Re: Fitch's paradox and OWA
Date: Fri, 1 Jan 2010 07:28:30 -0800 (PST)
On Dec 31 2009, 7:24 pm, Nam Nguyen <namducngu..._at_shaw.ca> wrote:
> Marshall wrote:
> Can you verify that your definition of the naturals meet the definition of
> formal system model, with say Q is the underlying system at hand, as I did
> verify M w.r.t to T above? [It's just a pure simple technical question!]
I expect so. I haven't gone through the exercise at length, but the whole process seems straightforward enough. I have done certain individual proofs, but not all of them.
> > What difficulties do you foresee?
> Ok. this is a much better and more technical question one could entertain.
> In a nutshell, one of difficulties that formula such as (1) or (1') presents is
> that there's no way you could define any model of Q such that a certain expected
> set of 2-tuples (i.e. _relation_) can be verified to exist. And if you can't,
> you can't tell whether or not you have would conform to the overall definition of a
> model of the underlying formal system (say Q in this case).
If you don't admit the existence of any possible technique of showing such a thing, it wouldn't be a good use of my time to try to convince you otherwise.
Note at least that yours is a minority opinion, here; it's certainly possible to show the necessary relations exist, and have the desired properties, though such ordinary methods as induction.
Marshall Received on Fri Jan 01 2010 - 16:28:30 CET