For WITTGENSTEIN Ludwig Revised . Position of Language. 2005-2012

For WITTGENSTEIN Ludwig Revised

Position of Language

TANAKA Akio
                          
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 3  and  mirror symmetry 4  are inevitable approach to the study of language especially for  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]
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  


Tokyo December 10, 2005
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
Tokyo December 8, 2014 Reprinted
SIL