out of the work of Immanuel Kant in the 1780s and 1790s, and was closely linked both with romanticism and the revolutionary politics of the Enlightenment...
, starting with Kant
Immanuel Kant
Immanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....
and culminating in his own philosophy, was the demonstration that reality is shaped through and through by mind and, when properly understood, is mind. Thus ultimately the structures of thought and reality, subject and object, are identical. And since for Hegel the underlying structure of all of reality is ultimately rational, logic is not merely about reasoning or argument but rather is also the rational, structural core of all of reality and every dimension of it. Thus Hegel's Science of Logic includes among other things analyses of being, nothingness, becoming, existence, reality, essence, reflection, concept, and method. As developed, it included the fullest description of his dialectic
Dialectic
Dialectic is a method of argument for resolving disagreement that has been central to Indic and European philosophy since antiquity. The word dialectic originated in Ancient Greece, and was made popular by Plato in the Socratic dialogues...
. Hegel considered it one of his major works and therefore kept it up to date through revision. The Science of Logic is sometimes referred to as the Greater Logic to distinguish it from the condensed version of it he presented in what is called the Lesser Logic, namely the Logic section of his Encyclopedia of the Philosophical Sciences.
Brief history of the book
Hegel wrote 'The Science of Logic' after he had completed his Phenomenology of SpiritPhenomenology of Spirit
Phänomenologie des Geistes is one of G.W.F. Hegel's most important philosophical works. It is translated as The Phenomenology of Spirit or The Phenomenology of Mind due to the dual meaning in the German word Geist. The book's working title, which also appeared in the first edition, was Science of...
and while he was in Nuremberg
Nuremberg
Nuremberg[p] is a city in the German state of Bavaria, in the administrative region of Middle Franconia. Situated on the Pegnitz river and the Rhine–Main–Danube Canal, it is located about north of Munich and is Franconia's largest city. The population is 505,664...
working at a secondary school and courting his fiancé. It was published in a number of volumes. The first, ‘The Objective Logic’, has two parts (the Doctrines of Being and Essence) and each part was published in 1812 and 1813 respectively. The second volume, ‘The Subjective Logic’ was published in 1816 the same year he became a professor of philosophy at Heidelberg
Heidelberg
-Early history:Between 600,000 and 200,000 years ago, "Heidelberg Man" died at nearby Mauer. His jaw bone was discovered in 1907; with scientific dating, his remains were determined to be the earliest evidence of human life in Europe. In the 5th century BC, a Celtic fortress of refuge and place of...
. The Science of Logic is too advanced for undergraduate students so Hegel wrote an Encyclopaedic version of the logic which was published in 1817.
In 1826 the book went out of stock. Instead of reprinting, as requested, Hegel undertook some revisions. By 1831 Hegel completed a greatly revised and expanded version of the ‘Doctrine of Being’, but had no time to revise the rest of the book. The Preface to the second edition is dated 7 November 1831, just before his death on 14 November 1831. This edition appeared in 1832, and again in 1834–5 in the posthumous Works. Only the second edition of Science of Logic is translated into English.
Antecedents
The main antecedents of the Science of Logic are these:1. In his Categories, Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
tried to list and define the most general types of predicates applicable to an entity: substance (ousia), quality, quantity, relation. Plato had attempted a similar task, especially in the Sophist, Hegel's favourite Platonic dialogue.
2. In his De Interpretatione, Aristotle considered the structure and constituents of the proposition or judgement. Plato had again explored this matter, especially in the Theaetetus and Sophist.
3. Aristotle's Prior Analytics
Prior Analytics
The Prior Analytics is Aristotle's work on deductive reasoning, specifically the syllogism. It is also part of his Organon, which is the instrument or manual of logical and scientific methods....
deals with the nature and validity of inferences or syllogisms, while his Posterior Analytics deals with proof or demonstration and with demonstrative science. 'Analutika' is Aristotle's word for 'logic'. Logiki (techne) ('(the art of) logic', from logos, 'word, reason', etc.) was first used by the stoics.
These and other logical works of Aristotle were later called the Organon
Organon
The Organon is the name given by Aristotle's followers, the Peripatetics, to the standard collection of his six works on logic:* Categories* On Interpretation* Prior Analytics* Posterior Analytics...
, the 'instrument' of correct thought. (Works entitled 'New Organon', such as Bacon's and Lambert's, are attempts to outdo, or update, Aristotle.)
4. In his Metaphysics, Aristotle attempted to justify the law of non contradiction and of the excluded middle. He considered them to be metaphysics or 'first philosophy', since they apply to all entities. By Hegel's time the 'laws of thought' also included the law of identity and, since Leibniz and Enlightenment, the principle of sufficient reason or ground.
5. Hegel also says that the Science of Logic incorporates the material of the 'old' metaphysics, which derives from Aristotle and Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
, but also embraces Leibniz, Spinoza, Wolff, etc. Many of the concepts he examined, especially in the 'Doctrine of Essence', were employed by metaphysicians.
6. In the first main section of Kant's Critique of Pure Reason
Critique of Pure Reason
The Critique of Pure Reason by Immanuel Kant, first published in 1781, second edition 1787, is considered one of the most influential works in the history of philosophy. Also referred to as Kant's "first critique," it was followed by the Critique of Practical Reason and the Critique of Judgement...
, the 'Transcendental Doctrine of Elements', Kant
KANT
KANT is a computer algebra system for mathematicians interested in algebraic number theory, performing sophisticated computations in algebraic number fields, in global function fields, and in local fields. KASH is the associated command line interface...
defines 'transcendental' logic as the science which, in contrast to formal logic, 'determines the origin, range and objective validity of a priori cognitions' (Critique of Pure Reason, A57, B8I). Transcendental logic falls into two parts: (a) the logic of truth (transcendental analytic), and (b) the logic of illusion (Schein) (transcendental dialectic). In (a) he attempts to systematize and justify the categories (e.g. causality) presupposed by objective judgements and experience. In (b) he attempts to curb the speculative
Speculative reason
Speculative reason or pure reason is theoretical thought , as opposed to practical thought...
use of reason, arguing, e.g., that it leads to antinomies. Many of the concepts considered in (a) and (b) reappear. But Hegel combines analytic and dialectic at every stage, arguing that every concept (except the absolute idea, which even so is instantiated in these proliferating contradictions) gives rise to antinomies or contradictions. The second main section of Kant's book, the 'Transcendental Doctrine of Method', which determines the 'formal conditions of a complete system of pure reason' (A708, B735), is also relevant, especially to Hegel's concern for system. Hegel's knowledge of, and indebtedness to, Kant were great. But the extent to which his fundamental motivations and procedures are Kantian is still a matter of controversy.
7. Hegel also explores concepts such as force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
, polarity or opposition and infinity
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...
, which figured not only in metaphysics and theology
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...
, but also in the natural science and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
of the day.
(2), (3), (4) and, in part, (1) made up the subject-matter of the 'formal', 'classical' or 'traditional' logic of Hegel's day. Hegel, like Kant, held that this had made no important advance since Aristotle. This underrates the medieval and stoic
STOIC
STOIC was a variant of Forth.It started out at the MIT and Harvard Biomedical Engineering Centre in Boston, and was written in the mid 1970s by Jonathan Sachs...
contributions to logic, as well as the mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
that began with Leibniz's 'universal characteristic', and which Hegel argued against.
General Circular Progression: Objective to Subjective and Back
The overall progression of the Science of Logic is from the objective to the subjective. Hegel starts simply with the concept of being, objective being which you can simply point at, such as the chair in front of you. He progresses by a series of painstaking (and unfortunately patently obfuscating) moves to an increasingly subjective viewpoint. For example, he transitions from objective being (the chair) to "illusory being," which is still real but the product of one's imagination, such as the likeness of two chairs. Eventually Hegel pulls in KantKANT
KANT is a computer algebra system for mathematicians interested in algebraic number theory, performing sophisticated computations in algebraic number fields, in global function fields, and in local fields. KASH is the associated command line interface...
's ideas of judgement and categorical classification, more or less wholesale copied from the Critique of Pure Reason
Critique of Pure Reason
The Critique of Pure Reason by Immanuel Kant, first published in 1781, second edition 1787, is considered one of the most influential works in the history of philosophy. Also referred to as Kant's "first critique," it was followed by the Critique of Practical Reason and the Critique of Judgement...
and adapted into his system. In the end of the book Hegel wraps all of reality into a single Absolute
Absolute (philosophy)
The Absolute is the concept of an unconditional reality which transcends limited, conditional, everyday existence. It is sometimes used as an alternate term for "God" or "the Divine", especially, but by no means exclusively, by those who feel that the term "God" lends itself too easily to...
. This absolute covers basically everything which can happen, has happened, and all viewpoints rolled into one. Importantly Hegel then links this final absolute idea with his ordinary concept of being which he introduced in the start of the book. Hence the Science of Logic is actually a circle and there is no starting point, no sequence, but rather a totality.
Quality, Being, Sublation, and Becoming
Hegel takes Quality as the first major topic of the book. In the simplest case we take a quality such as being—Hegel uses "pure being." The opposite of pure being is pure nothing. The important point is that we cannot have the quality being unless we also take into consideration nothing. It is impossible to conceive of being without nothing included in the thought. As another example, it is impossible to understand the idea of continuous unless we have an understanding of discrete. Continuous would be entirely meaningless if it could not be held in contrast with discrete. This process is Hegel's concept of quality "sublation" and this type of dialecticDialectic
Dialectic is a method of argument for resolving disagreement that has been central to Indic and European philosophy since antiquity. The word dialectic originated in Ancient Greece, and was made popular by Plato in the Socratic dialogues...
thinking permeates all the Science of Logic under one heading or another.
If reality were static there wouldn't be much to explain, but reality is a continual oscillation from being to nothing, from quality to quality, from something to other. Hegel identifies "becoming" as the substrate upon which changes takes place.
Determinate Being
Once being has achieved a steady quality, Hegel describes this status as "determinate being." For example, a stop light may change from green, yellow, to red. When in a single color the light has a determinate being of that color, yet the other colors "are" still in existence, but in a state of sublation. It is just as important that when the light is green it is also NOT yellow nor red. Just because the light shows green does not mean that red and yellow have entirely fallen out of existence. The critical point is that we should certainly have the concept of the upcoming red light in the center of our attention—thus the red is still "in" existence in this fashion .Most of reality is like that to some extent . A person is alive—but will be dead. When you look at a person you know death is only sublated. Death is still there. The important point to Hegel is that reality is not simply a set of discrete states akin to a computer state machine . Hegel notes that "there is nothing on heaven and earth which does not contain within itself both being and nothing." By this he means that being is continually changing from something to nothing and back, and "becoming" is the substrate upon which change takes place. In order to process reality we need to take the totality of an object's states into consideration, not just the present determinate being.
Constitution, Limit, and the Ought
If we take all the possible determinate being states of some object we can determine the object's constitution. Take any person's moods as an example: the totality of moods reveal constitution. Returning to the simple stop light example above, we see that it can be in three states: green, yellow, and red. This totality of states we can think of as the object's constitution. Hegel associates "limit" with whatever conditions surround the determinate being in question. Hence, if the light is green it is limited to that state. But, the light "ought" to be able to advance to a different quality like yellow or red. Reality is saturated with the continual transcending of "limits." We see a thing "ought" to be able to change from its present "limit" and this is often what happens.Finite, Infinite, Being-For-Self, Transition to Quantity
To Hegel an object in a particular state is limited and finite. Reality, however, displays the continual transcending of limits, inducing in us the belief in the infinite. There are just too many possible states to count so we believe in the infinite.But, to Hegel, however, this transition to the infinite is a fallacy. There is no such infinite. What results from one finite state is always just a new finite state. Even if we take an enormous number of different qualities, this is still finite, although too large even to perhaps be counted. We can still add one to the enormous number and we still have another finite enormous number of qualities for as long as it pleases us. Because a new finite always results, no matter how large, Hegel states that this "infinite" is in fact the "spurious infinite." We are fooled into the belief of a truly objective infinite, but we will always just have another finite.
Regardless of this seeming contradition of infinites, reality nevertheless presents itself to all persons as a single unified whole. Hegel introduces the concepts of "Being-For-Self" and "Being-For-One" to describe this state of affairs. Due to this system of presenting one single unified whole to any person, the concept of quantity emerges directly out of Being-For-One. If we have Being-For-One we definitely have a quantity of one to start off with. No matter how infinite reality appears to us, it is still one single reality for one person to us. One reality, one person, and there is no mistaking the concept of one and quantity is easy to envision. Hegel uses this as his springboard from quality to quantity.
Does that mean there is no true infinite? According to Hegel the true infinite appears as thought itself.
Quantity
Importantly Hegel notes that reality is saturated in ones. We are constantly using our one reality to subdivide and rearrange new sets of ones. According to Hegel quantity exists within a "void" -- probably a sort of qualitative numerical substratum which is the subject's working space for quantity, as yet not determinate (i.e., as yet having no value assigned). Important concept having directly to do with quantum include "attraction," "repulsion," "intensive magnitude," "extensive magnitude," "continuous," "discrete," "amount," "unit," and "number."Hegel groups attraction and repulsion together. Attraction simply means that a set of ones can be grouped together resulting in a new one. For example, a group of students is one. Repulsion is the reverse: we take a group and split it into subcomponents. Now we have a set of ones.
Intensive magnitude refers to the numerical size of some object, for example the intensive magnitude of a person may be five and a half feet tall. Extensive magnitude refers to the effect that this intensive magnitude has on everything else.
Continuous and discrete are straightforward. An example would be a line painted on a highway that is continuous, alternatively the same line could have been discrete (split into sections).
Number to Hegel is basically a determinate quantum like 35. Note however that this 35 is still "one," i.e., it is one 35 and not other numbers like 34 and 36; it is limited at 35. That a thing (here a quantity) is limited and is not something else is of great importance to Hegel and a recurring theme of the work. Amount refers to a set of ones within the number 35. Unit is the standard understanding—for example force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
may be expressed in newtons. So we may for example have one "number" equal to 35 newtons, one "amount" referring to the set of newtons, and finally individually 35 of one unit. Note that we are continuing down a kind of hierarchy of ones.
Ratios
Once Hegel establishes the basics with respect to quantum as described above, the next issue he takes up is ratios after another discussion of the infinite (this time taken from a quantitative starting point but with the same results as qualitative infinity above—i.e., we never reach a true quantitative infinity but always reach just a new finite quantum: thus such infinity is mere "spurious infinity"). Recall that with Hegel there is nothing in reality in isolation, and this is immediately apparent within the area of quantitative ratio: With a ratio we are obviously holding two distinct things in contrast, yet the result is a single thing which binds the arguments into a whole. The result of a ratio is something new which is based upon and includes the arguments.Hegel's "direct ratio" is the ordinary ratio, such as 2/3. We can alter the arguments in keeping with the ratio, such as 40/60 but the result (which Hegel curiously calls the "exponent" throughout the discussion) remains the same. The "inverse ratio" refers to the basic mathematical relationship in which the product of two arguments stays the same while the arguments vary in an inverse fashion to each other. For example, 20 = 10 * 2, but if we change 10 to 5 we are obliged to change 2 to 4, yielding 20 = 5 * 4. The result is the same as the arguments depend upon each other.
The upshot of Hegel's discussion is that within the realm of ratio, the arguments are bound to each other so much so that each argument "is" the other, not existing in isolation. By the time Hegel's reaches his last ratio, the so-called "ratio of powers," he begins a shift back from quantity to quality because we attach a quality to ratios.
Measure
In general "measure" for Hegel is the result of quantity and quality together held in relation to something else—possibly the same thing in a previous state. Take a pile of bricks as an example. If we had a quantity of just two bricks we could assign "small pile" to its quality. This is only true, however, that we determine a "small pile," if it is held directly in relation to a second unit of bricks with the quality "large pile" and quantity much increased. Thus by this point Hegel has brought quality into play with his discussion of quantitative ratios as above.Hegel specifies two forms of measure: "Specifying Measure" and "Real Measure."
Specifying measure can rely on a rule established beforehand by taking an instance of measure as the reference point. Let us use average car as a reference point. Here we have a general idea of the size in terms of quantity of dimensions, for example in meters. We assign to this quantity of the dimensions of the car the quality average. Now suppose we see somebody driving a little 1960s VW Bug: we utilize our specifying measure and assign the value small car to this instance because the quantity in terms of dimensions of the VW is much smaller than our average reference. Now somebody drives by in a roomy 1975 Buick sedan. In relation to our average car measure, the quantity of roominess in the Buick held in relation to our average car dimensions results in the quality "big." It is important to note that by this time in Hegel's system we are utilizing elements of ratio as above expressly for quantitative comparison for qualitative reasons.
By the time Hegel reaches his "Real Measure" he has begun to compound relations between measures. For example, establishing a measure that is the contrast of two previous measures, such as a measure that shows an overall increase or decrease. For example suppose we see a succession of persons based upon increasing age. Each person could have a specific measure in terms of quantity (age) and quality (young, middle age, old). Yet, we could establish a secondary, overall measure that indicates increasing age in succession. As another point he discusses the importance of realizing all the qualities that a specific measure is not, such as obviously a young person is not an old person. What something is not is just as relevant as what something is to Hegel. Hegel also mentions that just because quantity changes, it does not immediately signal a change of quality. Usually a couple of years will not immediately change a young person to middle aged for example.
Absolute Indifference, Transition to Essence
It is at this stage (still within the topic of measure) that Hegel begins the long transition from the domain of objective logic to subjective logic. He shortly introduces essence, which he will classify as "illusory being" in contrast to "determinate being" as above. The point is that now we are transitioning to an increasingly mind-dependent viewpoint of reality.In previous sections, Hegel established that being can shift from some determinate something to another determinate other, and becoming was the substrate upon which these transitions took place. For example your shoes might be off or they might be on, and that is all there is to it. However, now we have to deal in things that are naturally not in a single discrete state but have some imprecise value on a continuum.
So at this stage Hegel takes his idea of sublation a bit further and introduces "absolute indifference." He claims absolute indifference is the substrate upon which a thing can basically be in two states at once to different varying degrees. Some things in reality are never completely in one discrete state or another (this is an idea akin to fuzzy logic
Fuzzy logic
Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...
) yet we seem to be able to handle this situation easily. For example suppose we may have a partly cloudy, partly sunny day and we desire to state some objective measurement of the weather conditions to a friend. It is up to us to mediate multiple, non-discrete states, yet still arrive at a single "posited reflection." To continue the example we could say that "the weather today is fair," being neither totally cloudy nor totally clear.
Doctrine of Essence
When Hegel reaches essence, he starts a new "book," still under the heading of objective logic. Thus, he considers essence to fall more readily under an objective rather than subjective heading. He immediately introduces the term "illusory being" which signals a sharp break from the more tactile qualities, quantities, and measures that serve as the basis for the first "book" of his objective logic described above.Essential/Unessential, Illusory Being, Reflection
Although any fairminded reader would consider this stage of the Science of Logic plainly at obfuscating heights, essenceEssence
In philosophy, essence is the attribute or set of attributes that make an object or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity. Essence is contrasted with accident: a property that the object or substance has contingently, without...
for Hegel seems to take as its starting point the traditional conception of essence descended down from the ancient Greeks.
Hegel points out that the object of our attention may contain the unessential as well as the essential. Later on he will note that all of appearance contains the essential and unessential. A horse might be brown or black, but in any case it is still a horse. It is not essential the horse be black to be a horse. When we experience something, we consider its essential features, but at the same time are also able to "throw out" unessential features and ultimately arrive at a true objective essential conception. This process he terms reflection: a wholly "illusory" process which filters the essential from the unessential and ultimately results in some determinate conception which Hegel calls "illusory being." Yet illusory being, the mediation of essential and unessential, Hegel terms an outright mind dependent "nullity" when considered in contrast to the more
stable and simpler qualities above.
Let us take for an example "happy group of people" as our object. It is essential that the people be smiling, laughing, and so forth, but unessential as to location and dress. They may be in an elevator or walking on a sidewalk dressed in suits or shorts. It makes no difference. We reflect on the situation and hold the essential (smiling, laughing, etc.) together with the unessential (location, dress, etc.), and the result is an "illusory being" -- nothing more than a "nullity" that arises as a result of our mediation of essential and unessential. We are able to determine, by reflection, the essence of our group of observed people as a "happy group of people."
Hegel claims there are three general types of reflection: "positing reflection," in which one forms a reflection internally (i.e., completely within one's mind); "external reflection," in which one reflects upon two objects external to oneself; and finally "determining reflection," in which one draws a relation between an internal representation and something external. The result of a completed reflection is "already in propositional form."
Identity, Difference, Contradiction
Identity holds high importance for Hegel, writing that "all thinking involves identity and difference." Indeed it is hard to imagine any sort of life at all if we could not make use of identity, difference, and related concepts such as likeness; these principles constitute the backbone of Hegel's view of essence. Initially he claims that "so far, then, identity is still in general the same as essence" and reminds us that identity is usually held to be the "First Original Law of Thought." The problem with identity, however, is that a statement such as A=A is a limited, one-sided statement of identity, a mere "empty tautologyTautology (logic)
In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...
" that has "no content." If someone declares that the book in front of him is the book in front of him it leads nowhere, in the same way that a person claiming that "God is--God" is wasting our time. These are "boring and tedious" statements utilizing the "pure law of identity" which merely "reiterate the same thing" in Hegel's view.
As soon as "A is..." completes (is predicated by something), says Hegel, difference emerges. Thus he claims broadly that "everything is inherently contradictory." Taking "the camera is black" as our example, a camera is not the same thing as the color black, yet it is what it is (a black camera) through this resolved contradiction.
Hegel identifies three types of difference. "Absolute difference" is the most general and abstract (mental reflection) sense. "Diversity" includes the "otherness of reflection" meaning that we essentially think of how "A" is different from all other possible cases. Finally, "Opposition" is the "completion of determinate difference" with "moments that are different in one identity."
Regarding diversity, let's assume there is some American person "A" who is overweight. In considering the obesity of "A" in our mental reflection we at the same time consider all the potential and possible weights that "A" is not along some continuum. "A" is not thin nor of normal weight either and this needs to be taken into consideration. Hegel says that things are different through unlikeness: this is the so-called "Law of Diversity."
Ground
Simply put ground is the "essence of essence," which for Hegel arguably means the lowest, broadest rung in his ontology because ground appears to fundamentally support his system. Hegel says, for example, that ground is "that from which phenomena is understood." Within ground Hegel brings together such basic constituents of reality as form, matter, essence, content, relation, and condition. The chapter on ground concludes by describing how these elements, properly conditioned, ultimately will bring a fact into existence (a segue to the subsequent chapter on existence).Hegel considers form to be the focal point of "absolute ground," saying that form is the "completed whole of reflection." Broken into components, form taken together with essence gives us "a substrate for the ground relation" (Hegel seems to mean relation in a quasi-universal sense). When we combine form with matter the result is "determinate matter." Hegel thinks that matter itself "cannot be seen": only a determination of matter resulting from a specific form can be seen. Thus the only way to see matter is by combining matter with form (given a literal reading of his text). Finally, content is the unity of form and determinate matter. Content is what we perceive.
"Determinate ground" consists of "formal ground," "real ground," and "complete ground." Remember with Hegel that when we classify something as determinate we are not referring to absolute abstractions (as in absolute ground, above) but now (with determinate ground) have some values attached to some variables—or to put it in Hegel's terminology, ground is now "posited and derived" with "determinate content."
In formal ground Hegel seems to be referring to those causal explanations of some phenomena that make it what it is. In a (uncharacteristically) readable three paragraph remark, Hegel criticizes the misuse of formal grounds, claiming that the sciences are basically built upon empty tautologies. Centrifugal force, Hegel states as one of several examples drawn from the physical sciences,
may be given as prime grounds (i.e. "explanation of") some phenomena, but we may later find upon critical examination that this phenomenon supposedly explained by centrifugal force is actually used to infer centrifugal force in the first place. Hegel characterizes this sort of reasoning as a "witch's circle" in which "phenomena and phantoms run riot."
Real ground is external and made up of two substrates, both directly applicable to content (which evidently is what we seem to perceive). The first is the relation between the ground and the grounded and the second substrate handles the diversity of content. As an example Hegel says that an official may hold an office for a variety of reasons—suitable connections, made an appearance on such and such occasion, and so forth. These various factors are the grounds for his holding office. It is real ground that serves to firstly make the connection between holding office and these reasons, and secondly to bind the various reasons, i.e. diverse content, together. Hegel points out that "the door is wide open" to infinite determinations that are external to the thing itself (recall that real ground is external). Potentially any set of reasons could be given for an official to be holding office.
In complete ground Hegel brings together formal and real ground, now saying that formal ground presupposes real ground and vice versa. Complete ground Hegel says is the "total ground-relation."
(In progress)
Editions of Science of Logic
- translated by W. H. Johnston and L. G. Struthers. London: George Allen & Unwin, 1929
- translated by Henry S. Macran (Hegel's Logic of World and Idea) (Bk III Pts II, III only). Oxford, Clarendon Press, 1929
- translated by A. V. Miller, Foreword by J. N. Findlay. London: G. Allen & Unwin, 1969
- translated by George di Giovanni, Cambridge: Cambridge University Press, 2010
Secondary literature
- Bencivenga, Ermanno 2000. Hegel's dialectical logic Oxford.
- Burbidge, John W., 1995. On Hegel's logic. Fragments of a commentary Atlantic Highlands, N.J.
- Burbidge, John W. 2006. The logic of Hegel's logic. An introductionPeterborough, ON.
- Butler, Clark. 1996. Hegel's logic. Between dialectic and history Evanston.
- Carlson, David 2007. A Commentary on Hegel's Science of Logic New York: Palgrave MacMillan. 978-1403986283
- Di Giovanni, George (ed) 1990. Essays on Hegel's logic Albany: New York State University Press.
- Harris, Errol E. 1983. An interpretation of the logic of Hegel Lanham.
- Harris, William T. 1895. Hegel's logic : a book on the genesis of the categories of the mind. A critical exposition Chicago.
- Hartnack, Justus, 1998. An Introduction to Hegel's Logic. Indianapolis: Hackett. ISBN 0-87220-424-3
- Houlgate, Stephen, 2006. The Opening of Hegel's Logic: From Being to Infinity Purdue: University Press.
- Rinaldi, Giacomo, 1992. A History and Interpretation of the Logic of Hegel Lewiston: Edwin Mellen Press.
- Roser, Andreas, 2009. Ordnung und Chaos in Hegels Logik. 2 Volumes, New York, Frankfurt, Wien. ISBN 978-3-631-58109-4
- Winfield, Richard Dien, 2006. From Concept to Objectivity. Thinking Through Hegel's Subjective Logic Aldershot: Ashgate. ISBN 0-7546-5536-9.
External links
- Source text (German) Wissenschaft der Logik Vol. 1 Vol. 2
- Outline of Hegel's Logic at marxists.org
- The Meaning of Hegel's Logic (commentary at Wikisource)