Re: Fitch's paradox and OWA
From: Nam Nguyen <namducnguyen_at_shaw.ca>
Date: Thu, 31 Dec 2009 18:10:33 -0700
Message-ID: <fYb%m.285$Mv3.94_at_newsfe05.iad>
>> Marshall wrote:
>>> On Dec 31, 3:40 pm, Nam Nguyen <namducngu..._at_shaw.ca> wrote:
>>>> Barb Knox wrote:
>>>>> They are true or false in any *particular* model. Since we apparently
>>>>> cannot formally pin down arithmetic to have just one particular model
>>>>> (the Standard one) then there will always be some arithmetic statements,
>>>>> the undecidable ones, which are true in some models and false in others.
>>>> Agree. The question - and the heart of my argument - is whether or not there
>>>> exists a formula F such that it's impossible to know/assert a truth value
>>>> in the collection K of _all_ arithmetic models: K = {the standard one, the
>>>> non-standard ones}? I've argued that there exist such statements.
>>> Why would the existence of such statements imply that there
>>> are truth values other than true or false?
>> Because a) FOL truth is no longer absolute: it has to be relativized to some
>> models; and yet b) what one constructs and _label_ as a model might indeed
>> be impossible to be technically verified as a model. How could a statement be
>> true or false if in the first place it can't be true-able or false-able?
>>
>> I think I've asked/raised this question a few times but have yet to hear
>> a response to it!
Date: Thu, 31 Dec 2009 18:10:33 -0700
Message-ID: <fYb%m.285$Mv3.94_at_newsfe05.iad>
Marshall wrote:
> On Dec 31, 4:18 pm, Nam Nguyen <namducngu..._at_shaw.ca> wrote:
>> 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!
> > There is simply no issue here to respond to. Everything you've > said here is either false or else it's the same as the conclusion > you're trying to establish.
Great "refute" you seem to have had here! Among "everything" I've said here are a) and b). Why do you think they're false? Or you just said so out of the habit of saying things with no back-up reasons?
Btw, usually "conclusion" is "the same" thing as what one would be "trying to establish". You seemed to be surprise of that. Why? Received on Fri Jan 01 2010 - 02:10:33 CET