Science of Logic

Hegel's work The Science of Logic 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.

Circular Progression: Objective to Subjective and Back

The overall progression of the Science of Logic is from the objective to subjective, but Hegel reveals that his system has no starting point per se and is a circular totality. In other words, Hegel starts simply with the concept of being, such as a chair has objective being you can simply point at. He progresses by a series of painstaking (and unfortunately patently obfuscating) moves to an increasingly subjective viewpoint. For example, he transitions from objective being (such as a chair) to what he calls "illusory being" which is still real but the product of one's imagination, such as the likeness of two chairs. Eventually Hegel pulls in Kant's ideas of judgement and 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 subjective idea. This absolute covers basically everything which can happen, has happened, and all viewpoints rolled into one. Importantly Hegel then links this final absolute idea rollup with his ordinary concept of being which he introduced in the start of the book. Hence the SOL is actually a circle and there is no starting point, no sequence, but rather a totality. It is important to note that Hegel picks objective being as his starting point simply because of convenience; there is actually no "start" in Hegel's system.

Quality, 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 dialectic 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: picture a jazz musician on heroin for 20 years. 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 (ie., 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," ie, 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 heirachy 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 -- ie., 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 in to 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 which Hegel says is the "immanent quantitative relationship of two qualities to each other." In this instance we take an established instance of measure as the reference point. Let us use small 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 size of car the quality small. Now suppose we see sombody driving a little 1960s VW Bug: we utilize our specifying measure and assign the value small car to this instance. Now somebody drives by in a roomy 1975 Buick sedan. In quantitative terms the dimensions of the two cars are much different, and this results in the qualities of big and small. It is important to note that by this time in Hegel's system we are utilizing elements of ratio expressly for comparison, but we have begun to think in qualitative terms.

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, including increase and decrease. For example if 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 measure that indicates the display of increase.

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

Secondary literature

Hartnack, Justus, 1998. An Introduction to Hegel's Logic. Indianapolis: Hackett. ISBN 0-87220-424-3
Wallace, Robert M., 2005. Hegel's Philosophy of Reality, Freedom, and God. Cambridge University Press. ISBN 0-521-84484-3.
Houlgate, Stephen, 2006. The Opening of Hegel's Logic: From Being to Infinity. Purdue University Press
Carlson, David, 2007. A Commentary on Hegel's Science of Logic. Palgrave MacMillan. 978-1403986283