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Topic: Matheology § 224
Replies: 2   Last Post: Apr 16, 2013 11:38 PM

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Alan Smaill

Posts: 757
Registered: 1/29/05
Re: Matheology § 224
Posted: Apr 16, 2013 5:49 AM
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Nam Nguyen <namducnguyen@shaw.ca> writes:

> On 15/04/2013 5:38 AM, Alan Smaill wrote:
>> Nam Nguyen <namducnguyen@shaw.ca> 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.


Life is too short for that, I'm afraid.

--
Alan Smaill



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