[FOM] Kripke's outline of a theory of truth

[Aatu Koskensilta]

Quoting "Timothy Y. Chow" <tchow at alum.mit.edu>:

> In Kripke's "Outline of a Theory of Truth," he makes the following
> comment, "To my surprise, I have found that the problem of defining the
> languages of transfinite level presents substantial technical difficulties
> which have never seriously been investigated."  He then goes on to say
> that he has some partial results but doesn't go into detail.

   Kripke mentioning some result without going into detail? Surely  
you're joking, surely this can't be.

> What difficulties was Kripke talking about and have they been surmounted
> by subsequent researchers?

   I wouldn't know about such things, but one difficulty here is  
readily apparent once we actually try to set up suitable formalisms  
and technical scaffolding, in order to model and support the sort of  
construction Kripke no doubt had in mind: ordinals are extensional set  
theoretic objects it makes no sense to talk of plugging into formulas,  
or introduce as formal parameters for truth predicates in theories  
intended for human consumption. So if we want a theory, in any sense  
relevant to human understanding of transfinitely iterated Tarskian  
truth, reasoning about such truth, and so on, we need more than just  
the idea of an extensional ordinal indexed hierarchy of truth  
predicates. Torkel Franzén explains in his wonderful  
_Inexhaustibility_ what goes into the relevant formal constructions  
and results, how that relates to the actual "informal" issue at hand,  
what to make of all this, all the jazz.

-- 
Aatu Koskensilta (aatu.koskensilta at uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus