Re: Fitch's paradox and OWA

Daryl McCullough wrote:
> Nam Nguyen says...

>> Daryl McCullough wrote:
>>> Nam Nguyen says...
>>>> Daryl McCullough wrote:
>>>>> By the way, I haven't thought about it a huge amount, but I
>>>>> don't have any problems with the paradox, because I don't
>>>>> accept the premise: Every true proposition is potentially knowable.
>>>>> It seems to me that sufficiently complex true propositions may never
>>>>> be known. 
>>>> But how can we know it's true in the first place, when its being true
>>>> can't be known?
>>> I didn't say that we can *know* it is true. That's my point---something
>>> can be true without anyone knowing that it is true. It might be true,
>>> for example, that there is an even number of grains of sand in the world,
>>> but we may never find that out. Is e^pi rational? We may never find out.
>> Don't want to beat a dead horse so to speak but not knowing a truth because
>> its proof (knowledge) is _finitely_ larger than what one can possibly know
>> is *not* the same as not knowing a truth value because the statement is not
>> *genuinely* truth-assigned-able. The "sand in the world" being an even number
>> example above is of the 1st kind: not the 2nd kind.

So, are you with me that there could be statements that are neither true or false, on the ground that we can't assign a truth value to them; i.e., on the ground what we've _intuitively perceived_ as the "natural numbers" is _not adequate_ for us to say they are true or false?

> we will never know that they are true. There can also be statements
> that are true, but which we have no way of ever knowing that they are
> true. For example, I flip a coin, and before I see whether it lands
> heads up or tails up, it is run over by train, smashing it into a
> flat, smooth chip of metal. Now, there is no way of ever knowing
> whether it was heads-up or tails-up. But it is possible that
> "It was heads-up before it was smashed" is true.
>
> Statements can be true even if there is no way to ever know that they
> are true.

But that's _not_ my point! The statements I have in mind are the ones that can _not_ be assigned true or false, in the first place! Do you see that they aren't of the same kind of statements you've alluded to?

>
> --
> Daryl McCullough
> Ithaca, NY
>
Received on Thu Dec 31 2009 - 22:07:07 CET