BREV TIL: Louis Hjelmslev FRA: Hans Jørgen Uldall (1941-01-16)

16/1/41. Dear Hjelmslev, V/e have only just found out that It is possible to send letters to Denmark, that is why I have not written for so long. In any case, there have been no scientific results to report for ouite a while, as my papers were lost in transit for a couple of months, but j am now happily at work again and, I think, making some progress. I think I told you in my last letter, dated some time in August or September, that I was trying to get behind the concepts of ’’constant" and "variable", but at the time I got no further with it. I have now started on the same line, and it seems that it can be done as follows: the first constant to be met with in any deduction is the object of the first analysis, the original entity; this is an b absolute constant as far as that deduction is concerned, but as all deductions are ultimately part of one comprehensive deduction, all these Initial constants are reduced to one, viz. the Universe. The next constants are the functives connected by constellation (combination), but these are not absolute constants, because, even though their first-degree relation may be constellation (a relation takes the same degree as the functives engaged in It), they invariably engage in some relation or correlation of a higher degree, which is Interdependence, since It appears to be a law that the first analysis of a deduction must dis- cover an interdependence. But I think the be^t way to explain what I mean is to copy out the relevant sections of the definitions, which I have altered accordingly, so please read that before you go on. The Important thing in the theory of functions seems to be the ability of a unit to belong to two successive stages of the hierarchy. The first example of that Is a unit occurring at the same time as a nexia and as a nexus or, rather, a nexia and a nexus having the same heteroplane relation, e.g. 'I went', which can occur both as an Inde- pendent nexia and as part of a nexia as In ’when he came, I went*. I now think that this can be generalized to account for every case of what we used to think of as ’occurring alone’, either direct or so that

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a riixEEted determined unit is deduced from a unit having this dual function. If this is true, the whole thing is much simpler than we thought before or, at least, than I thought last spring, when the categories of functions grew so alarmingly from four to nine to fifteen. It now seems to me that there are only the three possible functions mentioned in the delinitions, and that all the complication comes from the possibility of each functlve having a number of different functions of different degrees. In other words, the hierarchy is the important factor, which beautifully vindicates our terminology: the system determines the syntaxia. There are a number of cases of a unit belonging to two stages of the hierarchy, e.g. aMxtiiaryxxsriDKxsMJshxaKxAdH* verbs such as 'go' and other "full" verbs, which occur at the same time as a complete verbal unit and as part of a verbal unit such as 'can go', where 'can' is the determining functive, since it cannot occur without another verb. You get a nicely graded series with auxiliary verbs like 'do' and 'have'. Diphthongs and Maidu t also appear in a new light, and so do long vowels with no short counterpart, if they share the functions of other long vowels In the language rather than those of the short vowels. The fifteen functions and the beautiful four-dimensional diagram of last spring are hereby solemnly declared null and void, though it hurts me grievously to have to give them up. Oh, there is another lovely example of a unit belonging to two stages of the hierarchy: in Miwok (I think it is, but I can't verify that at the moment), in Miwok kinship terminology the women are treated as a generation younger than the men: a woman looks up to her brother as to a father, etc. I am in difficulties at the mompnt about how to make a graphic representation of the hierarchy from the point where homoplane and heteroplane units no longer coalesce. It will have to be three-dimension- al in some sort of way, but I can't at the moment see just how.