1. The development from affixes to separate word classes in languages referred to here seems as a clear illustration of the main features in the applied model: the debranching degrees in steps outwards toward lower d-degrees.
   In simple terms of our dimension model:

Prepositions are

a) the vector character of d-degree 4 debranched to a position before nouns in the step 4 → 3, where the verb also transforms to radius, a pole of d-degree 3,
(4 = 1 + 3),

b) the same vector character, debranched to d-degree 1 in the loop model ("the other way around") become vector-adverbs, closely related to prepositions.
4 → 3 ... +1.
   (Through step 1 → 0/00, when verbs become equivalent with Motions, d-degree 0/00, the prepositions express the vector character in our concepts "motions to and from each other".)

Pronouns may, as proposed before, be regarded as originating from outer poles 0 and 00 of d-degree 4 of verbs in the primary speech situation speaker - addressee(s).
   In secondary types of sentences they become "references". In this sense they too reveal the vector character of "Direction", d-degree 4 in our model. Verb affixes get debranched to secondary "pro-nouns", replacing nouns as the "circular", enclosing pole of d-degree 3.

Both pronouns and prepositions appear as quanta of the binding force in sentences: pronouns expressing relations in the whole speech situation and displacements in types of sentences, prepositions expressing the very transformational relation in word classes V-N, verbs-nouns.
   Prepositions could perhaps be compared with "group-transporting enzymes" on the biochemical level: prepositions as expressions for the transporting mechanism itself.
   As such they may be compared with lexical derivations on a superposed level.

"Form-words" or "functional words" are the linguists' name for this kind of released elements.
   A development towards such free form words has been going on not only in Indo-European languages but also in other ones. A couple of statements:
   Only about 50 % of pronouns were developed in the daughter languages of Latin in the 12th century. Etruscan had pronouns but not many traces of prepositions.

Prepositions

1. To sum up they express a) directions, b) positions and can in application of our dimension model be regarded as essential elements of d-degree 4 (Directions) and d-degree 3a (Space, "pre-position"): elements which debranched give prepositions as a separate word class.

They represent the most pure geometrical elements of word classes. Many of them also with the most obvious polar character, divided in pairs of opposites as to - from, in - outside, above - below, over - under…

Prepositions as displacements of elements in higher d-degrees 4 and 3 becomes also expressions for the displacement of nouns as subjects to nouns of secondary (oblique) and tertiary roles in the sentences, as to dative, locative, instrumental function…
   Compare for instance "he saw her" with "he looked on/at her": in first expression "her" is only linguistically an "object", in the second expression also semantically more of an object, a locative or ...

2. Some statements by linguists about origin of prepositions, probably (?) limited to certain languages as those from Latin:

a. Case forms are described as derivations from noun stems. (BC,s)
b. A case form of a noun becomes prepositions, e.g. in Hungarian benn → bél.*
c. Prepositions have developed from case forms of nouns and pronouns - and from comparison forms of adjectives and adverbs.
d. Prepositions may in general be traced back to adverbs. (BC).
[Cf. that that many Latin adverbs were said to be case forms of nouns that "have gone astray".]
e. One example: A unit kata (meaning "in the descension") with adverbial sense, moved to a position before the noun or before a verb, transforms it to a preposition, and creates these as a word class (PW).

*b. Compare in this example n and l with interpretation
of phonemes and their semantic roles.

Hence, one main statement or proposition here implies that prepositions first appeared as cases in what we here have regarded as the secondarily developed dimension chain within nouns, before they got released to form-words. The second that prepositions would have their origin in adverbs, more in agreement with our view on the loop model above.

It's curious that prepositions with an obvious vector meaning don't seem to have been parts of verbs. In Swedish for instance the verb tillhöra (belong to) may just as well be expressed as höra till, the preposition till (to) separated to position after the verb: 4 → 3 + 1 in terms of d-degrees.
    It would imply that most verbs early were transformed to radii in d-degree 3 in relation to nouns in roles of subject and objects - according to views on verbs above. Only in verbs as come - go does the higher d-degree of speech situation remain.

However, the near connection between many kinds of adverbs for directions and prepositions reveal such relations between verbs and prepositions.
   The only difference here is that in the adverbs (the type "vector-adverbs") the direction is the main topic, while preposition need a following noun (per definition!), a definite localization, representing the step 4 → 3 in our terms.

This differences seems as originally connected with the one between intransitive and transitive verbs, the step from d-degree 4 unpolarized, "double-direction", to its polarization, implying transitive verbs:

   - the vector-adverbs derived from intransitive verbs originally,
   - the prepositions from transitive verbs, radii directly connected nouns.

Cf. the difference in the preposition på (= on) in Swedish: "köra på (stressed) någon" (= drive into somebody) and "köra på vägen" (= drive on the road). In the first phrase "på" belongs to the verb as "ad-verb" on its way to a preposition, in the second phrase, unstressed, clearly pointing out a position as "pre-position".

It was said that case forms of nouns also influenced attached adjectives, hence perhaps also the comparable "How"-adverbs (?), so to speak the straight way outwards in the dimension chain.
   It was a third point in the linguists' statements above that prepositions also would derive from comparatives of adjectives and adverbs. Why precisely comparatives?
   One answer could eventually be that these comparatives represent steps in gradients towards higher or lower d-degrees - as in fact the whole dimension chains in the interpretations here? In a deeper sense the comparatives may be regarded as derivations (or integrations) as such?

About pronouns it has been assumed that certain case forms (syllabic ones) originally have been pronouns. (BC,u).
   Together with the statements about propositions we could get a picture of a trend as this below, with pronouns, case affixes and prepositions representing first three levels in the level chain of linguistic analysis:

- Pronouns suggested as derived from the situation of speech as most underlying level, originally the relation speaker - addressee and references from there to 3rd parts.
- Cases regarded as expressions for next level, the Syntax, representing the differentiated geometries between parts of speech.
- Prepositions more restricted to word classes as verbs and nouns.

A rough outline of the relations if imagined as 3 crossing coordinate axes?

Or as angle steps (projected in the plane):

Pronouns

Pronouns are a very differentiated word class, by linguists divided in a bit different ways.
   Here suggestions on how to look at these different categories of pronouns in agreement with the dimension chain:

(5) → 4
Demonstrative <—> Interrogative:
- These types seem directly dependent on the situation of speech, connected with directions of the whole sentence. Demonstratives have a typical vector character of d-degree 4 and simultaneously define a centre, as in first place a 0-pole.

- The interrogatives represent the undefined anticentre, the 0-pole, and also inward direction of sentences in opposition to statements as outwards, marking the "definitive". The pointing out versus questioning becomes related to moods of verbs.

(English has two demonstrative pronouns, this and that. Eskimo has about 30 such demonstrative pronouns (!). (CEL). (30 = sum of poles in a dimension chain.)

4 → 3:
Personal: nominative, accusative, dative... :
- Personal pronouns in nominative as he, she, are believed to originate from demonstrative pronouns, if so from the preceding step above.
   (1st and 2nd person are here regarded as related to first poles in the situation of speech (0 — 00), speaker - addressee.)
   The angle change to describing sentences and subject - object relations implies also a displacement of personal pronouns to secondary relations as objects, accusative and dative forms...
   The fact that these steps to object, dative etc. include vowel changes in the word stems of our IE-languages, indicates their very central function (of high degree) in speech and their close relations to verbs that have the same change.
   With verbs originally characterized by d-degree 4, as vectors, it's logical that verb endings developed to separate pronouns (in Latin) preceding the word class nouns of d-degree 3 as "pro-nouns".

4a —>3 <—4b:
Reflexive pronouns (yourself, oneself) may be compared with secondary forms of personal pronouns in e. g. accusative or dative but refer back to the subject itself.
   They may be related to the polarization of verbs into active - passive forms (poles 4b = outward direction, pole 4a = inward direction).
   About Swedish, it's said that the s as in the passive verb suffix, e.g. kallas (= is called) has developed from the reflexive pronoun sig (= himself, herself...).
   There is the clear difference between kallar sig (he calls himself) and kallas (is called): In the reflexive pronoun he is the Subject, while he in the passive verb form is only, in reality, an object. Hence, the development from reflexive pronouns to passive verbs agrees with the displacement Subject → Object of nouns and pronouns.
   The reflexive pronoun sig originates in its turn from words for self or own, words for the "I" that has been certified and confirmed, substantiated. Cf. possessive pronouns in next step.
   To reflexive pronouns the reciprocal may be added, as each other, a dual or plural version.

3 — 2:
Possessive pronouns as mine, his, theirs, implies a referring inwards, the owner at his anticentre, at the surface of what is possessed, the real noun or topic as enclosed within. (Cf. about the auxiliary verb "have" in the verb-file..
   Possessive pronouns originate from case forms of "reflexive verbs", that's passive verb forms, so it's said about Swedish (SEO). They are also expressed through the verb ending -s in Swedish, the same as in passive verbs.
   We should thus observe that the owner in fact becomes displaced as to the role of an object at anticentre semantically, while that which is owned has raised to the Subject, more or less owing its owner. A turn in the relation in this middle step 3–2 when regarded in the loop model.

3 —> ↑ < — 2: Subordinate clauses:
Relative pronouns as "which", refer forwards (or "upwards") to something coming, introduces subordinate clauses.
   It has been proposed above that subordinate clauses could be regarded as level developments in step 3 → ← 2 through the opposite directions in the loop model of a dimension chain. These clauses (more or less elliptic) make something mentioned to a new start as subject, a centre.
   All the mentioned types of pronouns above but for the interrogatives are called "definite" or "determinative" as references to certain things, in opposition to more generalizing things, the "indefinite" pronouns. Compare the opposition between centres and primarily undefined anticentres, the underlying polarity 0 <==> 00.

In the loop version of the dimension model we get secondarily as in a haploid chain degree 00/0 in the middle step:

The indefinite pronouns have been divided into "quantitative" and "relational" ones*,

   - Quantitative as all, each, many, few, much, one, somebody, nobody...
   - Relational as another, same, such, first - last, inner- outer, upper - lower, east - west

* (Source here: Swedish Wikipedia, from Hultman, Tor G.:
Svenska Akademiens språklära, Stockholm 2003.)

Most of them can appear as in an adjectival function before nouns (and may as adjectives become inflected in agreement with the nouns). Some are also substantival and can stand alone as nouns in sentences.

2 - 1:
The "quantitative" pronouns could thus at first be regarded as connected with the word class in step 2 - 1 for adjectives. Note that outer poles of d-degree 2 is 3a and 3b, (3b — 2 — 3a) poles which represents a dissolution of d-degree 3 as nouns but can replace these as substantival.
   Swedish någon (somebody) is said to be an abbreviation of a subordinate clause "jag vet inte vem" (I don't know who...), which also connects this pronoun with the mood type of questions and interrogative pronouns.
   Swedish Ingen (= nobody) comes from en (one) and a suffix -ghi(n) that first represented a generalizing sense, (cf. the 00-pole), later a denying sense. Compare the opposite direction to the mood indicative: pole 00 representing inward direction in types of sentence, associated with negations or questions.

Many quantitative pronouns are naturally also closely related to the "word class" of numbers, here earlier regarded as basically built on d-degree 1.

1 - 00:
The "relational" pronouns mentioned in this grouping include relations in positions as upper - lower and for instance points of the compass... The are all "adjectival" in possible position before nouns like the quantitative. Yet, many of them appear as parts of adverbial expressions and are related to vector-adverbs and corresponding prepositions.
   Most of them have the typical vector character of directions of the type right - left and express polarizations between complementary poles.

In these respects they could be regarded as pronouns originating from the word class step of adverbs 1- 0/00.
   It should be observed that with the loop model we have inward direction in the chain from 00: 3 → ← 2 <— 1 <— 00, which would imply that adverbs can develop to adjectival function and these to substantival positions in sentences as often is the case.*

Both the quantitative and the relational pronouns include many of comparing type. This character is also a typical feature for adjectives and "how"-adverbs, which supports the interpretations here.

* In the elementary geometries of the dimension model inward direction from the 00-pole in d-degree 4 transforms to circular (enclosing) structure in the step d-degree 4 → 3, in languages the nouns.
   In the inward, synthesizing direction of the whole chain as "haploid" the same implies an aggregating, enclosing force, which stepwise may transform adjectival an adjectival properties into encircled noun character, that is in a more generalized way.
   We could compare with the formation of an atom as created so to speak from inside the 0-pole, with the aggregation of big celestial masses (one multitude) through the gravitational force from the 00-pole.
   Compare also the spontaneous creation of e. g. the nucleic acid Adenine in adequate solutions when energy is supplied, with the very circumstantial way of its synthesis in our bodies: Note circum-stantial, as "the other way around" in our loop model, a turn to the synthetic direction inwards.

————————————

Conjunctions:

About two other so-called word classes:
   Interjections should perhaps more adequately be interpreted as one kind of mood (?), a very elementary first one, and not a word class.
   Conjunctions such as and, or, if, because etc., representing additions or alternatives or relations to subordinate clauses, are here hypothetically proposed as elements of syntax in the middle step 3 → conjunctions← 2 of the loop model, leading to subordinate clauses (if, because...) as a new level - or (words as and, or) just repetitions or alternations ("straight outwards towards 0/00 in the chain) between words of the same class.

*

To Lexical derivations