[FOM] Between Russell's Twins and Tarski's Chimera

[Segunai]

Hello all,

This is my first posting although I've been visiting FOM longer than a 
year. I think it's the best way to introduce myself that I invite you to 
visit me at http://maincc.hufs.ac.kr/~germanistik/segunai.htm, where I 
offer two unpublished papers of mine. I give here only the abstract of one 
of them titled "Mathematical Logic between Russell's Twins and Tarski's 
Chimera":

"This sentence is short" is true of itself and we can use it to assert that 
fact. That leads to the loss of its entire syntactic links to other 
sentences including its negation in normal use, "This sentence is not 
short", which attributes a different property to a different string if it 
refers to itself.

Since truth is disquotation, i.e. a truth-assertion is disquotable, "This 
sentence is true" expires after it approves of the proposition of another 
sentence. In case it refers to itself, the truth-teller is therefore 
neither true nor false since entirely devoid of propositional contents. 
Exactly the same applies also to the liar, its alienated negation.

Semantical anomaly results only from self-referential use of disquotable 
sentences, undisquotable sentences such as address the length of strings 
never leading to related problems. Completely unfounded is therefore 
Tarski's ban on the use of sentences of level 3 or higher.

Respectfully and cordially, Yours Segunai