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Greek mythology, pt. 3: rectangular linguistic investigations

October 20, 2011

[The impetus for this series of posts came from some thoughts I had after writing about the Milosz poem “Bypassing rue Descartes” in the post titled “Empire, City, and Earth”. The first post took the form of a series of diagrams, with commentary, laying out the relationships between various archetypal figures. The second post carried the inquiry slightly further and commented on the form of the inquiry and whether it was valuable. This post will discuss whether that inquiry is valuable and what it tells us about language. N.B.: while I am not going to talk about truth tables explicitly at any point in this post, it would be meet to keep them in mind for the entirety of it.]

I ended the previous post with a question: If we can always use the square, the cube, etc, to generate another dichotomy, should we? More generally, is this square mode of investigation valuable?

I said there that I would not fill out the rest of the hyper-cube because finding male and female counterparts for the eight figures I already listed sounds–what? Daunting, or pointless? Probably the latter. I could have easily found such figures for most of them–Apollo would be Athena or Artemis, for example–but the choices would have been somewhat arbitrary. And why is this? Because the male/female dichotomy does not help us to understand the earlier ones. It cannot be fruitfully juxtaposed with them. It helps for us to see the difference between earth/sky and body/spirit made concrete through examples; it does not help to see that for man/god with female/male, because I already know what all of those words mean.

Perhaps the purpose of this mode of investigation is to clarify our vocabulary. It would then be a systematic application of the principle that we don’t know the difference between two words unless there is an instance when one can be used and the other can’t. It sounds almost Saussurean (as in Ferdinand de Saussure, founder of modern linguistics). But it also provides a type of relation besides “difference.” If language is simply a system of difference, the deconstructionists win. We want to show that while our original two dichotomies are not the same, nevertheless there is one quality that goes with taking the ‘same’ side on each, and another that goes with splitting the difference. By saying this, we say something about these dichotomies and about the new one. In our original example, we suggest that there is something divine about being pure body and earth, or pure spirit and sky, and that there is something human about being a mix of body and sky, or spirit and earth.

Unfortunately, suggesting such a relation depends on not offering a figure for each possible combination of dichotomies. If there are n dichotomies, there must be less than 2^n figures. To use a geometric metaphor: we began with a square, a rather unstable configuration; it can easily be bent into a rhombus or even flattened into a straight line. When we added the man/god dichotomy, we might say that we added crossbars, thus stabilizing it. We might also that that we then twisted the square into a tetrahedron–still a stable shape. Very well. But when we insist on finding more figures to “fill in” the tetrahedron so it becomes a cube, we change our stable shape into an unstable one.

We are thus left, it seems, with two options.

  1. That this sort of inquiry will necessary shift back and forth between stability and instability, and we recognize a dichotomy with which to add stability to our n-cube, then use it to extend to an n+1-cube, then recognize another dichotomy, etc.
  2. That my postulates as to the difference between Punnet squares and archetype squares were false. Those were, to remind us:
    1. That the diagonal dichotomy is the same sort of dichotomy as the original two. So, if X=a and X=B, then X=c in the same sense.
    2. That it can always in principle be asked why, if X=a,B,c, there could not be a Y such that Y=a,B,C.

The second option is of course the far more interesting of the two. What would it be to choose it?

To reject the first postulate means accepting that Orpheus is associated with earth and spirit, but he is human. Which is to say that “the human” can be somehow both earth and spirit, even as it is both sky and body, while sky and spirit together are somehow not human. The dichotomy we arrive at, we realize, refers not just the four figures, but to the relationship between the original dichotomies. Thus “human” and “divine” are more complex concepts than “earth” and “sky” or “body” and “spirit”; and, perhaps, the purpose of the square is not to help us understand the original four terms, but the two new ones.

To reject the second postulate would, I think, be to bring us back to a consideration of what exactly it is we’re talking about, namely, archetypes. It’s silly to say “we can conceive of a figure with the characteristics of Orpheus but who is a god.” Of course any archetype could have some characteristic flipped. But archetypes are valuable because they bundle many characteristics together.  The question is not “can we conceive a figure,” or even “does such a figure exist”; the question is, why is it Orpheus whom we feel is best suited for that place on the square?

These are probably both the correct moves to make, in this instance. If we make them, the infinitely-extensible process described in the second post becomes, in fact, worthless, for we cannot go beyond the second dimension, at least in the way I described. But there must be some way to do so; language has, after all, many more than three dimensions. And also note, “in this instance.” My mind immediately ventures my Senior Novel paper on Cormac McCarthy; there, I contrasted not different archetypes, but different authorial approaches, and, I think, entered the “third dimension” in the sense used above. But I have neither desire nor ability to recapitulate the argument of that paper in but a few sentences.

So–is this mode of investigation valuable? I cannot entirely answer the question. I suspect so, but cannot entirely justify that suspicion. It may be that it is only useful as a way of writing down what we already believe, e.g. the diagram at the end of the first post, that it cannot generate any new knowledge.

I noted at the beginning that we ought to keep truth tables in mind during all of this. This is mainly because I almost used them instead of Punnet squares in the previous post, but did not. And when the subject turned to the relation between these diagrams and language, I could not evade the suspicion that it would have been more productive to do so, if I could have found a way to do so; unfortunately, I could not, and still cannot. I also find it interesting to note that Ludwig Wittgenstein is credited with the invention of truth tables. I am left with the distinct feeling that if I had read more Wittgenstein, I would be better able to proceed. Or, perhaps, simply to cure myself of my addiction to these squares.


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