[FOM] Between Russell's Twins and Tarski's Chimera
segunai at hufs.ac.kr
Mon Jul 19 23:53:13 EDT 2004
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offer two unpublished papers of mine.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
"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
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