[FOM] Kripke's outline of a theory of truth
Aatu.Koskensilta at uta.fi
Tue Feb 21 21:44:41 EST 2012
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
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