[FOM] On >>this sentence cannot be proven true<<

[Hartley Slater]

Following on from my previous message, here is more regarding the 
contextuality of possible-worlds talk.

One has to remember that other possible worlds are not entirely 
abstract objects, since we can imagine entering them, which is a 
process that takes place in this world.  In the case of linguistic 
fictions this commonly involves certain context markers, like 'Once 
upon a time'.  Maybe once upon a time an old man was reading page n 
of a book, B, the first sentence on that page [i.e. page n of book B] 
being 'The first sentence on page n of book B is not true'.  In this 
case, at its unquoted place the subsequently quoted referential 
phrase refers to the page the old man was reading in the fiction, 
i.e. the possible world.

Without the 'Once upon a time', the following story might be 
non-fiction, although the same kind of linguistic cross-reference 
would still occur, from the referential 'the first senternce...' back 
to the previous introductory description of the man.  In 
non-anaphoric uses of referential phrases, i.e. when they are 
'deictic', there is no context marker like 'Once upon a time'. or 
even explicit introductory description.  But the absence of these is 
not part of the sentence(s) that follow, so, even when there is 
direct reference to the actual world, it is a matter of the 
pragmatics and not the semantics of the utterance, i.e. not something 
in the sentence alone, in itself.

One is nowhere near appreciating any of this if one is at all closely 
attached to Russell's Theory of Descriptions.  For what otherwise 
would be a 'referential phrase' is taken there to include some 
introductory descriptive material, and so have a quantificational 
analysis.  Finding a better representation of properly referential 
phrases is first required, such as that given by epsilon terms rather 
than iota ones, as I have demonstrated in a number of publications. 
One other misleading aspect of the Formal Logic scene before WWII, 
besides the sidelining of context, and possible worlds, and the 
engrossment in Russell's theory, was the close connection, then, 
between Logic and Mathematics, especially the Foundations of 
Mathematics.  It is quite plausible to believe that one can have a 
truth predicate of elementary mathematical sentences such that, e.g. 
T'2 + 3 = 5' iff 2 + 3 = 5, and so that sort of case came to be taken 
as the paradigm.  The realisation that the cases where this kind of 
equivalence holds are very special cases has taken a long while to 
dawn - even given Tarski's own Indefinability Theorem showing there 
cannot be such a 'T' in general, even in Arithmetic.

Of course, outside the Formal Logic tradition there are plenty who 
have insisted, on other grounds, that it is not sentences but 
propositions that are truth bearers.  Thus there is no objection to a 
truth scheme in either of the propositional forms:
p iff it is true that p,
p iff that p is true.
Here, any referential term in 'p' is used (in this world), on both 
sides of the equivalence, unlike when it is  just mentioned on the 
RHS in the corresponding sentential form:
p iff 'p' is true,
and that leads to a lack of paradox in the former case.  The trouble 
with developing such a propositional theory of truth formally, 
however, has been the lack of any general symbol for the content of a 
sentence, like my previous '*p' - although notable logicians like 
Kneale and Cocchiarella have both provided one (see the papers I 
previously specified for the references).

-- 
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 6488 1246 (W), 9386 4812 (H)
Fax: (08) 6488 1057
Url: http://www.philosophy.uwa.edu.au/staff/slater