On 4/16/2013 12:38 AM, Nam Nguyen wrote: > On 15/04/2013 5:38 AM, Alan Smaill wrote: >> Nam Nguyen <email@example.com> writes: >> >>> My presentation over the years is that it does _not_ matter >>> what, say, Nam, fom, Frederick, Peter, ... would do to >>> "specify an infinite domain", including IP (Induction Principle), >>> a cost will be exacted on the ability to claim we know, verify, >>> or otherwise prove, in FOL level or in metalogic level. >>> >>> The opponents of the presentation seem to believe that with IP >>> we could go as far as proving/disproving anything assertion, >>> except it would be just a matter of time. >> >> I haven't seen anyone claim that, and I certainly don't. > > They claimed that my claim about the relativity of truth of cGC > would be in vain because like GC, we might _one day_ compute a > counter example, hence the absolute truth value would be > established. > > But such reasoning indirectly assumes _there is no statement_ > _that is relativistic_ hence my allegation above.
Explaining that there is a reasonable prior requirement to accept an assertion that a statement is "relative" seems to have fallen on deaf ears (or, in this case, blind eyes).
There is a standard that establishes such relativity. It would involve proving the independence of the given statement by demonstrating a model in which it holds and a model in which it fails.
Set theory is full of such statements. The literature involving set theory is full of "what ifs" involving independent statements that have been assumed to investigate results which follow from them.
The models required for your statements of "relativity" to be admissible do not have to be constructive models because that is not the paradigm.
The fact that you want to do something different does not change the paradigm or the responsibilities that come with telling people that you are following the paradigm when you are, in fact, not.
Once again, I have not cared.
Except when I have simply lost my temper, I have tried to indicate materials that would alleviate some of the consternation caused by these misrepresentations. I have also taken the time to write extensive posts directed toward the same end.
I do not appreciate having these matters misrepresented time and time again without apology or any attempt to repair the situation.
I withhold repeating the comments I have concluded with in the recent past.