Re: Fitch's paradox and OWA
Date: Thu, 31 Dec 2009 17:18:47 -0700
Message-ID: <Jbb%m.281$Mv3.23_at_newsfe05.iad>
Marshall wrote:
> On Dec 31, 3:40 pm, Nam Nguyen <namducngu..._at_shaw.ca> wrote:
>> Barb Knox wrote:
>>
>>> They are true or false in any *particular* model. Since we apparently
>>> cannot formally pin down arithmetic to have just one particular model
>>> (the Standard one) then there will always be some arithmetic statements,
>>> the undecidable ones, which are true in some models and false in others.
>> Agree. The question - and the heart of my argument - is whether or not there
>> exists a formula F such that it's impossible to know/assert a truth value
>> in the collection K of _all_ arithmetic models: K = {the standard one, the
>> non-standard ones}? I've argued that there exist such statements.
> > Why would the existence of such statements imply that there > are truth values other than true or false?
Because a) FOL truth is no longer absolute: it has to be relativized to some models; and yet b) what one constructs and _label_ as a model might indeed be impossible to be technically verified as a model. How could a statement be true or false if in the first place it can't be true-able or false-able?
I think I've asked/raised this question a few times but have yet to hear a response to it! Received on Fri Jan 01 2010 - 01:18:47 CET