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] 0 . WITTGENSTEIN Ludwig Theory Dictionary Writing Theory Dictionary Person Aim for Frame-Quantum Theory 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