> 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.
Saying "might" is different from saying "could go as far as proving/disproving anything assertion, except it would be just a matter of time", isn't it?
> But such reasoning indirectly assumes _there is no statement_ > _that is relativistic_ hence my allegation above.
You are reacting to a stronger statement than the one that was actually made.
>> You are the one making claims of impossibility for particular >> statements. > > Yes. But I don't just claim it. I do have some good evidences > and I did present a proof in the past. On the other hand, it seems > my opponents only have one thing to go by, something like: "we might > prove it one way or the other tomorrow".
Because you made the statement, the burden of proof is on you.
>>> Which sounds like >>> Hilbert's false paradigm of a different kind. >>> >>> That's the difference on the two sides. >> >> Whatever you think the "two sides" are, you misrepresent >> some posters here. > > Given that you seem to have opposed me I thought you might > have been on _that_ other side. But I withdraw that genuine > suspicion of mine. Though I'd like to ask you one question: > on the issue of the relativity of the truth value of cGC, > are you on my side or are you on the opposing side?
I have not seen any convincing argument from you on cGC, and I have presented evidence on the other side. On the other hand (and this is why I object to the "two sides" notion), clearly there is incompleteness around in foundations of arithmetic: after all there is an incompleteness theorem. Torkel's book about "inexhaustibility" is another example.
> In any rate, in the interest of time, for the issue of cGC, > if you could join in the sub thread conversation with Jesse F. > Hughes that would be great: that sub thread is a "re-organized" > debate where we'd go 1-step at a time, from the very basics of > the foundation.