[FOM] Unrestricted Quantification and Paradox

[Richard Heck]

laureano luna wrote:
> Robert Smith wrote:
>   
>> General prohibitions against "self-reference" are
>> untenable IMHO.
>>     
> My claim is that all forbidden self-references stem
> from the impossibility of an intentional act to be its
> own intentional object. Someone told me Ernst Mally
> wrote that no thought can think itself. In other
> terms, no thought is about itself.
But what about the familiar sorts of examples from Kripke? E.g, the 
Nixon-Dean case? So Nixon says, "Everything Dean says [timeless] about 
Watergate is true" and Dean says, "Most of what Nixon says about 
Watergate is false". They mean to include what each of them says. As 
Kripke then points out, there are circumstances in which it is utterly 
unproblematic to attribute definite truth-values, and there are 
circumstances in which you can't, due to paradox. So banning 
SELF-reference wouldn't be sufficient anyway. But then there are simple 
examples in which self-reference seems equally unproblematic. Nixon 
says, "Everything I shall ever say about Watergate, including this, is 
true". Well, it's easy to assign that a truth-value, isn't it? But under 
certain circumstances, it would be a truth-teller. And you can easily 
formulate Tarski-like examples, such as, "The one and only one 
proposition being expressed on such and such an occasion by such and 
such a person is not true". If you're a Russellian about descriptions, 
then there should be no problem about that expressing a proposition, 
even if the proposition described happens to be that very proposition.

And, as Smith said, self-reference is ubiquitous in foundational 
studies, anyway, and there are going to be plenty of true (indeed, 
provable) sentences of PA plus a Kripke-like truth-predicate that are 
self-referential. Anyone have a pretty example to hand? I'm guessing you 
could get one by playing around with Henkin's famous example "This is 
provable".

Richard


-- 
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Richard G Heck, Jr
Professor of Philosophy
Brown University
http://frege.brown.edu/heck/
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