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

Richard Heck rgheck at brown.edu
Thu Feb 23 10:55:15 EST 2012

On 02/21/2012 09:44 PM, Aatu Koskensilta wrote:
> Quoting "Timothy Y. Chow" <tchow at alum.mit.edu>:
>> 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.
This isn't so clear. I can quite easily write down a definition of 
formal sentence that allows sets---not names of sets, but sets 
themselves---to be substituted for free variables. That said, ...

> 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.
there are other problems for which one will need some system of ordinal 
notations, which is what the classic work by Turing and Feferman that 
Franzel discusses is based upon.

What's not clear to me is what problems *other than* the ones that arise 
in connection with ordinal notations Kripke might have had in mind.


Richard G Heck Jr
Romeo Elton Professor of Natural Theology
Brown University

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