Now language has some algebraic postulations below.
Word consists of elements R1. The element has proto-meaning.
Word’s meaning is generated by product(・) of the elements.
The product of elements is called primary meaning (R1, ・).
Word is group.
Another word ( R2, ・)is generated.
New word is generated by addition (＋) of the elements of two words.
The addition of elements is called secondary meaning (R1, R2, ・, + ).
New word is ring.
The upper group and ring are regarded as commutative.
Sentence consists of words T1.
Sentence is generated by product of words (T1, ・).
But sentence is seemed to be non-commutative, i.e.T1T2T3 is not T3T2T1. /I/ /read/ /book/ is not /book/ /read/ /I/. Word is expressed by / /.
I call the situation <deep fissure between word and sentence>.
This <fissure> is seemed to be relative with true-false argument of sentences.
Tokyo
September 10, 2007
September 10, 2007
Postscript January 21, 2008
[Basis]
<On differential structure between word and sentence>
[Foresight from past work]
<On true-false value>
Postscript February 10, 2008
[Conjecture]
<On finiteness and Infinity on language>
Postscript August 2, 2008
[Conjecture]
<On Definition of word and sentence>
<On warp and entropy of language>
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