[FOM] consistency and completeness in natural language

[Hartley Slater]

Just one final word on this topic.  Here is a more complete, formal 
reply to Sandy Hodges' question (FOM Digest Vol 4 Issue 7):

>So we posit that, on July 1st, 1972, Jones says, as his only utterance
>of the day:
>
>"Nixon's first statement made on June 19th, 1972 is false."
>
>and posit that, on June 19th, 1972, Nixon says, of his only utterance of
>the day:
>
>"The first statement Jones will make on July 1st, 1972, will be true."
>
>And posit that Jones does not know what Nixon said, and Nixon does not
>know what Jones will say.   Would you say that both Jones and Nixon made
>coherent utterances?

Consider, for a start, the case where Quint utters (at time t) 'What 
Quint states (at time t) is not true', where 'states' is deliberately 
not 'utters', but relates to the content of what is uttered.  Putting 
this remark into indirect speech we can say 'Quint states that what 
Quint states is not true' which we can symbolise 'Mq*~TerMqr' where 
'Mqr' is 'Quint states r', 'e' is epsilon, '*' is the nominaliser 
'that', and 'r' varies over referring phrases to 
propositions/statements, which include expressions like 'what Quint 
states' (i.e. 'erMqr'), and also that-clauses, like '*~TerMqr'. 
Supposing there is a determinate statement Quint makes, i.e. 
(E!r)Mqr, straightforward logic then gives 'erMqr = *~TerMqr', i.e. 
'what Quint states is that what Quint states is not true'.  But then 
TerMqr iff T*~TerMqr, and so we get, because of the propositional 
truth scheme 'T*p iff p' (where 'p' is a used sentence), TerMqr iff 
~TerMqr, which is a contradiction.  It follows that there is no 
determinate statement Quint makes.

Turning to the case where there are two speakers, Jones and Nixon, 
consider, first, the telling case which Hodges does not mention - 
where the second speaker in fact utters nothing.  The phrase 'What 
Nixon states' then refers to a fiction, but the epsilon analysis 
simply leaves it with an indeterminate referent.  We know that 
Mj*~TerMnr, so we have a representation for what many have called 
'the proposition' Jones expresses (*~TerMnr), and that necessarily 
contains a term for 'what Nixon states', i.e. 'erMnr'.  But there is 
no way to specify 'the statement'  which either Jones or Nixon makes, 
because there is nothing to determine what 'erMnr' refers to.  The 
distinction between propositions and statements was notably made by 
Strawson and Lemmon (see also Susan Haack's chapter on the matter in 
'Philosophy of Logics' CUP 1978).  The case of fictions was 
originally understood to provide a case where no statement was made, 
as with Russell's 'The King of France is bald' said at the present 
time.  But an epsilon representation of such definite descriptions as 
'The King of France' allows them to be complete individual terms, 
with merely an indeterminate referent in the fictional case.

So if we have Mj*~TerMnr, and Mn*TerMjr (by putting Hodges' case into 
indirect speech), then if (E!r)Mjr and (E!r)Mnr we get that erMjr = 
*~TerMnr, and that erMnr = *TerMjr, which means, using the truth 
scheme, that TerMjr iff ~TerMnr, and TerMnr iff TerMjr; and those are 
together a contradiction.  It follows that at least one of the 
speakers does not make an identifiable statement, in which case the 
other is talking about a fiction.  The representation and 
understanding of fictions is therefore what is most crucial.  I have 
written on this matter in several places now, and my 'The Logic of 
Fiction' is to appear shortly in John Woods' coming festschrift, 
edited by Kent Peacock and Andrew Irvine.
-- 
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