[FOM] Self-reference in natual, languages (re >>this sentence, cannot be proven true<<)"

[A.P. Hazen]

Quine's elegant recipe for self-referential sentences uses the construction
	(*) appended to its own quotation yields an F
(where F is to be replaced by some noun phrase: e.g. "falsehood"), 
and he claims that appending a phrase of this form to its own 
quotation produces a sentence naturally interpreted as saying of 
itself that it is an F.  If I understand Hartley Slater,  one of his 
objections to this is that (*) contains a dangling (antecedentless) 
pronoun, "its."   But surely THIS objection can be overcome with a 
minor  reformulation:
	(**) is a string of words which, when appended to its own
		quotation, yields an F.
This seems like a perfectly grammatical English VP (VP: "verb 
phrase," something which can be, in the jargon of older grammars, the 
"predicate" of a simple declarative sentence), and the only pronouns 
in it HAVE antecedents: "its" is anaphoric for "which" which in tun 
has the NP "a  string of words" as antecedent.

Question for Haim Gaifman: does this version have a direct 
translation into Hebrew?

Historical note: Gödel's double-substitution trick for obtaining 
self-referential sentences, whgich Quine imitates in English, seems 
to have been anticipated by Russell: cf. Judy Pelham & Alasdair 
Urquhart, "Russellian propositions,"in D. Prawitz et. al., eds., 
"Logic, Methodology and Philosophy of Science IX" 
(Elsevier-Horth-Holland, 1994), pp. 307-326.  Nice illustrative 
applications, including the definition of a formal language 
equivalent to First-Order Logic in which sentences have the 
subject-followed-by-predicate form exploited by Quine, can be found 
in Raymond Smullyan, "Languages in which self-reference is possible," 
JSL 22 (1957), pp. 55-67.

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Allen Hazen
Philosophy Department
University of Melbourne