Day fifty-two -- Constructed linguistic universe (V)

      From Tienzen:
      Perhaps, the (type 0) and (type 1) are ideal languages.

      Now, we know the difference between two languages. Is that difference superficial or fundamental? We need to introduce three more operators to answer this question. [/quote]

      What we are doing here is not only new to linguistics but is also new to science. Thus, we must make the terms that we are using very clear without any misunderstanding. The terms of axiom, postulate, assumption, hypothesis and premise are sometimes viewed as synonyms. The followings are the definitions for this work, the "constructed linguistic universe."
         1. Axiom -- it is a non-logical axiom and is selected arbitrary. Its purpose is to demarcate a domain.
         2. Hypothesis -- it is a statement which must be proved, generally via a theory.
         3. Postulate -- it is a statement that is assumed to be true without proof and to serve as a starting point for proving other statements. In practice, a postulate must have enough evidences to support (not to prove) its validity.

      Now, I will introduce two postulates for this "constructed linguistic universe."
         1. Postulate one -- the "Operator of pidginning" transforms a language Lx toward the direction to the "type 0" language.
            Definition 9 -- the "Operator of pidginning" transforms a language Lx to a pidgin (Lx).
         2. Postulate two -- the "Operator of creoling" transforms a pidgin (Lx) toward the direction to the "type 1" language.
            Definition 10 -- the "Operator of creoling" transforms a pidgin (Lx) to a creole (Lx).

      With these two postulates, we can make some predictions.

      Predication one -- Lx and Ly have different language structures. That is, [Lx - Ly] = D1. and [pidgin (Lx) - pidgin (Ly)] = D2, then,
      D2 < D1, D2 is smaller than D1. That is, the difference of the language structure in terms of "language type" between two pidgins is smaller than the difference between two original languages

      Predication two -- Lx is a natural language with a creole (Lx) and Ly with creole (Ly). And,
      [Lx - creole (Lx)] = D1
      [Ly - creole (Ly)] = D2
      [creole (Lx) - creole (Ly)] = D3

      Then, D3 < D1, D3 is smaller than D1, and
      D3 < D2, D3 is smaller than D2.

      The difference of the language structure in terms of "language type" between two creoles is smaller than the difference between it and its parent language.

      If we can find some evidences for these two predictions, the following hypothesis is proved.

      Hypothesis one -- this "constructed linguistic universe" forms a linear language spectrum, ranging from the "type 0" to the "type 1". That is, all natural languages are distributed in this language spectrum, and this "constructed linguistic universe" encompasses the entire "real" linguistic universe.

      If the "hypothesis one" is true, then the difference among natural languages is superficial, not fundamental. The great divide between the "type 0" and "type 1" can be bridged over with two operators, "Operator of pidginning" and "Operator of creoling".

      Thus far, we only concern about the "structures" of the languages, without any concern about the members (the word forms, sounds, cultures, etc.) in those structures. This is also an issue which must be discussed.

Signature --
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