[FOM] consistency and completeness in natural language

[Hartley Slater]

Franzen writes (FOM Digest Vol 4 Issue 5):

>Formulas are indeed what formal systems prove. Nevertheless we say
>such things as "it is provable in ZFC that every Polish group H
>satisfies WVC(H)", "S proves the consistency of T", and so on, all the
>time. What we mean by saying "S proves that A" is that S proves a
>standard formalization of A.

Directly to me he has said:

>truth in logic is predicated of sentences as
>a matter of definition. I don't agree that there is any use-mention
>confusion involved in "T proves that...",

Clearly Prior was not a logician, by these standards (see chapter 7 
of 'Objects of Thought' again).  But how does Franzen read the null 
or identity modality in system T, for instance?  That is such that |- 
Lp <-> p, so Tarski's theorem does not hold.  It's reading is, of 
course 'It is true that', showing that 'it is true that p' is 
provably different from ''p' is true'.


-- 
Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, School of Humanities
University of Western Australia
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