[FOM] consistency and completeness in natural language

[Hartley Slater]

Dean Buckner writes (FOM Digest Vol 4, Issue 1):
>This has obvious resemblances to the Tractarian doctrine, about what 
>can be shown but
>not said.  Failure to recognise this led to Russell's problem about the
>"relating relation" that connects the terms of a proposition into a
>judgment.  He thought a relating relation is the same entity as its
>nominalization, "that grass is green" has the same meaning as "grass is
>green", and was puzzled that it hasn't.

Torkel Franzen writes (FOM Digest Vol 4, Issue 2):
>What, specifically, in Tennant's paper do you find clarifying as regards
>such a possible need for a truth predicate [to establish reflection 
>principles]? You have in mind, perhaps, his discussion of "showing" 
>vs "saying", and of prosentential
>interpretations, on p 574f?

It would be better, I think, if Franzen's suggestion about the 
possible need for a truth predicate to establish reflection 
principles was made more concrete; and maybe even addressed directly 
to Tennant himself.  Certainly it is not what I am mainly concerned 
with; as I said 'my interest starts from the recognition that the 
reflection principles Tennant is concerned with have
abandoned entirely any truth-predicate. '.  I do have in mind, 
though, the kind of thing that Franzen goes on to mention:

Clearly there is a connection between the use of reflection 
principles and the Tractarian doctrine about the ineffability of 
semantics, but Tennant's brief discussion is not the whole story, and 
I am not myself persuaded of the prosentential theory of Truth, even 
though I still count myself a kind of Priorian.  What Prior's 
propositional quantification missed (see my 'Priori's Analytic 
Revised' Analysis 61.1 Jan 2001, 86-90) was the nominaliser 'that' 
which Buckner mentions.  An appropriate symbol for this Kneale and 
Kneale introduced in 'The Development of Logic' (Clarendon 1962) 
p585f, and William Kneale later dwelt on its significance at greater 
length in 'Propositions and Truth in Natural Languages', Mind 1972.

Twentieth century history in this area went through three broad 
phases, on my understanding of the matter. First there was the 
Tractarian idea that tautologousness could only be shown, then came 
the representation of modal status by means of meta-linguistic 
predicates, as in Quine, but then thirdly (and rightly) the 
representation using modal operators.  In the latter two phases the 
ineffability of semantics was given up, with explicit judgements 
becoming possible concerning such notions as necessity and truth; but 
the linguistic subject of judgements of truth and necessity changed 
between the second and third phases, from mentioned sentences to 
that-clauses.  Thus most of the intention behind the mid-century 
interest in '"P v ~P' is necessary'", and the like, turns out to be 
better expressed in forms such as 'It is necessary that P v ~P'.  In 
addition, with the latter mode of speech more fully understood, it is 
readily seen that the former mode of speech can only be the 
(meta-)statement of a (contingent) linguistic convention, leaving the 
latter alone to register a proposition-form as non-contingent.  Of 
course it does so, also, while remaining in, and not speaking about, 
the object language.

Goedel's results come out of the second of these phases, and the many 
discussions of our differences from Turing Machines in this area, as, 
for instance, in Penrose's 'The Emperor's New Mind' (Oxford 1989), I 
take to be part of the struggle some people are still having moving 
into the third phase.  Tennant's use of reflection principles, which, 
as I said before, reduce the machine-human question essentially to 
the difference between mention and use, will maybe help people who 
are still attached to Tarskian semantics to take this step.  See 
Chapter 7, 'Tarskian and Non-Tarskian Semantics' of Prior's 'Objects 
of Thought' (Oxford 1971) for earlier moves in this area.


-- 
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