Re: Fitch's paradox and OWA

Bob Badour wrote:
> Nam Nguyen wrote:
>

>> Daryl McCullough wrote:
>>
>>> Marshall says...
>>>
>>>> I believe Nam is roughly of the opinion that if we can't know which
>>>> one of {true, false} a sentence is, then we have no basis for saying
>>>> it must be one or the other.
>>>
>>> But typically, for some statements such as "The Greek philosopher
>>> Plato was left-handed" I don't know whether the statement is true
>>> or not, and I also don't know whether anyone else knows whether it
>>> is true or not, and I don't know whether it is *possible*, at this
>>> late date, to find out whether it is true or not. 
>>
>>> But surely, it's either true or false, right?
>>
>> No. Not surely. Since by our assumption here is nobody would know about
>> his handed-ness, his nervous system to both arms might not have 
>> functioned
>> at all to begin with and hence whether or not he was left-handed is moot
>> and is not-truth assignable. As well, there are people are strong equally
>> on both arms and therefore handed-ness is not applicable to them.

The _analogy_ was under the assumption that we'd logically live under a binary world where the negation of "left-handed" is "right-handed". I don't think we were arguing about precise meanings of biological/physiological matters.

My point still stands: if it's _impossible_ (as opposed to just being difficult) to assign truth values to a formula then the formula is neither true nor false, which means that collectively the naturals isn't a _complete_ model of Q or its extensions.

>
> It doesn't get tricky until handedness is equally strong in both arms
> but not for the same things like a person who writes left-handed but
> shoots right-handed etc.
>
Received on Thu Dec 31 2009 - 09:18:18 CET