**For WITTGENSTEIN Ludwig ^{0}**

** **

**Position of Language**

1 **Quantization ^{1}** is a cliff for consideration of language.

2 Mathematical interpretation of quantized language is now a first step to the theoretical ascent.

3 If there is not mathematics, next conjectures are impossible.

(i) Difference between word and sentence—**Commutative and noncommutative ring**

(ii) Continuation from word to sentence—**Tomita’s fundamental theorem**

(iii) Word’s finiteness and sentence’s infinity—**Property infinite** and **purely infinite**

(iv) Cyclic structure of word’s meaning—**Infinite cyclic group**

4 **Meaning minimum ^{2}**,

**mirror language**and

^{3}**mirror symmetry**are inevitable approach to the study of language especially for

^{4}**language universals**.

^{5}5 Symplectic Language Theory, Floer Homology Language and Arithmetic Geometry Language are adopted as the model theory for natural language in the recent.

6 Hereinafter the model theory will be entered to the new concept. **The Model****s**** of Language Universals**** ****6** will be shown by the description of mathematics.

[References]

0. WITTGENSTEIN Ludwig

1. Quantized Language

Quantization of Language /Floer Homology Language

2. Meaning minimum

Structure of Meaning / Symplectic Language Theory

3. Mirror language

Mirror Symmetry on Rational Curve / Symplectic Language Theory

4. Mirror symmetry

Homology Mirror Symmetry Conjecture by KONTSEVICH / Symplectic Language Theory

5. Language universals

Generating Function / Symplectic Language Theory

6. Models of Language Universals

Language Universal Models till 2011

**Tokyo December 10, 2005**

**Now traveling to a northern more place from the encounter
**

**Tokyo November 27, 2008 Revised**

**Tokyo March 24, 2009 Revised**

**Tokyo June 27, 2009 Revised**

**Tokyo February 28, 2011 Revised
Tokyo August 3, 2012 Revised**