The number of grammatical differentiations of verbs (potentially
or in Indo-European languages?) seems to be of the magnitude
5 - 6. Perhaps these different aspects on verbs could be connected
with d-degrees or steps in our model, in a secondary dimension
chain of verbs? Here a suggestion, where the situation for
speech could be regarded as one determining factor in moods:
There is a connection between moods and tenses as between
steps 5 - 4 and 1-0/00 in the loop model of a dimension chain:
Suffixes for moods became auxiliary verbs
in the development from Latin in Indo-European languages,
auxiliaries also for determination of tenses.
We can also find a semantic connection between steps 4 -
3 and 1 - 2: between intransitive - transitive character and
the aspect of duration:
Intransitive verbs have the character of a state (or condition),
something continuous as "duration", transitive verbs
with more character of bordered, delimited actions.
Active - passive verb forms is a secondary polarization
of transitive verbs, of unidirection outwards (pole 4b) towards
an object versus inwards the subject (pole 4a).
In passive verbs this displacement to a
change in direction inwards the subject is expressed by simply
addition of the suffix -s in Swedish, derived from a reflexive
Here we have a connection to next differentiation
with inclinations after 1st, 2nd, 3rd person etc., as the
polarization of d-degree 4 in 4b/4a gives d-degree 3 in the
dimension chain: start of substantiations towards the category
of nouns, deciding the inclination after person.
In certain Uralic languages the verbs have double suffixes,
marking both the subject and the object (BC,u) of transitive
(In a language as Swedish oppositions concerning moods and
intransitive - transitive verbs as in tense inclinations are
stronger marked through vocal changes in word stems than in
active - passive forms and person suffixes. Possibly while
these differentiations represent a deeper level in the loop
version of our dimension chain?)
Moods: — step 5 -
Moods are described as "a form category that indicates
the speaker's apprehension of what is said". Linguists
talk about 5 to 4 moods, in Greek 5, in Latin (or languages
from Latin?) 4. With differentiations in moods we get a third
level in the "fractal" developments within the dimension
- Indicative (something stated, related)
- Imperative (exhorting, urging)
- Subjunctive (something thought, possible, conditional)
- Optative (Greek: what is wished)
An Uralic language as Yurak (Nenets) is said to have 10 moods
(BC,u). Uralic and some other languages have also negation
verb forms; Turkish has a "mood negatives".
The question form should reasonably be possible
to apprehend as a mood too when the imperative is a mood and
it seems really to exist as a mood in certain languages (same
source BC,u). It's said that negation particles and
question particles originally have been identical in Indo-European
and Semitic languages (LB). Hence it sounds right to
connect moods with the whole situation for speech and the
relation speaker — addressee.
With the indicative taken as the basic form
of a full sentence, as developed straight "outwards"
in the sense of attitude, it seems possible to interpret the
other moods as representing geometries of different degrees
in the direction inwards as from 00-pole and "a-poles"
in the model:
In geometrical terms:
- 4a: straight inward direction, towards 2nd person, imperative.
- 3a: circular geometry: the infinitive with character
- 2a: convex form, open curve: the subjunctive, the
- 1a: defined as "motions towards each other" in
the model: the optative,
see annotations below.
- 00: the opposite direction in the whole chain, the indicative
turned in direction to negation or question mood.
The imperative is the purest example of the
direct relation speaker - addressee, as centre - anticentre
poles, the elementary direction, d-degree 4, in the situation
They include he most single-worded type
of sentences as "Run!", one single verb (verbs
in d-degree 4).
The speaker is centre-displaced as to the
surface of the addressee, which implies that the sentence
in a real semantic meaning lacks a subject. The direction
of imperatives is essentially inwards.
(The imperative could also be said to represent "law"
and rules, as syntax is proposed as from d-degree 4 in the
big level chain of linguistic analysis.
In languages like Swedish the verb gets often reduced to
the pure verb stem, without any suffixes.
The infinitive represents linguistically the
"infinite" (the 00-pole). It has a recognized subjectival
character of d-degree 3 and can function both as subject and
object, as an objective complement.
Uralic languages have instead of infinitives
case forms of verbal nouns (BC,u).
The subjunctive, the only imagined, possible
or conditional, may perhaps be expressed as if- sentences.
The speaker's psychological attitude is a kind of detour,
or "the other way around" in relation to statements
about facts, as it were connected with the loop model of the
In relation to indicatives as "substantiated"
actual facts, the subjunctive implies a dissolution, an opening,
something unsubstantiated of more wavy character. Hence here
suggested as in from step 2 ← 1.
The optative as "wished" could be
interpreted as a catching motion and has in relation to the
subject the inward direction. It could illustrate the definition
of d-degree pole 1a as "motions towards each other"
in our model, psychologically:
(It's said that an expression as the Swedish "Leve
konungen" (English "cheer the king
is the rest of present tense subjunctive in optative use.
Hence a wish as a positive possibility, connected with the
It sounds probable that auxiliary verbs have developed
from these later moods within Indo-European languages, those
moods that represent the only potential, imagined or wished
- in this sense the internal of the subject? Subjunctive verb
forms are in Swedish for instance alternatively expressed
through auxiliary verbs for passed time, in this sense in
the inward direction of time:
("Om det vore så = Om det hade varit så
= If it were so... If it had been so...)
Tenses, auxiliary verbs, —
step 1 ← 0/00:
1. Tenses are tools for the time aspect relative the present
in the situation of speech. They become parts in the angle
steps of time displacements through levels.
2. The subject as a centre, geometrically first as origin
(the 0-pole) becomes toward higher levels a growing circle,
The auxiliary verbs for past time could be regarded as internal
radii within the subject. (A verb as "be"
is a basic form as a radius without directions.)
3. With the subject centre displaced to its surface, its
circumference, as in possessive position, the radius gets
the direction inwards the past: the auxiliary verb marks the
time displacement inwards.
The possessive as the case for "ownership"
(normally for nouns) is an expression for this position of
the subject at its own surface, enclosing its belongings or
possessions. In Lappish also verb stems may be in the genitive
and in Uralic languages more generally the genitive is also
used to indicate points of time and time periods.
According to one opinion possessive suffixes
in Uralic and Turkish languages have originally been combined
with expressions for completed actions. (BC,u). With
the geometrical view above this seem natural.
In an Indo-European languages as Swedish (also in English)
the auxiliary verb for past time is ha (have)- hade...,
a verb for ownership too (Swedish "innehav").
An enclosing word. In opposition to this the auxiliary verb
for the future is skall (= shall), a word which originates
from skuld, (meaning debt), the opposition to ownership
in economic terms (!).
These auxiliary, "possessive" verbs imply also
terminated activities. Demarcations as shells are creations
of inward direction.
Perfectives of auxiliary verbs for the future as shall
- should become connected with e.g. subjunctive moods
above. They get an anticipating character, as from a still
larger incorporating circle (In real outward direction towards
the future there are strictly speaking no such angle steps
defined. "He will have finished this work tomorrow":
in such a phrase the speaker has already positioned himself
at a point in the future.)
The relation between auxiliary verbs and main verbs should
be possible to interpret as a relation between different coordinate
axes, including a displacement in tense. (A language as Swedish
has 5 tenses, 3 for the past, 1 for the present and 1 for
The changes between progressive and terminated
activities as between continuum and quantum jumps could be
compared to the steps in a ladder: horizontal resting-planes
varying with level steps.
Time displacements inwards "inflect" verbs
in languages as Indo-European through a change backwards in
the word stem of the vowel. The "strong verbs".
This "mutation" goes often to
a more inner vocal. Both seem to express the past as a "genealogical
The vowel changes in word stems when the
verb is substantivized is of the same kind. Swedish examples:
springa (run) - sprang (ran) - språng
(a jump); - ligga (lie) - låg (lay) -
läge (location); stjäla (steal) -
stal (stole) - stulit (stolen) - stöld
These vowel changes for past time and nouns
for the activity are both characterized in direction and enclosures
respectively by inward direction. So does direction inwards,
~ past time, transform to "circular" structure,
~ nouns, in the dimension model.
Duration, — step
The differentiation between progressive and terminated activities
has the general character of continuous versus quantified
(00 versus 0 in our model - or perhaps d-degree steps versus
d-degrees). One argument here for interpreting this differentiation
as an expression in d-degree step 2 —
1 is that it concerns borders for actions, "perfective",
borders similar to enclosing surfaces (d-degree 2). (Inside
~ finished, enclosed; outside ~ open, not terminated.) Cf.
the poles 2a / 2b of d-degree 1.
In Uralic languages there seems to be 3 polarizations as
for duration aspects:
a) The first polarity is easily identifiable with the poles
0 and 00, quantified - continuous. They could be compared
with poles 1a and 1b in our model: "motions to each other",
defining a centre, quantifying, and "motions from each
other", defining distances, a durative type.
b) The second polarity could possibly be interpreted as d-degree
1 ("rapidly", a quantified linear series?) - with
its outer poles 2b/2a.
c) The third polarity should then be these poles 2b and 2a,
for start of a durative activity and the closing down of it.
That implies borders (in this sense 2-dimensional, for the
Intransitive / transitive verbs, —
step 4 → 3:
Intransitive activity concerns the subject itself, as a person
is a whole in itself when sleeping. That means it's double-directed
outwards/inwards as d-degree 4 unpolarized.
As said above it implies a state, related
to the concept "condition", therewith also including
a connection with the concept duration as in the loop model.
Transitive verbs are unidirected as activated working forces
with explicit directions.
We get the polarization into active - passive forms:
- The active form binding the subject with an object
as 00-pole and anticenter on the circumference.
- The passive making the subject an object in itself.
Hence the relation Intransitive →
Transitive corresponds to a step 4 →
Outer poles of d-degree 3 are 4a and 4b, in our model assumed
as perpendicular to one another, the inward direction transformed
to a circular geometry.
How such a geometry eventually appears in passive verb forms
of languages may be left as an open question. Semantically
the passive could be said to make the subject to an encircled
The opposition intransitive - transitive is in a language
as Swedish often expressed through vowel change
in word stems: sova (sleep) - söva (get
to sleep), ligga (lie) - lägga (lay), in
similarity with tense changes in strong verbs.
Conjugations after person, singular - plural, —
This differentiation concerns persons, that is nouns, here
d-degree 3 as class of words.
Verb suffixes get the character of "pro-nouns".
They may be regarded as a result of the displacement from
the "I-You"-situation of speech to the describing
sentence and principally 3rd person, where also the I and
the You may get character of references.
While most of the verb suffixes for persons seem to originate
from the word class pronouns, it's doubted now that those
for 1st and 2nd person really do so in Indo-European languages.
(BC,s). Here the original situation of speech with
Speaker - Addressee as 0 - and 00-poles, before the "tangential"
coordinate axes of relating sentences develop, could be responsible
for that doubt.
In Uralic languages it seems that 3rd person not was expressed
as verb suffixes but in a substantival construction, a noun
derived from a verb, something which further supports the
interpretation of this differentiation with d-degree 3 and
the step 4→ 3 as verbs to nouns.
It's curious but significant that the suffixes for person
originate from possessive pronouns, not the nominative ones.
Also this fact seems pointing to the centre
displacement in the situation of speech, and pronouns as referring
backwards to something mentioned, geometrically similar
to the person at its circumference as an "owner"
of his content.