Linguists talk about lexical derivations when word stems
through addition of derivative endings changes the word
Such transitions become very natural with
application of the dimension model and word classes identified
as have been done above.
Derivation in mathematics implies a stepwise decrease
in degrees of a function as in the dimension model. In the
enlarged context here the "derivations" go in
both directions - and also within the same word class, for
variation of sense: e.g. the verbs form - formalize.
(See a Swedish example at end of this file.)
The derived word is "subject to"
the special differentiations belonging to that word class
which is created: tenses, cases, comparisons...
The general principle reminds of ionizations in
chemistry when a molecule as for instance CH4 is ionized
and the H-atoms are replaced by other elements.
The derivative endings seem to have a certain similarity
with "determinants" in early ideograph
writing, the special signs in hieroglyphic writing that
were added for the meaning to get closer specified, for
narrowing down the class of meanings.
The origins of lexical, derivative endings can be traced
back to other verbs, nouns (also adjectives?) or rests of
such morphemes. One Swedish example: the ending -lig
transforms many noun stems to adjectives: form →
formlig. This ending originates from a word lik
= body, figure or shape.
Here we can remind of the 5 types of quality
adjectives (RB) mentioned about adjectives before:
3 from verbs including participles, 2 from nouns.
The "noun disease", tendency to use substantivized
verbs instead of verbs in formulations in our languages
as Swedish and perhaps related ones, is e.g. apply -
applying - the application of could lie inherent in
the linguistic laws: the natural step of development from
d-degree 4 to d-degree 3. This on the level of word classes,
in outward direction. (Perhaps limited to some types of
languages, as the inflecting ones?)
The many transitions from nouns to adjectives
and "How-adverbs" is another: stone →
stony, heaven → heavenly
Number of derivative endings, used for the transitions
between word classes (V-N-A...) in our related languages
of today, are limited, which indicates that these
derivations are part of a principle in a system, not only
They could in numbers and function be
compared with the limited number of coenzymes
in relation to protein enzymes in cell biology: coenzymes
subdivided according to what they transfer: protons, electrons
or small molecules, the "group-transporting" ones...
One reason for the limited number of these derivative endings
could be that they at first and separately only represent
the abstract structure of a word class, the steps between
categories of words.
Calculating with both the primary and secondary dimension
chains (the latter for differentiation within a word category)
in a 2-dimensional coordinate system, we could get 5 x 5
derivative endings (in a first round?). 25 is also the number
of coenzymes in the file referred to above.
Compare the 25 case affixes in Hungarian?
It seems to be an old linguistic question how lexical
derivations relate to inflectional patterns (RB),
to syntactic affixes, case endings etc.
Linguists have found many similarities between subcategories
of case endings and lexical derivations (RB). Hence,
it would be possible to regard these as results of corresponding
principles on different levels of language.
The correspondences, which give the similarities,
are here suggested to be dimensional differentiations according
to the model here.
Cases are a differentiation within the word category
- Cases -represent a secondary developed level, however
with many syntactical implications, as the difference Subject
- Object with impact on word order and with endings having
adjectival sense as instrumental case etc.
Hence, cases have a relation to syntax,
which the lexical derivative endings haven't.
A suspect figure:
- Both nouns as such and cases in the chain
of differentiations within nouns are here identified as
in d-degree steps 3 - 2, in different dimension chains related
x → x'.
(The geometrical character becomes naturally
of a more secondary derived type on the level of cases.)
- Compare too that in the super-chain of levels here the
word categories as such are assumed identified in d-degree
step 3-2 (in relation to Syntax in step 4-3 and Morphemes
in step 2-1).
A third fact to mention here is that verbs, nouns - and
adjectives often originate from the same morpheme (LB)
or originate from verbs (in Indo-European and Semitic languages),
e.g. grow - grass
This branching of morphemes
could represent a third level, a deeper one in the gradient
from phonemes towards whole sentences (in synthesizing direction).
Should these three things, morpheme branching, case
endings and lexical derivations be regarded as
three historical phases in development of IE and Semitic
languages, creations of the same principle? And/or as referring
to three different levels of language: the morpheme level
- the word class level and syntax level in our scheme level
2 - 3 - 4 ? (Both the levels of word classes and of morphemes,
3 and 2, are more or less lexical.)
The geometrical poles out of step 3-2 are in our model
elementary proposed as radial versus circular:
The lexical derivations may be regarded as the circular
component, bridging over between word classes, while the
branching of phonemes implies a radial component.
Or: from Syntax - in outward direction
- from the whole sentence to phonemes: the radial component
giving the word class differentiations. While, from the
level of Morphemes - in inward direction - additions of
morphemes (from reduced word class words) give the "circular"
component, the bridges between word classes.
Note the two opposite gradients of the
big level chain of linguistic analysis.
Compare also the two kinds of generality connected
with 0- and 00-poles respectively, the deeper integrating
one from a common centre, the 0-pole, and the superficial
aggregating, surrounding one from outside, 00-pole, in terms
of the dimension model.
The lexical character of derivations (something learned
from outside) seems also emphasized in the statement (RB)
that many such derivative endings are loans
from other languages. (In accordance with RB's distinction
between individual affixes and abstract lexical rules.)
Much in accordance with our model is the view (RB)
on the relation cases - derivative endings as
along 2 coordinate axes:
We should naturally regard each axis as representing a whole
dimension chain and count on more than two.
Affixes are seen as points
on one axis with 1 coordinate, or in one of the plane quadrants
with 2 coordinates, or in a space quadrant with 3 coordinates?
The same affix can be used in more than one of the roles.
Each coordinate axis can be moved along
another one, which provides a basis for the many parallels
between case forms and subcategories of "lexical derivations"
that RB and others have pointed out.
Perhaps the chain for differentiation
of verbs should represent the 3rd axis with such aspects
for instance as active-passive form, unlimited/limited action
or in tense as completed or future / possible action. A
relation between an axis for morphemes, one for word classes
and this verb axis could relate the words drink (V)
and drunk (Adj.) and drinkable (Adj.).
* A note:
English examples: form →
form-a, → form-alist.
- some reflections