[FOM] consistency and completeness in natural language

[Hartley Slater]

A further thought occurs to me regarding Hodges' question about 
sentences being true, in FOM Digest Vol 4 Issue 4.  If he has been 
unable to look at Ch7 of Prior's 'Objects of Thought', he may not be 
alert to the possibility and relevance of ambiguity with sentences. 
Certainly we can say, for instance, that a sentence s *states the 
facts* (Ss), and Prior (as I have amended him) would then say Ss iff 
(r)(Msr -> Tr), where 'Msr' says 's means r', 'Tr' says 'r is true', 
and the variable 'r' ranges over referring phrases to 
propositions/statements.  Given (E!r)Msr one can then obtain, by 
straightforward logic, the sentential T-scheme, Ss iff TerMsr (where 
'e' is epsilon, and 'erMsr' is 'that statement s makes').  Charles 
Sayward, in 'Prior's Theory of Truth', Analysis 1987, uses the 
contingency of this sentential T-scheme to prove, indirectly, that in 
the case of the Epimenides Paradox the self-referential sentence must 
be non-univocal (i.e. ~(E!r)Msr).  The distinction of my new paper 
'Choice and Logic' is that it does not argue indirectly, but locates 
directly the ambiguity in this and similar cases, and finds 
comparable explicit ambiguties in the Paradox of Predication, 
Russell's Paradox, and Grelling's Paradox (Heterologicality), also 
Berry's Paradox, and Simmons' Denotation Paradox.
-- 
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 9380 1246 (W), 9386 4812 (H)
Fax: (08) 9380 1057
Url: http://www.arts.uwa.edu.au/PhilosWWW/Staff/slater.html