Hegel on quality and quantity
These are thoughts I jotted down a while ago, when reading John Hibben’s and Justin Hartnack’s books on Hegel’s Logic. They are relevant to a current Twitter conversation with my colleague J W Mason.
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Hibben makes it clear how Hegel’s Logic has a sort of fractal organization. In its examination of each triad of categories, Hegel rehearses the whole structure of his Logic as if in miniature. When he says that, as an abstraction, therefore empty of any other concrete determination, “Being is the same as non-being,” he seems to be simply noting that saying that something is, leaving it at that, is equivalent to saying nothing about the thing. The abstraction of Being goes as far as the abstraction of Nothing. This is the sense in which Being and Nothing fuse into each other. The attribute of “pure being” hangs in the air, with nothing concrete to de-fine, de-termine, or de-limit its boundaries.
Here one notes that Hegel viewed historically evolved human language as the mode of existence par excellence or vehicle of the universal character of logical categories, from their rawest to their ripest forms. “The most valuable thoughts of mankind are often found crystallized in language,” wrote John Hibben. But Hegel was much more expansive about it: “Language has compressed within it what man has made his own; and what he has fashioned and expressed in speech contains, either embedded or elaborated, a category: so natural does logic come to him, or rather it is his own very nature.”
The usual definition of a thing (“intensional,” rather than “extensional,” which requires exhaustively listing the instances of the thing) requires a statement of its genus (a chair is a piece of furniture) and of its differentia specifica (it is used mainly for one person to sit on it, though unlike a stool it has back support, typically has four legs, etc.). The genus connects it to the rest of the universe, establishing its belonging to one of its domains, while the differentia separates it, i.e. de-fines it with respect to the rest of its genus, and thereby the rest of the universe.
Thus, to de-fine something is to remark its finitude or finiteness. Likewise, to de-termine it is to set its terminus — its end or conclusion. It is no accident that the English word “term” has come to evoke both the name of a thing and an interval of time. Spinoza’s famous remark comes to mind here, “Determinatio est negatio,” or as people say nowadays, “What opposes you, supports you.” I.e. to define something is to negate it at once in that establishing its quality is akin to marking the boundaries beyond which it ceases to be what it is and becomes what is not, thus abandoning its de-finite or de-fining quality, turning itself into its very negation. Similarly, to de-limit a thing is to establish its limit. In the Preface to the Phenomenology, Hegel wrote that “the specific difference of a thing is rather its limit; it is where the thing stops, or it is what the thing is not.” This is the sense in which the determination of quality is identical to the determination of quantity.
Thus, when Hegel says that “Quantity is quality sublated” (sublated is negated and preserved, transcended dialectically) he seems to mean that qualifying something is already quantifying it, directly and immediately, even if such quantification is still highly abstract, i.e. quantification in its roughest, most elementary manner. In modern terms, qualifying or formally defining something means quantifying it in the binary domain. Like a switch turning from on to off, or vice versa. Something is or is not. It either retains or abandons its self same quality without further ado.
But the human mind is compelled to go beyond this most superficial form of quantification. Because in a closer inspection, things rarely leap from a quality to its negation, from an old to a new quality. Instead, with the progression of human practice, it becomes clear that things of interest gradually transition into their non-being along a sort of continuum, not smoothly, but still gradually; but this up to a point — the point at which they suddenly snap into their new quality.
According to Paul Lafargue (and, if I remember correctly, Franz Mehring), Marx believed that an intellectual discipline became a true science when it was capable of quantifying what previously was regarded as unquantifiable, or — more properly — what was previously qualified but kept in the realm of a relatively empty abstract definition, i.e. quantified in the roughest, most superficial manner. This highlights how thinking that by denying the possibility or necessity of quantification in the social sciences one escapes quantification altogether is a mirage. In fact, by seeking to prevent quantification, one incurs in it unconsciously and, therefore, less effectively. By so doing, one does not advance science but contains it. The proper scientific attitude is not to reject existing quantification but to critique it, transcend it, and improve on it. This is the path from abstraction to the organized concrete.
Re-examining Hegel’s remark on language is also illuminating here: “Language has compressed within it what man has made his own; and what he has fashioned and expressed in speech contains, either embedded or elaborated, a category: so natural does logic come to him, or rather it is his own very nature.” What humans have appropriated. Remember Marx here: Production is appropriation. The mere production of ourselves is appropriation, and appropriation through language is conscious appropriation. The development of language is the development of human consciousness, and thus the development of the productive force of labor.
When we appear in the world, we appear occupying physical space and time. And producing our lives leaves a footprint on the rest of nature. Because the objects that we produce embody our designs. And our designs, as humans, gain articulation and meaning in and through our language, the vehicle of our thoughts— internal and external speech, the language we use to communicate with ourselves (to think) and the one we use to communicate with others. Language is embedded (the instinctive body language with which our babies start their cognitive journey) or elaborated (the result of history, production, scientific development). In the introduction, Hegel does say that he is not dealing with the laws of thought as they should be but as they are in fact. Just like Molliere’s character speaks prose without knowing it, our cognition is dialectical thinking, embedded or elaborated.
Measuring a thing means simply comparing it to a standard. The standard and the thing measured must share a common quality or “substance,” but at the very least all things have as a common (though admittedly abstract) quality that of being. With slim prior knowledge, if all we know about two things is that they exist, their sheer existence as distinguishable things suffices as a basis for comparing them, which requires that one grants one of them the role of the standard of measurement. In fact, distinguishing a thing from others, defining its quality, entails ipso facto a comparison, i.e. a measurement! In sum, the very definition of the distinctive quality a thing implies its quantification, however rough or abstract such quantification may be.
