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[xmca] Generality Is Not Abstraction

I'll try to keep this short and to the point, but it's really a note about different kinds of vagueness. Marshall Brown notes in his book Turning Points: Essays in the History of Cultural Expressions that a particular kind of music which BEGINS with an apparent chaos of chromaticity and then allows the formation of clear musical concepts by the opposition of and generalization from emergent motifs (e.g. tonal oppositions, tunes, or simply an octave, a fifth, etc.)
In Chapter One, Chapter Five, and again in Chapter Six, Vygotsky presents two different mechanisms of concept formation: generality, and abstraction. What is the difference? Well, it seems to me the easiest way to understand it is Vygotsky's metaphor of a water molecule (which he does NOT use the way it is used in Mill, simply to say that the whole is more than the sum of its parts). 
For Vygotsky, the formula H20 is simply an example of generality, because it is true of every form of water without exception. It is NOT a successful application of abstraction, because it tells us nothing about the essence of water in concrete processes. In order to understand what we wish to understand about water (e.g. whether it assists combustion or extinguishes it) we need to understand not what it is but how it acts, and that requires abstraction rather than generality.
The problem is that this easy way of understanding it does not show us generality and abstraction working together. That is what we see in Vygotsky's "globe", the "measure of generality" in Chapter Six. At one pole, we have object-related meaning, which is unique (i.e. not general) and concrete (i.e. not abstract). 
At the other pole (which Ana calls the South Pole, but which I have always thought of as the North Pole) we have number, which is also unique (in the sense that one is not two or any other number) but which is entirely abstract (in the sense that it is not tied to any actual form of matter and as a consequence can be expressed in an infinitude of ways).
And where is generality? Ah, that is lies somewhere in the middle, where words are used to include the most variegated objects and their ideal representations and actions and processes, all of which are expressible in a myriad but not an infinity of different ways. And out of this chaos, Mozart, and Mendelssohn and later Beethoven, who were after all musicians of Kant's and Hegel's historical moment, can precipitate precise oppositions and concepts.
David Kellogg
Seoul National University of Education 

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