Re: Fitch's paradox and OWA

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?

> Certainly there are candidate mathematical truths, such
> as Goldbach's conjecture, that we have no idea how to ever prove,
> so it seems plausible (to me) that we may never come to know that
> they are true.

Let me add more to what you've said.

One of the shortcomings of modern mathematical logic is that it assumes every single formula written in the language of arithmetic "must be" arithmetically either true or false.

There is a class of formulas (written in the language) whose arithmetic truths or falsehoods can't be established as a matter of principle. [The existence of this class could be demonstrated]. GC and the formula "There are infinite counter examples of GC" are candidates of being in such class. Received on Thu Dec 31 2009 - 03:22:41 CET